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A polyploid complex , also called a diploid-polyploid complex , is a group of interrelated and interbreeding species that also have differing levels of ploidy that can allow interbreeding .
A polyploid complex was described by E. B. Babcock and G. Ledyard Stebbins in their 1938 monograph The American Species of Crepis : their interrelationships and distribution as affected by polyploidy and apomixis . In Crepis and some other perennial plant species, a polyploid complex may arise where there are at least two genetically isolated diploid populations, in addition to auto- and allopolyploid derivatives that coexist and interbreed. Thus a complex network of interrelated forms may exist where the polyploid forms allow for intermediate forms between the diploid species that are otherwise unable to interbreed. [ 1 ]
This complex situation does not fit well within the biological species concept of Ernst Mayr which defines a species as "groups of actually or potentially interbreeding natural populations which are reproductively isolated from other such groups".
In many diploid-polyploid complexes the polyploid hybrid members reproduce asexually while diploids reproduce sexually. [ 2 ] Thus polyploidy is related to the phenomenon called "geographic parthenogenesis" by zoologist Albert Vandel , [ 3 ] that asexual organisms often have greater geographic ranges than their sexual relatives. It is not known which of the associated factors is the major determiner of geographic parthenogenesis, hybridization , polyploidy, or asexual reproduction. [ 2 ] | https://en.wikipedia.org/wiki/Polyploid_complex |
Polyprenols are natural long-chain isoprenoid alcohols of the general formula H-(C 5 H 8 )n-OH, where n is the number of isoprene units. Any prenol with more than 4 isoprene units is a polyprenol. Polyprenols play an important function, acting as natural bioregulators and are found in small quantities in various plant tissues. Dolichols , which are found in all living creatures, including humans, are their 2,3-dihydro derivatives. [ 1 ]
Live trees are known to contain polyprenols. The needles of conifer trees are one of the richest sources of polyprenols. [ 2 ] They are also present in shiitake mushrooms in trace amounts. [ 3 ]
Polyprenols have been studied for more than 30 years. Interest has been strongest in Russia, Europe, Japan, India, and the United States. In the early 1930s, a scientific team at the Forest Technical Academy in St. Petersburg, Russia led by Fyodor Solodky, the founder of Forest Biochemistry, and Asney Agranet, began research into the composition of conifer tree needles. [ 4 ] They were intrigued by the trees' ability to remain disease free in extremes of temperature ± 40 °C.
Development of Solodky's research led Russian scientists to isolate a completely different class of organic substance from the needles, including polyprenols.
Polyprenols are low molecular natural bioregulators (physiologically active), playing a significant modulating role in the cellular process in plants referred to as biosynthesis .
What polyprenols are to plants, dolichols are to all living creatures, including man. They are in fact of a very similar chemical composition. Dolichols are a derivative of polyprenols with a saturated isoprene unit.
Through dolichols, the dolichol phosphate cycle occurs. The dolichol phosphate cycle plays a major role in the synthesis of glycoproteins .
All proteins from secretions , membranes and intracellular glycoproteins form the basis for the building of membrane receptors which are used in the production of insulin , adrenaline , estrogen , testosterone and other hormones and enzymes . Seemingly, dolichols have an important role in maintenance of the correct lipid composition of membranes . Decreased levels of dolichols have been connected to higher levels of peroxidation of lipids. [ 5 ]
The dolichol phosphate cycle facilitates the process of cellular membrane glycosylation , that is, the synthesis of glycoproteins that control the interactions of cells, support the immune system and the stabilization of protein molecules. Out of all these glycoproteins, polyglycoprotein has been found to create drug resistance to multiple cancer treatments and keep cancer cells alive. [ 6 ]
The pharmacological activity of polyprenols takes place in the liver, where they are metabolized into dolichols. [ 7 ]
The interest in polyprenols and dolichols is associated with their wide range of demonstrated biological activity and extremely low toxicity .
Polyprenols cellular reparation and spermatogenesis , and have antistress, adaptogenic , antiulcerogenic and wound-healing activity. [ 8 ] Dolichols have antioxidant activity and protect cell membranes from peroxidation . [ 9 ] Experiments on mice have demonstrated that polyprenols have antiviral activity, in particular against influenza viruses. [ 10 ] It has been established that the dolichol level in liver tumor cells are reduced in comparison with healthy hepatic cells. [ 11 ]
The Australian pharmaceutical company Solagran Limited has been investigating the medical significance of polyprenols. [ 12 ] [ 13 ] | https://en.wikipedia.org/wiki/Polyprenol |
The polypyrimidine tract is a region of pre-messenger RNA (mRNA) that promotes the assembly of the spliceosome , the protein complex specialized for carrying out RNA splicing during the process of post-transcriptional modification . The region is rich with pyrimidine nucleotides , especially uracil , and is usually 15–20 base pairs long, located about 5–40 base pairs before the 3' end of the intron to be spliced. [ 1 ]
A number of protein factors bind to or associate with the polypyrimidine tract, including the spliceosome component U2AF and the polypyrimidine tract-binding protein (PTB), which plays a regulatory role in alternative splicing . PTB's primary function is in exon silencing, by which a particular exon region normally spliced into the mature mRNA is instead left out, resulting in the expression of an isoform of the protein for which the mRNA codes . Because PTB is ubiquitously expressed in many higher eukaryotes , it is thought to suppress the inclusion of "weak" exons with poorly defined splice sites . [ 2 ] However, PTB binding is not sufficient to suppress "robust" exons. [ 3 ]
The suppression or selection of exons is critical to the proper expression of tissue -specific isoforms. For example, smooth muscle and skeletal muscle express alternate isoforms distinguished by mutually exclusive exon selection in alpha- tropomyosin . [ 4 ] | https://en.wikipedia.org/wiki/Polypyrimidine_tract |
Polypyrrole ( PPy ) is an organic polymer obtained by oxidative polymerization of pyrrole . It is a solid with the formula H(C 4 H 2 NH) n H. It is an intrinsically conducting polymer , used in electronics, optical, biological and medical fields. [ 2 ] [ 3 ]
Some of the first examples of PPy were reported in 1919 by Angeli and Pieroni, who reported the formation of pyrrole blacks from pyrrole magnesium bromide. [ 4 ] Since then pyrrole oxidation reaction has been studied and reported in scientific literature.
Work on conductive polymers including polypyrrole, polythiophene , polyaniline , and polyacetylene was awarded the Nobel Prize in Chemistry in 2000 to Alan J. Heeger, Alan G. MacDiarmid and Hideki Shirakawa . [ 5 ]
Different methods can be used to synthesize PPy, but the most common are electrochemical synthesis and chemical oxidation. [ 6 ] [ 3 ] [ 7 ]
Chemical oxidation of pyrrole:
The process is thought to occur via the formation of the pi- radical cation C 4 H 4 NH + . This electrophile attacks the C-2 carbon of an unoxidized molecule of pyrrole to give a dimeric cation [(C 4 H 4 NH) 2 ] ++ . The process repeats itself many times.
Conductive forms of PPy are prepared by oxidation ("p-doping") of the polymer:
The polymerization and p-doping can also be effected electrochemically. The resulting conductive polymer are peeled off of the anode. Cyclic voltammetry and chronocoulometry methods can be used for electrochemical synthesis of polypyrrole. [ 8 ]
Most recent micro and nano droplet researches have been conducted in the synthesis of polypyrrole microstructures using various fluid templates formed on different solid surfaces. [ 9 ]
Films of PPy are yellow but darken in the air due to some oxidation. Doped films are blue or black depending on the degree of polymerization and film thickness. They are amorphous, showing only weak diffraction. PPy is described as "quasi-unidimensional" vs one-dimensional since there is some crosslinking and chain hopping. Undoped and doped films are insoluble in solvents but swellable. Doping makes the materials brittle. They are stable in the air up to 150 °C at which temperature the dopant starts to evolve (e.g., as HCl). [ 2 ]
Doping the polymer requires that the material swell to accommodate the charge-compensating anions. The physical changes associated with this charging and discharging have been discussed as a form of artificial muscle. [ 10 ] The surface of polypyrrole films present fractal properties and ionic diffusion through them show anomalous diffusion pattern. [ 11 ] [ 12 ]
PPy and related conductive polymers have two main application in electronic devices and for chemical sensors and electrochemical applications. [ 13 ]
PPy is a potential vehicle for drug delivery . The polymer matrix serves as a container for proteins. [ 14 ]
Polypyrrole has been investigated as a catalyst support for fuel cells [ 15 ] and to sensitize cathode electrocatalysts. [ 16 ]
Together with other conjugated polymers such as polyaniline, poly(ethylenedioxythiophene) etc., polypyrrole has been studied as a material for "artificial muscles", a technology that offers advantages relative to traditional motor actuating elements. [ 17 ]
Polypyrrole was used to coat silica and reverse phase silica to yield a material capable of anion exchange and exhibiting hydrophobic interactions. [ 18 ]
Polypyrrole was used in the microwave fabrication of multiwalled carbon nanotubes, a rapid method to grow CNT's. [ 19 ]
A water-resistant polyurethane sponge coated with a thin layer of polypyrrole absorbs 20 times its weight in oil and is reusable. [ 20 ]
The wet-spun polypyrrole fibre can be prepared chemical polymerization pyrrole and DEHS as dopant. [ 21 ] | https://en.wikipedia.org/wiki/Polypyrrole |
Polyquaternium is the International Nomenclature for Cosmetic Ingredients designation for several polycationic polymers that are used in the personal care industry. Polyquaternium is a neologism used to emphasize the presence of quaternary ammonium centers in the polymer. INCI has approved at least 40 different polymers under the polyquaternium designation. Different polymers are distinguished by the numerical value that follows the word "polyquaternium". Polyquaternium-5, polyquaternium-7 , and polyquaternium-47 are three examples, each a chemically different type of polymer. The numbers are assigned in the order in which they are registered rather than because of their chemical structure.
Polyquaterniums find particular application in conditioners , shampoo , hair mousse , hair spray , hair dye , personal lubricant , and contact lens solutions. Because they are positively charged, they neutralize the negative charges of most shampoos and hair proteins and help hair lie flat. Their positive charges also ionically bond them to hair and skin. Some have antimicrobial properties.
This article about polymer science is a stub . You can help Wikipedia by expanding it .
This article about cosmetics chemicals is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polyquaternium |
Polyrotaxane is a type of mechanically interlocked molecule consisting of strings and rings, in which multiple rings are threaded onto a molecular axle and prevented from dethreading by two bulky end groups. As oligomeric or polymeric species of rotaxanes , polyrotaxanes are also capable of converting energy input to molecular movements because the ring motions can be controlled by external stimulus. [ 1 ] Polyrotaxanes have attracted much attention for decades, because they can help build functional molecular machines with complicated molecular structure. [ 2 ]
Although there are no covalent bonds between the axes and rings, polyrotaxanes are stable due to the high free activation energy ( Gibbs energy ) needed to be overcome to withdraw rings from the axes. Also, rings are capable of shuttling along and rotating around the axes freely, which leads to a huge amount of internal degree of freedom of polyrotaxanes. Due to this topologically interlocked structure, polyrotaxanes have many different mechanical, electrical, and optical properties compared to conventional polymers. [ 3 ]
Additionally the mechanically interlocked structures can be maintained in slide-ring materials, which are a type supramolecular network synthesized by crosslinking the rings (called figure-of-eight crosslinking) in different polyrotaxanes. In slide-ring materials, crosslinks of rings can pass along the axes freely to equalize the tension of the threading polymer networks, which is similar to pulleys. With this specific structure, slide-ring materials can be fabricated highly stretchable engineering materials due to their different mechanical properties . [ 4 ]
If the rings and axes are biodegradable and biocompatible, the polyrotaxanes can also be used for biomedical application, such as gene/drug delivery. The advantage of polyrotaxanes over other biomedical polymers, such as polysaccharides , is that because the interlocked structures are maintained by bulky stoppers at the ends of the strings, if the bulky stoppers are removed, such as removed by a chemical stimulus, rings dethread from the axes. The drastic structural change can be used for programmed drug or gene delivery, in which the drug or gene can be released with the rings when the stoppers are cut off at the specific destination. [ 5 ]
According to the location of the rotaxanes units, polyrotaxanes can be mainly divided into two types: main chain polyrotaxanes, in which the rotaxane units locate on the main chain (axis), and side chain polyrotaxanes, in which the rotaxane units are located on the side chain. Corresponding polypseudorotaxanes can also be divided based on the same principle: main chain polypseudorotaxnes or side chain polypseudorotaxanes, in which there is no stopper at the ends.
In both main chain polyrotaxanes or side chain polyrotaxanes, the unique feature from other polymers is the potential for different motion of the ring unit relative to the string units. Because the shape and location of the assembly are capable of showing different responses to changes in temperature, pH or other environment conditions, polyrotaxanes have many distinctive properties. [ 6 ]
Main chain polyrotaxanes are formed by host–guest interactions of polymer backbones (main chain) with cyclic molecules that are interlocked by bulky stoppers.
There are five major synthesis routes for main chain polyrotaxanes. [ 7 ] [ 8 ] [ 9 ]
(1) Cyclization in the presence of main chain.
This synthesis route requires high dilution conditions of cyclization reactions. However, to most cases, it is difficult to sustain the high dilution conditions for rotaxane formation. Other possible methods to solve this problem are template cyclizations, such as cyclization based on metal chelation , change-transfer complexation or inclusion complexes.
(2) Polymerization of monomeric rotaxanes units.
Through polymerizing stable rotaxane monomers, polyrotaxanes are obtained. This method requires that the monomeric rotaxane units are stable in the solvent and have active groups that can be polymerized, which means the rings will not dethread from the main chain.
(3) Chemical conversion.
Specially designed linear polymers are required in this method. Designed monomers are polymerized to obtain special linear polymers with precursors of cyclic compounds. After bulky stoppers are modified onto two sides of polymer chains, the "temporary" chemical bonds in the precursors are cleaved to generate cyclic structure on the main chain, which becomes a polyrotaxane. The disadvantage of this method is the complex chemistry needed in the process of design and synthesis of the special linear polymers with precursors and the transitions to polyrotaxanes, e.g. the selective chemical bond cleavage. Many synthesis steps are required in this method.
(4) Threading of preformed main chain molecules through preformed rings.
The fourth approach is the simplest method to synthesize polyrotaxanes. Through mixing the main chain polymers and the rings in the solution, polyrotaxanes can be obtained after adding bulky stoppers to prevent the rings from dethreading from the chains. The number of rings on each chain depends on the threading equilibrium. Kinetic limitations due to the low concentration of chain ends and entropic effects also need further consideration. To overcome these obstacles, template threading (see below) is also a feasible alternative that can improve dynamically the number of threading rings by changing the equilibrium constant.
(5) Production of linear macromolecule in the presence of preformed rings.
Two general methods are included in this approach: the "statistical approach" and "template threading approach".
In the "statistical approach", the interaction between rings and strings is weakly attractive or repulsive or even negligible. Through employing an excess of rings, the equilibrium for threading or dethreading is forced to the threading side before polymerization. Compared with synthesis route 1, rings are a major constituent of the system instead of the rotaxanes, so the high dilution conditions are not required for this methods.
In "template threading approach", unlike the statistical approach, the interactions between rings and strings need to be attractive, such as metal chelations or charge transfer interactions which have been mentioned in the synthesis route 1. Because of this, the equilibrium is enthalpically driven, where the enthalpy is negative. In this method, high numbers of threading rings can be achieved, thus it is a useful way to stoichiometrically control the rings ratio of polyrotaxanes.
An example of the "statistical approach" is that a polyrotaxane was synthesized through polymerizing the rotaxane monomer that was assembled by oligomeric ethylene glycols (string) and crown ethers (ring) and naphthalene-1,5-di-isocyanate (stopper), which involves the threading equilibrium in the chain-ring system. [ 10 ]
Cyclodextrins have been extensively studied as host molecules (ring) in polyrotaxanes. The poly(ethylene glycol)s can assemble with α-cyclodextrins to form a molecular necklace. [ 11 ] Every two ethyleneoxy repeat units in poly(ethylene glycol)s can thread in one α-cyclodextrin. The models confirm that the distance of form zig-zag structure of repeat units corresponds to the size of cavity in α-cyclodextrins. This is a classical example of "template threadings" which also explains why poly(ethylene glycol)s are not able to form rotaxanes with β-cyclodextrin.
Crown ethers are another type of monomacrocyclic polymers that are used in synthesis of polyrotaxanes. The polyrotaxanes can be prepared by carrying out step-growth polymerizations in the presence of aliphatic crown ethers. In most of the cases, hydrogen bonding between the crown ethers and OH or NH/NHCO moieties are involved in the form of the assemblies. The threading efficiency will increase with the growth of sizes of the crown molecules. [ 12 ] Additionally, stoppers will also greatly increase the threading efficiency. [ 13 ]
Metal coordination also can be used to construct polyrotaxane structures. In this method, metal ions are employed as the synthesis templates to determine the coordinating sites of rotaxane structures. Conjugated polyrotaxanes can be synthesized through metal-template strategies followed by electropolymerization that ensures tuning of the electronic coupling between the ring cites and the conjugated backbone (string).
Side chain polyrotaxanes are formed by host–guest interactions of polymer side chains with cyclic molecules that are interlocked by bulky stoppers.
There are mainly three types of side chain polyrotaxanes: [ 14 ]
(1) Polyaxis/rotor: Comb-like polymers assembled with the cyclic molecules that are not interlocked on the side chain.
(2) Polyrotor/axis: polymers possess cyclic molecules on the side chain, which assemble with guest molecules to form polypseudorotaxanes.
(3) Polyrotor/polyaxis: polymers possess covalently bonded cyclic molecule-moieties assembled with polymers possess guested in the side chain.
Similar to the synthesis routes to main chain polyrotaxanes, there are mainly six approaches to side chain polyrotaxane.
(1) Ring-threading of performed graft polymer [ 15 ]
(2) Ring-grafting [ 16 ]
(3) Rotaxane-grafting [ 17 ]
(4) Polymerization of macromonomer with rings
(5) Polymerization of rotaxane-monomer
(6) Chemical conversion
Similarly, the positions of chain and rings can be switched, which results in corresponding side-chain polyrotaxanes.
In a polyrotaxane, unlike a conventional polymer, the molecules are linked by mechanical bonding, such as hydrogen boding or charge transfer, not covalent bonds. Also, the rings are capable of rotating on or shuttling around the axles, resulting in the large amount of freedom of polyrotaxanes. This unconventional combination of molecules leads to the distinctive properties of polyrotaxanes.
Due to the existence of stoppers on the ends of the rotaxanes units, polyrotaxanes are more thermodynamically stable than polypseudorotaxanes (similar structure to polyrotaxane but without stoppers at two ends). Also, if the interactions between guest and host molecules are attractive, such as hydrogen bonding or charge transfer, they have better stabilities than those without attractive interactions. However, specific salts, changes of pH condition or temperature that can disturb or interrupt the interactions between ring-ring, ring-backbone, or backbone-backbone will destroy the structural integrity of polyrotaxanes. For example, dimethylformamide or dimethyl sulfoxide is able to interrupt the hydrogen bonding between cyclodextrins in the cyclodextrin-based polyrotaxanes. Also, change of pH or high temperature can also destroy the crystalline domains. Some chemical bonds between stoppers and chains are not stable in acidic or basic solution. As the stoppers cut from the chain, the rings will dethread from the axles, which leads to the dissociation of the polyrotaxanes.
For example, a "molecular necklace" assembled by α-cyclodextrins and polyethylene glycol [ 18 ] is insoluble in water and dimethylfomamide, although their parents' components α-cyclodextrin and polyethylene glycol can be dissolved and this synthesis can happen in water. The product is soluble in dimethyl sulfoxide or 0.1 M sodium hydroxide solution. This is because the hydrogen bonding between the cyclodextrins. As the hydrogen bonding is destroyed by dimethyl sulfoxide or base solution, it can be dissolved, but the water does not deform the hydrogen interaction between cyclodextrins. In addition, the complexation process is exothermic in thermodynamic tests, which is also corresponding with the existence of hydrogen bonding.
One of the properties of polytorotaxanes involves the photoelectronic response when introducing photoactive or electrionic-active units into the mechanically interlocked structures.
For examples, the polyrotaxane structures are capable of enhancing the fluorescence quenching molecules that grafting on the rings and the other molecules at the ends. [ 19 ] Amplification of a fluorescence chemosensory can be achieved by using polyrotaxane structure, which enhances the energy migration in the polymer. It was found that a rapid migration of the hole-electron pair to the rotaxanes sites is followed by a rapid combination which leads to the enhancement of the energy migration. In addition, the conductivity of these polyrotaxanes was lower than the parent components.
Also conductive polyrotaxanes can be obtained by employing metal binding in the polyrotaxanes structure. For example, a polyrotaxane containing a conjugated backbone can be synthesized through metal template and electropolymerization. [ 20 ] The metal ion binding is reversible when another metal with stronger binding ability is employed to remove the previous ion, which results in the "scaffolding effect reversibility". The free coordination sites and the organic matrix are able to be maintained by the labile scaffolding.
Many mechanically interlocked molecules have been studied to construct molecular machines . Because the molecules are linked by mechanical bonds instead of conventional covalent bonds, a component can move (shuttle) or rotate around the other parent component, which results in the large amount of freedom of mechanically interlocked molecules. Polyrotaxanes, as the polymer form of corresponding rotaxanes, are also applied in molecular machines.
For example, the shuttling behavior of the molecular shuttle can be controlled by the solvent or temperature. [ 21 ] Due to the hydrophobic interaction between rings and strings, and the repulsive interaction between rings and linkers, conditions that are capable of influencing these interactions can be used to control the mobility of the rings in the molecular shuttle. In addition, if cationic or anionic units are employed to form the polyrotaxanes, the salts or pH in the solution also will influence the charge interactions between rings and strings, which is an alternative method to control the ring motion of the molecular shuttle. [ 22 ]
Poly[2]rotaxane " daisy chains " (like a string of daisies with stems linked to form a chain)is an example of a molecule that can be used to form a molecular muscle. [ 23 ] Poly[2]rotaxane can expand or shrink in response to external stimulus, which is similar to behaviors of muscle, an ideal model to construct a "molecular muscle". The ring stations on the chain can be controlled by pH or light. Due to "daisy chain" structure, two rings on the daisy chain will shift from one station to another station, which changes the distance between two rings as well as the state of the whole daisy chain. When the rings come close, the whole size of the daisy chain will increase, which is the "expand" state. As the rings get to the further station, the molecule become the "shrink" state as the decreased size. [ 24 ]
By chemically crosslinking the rings contained in the polyrotaxanes, sliding gels are obtained by being topologically interlocked by figure-of-eight crosslinks. Although it is a polymer network (gel), the rings are not fixed on the polyrotaxanes in the polymer network, the crosslinks of rings are able to freely move along the polymer chain. This can equalize the tension of the network, just like a pulley manner, which is referred to pulley effect. In chemical gels, the polymer chains are easy to be broken because the lengths of the heterogeneous polymer are limited or fixed. As a result, when the chemical gel is under a high pressure, the tension can not be equalized to the whole. On the opposite, the weakest part in the network will be broken easier, which leads to the damage of the gel. However, in the slide-ring materials, the polymer chain are able to pass through the figure-of-eight crosslinks which is like pulleys, and equalize the tension of network. As a result, slide-ring materials are applied to construct highly stretchable materials, up to 24 times its length when stretching and this process can be reversible. [ 25 ]
Although polyrotaxanes are formed from components, their solubilities are different from the host or guest molecules. For examples, in the cyclodextrin-based polyrotaxanes, due to the hydrophilicity or high polarity of exterior structure of the cyclodextrins, some polyrotaxanes are able to be dissolved in water or other polar solvents though the guest molecules are hydrophobic or nonpolar. These water-soluble can be applied into drug or gene carriers.
There are two main advantages for polyrotaxanes applied to drug/gene delivery:
Because the mechanically interlocked structures are maintained by bulky stoppers at the ends of the strings, if the bulky stoppers are removed, such as removed by a chemical stimulus, rings dethread from the axes. The drastic structural change can be used for programmed drug or gene delivery, of which drug or gene can be released with the rings when the stoppers are cut off at the specific destination.
For example, an enhanced gene delivery vehicle can be obtained by using a polyrotaxane formed by rings, backbones, then stoppers that linked by a disulfide bond (or other chemical bond that can be selected cleave in the body). [ 26 ] The cation-functionalized polyrotaxanes can bind with pDNA to form complex through the electronstatic interaction . Glutathione (or other corresponding chemicals that can cleave the sensitive chemical bond) is over-expressed in the target cells. When the polyrotaxane/plasmid DNA (pDNA) complexes are uptaken by the target cells, intercellular glutathione could cleave the disulfide bond to cut off the stoppers at the end of polyrotaxanes, which results in the dissociation of the polyrotaxanes. As the rings dethread from the chain, pDNA is released with the ring molecules.
Another advantage of poly(pseudo)rotaxanes is the ability for long-term release of drugs or genes. Some polyrotaxanes can used to form a physical hydrogel, which is called supramolecular hydrogel. In these cases, a three-dimensional physically crosslinked network formed by the poly(pseudo)rotaxanes, can be obtained, which is able to retain a large amount of water inside this network. If water-soluble drugs or genes are added in the solution, it could be capsulated in the supramolecular hydrogels. Also, functional units can be employed in the units of the poly(pseudo)rotaxanes, which enhances the interaction between the poly(pseudo)rotaxanes and capsulated drugs/genes and provides the carriers with other predetermined functions. As the network is further swollen in the water-based environment, part of the carrier will be dissolved gradually, so the capsulated drug or gene can be released from the hydrogels over a long period of time. [ 27 ] [ 28 ] | https://en.wikipedia.org/wiki/Polyrotaxane |
Polysaccharides ( / ˌ p ɒ l i ˈ s æ k ə r aɪ d / ), or polycarbohydrates , are the most abundant carbohydrates found in food . They are long-chain polymeric carbohydrates composed of monosaccharide units bound together by glycosidic linkages . This carbohydrate can react with water ( hydrolysis ) using amylase enzymes as catalyst, which produces constituent sugars (monosaccharides or oligosaccharides ). They range in structure from linear to highly branched. Examples include storage polysaccharides such as starch , glycogen and galactogen and structural polysaccharides such as hemicellulose and chitin .
Polysaccharides are often quite heterogeneous, containing slight modifications of the repeating unit. Depending on the structure, these macromolecules can have distinct properties from their monosaccharide building blocks. They may be amorphous or even insoluble in water. [ 1 ]
When all the monosaccharides in a polysaccharide are the same type, the polysaccharide is called a homopolysaccharide or homoglycan, but when more than one type of monosaccharide is present, it is called a heteropolysaccharide or heteroglycan . [ 2 ] [ 3 ]
Natural saccharides are generally composed of simple carbohydrates called monosaccharides with general formula (CH 2 O) n where n is three or more. Examples of monosaccharides are glucose , fructose , and glyceraldehyde . [ 4 ] Polysaccharides, meanwhile, have a general formula of C x (H 2 O) y where x and y are usually large numbers between 200 and 2500. When the repeating units in the polymer backbone are six-carbon monosaccharides , as is often the case, the general formula simplifies to (C 6 H 10 O 5 ) n , where typically 40 ≤ n ≤ 3000 .
As a rule of thumb, polysaccharides contain more than ten monosaccharide units, whereas oligosaccharides contain three to ten monosaccharide units, but the precise cutoff varies somewhat according to the convention. Polysaccharides are an important class of biological polymers . Their function in living organisms is usually either structure- or storage-related. Starch (a polymer of glucose) is used as a storage polysaccharide in plants, being found in the form of both amylose and the branched amylopectin . In animals, the structurally similar glucose polymer is the more densely branched glycogen , sometimes called "animal starch". Glycogen's properties allow it to be metabolized more quickly, which suits the active lives of moving animals. In bacteria , they play an important role in bacterial multicellularity. [ 5 ]
Cellulose and chitin are examples of structural polysaccharides. Cellulose is used in the cell walls of plants and other organisms and is said to be the most abundant organic molecule on Earth. [ 6 ] It has many uses such as a significant role in the paper and textile industries and is used as a feedstock for the production of rayon (via the viscose process), cellulose acetate, celluloid, and nitrocellulose. Chitin has a similar structure but has nitrogen -containing side branches, increasing its strength. It is found in arthropod exoskeletons and in the cell walls of some fungi . It also has multiple uses, including surgical threads . Polysaccharides also include callose or laminarin , chrysolaminarin , xylan , arabinoxylan , mannan , fucoidan , and galactomannan .
Nutrition polysaccharides are common sources of energy. Many organisms can easily break down starches into glucose; however, most organisms cannot metabolize cellulose or other polysaccharides like cellulose , chitin , and arabinoxylans . Some bacteria and protists can metabolize these carbohydrate types. Ruminants and termites , for example, use microorganisms to process cellulose. [ 7 ]
Even though these complex polysaccharides are not very digestible, they provide important dietary elements for humans. Called dietary fiber , these carbohydrates enhance digestion. The main action of dietary fiber is to change the nature of the contents of the gastrointestinal tract and how other nutrients and chemicals are absorbed. [ 8 ] [ 9 ] Soluble fiber binds to bile acids in the small intestine, making them less likely to enter the body; this, in turn, lowers cholesterol levels in the blood. [ 10 ] Soluble fiber also attenuates the absorption of sugar, reduces sugar response after eating, normalizes blood lipid levels and, once fermented in the colon, produces short-chain fatty acids as byproducts with wide-ranging physiological activities (discussion below). Although insoluble fiber is associated with reduced diabetes risk, the mechanism by which this occurs is unknown. [ 11 ]
Not yet formally proposed as an essential macronutrient (as of 2005), dietary fiber is nevertheless regarded as important for the diet, with regulatory authorities in many developed countries recommending increases in fiber intake. [ 8 ] [ 9 ] [ 12 ] [ 13 ]
Starch is a glucose polymer in which glucopyranose units are bonded by alpha -linkages. It is made up of a mixture of amylose (15–20%) and amylopectin (80–85%). Amylose consists of a linear chain of several hundred glucose molecules, and Amylopectin is a branched molecule made of several thousand glucose units (every chain of 24–30 glucose units is one unit of Amylopectin). Starches are insoluble in water . They can be digested by breaking the alpha -linkages (glycosidic bonds). Both humans and other animals have amylases so that they can digest starches. Potato , rice , wheat , and maize are major sources of starch in the human diet. The formations of starches are the ways that plants store glucose . [ 14 ]
Glycogen serves as the secondary long-term energy storage in animal and fungal cells, with the primary energy stores being held in adipose tissue . Glycogen is made primarily by the liver and the muscles , but can also be made by glycogenesis within the brain and stomach . [ 15 ]
Glycogen is analogous to starch , a glucose polymer in plants , and is sometimes referred to as animal starch , [ 16 ] having a similar structure to amylopectin but more extensively branched and compact than starch. Glycogen is a polymer of α(1→4) glycosidic bonds linked with α(1→6)-linked branches. Glycogen is found in the form of granules in the cytosol /cytoplasm in many cell types and plays an important role in the glucose cycle . Glycogen forms an energy reserve that can be quickly mobilized to meet a sudden need for glucose, but one that is less compact and more immediately available as an energy reserve than triglycerides (lipids). [ citation needed ]
In the liver hepatocytes , glycogen can compose up to 8 percent (100–120 grams in an adult) of the fresh weight soon after a meal. [ 17 ] Only the glycogen stored in the liver can be made accessible to other organs. In the muscles , glycogen is found in a low concentration of one to two percent of the muscle mass. The amount of glycogen stored in the body—especially within the muscles , liver , and red blood cells [ 18 ] [ 19 ] [ 20 ] —varies with physical activity, basal metabolic rate , and eating habits such as intermittent fasting . Small amounts of glycogen are found in the kidneys and even smaller amounts in certain glial cells in the brain and white blood cells . The uterus also stores glycogen during pregnancy to nourish the embryo. [ 17 ]
Glycogen is composed of a branched chain of glucose residues. It is primarily stored in the liver and muscles. [ 21 ]
Galactogen is a polysaccharide of galactose that functions as energy storage in pulmonate snails and some Caenogastropoda . [ 23 ] This polysaccharide is exclusive of the reproduction and is only found in the albumen gland from the female snail reproductive system and in the perivitelline fluid of egogens have applications within hydrogel structures. These hydrogel structures can be designed to release particular nanoparticle pharmaceuticals and/or encapsulated therapeutics over time or in response to environmental stimuli. [ 24 ]
Formed by crosslinking polysaccharide-based nanoparticles and functional polymers, galactogens have applications within hydrogel structures. These hydrogel structures can be designed to release particular nanoparticle pharmaceuticals and/or encapsulated therapeutics over time or in response to environmental stimuli. [ 25 ]
Galactogens are polysaccharides with binding affinity for bioanalytes . With this, by end-point attaching galactogens to other polysaccharides constituting the surface of medical devices, galactogens have use as a method of capturing bioanalytes (e.g., CTC's), a method for releasing the captured bioanalytes and an analysis method. [ 26 ]
Inulin is a naturally occurring polysaccharide complex carbohydrate composed of fructose , a plant-derived food that human digestive enzymes cannot completely break down. The inulins belong to a class of dietary fibers known as fructans . Inulin is used by some plants as a means of storing energy and is typically found in roots or rhizomes . Most plants that synthesize and store inulin do not store other forms of carbohydrates such as starch . In the United States in 2018, the Food and Drug Administration approved inulin as a dietary fiber ingredient used to improve the nutritional value of manufactured food products. [ 27 ]
Arabinoxylans are found in both the primary and secondary cell walls of plants and are the copolymers of two sugars: arabinose and xylose . They may also have beneficial effects on human health. [ 28 ]
The structural components of plants are formed primarily from cellulose. Wood is largely cellulose and lignin , while paper and cotton are nearly pure cellulose. Cellulose is a polymer made with repeated glucose units bonded together by beta -linkages. Humans and many animals lack an enzyme to break the beta -linkages, so they do not digest cellulose. Certain animals, such as termites can digest cellulose, because bacteria possessing the enzyme are present in their gut. Cellulose is insoluble in water. It does not change color when mixed with iodine. On hydrolysis, it yields glucose. It is the most abundant carbohydrate in nature. [ 29 ]
Chitin is one of many naturally occurring polymers . It forms a structural component of many animals, such as exoskeletons . Over time it is bio-degradable in the natural environment. Its breakdown may be catalyzed by enzymes called chitinases , secreted by microorganisms such as bacteria and fungi and produced by some plants. Some of these microorganisms have receptors to simple sugars from the decomposition of chitin. If chitin is detected, they then produce enzymes to digest it by cleaving the glycosidic bonds in order to convert it to simple sugars and ammonia . [ 30 ]
Chemically, chitin is closely related to chitosan (a more water-soluble derivative of chitin). It is also closely related to cellulose in that it is a long unbranched chain of glucose derivatives. Both materials contribute structure and strength, protecting the organism. [ 31 ]
Pectins are a family of complex polysaccharides that contain 1,4-linked α- D -galactosyl uronic acid residues. They are present in most primary cell walls and in the nonwoody parts of terrestrial plants. [ 32 ]
Acidic polysaccharides are polysaccharides that contain carboxyl groups , phosphate groups and/or sulfuric ester groups. [ 33 ]
Polysaccharides containing sulfate groups can be isolated from algae [ 34 ] or obtained by chemical modification. [ 35 ]
Polysaccharides are major classes of biomolecules. They are long chains of carbohydrate molecules, composed of several smaller monosaccharides. These complex bio-macromolecules functions as an important source of energy in animal cell and form a structural component of a plant cell. It can be a homopolysaccharide or a heteropolysaccharide depending upon the type of the monosaccharides.
Polysaccharides can be a straight chain of monosaccharides known as linear polysaccharides, or it can be branched known as a branched polysaccharide.
Pathogenic bacteria commonly produce a bacterial capsule , a thick, mucus-like layer of polysaccharide. The capsule cloaks antigenic proteins on the bacterial surface that would otherwise provoke an immune response and thereby lead to the destruction of the bacteria. Capsular polysaccharides are water-soluble, commonly acidic, and have molecular weights on the order of 100,000 to 2,000,000 daltons . They are linear and consist of regularly repeating subunits of one to six monosaccharides . There is enormous structural diversity; nearly two hundred different polysaccharides are produced by E. coli alone. Mixtures of capsular polysaccharides, either conjugated or native, are used as vaccines . [ 36 ]
Bacteria and many other microbes, including fungi and algae , often secrete polysaccharides to help them adhere to surfaces and to prevent them from drying out. [ 37 ] Humans have developed some of these polysaccharides into useful products, including xanthan gum , dextran , welan gum , gellan gum , diutan gum and pullulan .
Most of these polysaccharides exhibit useful visco-elastic properties when dissolved in water at very low levels. [ 38 ] This makes various liquids used in everyday life, such as some foods, lotions, cleaners, and paints, viscous when stationary, but much more free-flowing when even slight shear is applied by stirring or shaking, pouring, wiping, or brushing. This property is named pseudoplasticity or shear thinning ; the study of such matters is called rheology . [ citation needed ]
Aqueous solutions of the polysaccharide alone have a curious behavior when stirred: after stirring ceases, the solution initially continues to swirl due to momentum, then slows to a standstill due to viscosity and reverses direction briefly before stopping. This recoil is due to the elastic effect of the polysaccharide chains, previously stretched in solution, returning to their relaxed state.
Cell-surface polysaccharides play diverse roles in bacterial ecology and physiology . They serve as a barrier between the cell wall and the environment, mediate host-pathogen interactions. Polysaccharides also play an important role in formation of biofilms and the structuring of complex life forms in bacteria like Myxococcus xanthus [ 5 ] .
These polysaccharides are synthesized from nucleotide -activated precursors (called nucleotide sugars ) and, in most cases, all the enzymes necessary for biosynthesis, assembly and transport of the completed polymer are encoded by genes organized in dedicated clusters within the genome of the organism . Lipopolysaccharide is one of the most important cell-surface polysaccharides, as it plays a key structural role in outer membrane integrity, as well as being an important mediator of host-pathogen interactions.
The enzymes that make the A-band (homopolymeric) and B-band (heteropolymeric) O-antigens have been identified and the metabolic pathways defined. [ 40 ] The exopolysaccharide alginate is a linear copolymer of β-1,4-linked D -mannuronic acid and L -guluronic acid residues, and is responsible for the mucoid phenotype of late-stage cystic fibrosis disease. The pel and psl loci are two recently discovered gene clusters that also encode exopolysaccharides found to be important for biofilm formation. Rhamnolipid is a biosurfactant whose production is tightly regulated at the transcriptional level, but the precise role that it plays in disease is not well understood at present. Protein glycosylation , particularly of pilin and flagellin , became a focus of research by several groups from about 2007, and has been shown to be important for adhesion and invasion during bacterial infection. [ 41 ]
Polysaccharides with unprotected vicinal diols or amino sugars (where some hydroxyl groups are replaced with amines ) give a positive periodic acid-Schiff stain (PAS). The list of polysaccharides that stain with PAS is long. Although mucins of epithelial origins stain with PAS, mucins of connective tissue origin have so many acidic substitutions that they do not have enough glycol or amino-alcohol groups left to react with PAS. [ citation needed ]
By chemical modifications certain properties of polysaccharides can be improved. Various ligands can be covalently attached to their hydroxyl groups. Due to the covalent attachment of methyl-, hydroxyethyl- or carboxymethyl- groups on cellulose , for instance, high swelling properties in aqueous media can be introduced. [ 42 ]
Another example is thiolated polysaccharides. [ 43 ] (See thiomers .) Thiol groups are covalently attached to polysaccharides such as hyaluronic acid or chitosan . [ 44 ] [ 45 ] As thiolated polysaccharides can crosslink via disulfide bond formation, they form stable three-dimensional networks. Furthermore, they can bind to cysteine subunits of proteins via disulfide bonds. Because of these bonds, polysaccharides can be covalently attached to endogenous proteins such as mucins or keratins. [ 43 ] | https://en.wikipedia.org/wiki/Polysaccharide |
Polysialic acid is an unusual posttranslational modification that occurs on neural cell adhesion molecules (NCAM). Polysialic acid is considerably anionic . This strong negative charge gives this modification the ability to change the protein's surface charge and binding ability. In the synapse , polysialation of NCAM prevents its ability to bind to NCAMs on the adjacent membrane.
Polysialic acid (polySia) is polymer of linearly repeating monomer units of α2,8- and α2,9-glycosidic linked sialic acid residues. Sialic acid refers to carboxylated 9-carbon sugars, 2-keto-3-dexoxy-D- glycero -nononic acids. [ 1 ] An unusual property of this sugar is that it often polymerizes into polySia. This is accomplished by attaching the monomers to the nonreducing end of the glycan. This mostly consists of Neu5Ac subunits. [ 2 ] It is polyanionic and bulky, meaning there is little ability to reach its central molecules. polySia is useful in signaling in vertebrates and on the cell surface of few glycoproteins and glycolipids causing modifications, and it has been recently found that the function of polySia relates almost directly to its degree of polymerization . [ 2 ] The number of units can range from 8 to greater than 400. This vast range causes differences in the polySia's ability to adhere different cells, assist in cellular migration , synapse formation , and regulate adhesion in nerve cells by modeling and formating them. [ 3 ] polySia's most prominent role is in post-translational modifications in a few proteins, with the main one being NCAM. [ 4 ] polySia links to adhesion molecules causing their adhesive properties to be subdued allowing for the detailed control of cell migration and cell to cell relations. This is caused by polySia's bulky and polyanionic properties.
The human body produces polySia naturally and attaches it to a various number of proteins. This is done by linking polySia on the α2,3- or α2,6- terminal of the glycoprotein. O -linked glycosylation through threonine or N -linked glycosylation through asparagine is employed. This polySia linkage is found in proteins such as NCAM, E-selectin ligand 1 (ESL-1), C–C chemokine receptor type 7 (CCR7), synaptic cell adhesion molecule-1 (SynCAM-1), neuropilin-2 (NRP-2), the CD36 scavenger receptor found in the milk of humans, and the α-subunit of the voltage-sensitive sodium channel. [ 2 ] The synthesis of polySia is enzymatically formed by α2,8-sialyltransferase (ST8Sia) in a Type II transmembrane protein located on the Golgi Apparatus membrane. [ 2 ] ST8Sia does this by adding sialic acids to the terminal end of the glycan through the CMP-sialic acid donor at various lengths depending on necessity. The length is controlled extensively by the expression of polysialyltransferase enzymes, once again controlling the function of polySia.
polySia was discovered in E. coli K-235 by Barry and Goebel in 1957. [ 1 ] E. coli is an encapsulated, gram-negative bacteria in which Barry and Goebel studied, pinpointing polySia, which they called colominic acid. Following this discovery, multiple other bacterial capsules abundant in glycans were found to contain polySia. This included Neisseia meningitidis serogroups B and C in 1975. This was done by the use of a horse anti-polySia polyclonal antibody , being one of the first effective immunochemical probes. This was revolutionary as the anti-polySia antibodies were used to find polySia on proteins and cells. Mannheimia haemolytica A2, Moraxella nonliquifaciens , and E. coli K92 were found in 2013. [ 1 ] Due to the capsule containing polySia, many scientists have tried to generate vaccines for these specific bacteria, notoriously difficult to target. However, their successes have been numbered as α2,8-polySia is naturally produced by humans. Another issue is that polySia found in bacteria does not produce a solid or consistent immune response . [ 1 ]
Another method of polySia detection relies on molecular labeling with fluorescence . This process, started in 1998, involves exposing α2→8-linked N -acylneuraminic acid (Neu5Acyl) to periodate oxidation causing the terminals to be oxidized and in between untouched. If C 9 compounds are observed after this exposure it indicates the presence of polySia. The way these can be numbered is by anion exchange chromatography after periodate oxidation with the label 1,2-diamino-4,5-methylenedioxybenzene (DMB) on C 7 and C 9 . It is known that there are many different structures of polySia and these were difficult to recognize and detect until this fluorescent labeling, making it very advantageous. [ 1 ]
polySia is involved in many natural human functions. The major examples include membranes , neuron signaling, the immune system , neutrophil extracellular trap formation, and macrophage and microglia function. First, polySia makes membrane modifications due to interactions with a variety of factors. These could include repulsive forces between the polyanionic polySia and the mostly negatively charged glycocalyx . [ 2 ] Because of these interactions the membrane is edited in its ability to interact with other cells, its surface charge distribution, inter-membrane interaction, pH , and membrane potential . Hydration and charge were noted before and after removing polySia from a membrane and a 25% decrease in the distance between cells was observed. [ 2 ] This is due to the anti-adhesive properties of polySia. polySia does not only have repulsive interactions, as there are positive charge molecules located in lipid rafts , such as NCAM. The interaction between polySia and NCAM greatly affects NCAM's signaling ability as its composition is altered when they meet. Other forms of neuron signaling polySia is involved in include brain-derived neurotrophic factor (BDNF) and fibroblast growth factor 2 (FGF2). With nearly the same mechanism, the act of polysialylation causes BDNF or FGF2 complexes through electrostatic interactions . This allows for the binding of polySia and these complexes causing polySia to be a reservoir. polySia then regulates the concentration of neurotrophins . Because they are not allowed to diffuse, signaling is more efficient. polySia is also found on immune cell surfaces. Some of the proteins are known, but many are not and the mechanisms are still being studied. However, it is known that polySia is in regulatory functions in the immune system leading to protection from invaders and response to damaged tissue. [ 2 ] polySia is involved in NETosis which is a reactionary function of the body in the presence of foreign invaders. It is the intentional death of neutrophils. polySia ensures that this targeted cell death does not kill cells that are healthy and unaffected, as well as containing antimicrobial attributes. This is done by polySia by binding to lactoferrin , another antimicrobial molecule, surrounding neutrophils. polySia binding causes a tighter shell of lactoferrin around the cell membrane. [ 2 ] polySia binds with Siglec-11 allowing for the regulation of microglia through exosomes . This shows that polySia binding with Siglec-11 causes a delay in neurodegeneration and control of neuroinflammation. polySia also limits inflammation in macrophages. polySia was found to have limited the expression of tumour necrosis factor (TNF). [ 2 ] | https://en.wikipedia.org/wiki/Polysialic_acid |
Polysiphonous describes an algal branch with axial cells each surrounded by cells of the same length as the axial cells. [ 1 ]
This alga -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polysiphonous |
In crystallography , the term polysome is used to describe overall mineral structures which have structurally and compositionally different framework structures.
A general example is amphiboles , in which cutting along the {010} plane yields alternating layers of pyroxene and trioctahedral mica . [ 1 ]
This crystallography -related article is a stub . You can help Wikipedia by expanding it .
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polysome_(crystallography) |
Polysome profiling is a technique in molecular biology that is used to study the association of mRNAs with ribosomes . It is different from ribosome profiling . Both techniques have been reviewed [ 1 ] and both are used in analysis of the translatome , but the data they generate are at very different levels of specificity. When employed by experts, the technique is remarkably reproducible: the 3 profiles in the first image are from 3 different experiments. [ 2 ]
The procedure begins by making a cell lysate of the cells of interest. This lysate contains polysomes , monosomes (composed of one ribosome residing on an mRNA ), the small (40 S in eukaryotes ) and large (60S in eukaryotes) ribosomal subunits, "free" mRNA and a host of other soluble cellular components.
The procedure continues by making a continuous sucrose gradient of continuously variable density in a centrifuge tube. At the concentrations used (15-45% in the example), sucrose does not disrupt the association of ribosomes and mRNA. The 15% portion of the gradient is at the top of the tube, while the 45% portion is at the bottom because of their different density .
A specific amount (as measured by optical density ) of the lysate is then layered gently on top of the gradient in the tube. The lysate, even though it contains a large amount of soluble material, is much less dense than 15% sucrose, and so it can be kept as a separate layer at the top of the tube if this is done gently.
In order to separate the components of the lysate, the preparation is subjected to centrifugation. This accelerates the components of the lysate with many times the force of gravity and thus propels them through the gradient based upon how "big" the individual components are. The small (40S) subunits travel less far into the gradient than the large (60S) subunits. The 80S ribosomes on an mRNA travel further (note that the contribution of the size of the mRNA to the distance traveled is not significant). Polysomes composed of 2 ribosomes travel further, polysomes with 3 ribosomes travel further still, and on and on. The "size" of the components is designated by S, the svedberg unit. Note that one S = 10 −13 seconds, and that the concept of "big" is actually an oversimplification.
After centrifugation, the contents of the tube are collected as fractions from the top (smaller, slower traveling) to bottom (bigger, faster traveling) and the optical density of the fractions is determined. The first fractions removed have a large amount of relatively small molecules, such as tRNAs, individual proteins, etc.
It is possible to use this technique to study the overall degree of translation in cells (for examples [ 3 ] [ 4 ] [ 5 ] ), but it can be used much more specifically to study individual proteins and their mRNAs. As an example shown in the lower portion of the figure, a protein that composes part of the small subunit can first be detected in the 40S fraction, then nearly disappears from the 60S fraction (the separations on these gradients are not absolute), then reappears in the 80S and polysome fractions. This indicates that there is at most very little of the protein found in the cell that is not part of the small subunit. In contrast, in the upper row of the immunoblot figure, a soluble protein appears in the soluble fractions and associated with ribosomes and polysomes. The particular protein is a chaperone protein , which (in brief) helps to fold the nascent peptide as it is being extruded from the ribosome. As other work in the paper showed, there is a direct association of the chaperone with the ribosome. [ 2 ]
The technique can also be used to study the degree of translation of a particular mRNA [ 6 ] In these experiments, 5' and 3' sequences of an mRNA were investigated for their effects on amount of mRNA produced and how well the mRNAs were translated. As shown, not all mRNA isoforms are translated with the same efficiency even though their coding sequences are the same. [ 6 ] | https://en.wikipedia.org/wiki/Polysome_profiling |
Polysorbates are a class of emulsifiers used in some pharmaceuticals and food preparation. They are commonly used in oral and topical pharmaceutical dosage forms. They are also often used in cosmetics to solubilize essential oils into water-based products. Polysorbates are oily liquids derived from ethoxylated sorbitan (a derivative of sorbitol ) esterified with fatty acids . Common brand names for polysorbates include Kolliphor, [ 1 ] Scattics, Alkest, Canarcel, Tween, [ 2 ] and Kotilen.
The number following the 'polysorbate' part is related to the type of major fatty acid associated with the molecule. Monolaurate is indicated by 20, monopalmitate is indicated by 40, monostearate by 60, and monooleate by 80. The number 20 following the 'polyoxyethylene' part refers to the total number of oxyethylene (–CH 2 CH 2 O–) groups found in the molecule.
This food ingredient article is a stub . You can help Wikipedia by expanding it .
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polysorbate |
In biology, polyspermy describes the fertilization of an egg by more than one sperm . Diploid organisms normally contain two copies of each chromosome , one from each parent. The cell resulting from polyspermy, on the other hand, contains three or more copies of each chromosome—one from the egg and one each from multiple sperm. Usually, the result is an unviable zygote . This may occur because sperm are too efficient at reaching and fertilizing eggs due to the selective pressures of sperm competition . Such a situation is often deleterious to the female: in other words, the male–male competition among sperm spills over to create sexual conflict . [ 1 ]
In the classical case (at least from the historical human perspective), monospermic fertilization is the norm. For monospermic organisms, polyspermy is a detrimental process where eggs are incorrectly fertilized. It causes the formation of multiple microtubule-organizing centers from multiple, leading to disruption of mitosis, disarrayment in cleavage furrow formation, [ 2 ] and ultimately, cell death. As a result, a number of "blocks" have evolved to prevent polyspermy in such organisms. [ 3 ]
Polyspermy is very rare in human reproduction. The decline in the numbers of sperm that swim to the oviduct is one of two ways that prevents polyspermy in humans. The other mechanism is the blocking of sperm in the fertilized egg. [ 4 ] Only two cases of human polyspermy leading to birth of children have been reported. [ 5 ]
The eggs of sexually-reproducing organisms are adapted to avoid this situation. [ 6 ] The defenses are particularly well characterized in the sea urchin , which respond to the acceptance of one sperm by inhibiting the successful penetration of the egg by subsequent sperm. Similar defenses exist in other eukaryotes .
The prevention of polyspermy in sea urchins depends on a change in the electrical charge across the surface of the egg, which is caused by the fusion of the first sperm with the egg. [ 7 ] Unfertilized sea urchin eggs have a negative charge inside, but the charge becomes positive upon fertilization. When sea urchin sperm encounter an egg with a positive charge, sperm-egg fusion is blocked. Thus, after the first sperm contacts the egg and causes the change, subsequent sperms are prevented from fusing. This "electrical polyspermy block" is thought to result because a positively charged molecule in the sperm surface membrane is repelled by the positive charge at the egg surface. [ 8 ]
Electrical polyspermy blocks operate in many animal species, including frogs , clams , and marine worms , but not in the several mammals that have been studied ( hamster , rabbit , mouse ). [ 9 ] In species without an electrical block, polyspermy is usually prevented by secretion of materials that establish a mechanical barrier to polyspermy. Animals such as sea urchins have a two-step polyspermy prevention strategy , with the fast, but transient, electrical block superseded after the first minute or so by a more slowly developing permanent mechanical block. Electrical blocks are helpful in species where a very fast block to polyspermy is needed, due to the presence of many sperm arriving simultaneously at the egg surface, as occurs in animals such as sea urchins. In sea urchins, fertilization occurs externally in the ocean, such that hundreds of sperm can encounter the egg within several seconds.
In mammals, it occurs 2-3 seconds after the first sperm enters the egg. It is a chemical process which involves changing the potential of egg from a resting potential of -70 mv to 10 mv. It involves an influx of sodium ion into the egg. The membrane of the egg changes from negatively to positively charged. Sperm cannot enter a positively charged egg. The positive charge only lasts for 60 seconds. [ citation needed ]
In mammals, in which fertilization occurs internally, fewer sperm reach the fertilization site in the oviduct . This may be the result of the female genital tract being adapted to minimize the number of sperm reaching the egg. [ 10 ] Nevertheless, polyspermy preventing mechanisms are essential in mammals; a secretion reaction, the " cortical reaction " modifies the extracellular coat of the egg (the zona pellucida ), and additional mechanisms that are not well understood modify the egg's plasma membrane. [ 11 ] The zona pellucida is modified by serine proteases that are released from the cortical granules. The proteases destroy the protein link between the cell membrane and the vitelline envelope, remove any receptors that other sperm have bound to, and help to form the fertilization envelope from the cortical granules. [ 12 ]
The cortical reaction occurs due to calcium oscillations inside the oocyte. What triggers such oscillations is PLC-zeta, a phospholipase unique to sperm that is very sensitive to calcium concentrations. When the first spermatozoa get inside the oocyte, it brings in PLC-zeta, that is activated by oocyte's basal calcium concentrations, initiates the formation of IP3 and causes calcium release from endoplasmic reticulum stores, generating the oscillations in calcium concentration that will activate the oocyte and block polyspermy. [ 13 ]
Physiological polyspermy happens when the egg normally accepts more than one sperm but only one of the multiple sperm will fuse its nucleus with the nucleus of the egg. Physiological polyspermy is present in some species of vertebrates and invertebrates. Some species utilize physiological polyspermy as the proper mechanism for developing their offspring. Some of these animals include birds, ctenophora , reptiles and amphibians. Some vertebrates that are both amniote or anamniote, including urodele amphibians , cartilaginous fish , birds and reptiles, undergo physiological polyspermy because of the internal fertilization of their yolky eggs. Sperm triggers egg activation by the induction of free calcium ion concentration in the cytoplasm of the egg. This induction plays a very critical role in both physiological polyspermy and monomeric polyspermy species. The rise in calcium causes activation of the egg. The egg will then be altered on both a biochemical and morphological level. [ 14 ] In mammals as well as sea urchins, the sudden rise in calcium concentration occurs because of the influx of calcium ions within the egg. These calcium ions are responsible for the cortical granule reaction, and are also stored in the egg's endoplasmic reticulum. [ 15 ]
Unlike physiological polyspermy, monospermic fertilization (described above) deals with the analysis of the egg calcium waves, as this is the typical reproduction process in all species. Species that undergo physiological polyspermy have polyploidy -preventing mechanisms that act inside the egg. This is quite different from the normal polyspermy block on the outside of the egg. [ 16 ] Even though multiple sperm enter the cell and each form an aster (see: Fertilisation § The sperm aster and zygote centrosomes ), only one male pronucleus is chosen to merge with the female pronucleus. [ 3 ]
In amphibians, the sperm pronucleus needs to be in the animal hemisphere to be chosen. It's also known that the chosen pronucleus also has the biggest aster, though details on how this is achieved (and how precisely it affects choice) remains unknown. The addition pronuclei are degraded during cleavage. [ 17 ] In birds, the chosen pronucleus moves to the center of the germinal disk, while the others move to the periphery. [ 3 ]
In the journal Proceedings of the Royal Society B , [ 18 ] as reported in the New York Times , [ 19 ] Dr. Nicola Hemmings, an evolutionary biologist at the University of Sheffield, and one of the study's authors reported that the eggs of zebra finches and chickens require multiple sperm, from 10 to hundreds of sperm, to penetrate the egg to ensure successful fertilization and growth of the bird embryo.
Yet another case involves normally monospermic organisms that "tolerate" polyspermy without ill effects. In other words, they too can choose one sperm pronucleus to fuse with, discarding the rest. A number of species is known to exhibit this unusual behavior, but this case is very poorly studied. [ 3 ]
Pathological polyspermy is costly for females as it decreases their chances to produce offspring. This would make investing into defenses that block polyspermy viable. Female defenses select for ever more aggressive male sperm, however, leading to an evolutionary arms race . On the one hand, polyspermy creates inviable zygotes and lowers female fitness, but on the other, defenses may prevent fertilization altogether. This leads to a delicate compromise between the two, and has been suggested as one possible cause for the relatively high infertility rates seen in mammalian species. [ 20 ]
The existence of compensable polyspermy suggests an alternative solution: females could also evolve tolerance of polyspermy to reduce its costs. [ 3 ] | https://en.wikipedia.org/wiki/Polyspermy |
Polysporangiophytes , also called polysporangiates or formally Polysporangiophyta , are plants in which the spore-bearing generation ( sporophyte ) has branching stems (axes) that bear sporangia . The name literally means 'many sporangia plant'. The clade includes all land plants ( embryophytes ) except for the bryophytes (liverworts, mosses and hornworts) whose sporophytes are normally unbranched, even if a few exceptional cases occur. [ 1 ] While the definition is independent of the presence of vascular tissue , all living polysporangiophytes also have vascular tissue, i.e., are vascular plants or tracheophytes. Extinct polysporangiophytes are known that have no vascular tissue and so are not tracheophytes.
Paleobotanists distinguish between micro- and megafossils. Microfossils are primarily spores , either single or in groups. Megafossils are preserved parts of plants large enough to show structure, such as stem cross-sections or branching patterns. [ 2 ]
Dawson , a Canadian geologist and paleobotanist, was the first to discover and describe a megafossil of a polysporangiophyte. In 1859 he published a reconstruction of a Devonian plant, collected as a fossil from the Gaspé region of Canada, which he named Psilophyton princeps . The reconstruction shows horizontal and upright stem-like structures; no leaves or roots are present. The upright stems or axes branch dichotomously and have pairs of spore-forming organs ( sporangia ) attached to them. Cross-sections of the upright axes showed that vascular tissue was present. He later described other specimens. Dawson's discoveries initially had little scientific impact; Taylor et al. speculate that this was because his reconstruction looked very unusual and the fossil was older than was expected. [ 3 ]
From 1917 onwards, Robert Kidston and William H. Lang published a series of papers describing fossil plants from the Rhynie chert – a fine-grained sedimentary rock found near the village of Rhynie, Aberdeenshire , now dated to the Pragian of the Lower Devonian (around 413 to 411 million years ago ). The fossils were better-preserved than Dawson's, and showed clearly that these early land plants did indeed consist of generally naked vertical stems arising from similar horizontal structures. The vertical stems were dichotomously branched with some branches ending in sporangia. [ 3 ]
Since these discoveries, similar megafossils have been discovered in rocks of Silurian to mid-Devonian age throughout the world, including Arctic Canada, the eastern US, Wales, the Rhineland of Germany, Kazakhstan, Xinjiang and Yunnan in China, and Australia. [ 4 ]
As of 2019 [update] , Eohostimella , dated to the Llandovery epoch ( 443 to 433 million years ago ), is one of the earliest fossils that has been identified as a polysporangiophyte. [ 5 ] [ 6 ] Fossils assigned to the genus Cooksonia , which is more certainly a polysporangiophyte, have been dated to the succeeding Wenlock epoch ( 433 to 427 million years ago ). [ 7 ] [ 8 ]
The concept of the polysporangiophytes, more formally called Polysporangiophyta, was first published in 1997 by Kenrick and Crane. [ 9 ] (The taxobox at the right represents their view of the classification of the polysporangiophytes.) The defining feature of the clade is that the sporophyte branches and bears multiple sporangia. This distinguishes polysporangiophytes from liverworts , mosses and hornworts , which have unbranched sporophytes each with a single sporangium. Polysporangiophytes may or may not have vascular tissue – those that do are vascular plants or tracheophytes. [ citation needed ]
Prior to that, most of the early polysporangiophytes had been placed in a single order , Psilophytales, in the class Psilophyta, established in 1917 by Kidston and Lang. [ 10 ] The living Psilotaceae , the whisk-ferns, were sometimes added to the class, which was then usually called Psilopsida. [ 11 ]
As additional fossils were discovered and described, it became apparent that the Psilophyta were not a homogeneous group of plants. In 1975, Banks expanded on his earlier 1968 proposal that split it into three groups at the rank of subdivision. [ 12 ] [ 13 ] These groups have since been treated at the ranks of division, [ 14 ] class [ 15 ] and order. [ 16 ] A variety of names have been used, which the table below summarizes.
For Banks, rhyniophytes comprised simple leafless plants with terminal sporangia (e.g., Cooksonia , Rhynia ) with centrarch xylem ; zosterophylls comprised plants with lateral sporangia that split distally (away from their attachment) to release their spores, and had exarch strands of xylem (e.g., Gosslingia ). Trimerophytes comprised plants with large clusters of downwards curving terminal sporangia that split along their length to release their spores and had centrarch xylem strands (e.g., Psilophyton ). [ 19 ]
Research by Kenrick and Crane that established the polysporangiophytes concluded that none of Banks' three groups were monophyletic . The rhyniophytes included "protracheophytes", which were precursors to vascular plants (e.g., Horneophyton , Aglaophyton ); basal tracheophytes (e.g., Stockmansella , Rhynia gwynne-vaughanii ); and plants allied to the lineages that led to the living club-mosses and allies as well as ferns and seed plants (e.g., Cooksonia species). The zosterophylls did contain a monophyletic clade, but some genera previously included in the group fell outside this clade (e.g., Hicklingia , Nothia ). The trimerophytes were paraphyletic stem groups to both the crown group ferns and the crown group seed plants . [ 20 ] [ 21 ]
Many researchers have urged caution in the classification of early polysporangiophytes. Taylor et al. note that basal groups of early land plants are inherently difficult to characterize since they share many characters with all later-evolving groups (i.e., have multiple plesiomorphies ). [ 14 ] In discussing the classification of the trimerophytes, Berry and Fairon-Demaret say that reaching a meaningful classification requires "a breakthrough in knowledge and understanding rather than simply a reinterpretation of the existing data and the surrounding mythology". [ 22 ] Kenrick and Crane's cladograms have been questioned – see the Evolution section below.
As of February 2011 [update] , there appears to be no complete Linnean (i.e., rank-based) classification for early polysporangiophytes that is consistent with Kenrick and Crane's cladistic analysis and subsequent research, though Cantino et al. have published a Phylocode classification. [ 23 ] Banks' three groups continue to be used for convenience. [ 14 ]
A major cladistic study of land plants was published in 1997 by Kenrick and Crane; this both established the concept of the polysporangiophytes and presented a view of their phylogeny . [ 9 ] Since 1997 there have been continual advances in understanding plant evolution, using RNA and DNA genome sequences and chemical analyses of fossils (e.g., Taylor et al. 2006 [ 24 ] ), resulting in revisions to this phylogeny.
In 2004, Crane et al. published a simplified cladogram for the polysporangiophytes (which they call polysporangiates), based on a number of figures in Kenrick and Crane (1997). [ 10 ] Their cladogram is reproduced below (with some branches collapsed into 'basal groups' to reduce the size of the diagram). Their analysis is not accepted by other researchers; for example Rothwell and Nixon say that the broadly defined fern group (moniliforms or monilophytes) is not monophyletic. [ 25 ]
† Horneophytopsida ( Caia , Horneophyton , Tortilicaulis )
† Aglaophyton
† Rhyniaceae ( Huvenia , Rhynia , Stockmansella )
† basal groups ( Aberlemnia caledonica [= Cooksonia caledonica ], Cooksonia pertoni )
Cooksonia cambrensis, Renalia , Sartilmania , Uskiella , Yunia
† Hicklingia
Adoketophyton , Discalis , Distichophytum (= Rebuchia ), Gumuia , Huia , Zosterophyllum myretonianum , Z. llanoveranum, Z. fertile
Zosterophyllum divaricatum , Tarella , Oricilla , Gosslingia , Hsua , Thrinkophyton , Protobarinophyton , Barinophyton obscurum , B. citrulliforme , Sawdonia , Deheubarthia , Konioria , Anisophyton , Serrulacaulis , Crenaticaulis
Nothia , Zosterophyllum deciduum
extant and extinct members
† Eophyllophyton
† basal groups ( Psilophyton crenulatum, Ps. dawsonii )
moniliforms (ferns; extant and extinct members)
† basal groups ( Pertica , Tetraxylopteris )
spermatophytes (seed plants; extant and extinct members)
More recently, Gerrienne and Gonez have suggested a slightly different characterization of the early diverging polysporangiophytes: [ 26 ]
†'Protracheophytes'
†Paratracheophytes
Eutracheophytes
The paraphyletic protracheophytes, such as Aglaophyton , have water-conducting vessels like those of mosses, i.e., without cells containing thickened cell walls. The paratracheophytes, a name intended to replace Rhyniaceae or Rhyniopsida, have 'S-type' water-conducting cells, i.e., cells whose walls are thickened but in a much simpler fashion than those of true vascular plants, the eutracheophytes. [ 26 ]
If the cladogram above is correct it has implications for the evolution of land plants. The earliest diverging polysporangiophytes in the cladogram are the Horneophytopsida , a clade at the 'protracheophyte' grade that is sister to all other polysporangiophytes. They had essentially an isomorphic alternation of generations (meaning that the sporophytes and gametophytes were equally free living), which might suggest that both the gametophyte-dominant life style of bryophytes and the sporophyte-dominant life style of vascular plants evolved from this isomorphic condition. They were leafless and did not have true vascular tissues. In particular, they did not have tracheids : elongated cells that help transport water and mineral salts, and that develop a thick lignified wall at maturity that provides mechanical strength. Unlike plants at the bryophyte grade, their sporophytes were branched. [ 27 ]
According to the cladogram, the genus Rhynia illustrates two steps in the evolution of modern vascular plants. Plants have vascular tissue, albeit significantly simpler than modern vascular plants. Their gametophytes are distinctly smaller than their sporophytes (but have vascular tissue, unlike almost all modern vascular plants). [ 28 ]
The remainder of the polysporangiophytes divide into two lineages, a deep phylogenetic split that occurred in the early to mid Devonian, around 400 million years ago. Both lineages have developed leaves, but of different kinds. The lycophytes, which make up less than 1% of the species of living vascular plants, have small leaves ( microphylls or more specifically lycophylls), which develop from an intercalary meristem (i.e., the leaves effectively grow from the base). The euphyllophytes are by far the largest group of vascular plants, in terms of both individuals and species. Euphyllophytes have large 'true' leaves (megaphylls), which develop through marginal or apical meristems (i.e., the leaves effectively grow from the sides or the apex). ( Horsetails have secondarily reduced megaphylls resembling microphylls.) [ 29 ]
Both the cladogram derived from Kenrick and Crane's studies and its implications for the evolution of land plants have been questioned by others. A 2008 review by Gensel notes that recently discovered fossil spores suggest that tracheophytes were present earlier than previously thought; perhaps earlier than supposed stem group members. Spore diversity suggests that there were many plant groups, of which no other remains are known. Some early plants may have had heteromorphic alternation of generations, with later acquisition of isomorphic gametophytes in certain lineages. [ 30 ]
The cladogram above shows the 'protracheophytes' diverging earlier than the lycophytes; however, lycophytes were present in the Ludfordian stage of the Silurian around 430 to 420 million years ago , long before the 'protracheophytes' found in the Rhynie chert , dated to the Pragian stage of the Devonian around 410 million years ago . [ 31 ] However, it has been suggested that the poorly preserved Eohostimella , found in deposits of Early Silurian age (Llandovery, around 440 to 430 million years ago ), may be a rhyniophyte. [ 6 ]
Boyce has shown that the sporophytes of some Cooksonia species and allies ('cooksonioids') had stems that were too narrow to have supported sufficient photosynthetic activity for them to be independent of their gametophytes – inconsistent with their position in the cladogram. [ 32 ]
Because the stomata in mosses , hornworts and polysporangiophytes are viewed as homologous, it has been suggested they belong in a natural group named stomatophytes . [ 33 ]
The evolutionary history of plants is far from settled. [ citation needed ] | https://en.wikipedia.org/wiki/Polysporangiophyte |
Polystannanes are organotin compounds with the formula (R 2 Sn) n . These polymers have been of intermittent academic interest; they are unusual because heavy elements comprise the backbone. Structurally related but better characterized (and more useful) are the polysilanes (R 2 Si) n .
Oligo- or polystannanes were first described by Löwig in 1852, [ 1 ] only 2 years after Edward Frankland 's report on the isolation of the first organotin compounds. [ 2 ] Löwig's route involved treating an Sn/K and Sn/Na alloys with iodoethane , in the presence of quartz sand which was used to control the reaction rate . Products with elemental compositions close to those of oligo(diethyl stannane )s or poly(diethylstannane) were obtained. Cahours obtained similar products and attributed the formation of the so-called "stannic ethyl" to a reaction of the Wurtz type . [ 3 ] Already in 1858, "stannic ethyl" was formulated as a polymeric compound denoted with the composition n(SnC 4 H 5 ). [ 4 ] In 1917 Grüttner, [ 5 ] who reinvestigated results on hexaethyl- distannanes (H 5 C 2 ) 3 Sn-Sn(C 2 H 5 ) 3 (reported by Ladenburg in 1870) confirmed the presence of Sn-Sn bonds and predicated for the first time that tin could form chain like compounds. [ 6 ] In 1943, it was postulated that “diphenyltin” exists as a type of polymeric material because of its yellow color, [ 7 ] and indeed a bathochromic shift of the wavelength at maximum absorption with increasing number of Sn atoms was found later in the case of oligo(dibutylstannane)s comprising up to 15 Sn atoms. [ 8 ]
The Wurtz reaction is still used for the preparation of poly(dialkylstannane)s. Treatment of dialkyltin dichlorides with sodium lead to polystannanes of high molar mass , however, in low yields and with formation of (cyclic) oligomers. [ 9 ] [ 10 ] Other efforts to prepare high molar mass polystannanes by electrochemical reactions [ 11 ] or by catalytic dehydropolymerization of dialkylstannanes (R 2 SnH 2 ) were also made. [ 10 ] [ 12 ] Unfortunately, frequently, the polymers prepared by those methods were not isolated and typically contained significant fractions of cyclic oligomers.
Alternatively, alkyltin halides react with excess electride in ammonia solutions to give metal alkylstannides. Added alkyltin halides then couple to the stannides to give polystannanes. [ 13 ]
Dialkytin dihydrides (R 2 SnH 2 ) were reported in 2005 to undergo dehydropolymerization in the presence of Wilkinson’s catalyst . This method afforded polystannanes without detectable amounts of "cyclic"-byproducts. The polymers were yellow with number average molar masses of 10 to 70 kg/mol and a polydispersity of 2 – 3. [ 14 ] By variation of the catalyst concentration the molar masses of the synthesized polymers could be adjusted. A strong influence of the temperature on the degree of conversion was observed. Determination of the molar mass at different degrees of conversion indicated that polymerization did not proceed according to a statistical condensation mechanism, but, likely, by growth onto the catalyst, e.g. by insertion of SnR 2 -like units.
The poly(dialkylstannane)s were found to be thermotropic and displayed first-order phase transitions from one liquid-crystalline phase into another or directly to the isotropic state, depending on the length of the side groups. More specifically, poly(dibutylstannane) for example showed an endothermic phase transition at ~0 °C from a rectangular to a pure nematic phase, as determined by X-ray diffraction . [ 15 ]
Like polysilanes , polystannanes are semi-conductive . Temperature-dependent, time-resolved pulse radiolysis microwave conductivity measurements of poly(dibutylstannane) yielded values of charge-carrier mobilities of 0.1 to 0.03 cm2 V −1 s −1 , which are similar to those found for pi-bond-conjugated carbon-based polymers. By partial oxidation of the material with SbF 5 conductivities of 0.3 S cm −1 could be monitored. [ 16 ]
The liquid-crystalline characteristics of the poly(dialkylstannane)s permitted facile orientation of these macromolecules, for instance, by mechanical shearing or tensile drawing of blends with poly(ethylene). Poly(dialkylstannane)s with short side groups invariably arranged parallel to the external orientation direction, while the polymers with longer side groups had a tendency to order themselves perpendicular to that axis. | https://en.wikipedia.org/wiki/Polystannane |
Polysuccinimide (PSI), also known as polyanhydroaspartic acid or polyaspartimide , is formed during the thermal polycondensation of aspartic acid and is the simplest polyimide . [ 5 ] Polysuccinimide is insoluble in water, but soluble in some aprotic dipolar solvents . Its reactive nature makes polysuccinimide a versatile starting material for functional polymers made from renewable resources . [ 5 ]
The name is derived from the salt of succinic acid , the structurally related succinate.
The production of polysuccinimide was reported by Hugo Schiff as early as 1897. [ 6 ] When dry aspartic acid was heated for about 20 hours at 190 °C to 200 °C, a colorless product was obtained. Above 200 °C, a weak yellowing occurs, the yield was almost quantitative. [ 7 ]
In the experiments by Hugo Schiff, oligomers and low-molecular polymers were formed in a solid state reaction by polycondensation upon water elimination. This is generally the case in the absence of strong acids, which suppress the thermal decomposition of free amino end groups and thus chain interruption reactions. The formation of the polyimide polysuccinimide can be followed by the intensive absorption band in the infrared spectrum at 1714 cm −1 . Many process variants described in the patent literature yield besides a relatively low degree of polymerization often branched and yellow to brown discolored products. [ 8 ]
Recent work has focused on increasing the molar mass and achieving a linear chain structure while avoiding decomposition reactions. With a simple "oven process" in which a mixture or paste of crystalline aspartic acid and concentrated phosphoric acid or polyphosphoric acid in a thin layer is heated to 200 °C for 2 to 4 hours, polysuccinimide is produced with molar masses in the range of 30,000 g/mol and cream white shade. [ 9 ] The implementation of the polycondensation in several steps [ 10 ] (precondensation, comminution, postcondensation), with other dehydrating substances (for example zeolites , triphenyl phosphite [ 11 ] ) or in the presence of solvents [ 12 ] (for example propylene carbonate ) provides higher molecular weight products with molar masses in the range of 10,000 to 200,000 g/mol. However, the patent literature does not address the polymer morphology, in particular the degree of branching.
A recent patent [ 13 ] describes the simple preparation of high molecular weight, virtually colorless and linear, unbranched polysuccinimide. For this purpose, aspartic acid, which is present as crystalline zwitterion and practically water-insoluble, is firstly dissolved with an aqueous, volatile acid (preferably hydrochloric acid) and mixed with phosphoric acid as condensing agent. The resulting homogeneous solution is evaporated at 120 °C and the resulting glassy mass is then polycondensed at 180 °C to 200 °C for at least one hour. The phosphoric acid is washed out and the dried polysuccinimide is converted by mild alkaline hydrolysis into water-soluble polyaspartic acid; the molar mass of which can be determined by gel permeation chromatography . The process provides reproducible polysuccinimide with molar masses above 100,000 g/mol.
Synthetic routes for polysuccinimides based on maleic acid monoammonium salt, [ 14 ] maleic anhydride and ammonia [ 15 ] or based on the intermediately formed maleic acid monoamide [ 16 ] achieved only low molar masses of a few 1,000 g/mol and yielded colored products. The same was the case for " green " process variants in supercritical carbon dioxide and while avoiding mineral acids as catalysts. [ 7 ]
Due to the lower cost of maleic anhydride and ammonia, starting materials produced from fossil raw materials, no L-aspartic acid (of biogenic origin) is used in the production of the commercial product Baypure® polysuccinimide either.
Polysuccinimide is produced as an odourless, non-hygroscopic, cream-white to brown powder which is soluble in aprotic dipolar solvents such as dimethylformamide , dimethylacetamide , dimethylsulfoxide , N -methylpyrrolidone , triethylene glycol or mesitylene / sulfolane mixtures. Polysuccinimide hydrolyses in water only very slowly. In diluted alkaline media (e.g. 1M sodium hydroxide solution ), hydrolysis takes place in α- and β-position of the succinimide (2,5-pyrrolidinedione) ring structures and racemization follows at the chiral center of the aspartic acid, yielding the water-soluble sodium salt of the poly(α, β)-DL-aspartic acid. The α form is formed to approx. 30%, the β form to approx. 70% in random arrangement along the polymer chain. [ 17 ]
In more basic solutions or with longer reaction times, the amide linkages in the polymer chain are attacked upon degradation of the molar mass. The presence of amide bonds makes the polyaspartic acid obtained in the hydrolysis relatively biodegradable (about 70% in wastewater), even of initially highly crosslinked polysuccinimides. [ 18 ]
The polysuccinimide [ 4 ] developed [ 19 ] by Bayer AG and marketed by Lanxess AG under the brand name Baypure® DSP with an average molecular weight of 4,400 g/mol is partially hydrolyzed even at slightly elevated pH values and is thus swellable in highly crosslinked form or water-soluble in linear form. The copoly-(succinimide-aspartic acid) formed by partial hydrolysis and especially polyaspartic acid (trade name Baypure® DS 100) produced by partial hydrolysis is suitable as a long-lasting inhibitor against limescale deposition in water treatment and applications in the oil and mining industries , and as a setting retarder for cement in the construction industry. [ 19 ] Patent literature [ 11 ] mentions polysuccinimide applications as chelating agents, inhibitors against scale formation, dispersant, humectants, and fertilizer additives .
The opening of the pyrrolidinedione ring structures in polysuccinimide via aminolysis with ammonia water (containgin NH 4 OH) produces poly-(α, β)-DL-asparagine, with hydrazine poly-(α, β)-DL-aspartylhydrazide (PAHy) and with functional amines, e.g. ethanolamine poly-(α), β)-DL-2-hydroxyethylaspartate (PHEA). [ 9 ] PHEA can be used a plasma expander with good biocompatibility and biodegradability, high water solubility at low manufacturing costs and was investigated more intensive as a potential drug carrier) in medical applications. [ 20 ] [ 21 ]
Cross-linked poly(α, β)-DL aspartic acid sodium salt, which is the commercially most interesting polysuccinimide derivative , has been extensively tested for its suitability as a biodegradable superabsorbent compared to the non-biodegradable standard cross-linked sodium polyacrylate . [ 22 ] [ 23 ] The results obtained have not yet led to the use of crosslinked polyaspartic acid in large-volume applications for superabsorbents (e.g. baby diapers ). | https://en.wikipedia.org/wiki/Polysuccinimide |
Polysulfides are a class of chemical compounds derived from anionic chains of sulfur atoms. [ 1 ] There are two main classes of polysulfides: inorganic and organic. The inorganic polysulfides have the general formula S 2− n . These anions are the conjugate bases of polysulfanes H 2 S n . Organic polysulfides generally have the formulae R 1 S n R 2 , where R is an alkyl or aryl group . [ 2 ]
The alkali metal polysulfides arise by treatment of a solution of the sulfide with elemental sulfur , e.g. sodium sulfide to sodium polysulfide :
S 2− + n S → S 2− n +1
In some cases, these anions have been obtained as organic salts, which are soluble in organic solvents. [ 4 ]
The energy released in the reaction of sodium and elemental sulfur is the basis of battery technology. The sodium–sulfur battery and the lithium–sulfur battery require high temperatures to maintain liquid polysulfide and Na + -conductive membranes that are unreactive toward sodium, sulfur, and sodium sulfide.
Polysulfides are ligands in coordination chemistry . Examples of transition metal polysulfido complexes include (C 5 H 5 ) 2 TiS 5 , [Ni(S 4 ) 2 ] 2− , and [Pt(S 5 ) 3 ] 2− . [ 5 ] Main group elements also form polysulfides. [ 6 ]
In commerce, the term "polysulfide" usually refers to a class of polymers with alternating chains of several sulfur atoms and hydrocarbons. They have the formula R 1 S n R 2 . In this formula n indicates the number of sulfur atoms (or "rank"). Polysulfide polymers can be synthesized by condensation polymerization reactions between organic dihalides and alkali metal salts of polysulfide anions:
n Na 2 S 5 + n ClCH 2 CH 2 Cl → [CH 2 CH 2 S 5 ] n + 2 n NaCl
Dihalides used in this condensation polymerization are dichloroalkanes such as 1,2-dichloroethane , bis(2-chloroethoxy)methane ( ClCH 2 CH 2 OCH 2 OCH 2 CH 2 Cl ), and 1,3-dichloropropane . The polymers are called thiokols . In some cases, polysulfide polymers can be formed by ring-opening polymerization reactions.
Polysulfide polymers are also prepared by the addition of polysulfanes to alkenes. An idealized equation is:
2 RCH=CH 2 + H 2 S n → (RCH 2 CH 2 ) 2 S n
In reality, homogeneous samples of H 2 S n are difficult to prepare. [ 2 ]
Polysulfide polymers are insoluble in water, oils, and many other organic solvents. Because of their solvent resistance, these materials find use as sealants to fill the joints in pavement, automotive window glass, and aircraft structures.
Polymers containing one or two sulfur atoms separated by hydrocarbon sequences are usually not classified polysulfides, e.g. poly( p -phenylene) sulfide (C 6 H 4 S) n .
Many commercial elastomers contain polysulfides as crosslinks . These crosslinks interconnect neighboring polymer chains, thereby conferring rigidity. The degree of rigidity is related to the number of crosslinks. Elastomers, therefore, have a characteristic ability to return to their original shape after being stretched or compressed. Because of this memory for their original cured shape, elastomers are commonly referred to as rubbers . The process of crosslinking the polymer chains in these polymers with sulfur is called vulcanization . The sulfur chains attach themselves to the allylic carbon atoms, which are adjacent to C=C linkages. Vulcanization is a step in the processing of several classes of rubbers, including poly chloroprene ( Neoprene ), styrene-butadiene, and poly isoprene , which is chemically similar to natural rubber. Charles Goodyear 's discovery of vulcanization, involving the heating of polyisoprene with sulfur, was revolutionary because it converted a sticky and almost useless material into an elastomer that could be fabricated into useful products.
In addition to water and ammonia , the clouds in the atmospheres of the gas giant planets contain ammonium sulfides. The reddish-brownish clouds are attributed to polysulfides, arising from the exposure of the ammonium sulfides to light. [ 7 ]
Polysulfides, like sulfides, can induce stress corrosion cracking in carbon steel and stainless steel . | https://en.wikipedia.org/wiki/Polysulfide |
Polysulfobetaines are zwitterionic polymers that contain a positively charged quaternary ammonium and a negatively charged sulfonate group within one constitutional repeat unit . [ 1 ] [ 2 ] In recent years, polysulfobetaines have received increasing attention owing to their good biotolerance and ultralow-fouling behavior towards surfaces. These properties are mainly referred to a tightly bound hydration layer around each zwitterionic group, which effectively suppresses protein adsorption and thus, improves anti-fouling behavior. [ 3 ] [ 4 ] Therefore, polysulfobetaines have been typically employed as ultrafiltration membranes, [ 4 ] blood-contacting devices, [ 5 ] and drug delivery materials . [ 3 ]
The chemical structure of polysulfobetaines can be divided in several subgroups. Most widespread are amides of (meth) acrylic acid ('PSPP') or quaternary esters ('PSPE'). Also, compounds from poly(vinylpyridinium), poly(vinylimidazolium), or quaternary poly(pyrrolidinium) as well as zwitterionic ionenes, are often found. [ 2 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ]
Polysulfobetaines are generally synthesized via free radical polymerization . [ 6 ] [ 11 ] However, the synthesis of polysulfobetaines is often limited by their poor solubility in most solvents and at present, only few sulfobetaine monomers that are suited for free radical polymerization, are commercially available. The most popular ones are SPE and SPP, which provide a good combination of hydrophilicity and polymerizability. [ 11 ]
Almost all polysulfobetaines are insoluble in water at low temperatures, however many polysulfobetaines feature an upper critical solution temperature (UCST) in aqueous solution. This means they undergo a coil-to-globule collapse transition upon cooling. [ 12 ] [ 13 ] Such a behavior is highly unusual, since other zwitterionic polymers, e.g., poly(phosphatidylcholines) and poly(carboxybetaines) do generally not feature a responsive behavior towards a temperature stimulus. [ 14 ] [ 15 ] [ 16 ]
The reason for the UCST-type behavior of polysulfobetaines in solution is based on their electrically neutral behavior, i.e., the overall charge is zero, over a large pH range (approximately 2 – 14). Due to the neutralization of the charges, repulsive and attractive interactions are present between the individual polymer chains and inner salt are formed. The balance of this complex interplay of interactions between numerous charged groups with water and with themselves, strongly affects the solubility of polysulfobetaines in water and eventually, results in an UCST-type transition. The temperature of this phase transition, often called clearing point, is very sensitive to molar mass , polymer architecture, solvent isotopes , e.g., H 2 O/D 2 O, and especially to the addition of salts to the solution. [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ]
The presence of salt additives in aqueous solution leads to an altered balance of the attractive and repulsive interactions and therefore, also to an altered solubility. Especially, the nature of the salt anion has a strong effect on the solubility of the polysulfobetaines. While chaotropic anions cause an improved dissolution ( salting-in effect ), kosmotropic anions result in precipitation of the polysulfobetaines ( salting-out effect ). [ 23 ] [ 24 ] [ 25 ]
Thin films made from polysulfobetaines also feature a thermo-responsiveness , however, the phase transition is strongly shifted, which is mainly addressed to the increased polymer concentration and the altered polymer-polymer and polymer-water interactions. [ 12 ] [ 26 ] [ 27 ] Furthermore, and analogously to aqueous solutions, different water isotopes (H 2 O/D 2 O) and salt additives were found to affect the phase transition as well. [ 20 ] [ 28 ] Interestingly, polysulfobetaine thin films feature a cononsolvency effect in mixed water/methanol vapors, which is not found in water/methanol solution. Apparently, polysulfobetaines feature a miscibility with lower alcohols at the substance-rich side of their phase diagrams. [ 29 ] [ 30 ] | https://en.wikipedia.org/wiki/Polysulfobetaine |
Polysulfones are a family of high performance thermoplastics . These polymers are known for their toughness and stability at high temperatures. Technically used polysulfones contain an aryl - SO 2 -aryl subunit. Due to the high cost of raw materials and processing, polysulfones are used in specialty applications and often are a superior replacement for polycarbonates .
Three polysulfones are used industrially: polysulfone (PSU), polyethersulfone (PES/PESU) and polyphenylene sulfone (PPSU). They can be used in the temperature range from -100 to +200 °C and are used for electrical equipment, in vehicle construction and medical technology . [ 1 ] They are composed of para-linked aromatics , sulfonyl groups and ether groups and partly also alkyl groups . Polysulfones have outstanding resistance to heat and oxidation, hydrolysis resistance to aqueous and alkaline media and good electrical properties. [ 2 ]
The term "polysulfone" is normally used for polyarylethersulfones (PAES), since only aromatic polysulfones are used commercially. Furthermore, since ether groups are always present in these polysulfones, PAESs are also referred to as polyether sulfones (PES), poly(arylene sulfone)s or simply polysulfone (PSU).
The simplest polysulfone poly(phenylene sulfone), known as early as 1960, is produced in a Friedel-Crafts reaction from benzenesulfonyl chloride : [ 3 ]
With a melting point over 500 °C, the product is difficult to process. It exhibits attractive heat resistance, but its mechanical properties are rather poor. Polyarylether sulphones (PAES) represent a suitable alternative. Appropriate synthetic routes to PAES were developed almost simultaneously, and yet independently, from 3M Corporation , [ 4 ] Union Carbide Corporation in the United States , [ 5 ] and ICI 's Plastics Division [ 6 ] in the United Kingdom. The polymers found at that time are still used today, but produced by a different synthesis process.
The original synthesis of PAES involved electrophilic aromatic substitution of an di aryl ether with the bis (sulfonyl chloride) of benzene. Reactions typically use a Friedel-Crafts catalyst , such as ferric chloride or antimony pentachloride :
This route is complicated by the formation of isomers arising from both para- and ortho- substitution. Furthermore, cross-linking was observed, which strongly affects the mechanical properties of the polymer. [ 7 ] [ 4 ] This method has been abandoned.
PAES are currently prepared by a polycondensation reaction of di phenoxide and bis(4-chlorophenyl)sulfone (DCDPS). The sulfone group activates the chloride groups toward substitution. The required diphenoxide is produced in situ from a diphenol and sodium hydroxide . The cogenerated water is removed by azeotropic distillation using toluene or chlorobenzene ). The polymerization is carried out at 130–160 °C under inert conditions in a polar, aprotic solvent, e.g. dimethyl sulfoxide , forming a polyether concomitant with elimination of sodium chloride :
Bis(4-fluorophenyl)sulfone can be used in place of bis(4-chlorophenyl)sulfone. The difluoride is more reactive than the dichloride but more expensive. Through chain terminators (e.g. methyl chloride ), the chain length can be controlled for melt-processing.
The diphenol is typically bisphenol-A or 1,4-dihydroxybenzene . Such step polymerizations require highly pure monomer and precise stoichiometry to ensure high molecular weight products. [ 8 ]
DCDPS is the precursor to polymers known as Udel (from bisphenol A), PES, and Radel R. Udel is a high-performance amorphous sulfone polymer that can molded into a variety of different shapes. It is both rigid and temperature-resistant, and has applications in everything from plumbing pipes, to printer cartridges , to automobile fuses . DCDPS also reacts with bisphenol S to form PES. Like Udel, PES is a rigid and thermally-resistant material with numerous applications.
Polysulfones are rigid, high-strength and transparent. They are also characterized by high strength and stiffness, retaining these properties between −100 °C and 150 °C. The glass transition temperature of polysulfones is between 190 and 230 °C. [ 9 ] They have a high dimensional stability, the size change when exposed to boiling water or 150 °C air or steam generally falls below 0.1%. [ 10 ] Polysulfone is highly resistant to mineral acids , alkali , and electrolytes , in pH ranging from 2 to 13. It is resistant to oxidizing agents (although PES will degrade over time [ 11 ] ), therefore it can be cleaned by bleaches . It is also resistant to surfactants and hydrocarbon oils . It is not resistant to low-polar organic solvents (e.g. ketones and chlorinated hydrocarbons ) and aromatic hydrocarbons . Mechanically, polysulfone has high compaction resistance, recommending its use under high pressures. It is also stable in aqueous acids and bases and many non-polar solvents; however, it is soluble in dichloromethane and methylpyrrolidone . [ 8 ]
Polysulfones are counted among the high performance plastics . They can be processed by injection molding , extrusion or hot forming.
Poly(aryl ether sulfone)s are composed of aromatic groups, ether groups and sulfonyl groups . For a comparison of the properties of individual constituents poly(phenylene sulfone) can serve as an example, which consists of sulfonyl and phenyl groups only. Since both groups are thermally very stable, poly(phenylene sulfone) has an extremely high melting temperature (520 °C). However, the polymer chains are also so rigid that poly(phenylene sulfone) (PAS) decomposes before melting and can thus not be thermoplastically processed. Therefore, flexible elements must be incorporated into the chains, this is done in the form of ether groups. Ether groups allow a free rotation of the polymer chains. This leads to a significantly reduced melting point and also improves the mechanical properties by an increased impact strength . [ 7 ] The alkyl groups in bisphenol A act also as a flexible element.
The stability of the polymer can also be attributed to individual structural elements: The sulfonyl group (in which sulfur is in the highest possible oxidation state ) attracts electrons from neighboring benzene rings, causing electron deficiency . The polymer therefore opposes further electron loss, thus substantiating the high oxidation resistance. The sulfonyl group is also linked to the aromatic system by mesomerism and the bond therefore strengthened by mesomeric energy. As a result, larger amounts of energy from heat or radiation can be absorbed by the molecular structure without causing any reactions (decomposition). The result of the mesomerism is that the configuration is particularly rigid. Based on the biphenylsulfonyl group, the polymer is thus durable heat resistant, oxidation resistant and still has a high stiffness even at elevated temperatures. The ether bond provides (as opposed to esters ) hydrolysis resistance as well as some flexibility, which leads to impact strength. In addition, the ether bond leads to good heat resistance and better flow of the melt. [ 12 ]
Polysulfone has one of the highest service temperatures among all melt-processable thermoplastics. Its resistance to high temperatures gives it a role of a flame retardant , without compromising its strength that usually results from addition of flame retardants. Its high hydrolysis stability allows its use in medical applications requiring autoclave and steam sterilization. However, it has low resistance to some solvents and undergoes weathering ; this weathering instability can be offset by adding other materials into the polymer.
Polysulfone allows easy manufacturing of membranes , with reproducible properties and controllable size of pores down to 40 nanometers. Such membranes can be used in applications like hemodialysis , waste water recovery, food and beverage processing, and gas separation. These polymers are also used in the automotive and electronic industries. Filter cartridges made from polysulfone membranes offer extremely high flow rates at very low differential pressures when compared with nylon or polypropylene media.
Polysulfone can be used as filtration media in filter sterilization .
Polysulfone can be reinforced with glass fibers . The resulting composite material has twice the tensile strength and three times increase of its Young's modulus . [ citation needed ]
Polysulfone is often used as a copolymer . Recently, sulfonated polyethersulfones (SPES) have been studied as a promising material candidate among many other aromatic hydrocarbon-based polymers for highly durable proton-exchange membranes in fuel cells. [ 13 ] Several reviews have reported progress on durability from many reports on this work. [ 14 ] The biggest challenge for SPES application in fuel cells is improving its chemical durability. Under oxidative environment, SPES can undergo sulfonic group detachment and main chain scission. However the latter is more dominant; midpoint scission and unzip mechanism have been proposed as the degradation mechanism depending on the strength of the polymer backbone. [ 15 ]
Polysulfone food pans are used for the storage, heating, and serving of foods. The pans are made to Gastronorm standards and are available in the natural transparent amber colour of polysulfone. The wide working temperature range of -40°C to 190°C allow these pans to go from a deep freezer directly to a steam table or microwave oven. Polysulfone provides a non-stick surface for minimal food wastage and easy cleaning.
Some industrially relevant polysulfones are listed in the following table: | https://en.wikipedia.org/wiki/Polysulfone |
A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms , sorites , epicheirema , and dilemmas ) [ 1 ] that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism is called a prosyllogism except the last, because the conclusion of the last syllogism is not a premise for another syllogism.
An example of a categorical polysyllogism is:
This argument has the following structure:
Note two points: first, the makeup of a polysyllogism need not be limited to two component syllogisms. In fact, it can have any number of component syllogisms. Second, validity depends on all its parts. If any one is not valid then the whole polysyllogism is to be considered invalid. [ 2 ]
An example for a propositional polysyllogism is:
Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms:
A sorites (plural: sorites) is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise. Example:
The word sorites / s ɒ ˈ r aɪ t iː z / comes from Ancient Greek : σωρίτης , heaped up , from σωρός heap or pile . Thus a sorites is a heap of propositions chained together. A sorites polysyllogism should not be confused with the sorites paradox , a.k.a. the fallacy of the heap.
Lewis Carroll uses sorites in his book Symbolic Logic (1896). For example: [ 3 ]
Carroll's example may be translated thus:
This logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polysyllogism |
Polytetrahedron is a term used for three distinct types of objects, all based
on the tetrahedron :
This 4-polytope article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polytetrahedron |
Polythiazyl ( polymeric sulfur nitride ), (SN) x , is an electrically conductive , gold- or bronze-colored polymer with metallic luster . It was the first conductive inorganic polymer discovered [ 1 ] [ 2 ] and was also found to be a superconductor at very low temperatures (below 0.26 K). [ 3 ] [ 4 ] It is a fibrous solid, described as "lustrous golden on the faces and dark blue-black", depending on the orientation of the sample. It is air stable and insoluble in all solvents. [ 5 ]
The compound was first reported as early as 1910 by F.P. Burt, who obtained it by heating tetrasulfur tetranitride in vacuum over silver wool. [ 6 ]
The compound was the first compound with only non-metallic elements in which superconductivity could be demonstrated. However, the relatively low transition temperature at about 0.3 K makes a practical application unlikely. [ 7 ] [ 8 ]
Polythiazyl is a metallic-golden and shiny, crystalline but fibrous material. [ 8 ] The polymer is mostly inert to oxygen and water, but decomposes in air to a grey powder. [ 9 ] [ 10 ] At temperatures above 240 °C explosive decomposition can occur. [ 11 ] The compound also explodes on impact. [ 10 ] Explosion generally proceeds via decomposition to the elements.
Polythiazyl shows an anisotropic electrical conductivity. Along the fibres or SN chains, the bond is electrically conductive, perpendicular to it acts as an insulator. The one-dimensional conductivity is based on the bonding conditions in the S-N chain, where each sulfur atom provides two π electrons and each nitrogen atom provides one π electron to form two-center 3π electron bonding units. [ 8 ]
Two polymorphic crystal forms were observed in the compound. The monoclinic form I obtained from the synthesis can be converted into an orthorhombic form II by mechanical treatment such as grinding. [ 12 ]
The material is a polymer, containing trivalent nitrogen, and divalent and tetravalent sulfur. The S and N atoms on adjacent chains align. [ 2 ] [ 13 ] [ 14 ] Several resonance structures can be written. [ 15 ]
The structure of the crystalline compound was resolved by X-ray diffraction . This showed alternating S–N bond lengths of 159 pm and 163 pm and S–N–S bond angles of 120 ° and N–S–N bond angles of 106 °. [ 16 ] [ 17 ] [ 9 ] [ 8 ]
The oldest-known polythiazyl synthesis is the polymerization of the cyclic formal dimer disulfur dinitride ( S 2 N 2 ), which is in turn synthesized from the formal tetramer tetrasulfur tetranitride ( S 4 N 4 ), [ 2 ] in the presence of hot silver wool. [ 2 ] [ 1 ] [ 18 ] The reaction begins when silver abstracts sulfur from S 4 N 4 to produce a Ag 2 S catalyst; the resulting gaseous S 2 N 2 is then isolated through sublimation onto a cold surface :
When warmed to room temperature , the additional heat induces spontaneous polymerization:
An alternative is the azide reduction of thiazyl chloride trimer, [ 19 ] itself made from thiazyl fluoride : [ 20 ]
To eschew explosive reagents entirely, iron filings in nitromethane reduce the thiazyl chloride trimer to [(SN) 5 ] + [FeCl 4 ] − , [ 21 ] which a platinum cathode reduces to polythiazyl. [ 22 ]
Due to its electrical conductivity, polythiazyl is used in LEDs , transistors , battery cathodes, and solar cells . [ 18 ]
King, R.S.P.: Novel chemistry and applications of polythiazyl , Doctoral Thesis Loughborough University 2009, pdf-Download | https://en.wikipedia.org/wiki/Polythiazyl |
Polythiophenes (PTs) are polymerized thiophenes , a sulfur heterocycle . The parent PT is an insoluble colored solid with the formula (C 4 H 2 S) n . [ notes 1 ] [ 2 ] [ 3 ] The rings are linked through the 2- and 5-positions. Poly(alkylthiophene)s have alkyl substituents at the 3- or 4-position(s). They are also colored solids, but tend to be soluble in organic solvents.
PTs become conductive when oxidized. The electrical conductivity results from the delocalization of electrons along the polymer backbone. Conductivity however is not the only interesting property resulting from electron delocalization. The optical properties of these materials respond to environmental stimuli, with dramatic color shifts in response to changes in solvent , temperature , applied potential , and binding to other molecules. Changes in both color and conductivity are induced by the same mechanism, twisting of the polymer backbone and disrupting conjugation, making conjugated polymers attractive as sensors that can provide a range of optical and electronic responses. [ 4 ] [ 5 ] [ 6 ]
The development of polythiophenes and related conductive organic polymers was recognized by the awarding of the 2000 Nobel Prize in Chemistry to Alan J. Heeger , Alan MacDiarmid , and Hideki Shirakawa "for the discovery and development of conductive polymers".
PT is an ordinary organic polymer, being a red solid that is poorly soluble in most solvents. [ 7 ] Upon treatment with oxidizing agents (electron-acceptors) however, the material takes on a dark color and becomes electrically conductive. Oxidation is referred to as "doping". Around 0.2 equivalent of oxidant is used to convert PTs (and other conducting polymers) into the optimally conductive state. [ citation needed ] Thus about one of every five rings is oxidized. Many different oxidants are used. Because of the redox reaction, the conductive form of polythiophene is a salt. An idealized stoichiometry is shown using the oxidant [A]PF 6 :
In principle, PT can be n-doped using reducing agents, but this approach is rarely practiced. [ 8 ]
Upon "p-doping", charged unit called a bipolaron is formed. The bipolaron moves as a unit along the polymer chain and is responsible for the macroscopically observed conductivity of the material. Conductivity can approach 1000 S/cm. [ 9 ] In comparison, the conductivity of copper is approximately 5×10 5 S/cm. Generally, the conductivity of PTs is lower than 1000 S/cm, but high conductivity is not necessary for many applications, e.g. as an antistatic film.
A variety of reagents have been used to dope PTs. Iodine and bromine produce highly conductive materials, [ 9 ] which are unstable owing to slow evaporation of the halogen. [ 10 ] Organic acids , including trifluoroacetic acid , propionic acid , and sulfonic acids produce PTs with lower conductivities than iodine, but with higher environmental stabilities. [ 10 ] [ 11 ] Oxidative polymerization with ferric chloride can result in doping by residual catalyst , [ 12 ] although matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) studies have shown that poly(3-hexylthiophene)s are also partially halogenated by the residual oxidizing agent. [ 13 ] Poly(3-octylthiophene) dissolved in toluene can be doped by solutions of ferric chloride hexahydrate dissolved in acetonitrile , and can be cast into films with conductivities reaching 1 S/cm. [ 14 ] Other, less common p-dopants include gold trichloride [ 15 ] and trifluoromethanesulfonic acid . [ 16 ]
The extended π-systems of conjugated PTs produce some of the most interesting properties of these materials—their optical properties. As an approximation, the conjugated backbone can be considered as a real-world example of the "electron-in-a-box" solution to the Schrödinger equation ; however, the development of refined models to accurately predict absorption and fluorescence spectra of well-defined oligo(thiophene) systems is ongoing. [ 17 ] Conjugation relies upon overlap of the π-orbitals of the aromatic rings , which, in turn, requires the thiophene rings to be coplanar.
The number of coplanar rings determines the conjugation length—the longer the conjugation length, the lower the separation between adjacent energy levels , and the longer the absorption wavelength. Deviation from coplanarity may be permanent, resulting from mislinkages during synthesis or especially bulky side chains ; or temporary, resulting from changes in the environment or binding. This twist in the backbone reduces the conjugation length, and the separation between energy levels is increased. This results in a shorter absorption wavelength.
Determining the maximum effective conjugation length requires the synthesis of regioregular PTs of defined length. The absorption band in the visible region is increasingly red-shifted as the conjugation length increases, and the maximum effective conjugation length is calculated as the saturation point of the red-shift. Early studies by ten Hoeve et al. estimated that the effective conjugation extended over 11 repeat units, [ 18 ] while later studies increased this estimate to 20 units. [ 19 ] Using the absorbance and emission profile of discrete conjugated oligo(3-hexylthiophene)s prepared through polymerization and separation, Lawrence et al. determined the effective conjugation length of poly(3-hexylthiophene) to be 14 units. [ 20 ] The effective conjugation length of polythiophene derivatives depend on the chemical structure of side chains, [ 21 ] and thiophene backbones. [ 22 ]
The absorption band of poly ( 3-thiophene acetic acid ) in aqueous solutions of poly(vinyl alcohol) (PVA) shifts from 480 nm at pH 7 to 415 nm at pH 4. This is attributed to formation of a compact coil structure, which can form hydrogen bonds with PVA upon partial deprotonation of the acetic acid group. [ 23 ]
Shifts in PT absorption bands due to changes in temperature result from a conformational transition from a coplanar, rodlike structure at lower temperatures to a nonplanar, coiled structure at elevated temperatures. For example, poly(3-(octyloxy)-4-methylthiophene) undergoes a color change from red–violet at 25 °C to pale yellow at 150 °C. An isosbestic point (a point where the absorbance curves at all temperatures overlap) indicates coexistence between two phases, which may exist on the same chain or on different chains. [ 24 ] Not all thermochromic PTs exhibit an isosbestic point: highly regioregular poly(3-alkylthiophene)s (PATs) show a continuous blue-shift with increasing temperature if the side chains are short enough so that they do not melt and interconvert between crystalline and disordered phases at low temperatures. [ citation needed ]
The optical properties of PTs can be sensitive to many factors. PTs exhibit absorption shifts due to application of electric potentials (electrochromism), [ 25 ] or to introduction of alkali ions (ionochromism). [ 26 ] Soluble PATs exhibit both thermochromism and solvatochromism (see above ) in chloroform and 2,5-dimethyltetrahydrofuran. [ 27 ]
Polythiophene and its oxidized derivatives have poor processing properties. They are insoluble in ordinary solvents and do not melt readily. For example, doped unsubstituted PTs are only soluble in exotic solvents such as arsenic trifluoride and arsenic pentafluoride . [ 28 ] Although only poorly processable, "the expected high temperature stability and potentially very high electrical conductivity of PT films (if made) still make it a highly desirable material." [ 29 ] Nonetheless, intense interest has focused on soluble polythiophenes, which usually translates to polymers derived from 3-alkylthiophenes, which give the so-called polyalkylthiophenes (PATs).
Soluble polymers are derivable from 3-substituted thiophenes where the 3-substituent is butyl or longer. Copolymers also are soluble, e.g., poly(3-methylthiophene-'co'-3'-octylthiophene). [ 29 ]
One undesirable feature of 3-alkylthiophenes is the variable regioregularity of the polymer. Focusing on the polymer microstructure at the dyad level, 3-substituted thiophenes can couple to give any of three dyads:
These three diads can be combined into four distinct triads. The triads are distinguishable by NMR spectroscopy . [ 30 ] [ 31 ]
Regioregularity affects the properties of PTs. A regiorandom copolymer of 3-methylthiophene and 3-butylthiophene possessed a conductivity of 50 S/cm, whereas a more regioregular copolymer with a 2:1 ratio of HT to HH couplings had a higher conductivity of 140 S/cm. [ 32 ] Films of regioregular poly(3-(4-octylphenyl)thiophene) (POPT) with greater than 94% HT content possessed conductivities of 4 S/cm, compared with 0.4 S/cm for regioirregular POPT. [ 33 ] PATs prepared using Rieke zinc formed "crystalline, flexible, and bronze-colored films with a metallic luster". On the other hand, the corresponding regiorandom polymers produced "amorphous and orange-colored films". [ 34 ] Comparison of the thermochromic properties of the Rieke PATs showed that, while the regioregular polymers showed strong thermochromic effects, the absorbance spectra of the regioirregular polymers did not change significantly at elevated temperatures. Finally, Fluorescence absorption and emission maxima of poly(3-hexylthiophene)s occur at increasingly lower wavelengths (higher energy) with increasing HH dyad content. The difference between absorption and emission maxima, the Stokes shift , also increases with HH dyad content, which they attributed to greater relief from conformational strain in the first excited state. [ 35 ]
Water-soluble PT's are represented by sodium poly(3-thiophenealkanesulfonate)s. [ 36 ] In addition to conferring water solubility, the pendant sulfonate groups act as counterions, producing self-doped conducting polymers. Substituted PTs with tethered carboxylic acids also exhibit water solubility. [ 37 ] [ 38 ] [ 39 ] and urethanes [ 40 ]
Thiophenes with chiral substituents at the 3 position have been polymerized. Such chiral PTs in principle could be employed for detection or separation of chiral analytes. [ 41 ]
Poly(3-(perfluorooctyl)thiophene)s is soluble in supercritical carbon dioxide [ 42 ] [ 43 ] Oligothiophenes capped at both ends with thermally-labile alkyl esters were cast as films from solution, and then heated to remove the solublizing end groups. Atomic force microscopy (AFM) images showed a significant increase in long-range order after heating. [ 44 ]
Fluorinated polythiophene yield 7% efficiency in polymer-fullerene solar cells. [ 45 ]
The 3,4-disubstituted thiophene called ethylenedioxythiophene (EDOT) is the precursor to the polymer PEDOT . Regiochemistry is not an issue in since this monomer is symmetrical. PEDOT is found in electrochromic displays , photovoltaics , electroluminescent displays, printed wiring, and sensors. [ 46 ]
In an electrochemical polymerization, a solution containing thiophene and an electrolyte produces a conductive PT film on the anode . [ 29 ] Electrochemical polymerization is convenient, since the polymer does not need to be isolated and purified, but it can produce polymers with undesirable alpha-beta linkages and varying degrees of regioregularity. The stoichiometry of the electropolymerization is:
The degree of polymerization and quality of the resulting polymer depends upon the electrode material, current density, temperature, solvent, electrolyte, presence of water, and monomer concentration. [ 47 ]
Electron-donating substituents lower the oxidation potential, whereas electron-withdrawing groups increase the oxidation potential. Thus, 3-methylthiophene polymerizes in acetonitrile and tetrabutylammonium tetrafluoroborate at a potential of about 1.5 V vs. SCE , whereas unsubstituted thiophene requires an additional 0.2 V. Steric hindrance resulting from branching at the α-carbon of a 3-substituted thiophene inhibits polymerization. [ 48 ]
In terms of mechanism, oxidation of the thiophene monomer produces a radical cation , which then couple with another monomer to produce a radical cation dimer.
Chemical synthesis offers two advantages compared with electrochemical synthesis of PTs: a greater selection of monomers, and, using the proper catalysts, the ability to synthesize perfectly regioregular substituted PTs. PTs were chemically synthesized by accident more than a century ago. [ 49 ] Chemical syntheses from 2,5-dibromothiophene use Kumada coupling and related reactions [ 50 ] [ 51 ]
Regioregular PTs have been prepared by lithiation 2-bromo-3-alkylthiophenes using Kumada cross-coupling . [ 52 ] This method produces approximately 100% HT–HT couplings, according to NMR spectroscopy analysis of the diads. 2,5-Dibromo-3-alkylthiophene when treated with highly reactive "Rieke zinc" is an alternative method. [ 53 ] [ 54 ]
In contrast to methods that require brominated monomers, the oxidative polymerization of thiophenes using ferric chloride proceeds at room temperature. The approach was reported by Sugimoto et al. in 1986. [ 55 ] The stoichiometry is analogous to that of electropolymerization.
This method has proven to be extremely popular; antistatic coatings are prepared on a commercial scale using ferric chloride. In addition to ferric chloride, other oxidizing agents have been reported. [ 29 ] Slow addition of ferric chloride to the monomer solution produced poly(3-(4-octylphenyl)thiophene)s with approximately 94% H–T content. [ 33 ] Precipitation of ferric chloride in situ (in order to maximize the surface area of the catalyst) produced significantly higher yields and monomer conversions than adding monomer directly to crystalline catalyst. [ 56 ] [ 57 ] Higher molecular weights were reported when dry air was bubbled through the reaction mixture during polymerization. [ 29 ] Exhaustive Soxhlet extraction after polymerization with polar solvents was found to effectively fractionate the polymer and remove residual catalyst before NMR spectroscopy. [ 30 ] Using a lower ratio of catalyst to monomer (2:1, rather than 4:1) may increase the regioregularity of poly(3-dodecylthiophene)s. [ 58 ] Andreani et al. reported higher yields of soluble poly(dialkylterthiophene)s in carbon tetrachloride rather than chloroform, which they attributed to the stability of the radical species in carbon tetrachloride. [ 59 ] Higher-quality catalyst, added at a slower rate and at reduced temperature, was shown to produce high molecular weight PATs with no insoluble polymer residue. [ 60 ] Factorial experiments indicate that the catalyst/monomer ratio correlated with increased yield of poly(3-octylthiophene). Longer polymerization time also increased the yield. [ 61 ]
In terms of mechanism, the oxidative polymerization using ferric chloride, a radical pathway has been proposed. Niemi et al. reported that polymerization was only observed in solvents where the catalyst was either partially or completely insoluble (chloroform, toluene , carbon tetrachloride, pentane , and hexane , and not diethyl ether , xylene , acetone, or formic acid ), and speculated that the polymerization may occur at the surface of solid ferric chloride. [ 62 ] However, this is challenged by the fact that the reaction also proceeds in acetonitrile, which FeCl 3 is soluble in. [ 63 ] Quantum mechanical calculations also point to a radical mechanism. The mechanism can also be inferred from the regiochemistry of the dimerization of 3-methylthiophene since C2 in [3-methylthiophene] + has the highest spin density.
A carbocation mechanism is inferred from the structure of 3-(4-octylphenyl)thiophene prepared from ferric chloride. [ 33 ]
Polymerization of thiophene can be effected by a solution of ferric chloride in acetonitrile. The kinetics of thiophene polymerization also seemed to contradict the predictions of the radical polymerization mechanism. [ 63 ] Barbarella et al. studied the oligomerization of 3-(alkylsulfanyl)thiophenes, and concluded from their quantum mechanical calculations, and considerations of the enhanced stability of the radical cation when delocalized over a planar conjugated oligomer, that a radical cation mechanism analogous to that generally accepted for electrochemical polymerization was more likely. [ 64 ] Given the difficulties of studying a system with a heterogeneous, strongly oxidizing catalyst that produces difficult to characterize rigid-rod polymers, the mechanism of oxidative polymerization is by no means decided. The radical cation mechanism is generally accepted.
As an example of a static application, poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate) (PEDOT-PSS) product ("Clevios P") from Heraeus has been extensively used as an antistatic coating (as packaging materials for electronic components, for example). AGFA coats 200 m × 10 m of photographic film per year with PEDOT:PSS because of its antistatic properties. The thin layer of PEDOT:PSS is virtually transparent and colorless, prevents electrostatic discharges during film rewinding, and reduces dust buildup on the negatives after processing. [ 46 ]
PEDOT also has been proposed for dynamic applications where a potential is applied to a polymer film. PEDOT-coated windows and mirrors become opaque or reflective upon the application of an electric potential, a manifestation of its electrochromic properties . [ 25 ] Widespread adoption of electrochromic windows promise significant savings in air conditioning costs. [ 65 ]
Another potential application include field-effect transistors , [ 66 ] electroluminescent devices , solar cells , photochemical resists , nonlinear optic devices , [ 67 ] batteries , diodes , and chemical sensors . [ 68 ] In general, two categories of applications are proposed for conducting polymers. Static applications rely upon the intrinsic conductivity of the materials, combined with their processing and material properties common to polymeric materials. Dynamic applications utilize changes in the conductive and optical properties, resulting either from application of electric potentials or from environmental stimuli.
PTs have been touted as sensor elements. In addition to biosensor applications , PTs can also be functionalized with receptors for detecting metal ions or chiral molecules as well. PTs with pendant crown ether functionalities exhibit properties that vary with the alkali metal. [ 69 ] and main-chain. [ 26 ]
Polythiophenes show potential in the treatment of prion diseases . [ 70 ] | https://en.wikipedia.org/wiki/Polythiophene |
An internal node of a phylogenetic tree is described as a polytomy or multifurcation if (i) it is in a rooted tree and is linked to three or more child subtrees or (ii) it is in an unrooted tree and is attached to four or more branches. [ 1 ] [ 2 ] A tree that contains any multifurcations can be described as a multifurcating tree.
Two types of polytomies are recognized, soft and hard polytomies. [ 3 ] [ 4 ]
Soft polytomies are the result of insufficient phylogenetic information: though the lineages diverged at different times – meaning that some of these lineages are closer relatives than others, and the available data does not allow recognition of this. Most polytomies are soft, meaning that they would be resolved into a typical tree of dichotomies if better data were available. [ 5 ]
In contrast, a hard polytomy represents a true divergence event of three or more lineages.
Interpretations for a polytomy depend on the individuals that are represented in the phylogenetic tree.
If the lineages in the phylogenetic tree stand for species, a polytomy shows the simultaneous speciation of three or more species. [ 6 ] In particular situations, they may be common, for example when a species that has rapidly expanded its range or is highly panmictic undergoes peripatric speciation in different regions.
An example is the Drosophila simulans species complex . Here, the ancestor seems to have colonized two islands at the same time but independently, yielding two equally old but divergently evolved daughter species
If a phylogenetic tree is reconstructed from DNA sequence data of a particular gene, a hard polytomy arises when three or more sampled genes trace their ancestry to a single gene in an ancestral organism. In contrast, a soft polytomy stems from branches on gene trees of finite temporal duration but for which no substitutions have occurred. [ 7 ]
As DNA sequence evolution is usually much faster than evolution of complex phenotypic traits, it may be that genetic lineages diverge a short time apart from each other, while the actual organism has not changed if the whole ancestral population is considered. Since few if any individuals in a population are genetically alike in any one population – especially if lineage sorting has not widely progressed – it may be that hard polytomies are indeed rare or nonexistent if the entire genome of each individual organism is considered, but rather widespread on the population genetical level if entire species are considered as interbreeding populations (see also species concept ).
"Speciation or lineage divergence events occurring at the same time" refers to evolutionary time measured in generations , as this is the only means that novel traits (e.g. germline point mutations ) can be passed on. In practical terms, the ability to distinguish between hard and soft polytomies is limited: if for example a kilobase of DNA sequences that mutate approximately 1% per million years is analyzed, lineages diverging from the same ancestor within the same 100,000 years cannot be reliably distinguished as to which one diverged first.
Founder effects and genetic drift may result in different rates of evolution. This can easily confound molecular clock algorithms to the point where hard polytomies become unrecognizable as such. | https://en.wikipedia.org/wiki/Polytomy |
In general topology , a polytopological space consists of a set X {\displaystyle X} together with a family { τ i } i ∈ I {\displaystyle \{\tau _{i}\}_{i\in I}} of topologies on X {\displaystyle X} that is linearly ordered by the inclusion relation where I {\displaystyle I} is an arbitrary index set . It is usually assumed that the topologies are in non-decreasing order. [ 1 ] [ 2 ] However some authors prefer the associated closure operators { k i } i ∈ I {\displaystyle \{k_{i}\}_{i\in I}} to be in non-decreasing order where k i ≤ k j {\displaystyle k_{i}\leq k_{j}} if and only if k i A ⊆ k j A {\displaystyle k_{i}A\subseteq k_{j}A} for all A ⊆ X {\displaystyle A\subseteq X} . This requires non-increasing topologies. [ 3 ]
An L {\displaystyle L} -topological space ( X , τ ) {\displaystyle (X,\tau )} is a set X {\displaystyle X} together with a monotone map τ : L → {\displaystyle \tau :L\to } Top ( X ) {\displaystyle (X)} where ( L , ≤ ) {\displaystyle (L,\leq )} is a partially ordered set and Top ( X ) {\displaystyle (X)} is the set of all possible topologies on X , {\displaystyle X,} ordered by inclusion. When the partial order ≤ {\displaystyle \leq } is a linear order then ( X , τ ) {\displaystyle (X,\tau )} is called a polytopological space . Taking L {\displaystyle L} to be the ordinal number n = { 0 , 1 , … , n − 1 } , {\displaystyle n=\{0,1,\dots ,n-1\},} an n {\displaystyle n} -topological space ( X , τ 0 , … , τ n − 1 ) {\displaystyle (X,\tau _{0},\dots ,\tau _{n-1})} can be thought of as a set X {\displaystyle X} with topologies τ 0 ⊆ ⋯ ⊆ τ n − 1 {\displaystyle \tau _{0}\subseteq \dots \subseteq \tau _{n-1}} on it. More generally a multitopological space ( X , τ ) {\displaystyle (X,\tau )} is a set X {\displaystyle X} together with an arbitrary family τ {\displaystyle \tau } of topologies on it. [ 2 ]
Polytopological spaces were introduced in 2008 by the philosopher Thomas Icard for the purpose of defining a topological model of Japaridze's polymodal logic (GLP) . [ 1 ] They were later used to generalize variants of Kuratowski's closure-complement problem . [ 2 ] [ 3 ] For example Taras Banakh et al. proved that under operator composition the n {\displaystyle n} closure operators and complement operator on an arbitrary n {\displaystyle n} -topological space can together generate at most 2 ⋅ K ( n ) {\displaystyle 2\cdot K(n)} distinct operators [ 2 ] where K ( n ) = ∑ i , j = 0 n ( i + j i ) ⋅ ( i + j j ) . {\displaystyle K(n)=\sum _{i,j=0}^{n}{\tbinom {i+j}{i}}\cdot {\tbinom {i+j}{j}}.} In 1965 the Finnish logician Jaakko Hintikka found this bound for the case n = 2 {\displaystyle n=2} and claimed [ 4 ] it "does not appear to obey any very simple law as a function of n {\displaystyle n} ". | https://en.wikipedia.org/wiki/Polytopological_space |
In astrophysics , a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form P = K ρ ( n + 1 ) / n = K ρ 1 + 1 / n , {\displaystyle P=K\rho ^{(n+1)/n}=K\rho ^{1+1/n},} where P is pressure, ρ is density and K is a constant of proportionality . [ 1 ] The constant n is known as the polytropic index; note however that the polytropic index has an alternative definition as with n as the exponent.
This relation need not be interpreted as an equation of state , which states P as a function of both ρ and T (the temperature ); however in the particular case described by the polytrope equation there are other additional relations between these three quantities, which together determine the equation. Thus, this is simply a relation that expresses an assumption about the change of pressure with radius in terms of the change of density with radius, yielding a solution to the Lane–Emden equation.
Sometimes the word polytrope may refer to an equation of state that looks similar to the thermodynamic relation above, although this is potentially confusing and is to be avoided. It is preferable to refer to the fluid itself (as opposed to the solution of the Lane–Emden equation) as a polytropic fluid or polytropic gas . Specifically, the polytropic gas is a gas for which the specific heat is constant. [ 2 ] [ 3 ] The equation of state of a polytropic fluid is general enough that such idealized fluids find wide use outside of the limited problem of polytropes.
The polytropic exponent (of a polytrope) has been shown to be equivalent to the pressure derivative of the bulk modulus [ 4 ] where its relation to the Murnaghan equation of state has also been demonstrated. The polytrope relation is therefore best suited for relatively low-pressure (below 10 7 Pa ) and high-pressure (over 10 14 Pa) conditions when the pressure derivative of the bulk modulus, which is equivalent to the polytrope index, is near constant.
In general as the polytropic index increases, the density distribution is more heavily weighted toward the center ( r = 0 ) of the body. | https://en.wikipedia.org/wiki/Polytrope |
Polyunsaturated aldehydes ( PUAs ) are a group of allelopathic chemicals typically associated with predator–prey interactions between diatoms (a type of single-celled alga ) and small crustaceans known as copepods . [ 1 ] These compounds are classified by an aldehyde group covalently bound to long carbon chains containing two or more carbon–carbon double bonds. Examples include isomers of heptadienal, octadienal, octatrienal, and decatrienal. [ 2 ]
Polyunsaturated aldehydes are oxylipins that are formed from lipids (specifically the fatty acid portion of lipids) when diatoms are exposed to environmental stresses . Stresses can include nutrient limitations, grazing by predators, and wounding . [ 3 ]
In particular, damage to diatom cells as a result of grazing by zooplankton invokes a chemical defense mechanism that produces PUA’s as secondary metabolites from fatty acids. [ 4 ] The production mechanism is as follows:
Thalassiosira rotula represents the most well-studied diatom species in terms of polyunsaturated aldehyde production. Wichard et al. determined that only 30% of PUA precursor molecules remain in T. rotula within minutes of cell membrane wounding, indicating a fast rate of response by diatoms to zooplankton grazing. [ 7 ]
T. rotula has been known to produce many types of polyunsaturated aldehydes, including (2 E ,4 E / Z )-hepta-2,4-dienal, (2 E ,4 E / Z ,7 Z )-deca-2,4,7-trienal, (2 E ,4 E / Z )-octa-2,4-dienal, and (2 E ,4 E / Z ,7 Z )-octa-2,4,7-trienal. These particular aldehydes are also produced by Stephanopyxis turris and Skeletonema costatum in response to wounding. [ 7 ] Phaeocystis pouchetii and Skeletonema marinoi also produce various octadienal and heptadienal isomers. [ 8 ]
Copepods are known to be the primary consumers of diatoms in the water column and initiate the production of PUA upon grazing. [ 8 ] The consumption of PUA-producing diatoms by copepods has been shown to diminish their reproductive success. Specifically, female copepods that consume diatoms spawn eggs with low viabilities and offspring with high teratogenesis rates. [ 1 ] The compounds mainly act by preventing cell division and promoting apoptosis in copepod embryos, [ 9 ] though the mechanism behind this is still poorly understood. [ 8 ] | https://en.wikipedia.org/wiki/Polyunsaturated_aldehyde |
Polyurea is a type of elastomer that is derived from the reaction product of an isocyanate component and an amine component. The isocyanate can be aromatic or aliphatic in nature. It can be monomer , polymer , or any variant reaction of isocyanates, quasi-prepolymer or a prepolymer . The prepolymer, or quasi-prepolymer, can be made of an amine -terminated polymer resin, or a hydroxyl -terminated polymer resin. [ 1 ]
The resin blend may be made up of amine-terminated polymer resins, and/or amine-terminated chain extenders. The amine-terminated polymer resins do not have any intentional hydroxyl moieties . Any hydroxyls are the result of incomplete conversion to the amine-terminated polymer resins. The resin blend may also contain additives or non-primary components. These additives may contain hydroxyls, such as pre-dispersed pigments in a polyol carrier. Normally, the resin blend does not contain a catalyst (s). This is because the reaction between an isocyanate and amine is extremely fast and hence does not need catalysis.
The word polyurea is derived from the Greek words πολυ- - poly- meaning "many"; and ουρίας - oûron meaning "to urinate" (referring to the substance urea , found in urine ). Urea or carbamide is an organic compound with the chemical formula (NH 2 ) 2 CO. The molecule has two amine groups (–NH 2 ) joined by a carbonyl functional group (C=O). In a polyurea, alternating monomer units of isocyanates and amines react with each other to form urea linkages. Ureas can also be formed from the reaction of isocyanates and water which forms a carbamic acid intermediate. This acid quickly decomposes by splitting off carbon dioxide and leaving behind an amine. This amine then reacts with another isocyanate group to form the polyurea linkage. This two step reaction is used to make what is commonly but improperly called polyurethane foam. The carbon dioxide that is liberated in this reaction is the primary blowing (foaming) agent especially in many polyurethane foams which more precisely should be called polyurethane/urea foams.
Polyurea and polyurethane are copolymers used in the manufacture of spandex , which was invented in 1959.
Polyurea was originally developed in automotive applications in the 1980s [ 2 ] [ 3 ] but other applications such as protecting tabletop edges followed. [ 4 ] Its fast reactivity and relative moisture insensitivity made it useful for coatings on large surface area projects, such as secondary containment, manhole and tunnel coatings, tank liners, and truck bed liners. Excellent adhesion to concrete and steel is obtained with the proper primer and surface treatment. They can also be used for spray molding and armor. [ 5 ] Some polyureas reach strengths of 40 MPa (6000 psi) tensile and over 500% elongation making it a tough coating. The quick cure time allows many coats to be built up quickly. The high strength, impact and abrasion resistance of polyurea coatings is a key reason for their use. [ 6 ]
In 2014, a polyurea elastomer -based material was shown to be self-healing, melding together after being cut in half. The material also includes inexpensive commercially available compounds. The elastomer molecules were tweaked, making the bonds between them longer. The resulting molecules are easier to pull apart from one another and better able to rebond at room temperature with almost the same strength. The rebonding can be repeated. Elastic, self-healing paints and other coatings recently took a step closer to common use, thanks to research being conducted at the University of Illinois. Scientists there have used "off-the-shelf" components to create a polymer that melds back together after being cut in half, without the addition of other chemicals. [ 7 ] [ 8 ]
Polyurea has become a preferred long term solution for narrowboats . The traditional coating with bitumen, known as "blacking" is being replaced with the practice of using polyurea coatings. The clearest advantage is that it is not necessary to reapply a coat every 3–4 years. It is thought that polyurea coatings last 25–30 years. [ 9 ]
Commercial trademarks for Polyurea include Line-X, GLS 100R, and Pentens SPU-1000, to name a few. [ 10 ] [ 11 ] [ 12 ] There are multiple possible polyurea formulations. The Polyurea Development Association is a trade association that represents the interests of polyurea coating manufacturers. [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/Polyurea |
Polyurethane ( / ˌ p ɒ l i ˈ jʊər ə ˌ θ eɪ n , - j ʊəˈr ɛ θ eɪ n / ; [ 1 ] often abbreviated PUR and PU ) is a class of polymers composed of organic units joined by carbamate (urethane) links. In contrast to other common polymers such as polyethylene and polystyrene , polyurethane term does not refer to the single type of polymer but a group of polymers. Unlike polyethylene and polystyrene , polyurethanes can be produced from a wide range of starting materials resulting various polymers within the same group. This chemical variety produces polyurethanes with different chemical structures leading to many different applications . These include rigid and flexible foams , and coatings, adhesives, electrical potting compounds, and fibers such as spandex and polyurethane laminate (PUL). Foams are the largest application accounting for 67% of all polyurethane produced in 2016. [ 2 ]
A polyurethane is typically produced by reacting a polymeric isocyanate with a polyol . [ 3 ] Since a polyurethane contains two types of monomers, which polymerize one after the other, they are classed as alternating copolymers . Both the isocyanates and polyols used to make a polyurethane contain two or more functional groups per molecule.
Global production in 2019 was 25 million metric tonnes, [ 4 ] accounting for about 6% of all polymers produced in that year.
Otto Bayer and his coworkers at IG Farben in Leverkusen, Germany, first made polyurethanes in 1937. [ 5 ] [ 6 ] The new polymers had some advantages over existing plastics that were made by polymerizing olefins or by polycondensation , and were not covered by patents obtained by Wallace Carothers on polyesters . [ 7 ] Early work focused on the production of fibers and flexible foams and PUs were applied on a limited scale as aircraft coating during World War II . [ 7 ] Polyisocyanates became commercially available in 1952, and production of flexible polyurethane foam began in 1954 by combining toluene diisocyanate (TDI) and polyester polyols. These materials were also used to produce rigid foams, gum rubber, and elastomers . Linear fibers were produced from hexamethylene diisocyanate (HDI) and 1,4-Butanediol (BDO).
DuPont introduced polyethers, specifically poly(tetramethylene ether) glycol , in 1956. BASF and Dow Chemical introduced polyalkylene glycols in 1957. Polyether polyols were cheaper, easier to handle and more water-resistant than polyester polyols. Union Carbide and Mobay , a U.S. Monsanto / Bayer joint venture, also began making polyurethane chemicals. [ 7 ] In 1960 more than 45,000 metric tons of flexible polyurethane foams were produced. The availability of chlorofluoroalkane blowing agents, inexpensive polyether polyols, and methylene diphenyl diisocyanate (MDI) allowed polyurethane rigid foams to be used as high-performance insulation materials. In 1967, urethane-modified polyisocyanurate rigid foams were introduced, offering even better thermal stability and flammability resistance. During the 1960s, automotive interior safety components, such as instrument and door panels, were produced by back-filling thermoplastic skins with semi-rigid foam.
In 1969, Bayer exhibited an all-plastic car in Düsseldorf , Germany. Parts of this car, such as the fascia and body panels, were manufactured using a new process called reaction injection molding (RIM), in which the reactants were mixed and then injected into a mold. The addition of fillers, such as milled glass, mica , and processed mineral fibers, gave rise to reinforced RIM (RRIM), which provided improvements in flexural modulus (stiffness), reduction in coefficient of thermal expansion and better thermal stability. This technology was used to make the first plastic-body automobile in the United States, the Pontiac Fiero , in 1983. Further increases in stiffness were obtained by incorporating pre-placed glass mats into the RIM mold cavity, also known broadly as resin injection molding , or structural RIM.
Starting in the early 1980s, water-blown microcellular flexible foams were used to mold gaskets for automotive panels and air-filter seals, replacing PVC polymers. Polyurethane foams are used in many automotive applications including seating, head and arm rests, and headliners.
Polyurethane foam (including foam rubber) is sometimes made using small amounts of blowing agents to give less dense foam, better cushioning/energy absorption or thermal insulation. In the early 1990s, because of their impact on ozone depletion , the Montreal Protocol restricted the use of many chlorine -containing blowing agents, such as trichlorofluoromethane (CFC-11). By the late 1990s, blowing agents such as carbon dioxide , pentane , 1,1,1,2-tetrafluoroethane (HFC-134a) and 1,1,1,3,3-pentafluoropropane (HFC-245fa) were widely used in North America and the EU, although chlorinated blowing agents remained in use in many developing countries. Later, HFC-134a was also banned due to high ODP and GWP readings, and HFC-141B was introduced in early 2000s as an alternate blowing agent in developing nations. [ 8 ]
Polyurethanes are produced by reacting di isocyanates with polyols , [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] often in the presence of a catalyst , or upon exposure to ultraviolet radiation. [ 15 ] Common catalysts include tertiary amines , such as DABCO , DMDEE , or metallic soaps , such as dibutyltin dilaurate . The stoichiometry of the starting materials must be carefully controlled as excess isocyanate can trimerise , leading to the formation of rigid polyisocyanurates . The polymer usually has a highly crosslinked molecular structure, resulting in a thermosetting material which does not melt on heating; although some thermoplastic polyurethanes are also produced.
The most common application of polyurethane is as solid foams , which requires the presence of a gas, or blowing agent , during the polymerization step. This is commonly achieved by adding small amounts of water, which reacts with isocyanates to form CO 2 gas and an amine , via an unstable carbamic acid group. The amine produced can also react with isocyanates to form urea groups, and as such the polymer will contain both these and urethane linkers. The urea is not very soluble in the reaction mixture and tends to form separate "hard segment" phases consisting mostly of polyurea . The concentration and organization of these polyurea phases can have a significant impact on the properties of the foam. [ 16 ]
The type of foam produced can be controlled by regulating the amount of blowing agent and also by the addition of various surfactants which change the rheology of the polymerising mixture. Foams can be either "closed-cell", where most of the original bubbles or cells remain intact, or "open-cell", where the bubbles have broken but the edges of the bubbles are stiff enough to retain their shape, in extreme cases reticulated foams can be formed. Open-cell foams feel soft and allow air to flow through, so they are comfortable when used in seat cushions or mattresses . Closed-cell foams are used as rigid thermal insulation . High-density microcellular foams can be formed without the addition of blowing agents by mechanically frothing the polyol prior to use. These are tough elastomeric materials used in covering car steering wheels or shoe soles .
The properties of a polyurethane are greatly influenced by the types of isocyanates and polyols used to make it. Long, flexible segments, contributed by the polyol, give soft, elastic polymer. High amounts of crosslinking give tough or rigid polymers. Long chains and low crosslinking give a polymer that is very stretchy, short chains with many crosslinks produce a hard polymer while long chains and intermediate crosslinking give a polymer useful for making foam. The choices available for the isocyanates and polyols, in addition to other additives and processing conditions allow polyurethanes to have the very wide range of properties that make them such widely used polymers.
The main ingredients to make a polyurethane are di- and tri- isocyanates and polyols . Other materials are added to aid processing the polymer or to modify the properties of the polymer. PU foam formulation sometimes have water added too.
Isocyanates used to make polyurethane have two or more isocyanate groups on each molecule. The most commonly used isocyanates are the aromatic diisocyanates, toluene diisocyanate (TDI) and methylene diphenyl diisocyanate , (MDI). These aromatic isocyanates are more reactive than aliphatic isocyanates.
TDI and MDI are generally less expensive and more reactive than other isocyanates. Industrial grade TDI and MDI are mixtures of isomers and MDI often contains polymeric materials. They are used to make flexible foam (for example slabstock foam for mattresses or molded foams for car seats), [ 17 ] rigid foam (for example insulating foam in refrigerators) elastomers (shoe soles, for example), and so on. The isocyanates may be modified by partially reacting them with polyols or introducing some other materials to reduce volatility (and hence toxicity) of the isocyanates, decrease their freezing points to make handling easier or to improve the properties of the final polymers.
Aliphatic and cycloaliphatic isocyanates are used in smaller quantities, most often in coatings and other applications where color and transparency are important since polyurethanes made with aromatic isocyanates tend to darken on exposure to light. [ page needed ] [ 18 ] The most important aliphatic and cycloaliphatic isocyanates are 1,6-hexamethylene diisocyanate (HDI), 1-isocyanato-3-isocyanatomethyl-3,5,5-trimethyl-cyclohexane ( isophorone diisocyanate , IPDI), and 4,4′-diisocyanato dicyclohexylmethane (H 12 MDI or hydrogenated MDI). Other more specialized isocyanates include Tetramethylxylylene diisocyanate (TMXDI).
Polyols are polymers in their own right and have on average two or more hydroxyl groups per molecule. They can be converted to polyether polyols by co-polymerizing ethylene oxide and propylene oxide with a suitable polyol precursor. [ 19 ] Polyester polyols are made by the polycondensation of multifunctional carboxylic acids and polyhydroxyl compounds. They can be further classified according to their end use. Higher molecular weight polyols (molecular weights from 2,000 to 10,000) are used to make more flexible polyurethanes while lower molecular weight polyols make more rigid products.
Polyols for flexible applications use low functionality initiators such as dipropylene glycol ( f = 2), glycerine ( f = 3), or a sorbitol/water solution ( f = 2.75). [ 20 ] Polyols for rigid applications use higher functionality initiators such as sucrose ( f = 8), sorbitol ( f = 6), toluenediamine ( f = 4), and Mannich bases ( f = 4). Propylene oxide and/or ethylene oxide is added to the initiators until the desired molecular weight is achieved. The order of addition and the amounts of each oxide affect many polyol properties, such as compatibility, water-solubility, and reactivity. Polyols made with only propylene oxide are terminated with secondary hydroxyl groups and are less reactive than polyols capped with ethylene oxide, which contain primary hydroxyl groups. Incorporating carbon dioxide into the polyol structure is being researched by multiple companies.
Graft polyols (also called filled polyols or polymer polyols) contain finely dispersed styrene–acrylonitrile , acrylonitrile , or polyurea (PHD) polymer solids chemically grafted to a high molecular weight polyether backbone. They are used to increase the load-bearing properties of low-density high-resiliency (HR) foam, as well as add toughness to microcellular foams and cast elastomers. Initiators such as ethylenediamine and triethanolamine are used to make low molecular weight rigid foam polyols that have built-in catalytic activity due to the presence of nitrogen atoms in the backbone. A special class of polyether polyols, poly(tetramethylene ether) glycols , which are made by polymerizing tetrahydrofuran , are used in high performance coating, wetting and elastomer applications.
Conventional polyester polyols are based on virgin raw materials and are manufactured by the direct polyesterification of high-purity diacids and glycols, such as adipic acid and 1,4-butanediol. Polyester polyols are usually more expensive and more viscous than polyether polyols, but they make polyurethanes with better solvent, abrasion, and cut resistance. Other polyester polyols are based on reclaimed raw materials. They are manufactured by transesterification ( glycolysis ) of recycled poly(ethyleneterephthalate) (PET) or dimethylterephthalate (DMT) distillation bottoms with glycols such as diethylene glycol. These low molecular weight, aromatic polyester polyols are used in rigid foam, and bring low cost and excellent flammability characteristics to polyisocyanurate (PIR) boardstock and polyurethane spray foam insulation.
Specialty polyols include polycarbonate polyols, polycaprolactone polyols, polybutadiene polyols, and polysulfide polyols. The materials are used in elastomer, sealant, and adhesive applications that require superior weatherability, and resistance to chemical and environmental attack. Natural oil polyols derived from castor oil and other vegetable oils are used to make elastomers, flexible bunstock, and flexible molded foam.
Co-polymerizing chlorotrifluoroethylene or tetrafluoroethylene with vinyl ethers containing hydroxyalkyl vinyl ether produces fluorinated (FEVE) polyols. Two-component fluorinated polyurethanes prepared by reacting FEVE fluorinated polyols with polyisocyanate have been used to make ambient cure paints and coatings. Since fluorinated polyurethanes contain a high percentage of fluorine–carbon bonds, which are the strongest bonds among all chemical bonds, fluorinated polyurethanes exhibit resistance to UV, acids, alkali, salts, chemicals, solvents, weathering, corrosion, fungi and microbial attack. These have been used for high performance coatings and paints. [ 21 ]
Phosphorus -containing polyols are available that become chemically bonded to the polyurethane matrix for the use as flame retardants . This covalent linkage prevents migration and leaching of the organophosphorus compound .
Interest in sustainable "green" products raised interest in polyols derived from vegetable oils , [ 22 ] [ 23 ] [ 24 ] fatty acids [ 25 ] , lignin, sorbitol [ 26 ] , etc. These are mostly contributing to polyol part. There are attempts made to prepare isocyanate part using bio-derived material. However, as far as commercialization is concern, polyol part is more targeted being easy and required in more quantity than isocyanate part. Various oils used in the preparation polyols for polyurethanes include soybean oil , cottonseed oil , neem seed oil , algae oil, [ 27 ] [ 28 ] and castor oil . Vegetable oils are functionalized in various ways and modified to polyetheramides , polyethers , alkyds , etc. Renewable sources used to prepare polyols may be fatty acids or dimer fatty acids . [ 29 ] Some biobased and isocyanate-free polyurethanes exploit the reaction between polyamines and cyclic carbonates to produce polyhydroxyurethanes . [ 30 ]
Chain extenders ( f = 2) and cross linkers ( f ≥ 3) are low molecular weight hydroxyl and amine terminated compounds that play an important role in the polymer morphology of polyurethane fibers, elastomers, adhesives, and certain integral skin and microcellular foams.
The elastomeric properties of these materials are derived from the phase separation of the hard and soft copolymer segments of the polymer, such that the urethane hard segment domains serve as cross-links between the amorphous polyether (or polyester) soft segment domains. This phase separation occurs because the mainly nonpolar, low melting soft segments are incompatible with the polar, high melting hard segments. The soft segments, which are formed from high molecular weight polyols, are mobile and are normally present in coiled formation, while the hard segments, which are formed from the isocyanate and chain extenders, are stiff and immobile. As the hard segments are covalently coupled to the soft segments, they inhibit plastic flow of the polymer chains, thus creating elastomeric resiliency. Upon mechanical deformation, a portion of the soft segments are stressed by uncoiling, and the hard segments become aligned in the stress direction. This reorientation of the hard segments and consequent powerful hydrogen bonding contributes to high tensile strength, elongation, and tear resistance values. [ 12 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] The choice of chain extender also determines flexural, heat, and chemical resistance properties.
The most important chain extenders are ethylene glycol , 1,4-butanediol (1,4-BDO or BDO), 1,6-hexanediol , cyclohexane dimethanol and hydroquinone bis(2-hydroxyethyl) ether (HQEE). All of these glycols form polyurethanes that phase separate well and form well defined hard segment domains, and are melt processable. They are all suitable for thermoplastic polyurethanes with the exception of ethylene glycol, since its derived bis-phenyl urethane undergoes unfavorable degradation at high hard segment levels. [ 10 ] Diethanolamine and triethanolamine are used in flex molded foams to build firmness and add catalytic activity. Diethyltoluenediamine is used extensively in RIM, and in polyurethane and polyurea elastomer formulations.
Polyurethane catalysts can be classified into two broad categories, basic and acidic amine . Tertiary amine catalysts function by enhancing the nucleophilicity of the diol component. Alkyl tin carboxylates, oxides and mercaptides oxides function as mild Lewis acids in accelerating the formation of polyurethane. As bases, traditional amine catalysts include triethylenediamine (TEDA, also called DABCO , 1,4-diazabicyclo[2.2.2]octane), dimethylcyclohexylamine (DMCHA), dimethylethanolamine (DMEA), Dimethylaminoethoxyethanol and bis-(2-dimethylaminoethyl)ether, a blowing catalyst also called A-99. A typical Lewis acidic catalyst is dibutyltin dilaurate . The process is highly sensitive to the nature of the catalyst and is also known to be autocatalytic . [ 36 ]
Another class of catalysts was published in a study in May 2024. In this study, polyurethane synthesis was investigated in the presence of acid catalysts, namely dimethylphosphite (DMHP), methanesulfonic acid (MSA), and trifluoromethanesulfonic acid (TFMSA). The thermodynamic profile was examined and described in detail through computational tools, showing that TFMSA had the best catalytic properties. The study aimed to open the door to a new class of catalysts. [ 37 ]
Factors affecting catalyst selection include balancing three reactions: urethane (polyol+isocyanate, or gel) formation, the urea (water+isocyanate, or "blow") formation, or the isocyanate trimerization reaction (e.g., using potassium acetate, to form isocyanurate rings). A variety of specialized catalysts have been developed. [ 38 ] [ 39 ] [ 40 ]
Surfactants are used to modify the characteristics of both foam and non-foam polyurethane polymers. They take the form of polydimethylsiloxane-polyoxyalkylene block copolymers, silicone oils, nonylphenol ethoxylates, and other organic compounds. In foams, they are used to emulsify the liquid components, regulate cell size, and stabilize the cell structure to prevent collapse and sub-surface voids. [ 41 ] In non-foam applications they are used as air release and antifoaming agents, as wetting agents, and are used to eliminate surface defects such as pin holes, orange peel, and sink marks.
Polyurethanes are produced by mixing two or more liquid streams. The polyol stream contains catalysts, surfactants, blowing agents (when making polyurethane foam insulation) and so on. The two components are referred to as a polyurethane system, or simply a system. The isocyanate is commonly referred to in North America as the 'A-side' or just the 'iso'. The blend of polyols and other additives is commonly referred to as the 'B-side' or as the 'poly'. [ citation needed ] This mixture might also be called a 'resin' or 'resin blend'. In Europe the meanings for 'A-side' and 'B-side' are reversed. [ citation needed ] Resin blend additives may include chain extenders, cross linkers , surfactants , flame retardants , blowing agents , pigments , and fillers . Polyurethane can be made in a variety of densities and hardnesses by varying the isocyanate, polyol or additives.
Fully reacted polyurethane polymer is chemically inert . [ 42 ] No exposure limits have been established in the U.S. by OSHA ( Occupational Safety and Health Administration ) or ACGIH ( American Conference of Governmental Industrial Hygienists ). It is not regulated by OSHA for carcinogenicity.
Polyurethanes are combustible. [ 43 ] Decomposition from fire can produce significant amounts of carbon monoxide and hydrogen cyanide , in addition to nitrogen oxides, isocyanates, and other toxic products. [ 44 ] Due to the flammability of the material, it has to be treated with flame retardants (at least in case of furniture), almost all of which are considered harmful. [ 45 ] [ 46 ] California later issued Technical Bulletin 117 2013 which allowed most polyurethane foam to pass flammability tests without the use of flame retardants. Green Science Policy Institute states: "Although the new standard can be met without flame retardants, it does NOT ban their
use. Consumers who wish to reduce household exposure to flame retardants can look for a TB117-2013 tag on furniture, and verify with retailers that products do not contain flame retardants." [ 47 ]
Liquid resin blends and isocyanates may contain hazardous or regulated components. Isocyanates are known skin and respiratory sensitizers. Additionally, amines, glycols, and phosphate present in spray polyurethane foams present risks. [ 48 ]
Exposure to chemicals that may be emitted during or after application of polyurethane spray foam (such as isocyanates) are harmful to human health and therefore special precautions are required during and after this process. [ 49 ]
In the United States, additional health and safety information can be found through organizations such as the Polyurethane Manufacturers Association (PMA) and the Center for the Polyurethanes Industry (CPI), as well as from polyurethane system and raw material manufacturers. Regulatory information can be found in the Code of Federal Regulations Title 21 (Food and Drugs) and Title 40 (Protection of the Environment). In Europe, health and safety information is available from ISOPA, [ 50 ] the European Diisocyanate and Polyol Producers Association.
The methods of manufacturing polyurethane finished goods range from small, hand pour piece-part operations to large, high-volume bunstock and boardstock production lines. Regardless of the end-product, the manufacturing principle is the same: to meter the liquid isocyanate and resin blend at a specified stoichiometric ratio, mix them together until a homogeneous blend is obtained, dispense the reacting liquid into a mold or on to a surface, wait until it cures, then demold the finished part.
Although the capital outlay can be high, it is desirable to use a meter-mix or dispense unit for even low-volume production operations that require a steady output of finished parts. Dispense equipment consists of material holding (day) tanks, metering pumps, a mix head, and a control unit. Often, a conditioning or heater–chiller unit is added to control material temperature in order to improve mix efficiency, cure rate, and to reduce process variability. Choice of dispense equipment components depends on shot size, throughput, material characteristics such as viscosity and filler content, and process control . Material day tanks may be single to hundreds of gallons in size and may be supplied directly from drums, IBCs ( intermediate bulk containers , such as caged IBC totes ), or bulk storage tanks . They may incorporate level sensors, conditioning jackets, and mixers. Pumps can be sized to meter in single grams per second up to hundreds of pounds per minute. They can be rotary, gear, or piston pumps, or can be specially hardened lance pumps to meter liquids containing highly abrasive fillers such as chopped or hammer-milled glass fiber and wollastonite . [ citation needed ]
The pumps can drive low-pressure (10 to 30 bar, 1 to 3 MPa) or high-pressure (125 to 250 bar, 12.5 to 25.0 MPa) dispense systems. Mix heads can be simple static mix tubes, rotary-element mixers, low-pressure dynamic mixers, or high-pressure hydraulically actuated direct impingement mixers . Control units may have basic on/off and dispense/stop switches, and analogue pressure and temperature gauges, or may be computer-controlled with flow meters to electronically calibrate mix ratio, digital temperature and level sensors, and a full suite of statistical process control software. Add-ons to dispense equipment include nucleation or gas injection units, and third or fourth stream capability for adding pigments or metering in supplemental additive packages.
Distinct from pour-in-place, bun and boardstock, and coating applications, the production of piece parts requires tooling to contain and form the reacting liquid.
The choice of mold-making material is dependent on the expected number of uses to end-of-life (EOL), molding pressure, flexibility, and heat transfer characteristics.
RTV silicone is used for tooling that has an EOL in the thousands of parts. It is typically used for molding rigid foam parts, where the ability to stretch and peel the mold around undercuts is needed.
The heat transfer characteristic of RTV silicone tooling is poor. High-performance, flexible polyurethane elastomers are also used in this way.
Epoxy, metal-filled epoxy, and metal-coated epoxy is used for tooling that has an EOL in the tens of thousands of parts. It is typically used for molding flexible foam cushions and seating, integral skin and microcellular foam padding, and shallow-draft RIM bezels and fascia. The heat transfer characteristic of epoxy tooling is fair; the heat transfer characteristic of metal-filled and metal-coated epoxy is good. Copper tubing can be incorporated into the body of the tool, allowing hot water to circulate and heat the mold surface.
Aluminum is used for tooling that has an EOL in the hundreds of thousands of parts. It is typically used for molding microcellular foam gasketing and cast elastomer parts, and is milled or extruded into shape.
Mirror-finish stainless steel is used for tooling that imparts a glossy appearance to the finished part. The heat transfer characteristic of metal tooling is excellent.
Finally, molded or milled polypropylene is used to create low-volume tooling for molded gasket applications. Instead of many expensive metal molds, low-cost plastic tooling can be formed from a single metal master, which also allows greater design flexibility. The heat transfer characteristic of polypropylene tooling is poor, which must be taken into consideration during the formulation process.
In 2007, the global consumption of polyurethane raw materials was above 12 million metric tons, and the average annual growth rate was about 5%. [ 51 ] Revenues generated with PUR on the global market are expected to rise to approximately US$75 billion by 2022. [ 52 ] As they are such an important class of materials, research is constantly taking place and papers published. [ 53 ]
Polyurethanes, especially those made using aromatic isocyanates, contain chromophores that interact with light. This is of particular interest in the area of polyurethane coatings, where light stability is a critical factor and is the main reason that aliphatic isocyanates are used in making polyurethane coatings. When PU foam, which is made using aromatic isocyanates, is exposed to visible light, it discolors, turning from off-white to yellow to reddish brown. It has been generally accepted that apart from yellowing, visible light has little effect on foam properties. [ 54 ] [ 55 ] This is especially the case if the yellowing happens on the outer portions of a large foam, as the deterioration of properties in the outer portion has little effect on the overall bulk properties of the foam itself.
It has been reported that exposure to visible light can affect the variability of some physical property test results. [ 56 ]
Higher-energy UV radiation promotes chemical reactions in foam, some of which are detrimental to the foam structure. [ 57 ]
Polyurethanes may degrade due to hydrolysis . This is a common problem with shoes left in a closet, and reacting with moisture in the air. [ 58 ]
Microbial degradation of polyurethane is believed to be due to the action of esterase , urethanase , hydrolase and protease enzymes. [ 59 ] The process is slow as most microbes have difficulty moving beyond the surface of the polymer. Susceptibility to fungi is higher due to their release of extracellular enzymes , which are better able to permeate the polymer matrix. Two species of the Ecuadorian fungus Pestalotiopsis are capable of biodegrading polyurethane in aerobic and anaerobic conditions such as found at the bottom of landfills . [ 60 ] [ 61 ] Degradation of polyurethane items at museums has been reported. [ 62 ] Polyester-type polyurethanes are more easily biodegraded by fungus than polyether-type. [ 63 ] | https://en.wikipedia.org/wiki/Polyurethane |
Polyurethane dispersion , or PUD , is understood to be a polyurethane polymer resin dispersed in water , rather than a solvent , although some cosolvent may be used. Its manufacture involves the synthesis of polyurethanes having carboxylic acid functionality or nonionic hydrophiles like PEG ( polyethylene glycol ) incorporated into, or pendant from, the polymer backbone. [ 1 ] Two component polyurethane dispersions are also available. [ 2 ]
There has been a general trend towards converting existing resin systems to waterborne resins , for ease of use and environmental considerations. [ 3 ] [ 4 ] [ 5 ] Particularly, their development was driven by increased demand for solventless systems since the manufacture of coatings and adhesives entailed the increasing release of solvents into the atmosphere from numerous sources. [ 6 ] Using VOC exempt solvents is not a panacea as they have their own weaknesses.
The problem has always been that polyurethanes in water are not stable, reacting to produce a urea and carbon dioxide . Many papers and patents have been published on the subject. [ 7 ] [ 8 ] For environmental reasons there is even a push to have PUD available both water-based and bio-based or made from renewable raw materials. [ 9 ] [ 10 ] [ 11 ] PUDs are used because of the general desire to formulate coatings, adhesives, sealants and elastomers based on water rather than solvent, and because of the perceived or assumed benefits to the environment.
The techniques and manufacturing processes have changed over the years from those described in the first papers, journal articles and patents that were published. There are a number of techniques available depending on what type of species is required. An ion may be formed which can be an anion thus forming an anionic PUD or a cation may be formed forming a cationic PUD. Also, it is possible to synthesize a non-ionic PUD. [ 12 ] This involves using materials that will produce an ethylene oxide backbone, or similar, or a water-soluble chain pendant from the main polymer backbone.
Anionic PUDs are by far the most common available commercially. To produce these, initially a polyurethane prepolymer is manufactured in the usual way but instead of just using isocyanate and polyol , a modifier is included in the polymer backbone chain or pendant from the main backbone. This modifier is/was mainly dimethylol propionic acid (DMPA). [ 13 ] This molecule contains two hydroxy groups and a carboxylic acid group. [ 14 ] The OH groups react with the isocyanate groups to produce an NCO terminated prepolymer but with a pendant COOH group. This is now dispersed under shear in water with a suitable neutralizing agent such as triethylamine . This reacts with the carboxylic acid forming a salt which is water soluble. Usually, a diamine chain extender is then added to produce a polyurethane dispersed in water with no free NCO groups but with polyurethane and polyurea segments. [ 15 ] Dytek A is commonly used as the chain extender. [ 16 ] [ 17 ] Various papers and patents show that an amine chain extender with more than two functionalities such as a triamine may be used too. [ 18 ] Chain extender studies have been carried out. [ 19 ]
There is also a push to have a synthesis strategy that is non-isocyanate based. [ 20 ] When blocked isocyanates are used there is no isocyanate (NCO) functionality and hence the water reaction producing carbon dioxide so dispersion is easier. [ 21 ] Modifiers other than DMPA have been researched. [ 22 ]
It is also possible to introduce hydrophilicity into the polymeric molecule by using a modified chain extender rather than doing so in the polymer backbone or a pendant chain. Lower viscosity materials are often the result, as well as higher solids. [ 23 ] A variation on this technique is to incorporate sulfonate groups. PUD/polyacrylate blends can be prepared this way also utilizing internal emulsifiers. [ 24 ]
Cationic PUD also introduce hydrophilic components when synthesized. This includes phosphonium entities. [ 25 ] Techniques have and are being researched to improve the performance and water resistance properties by various techniques. This includes introducing star-branched polydimethylsiloxane. [ 26 ]
Research has been done and published that shows it is not the dispersion speed, mechanical agitation or high shear mixing that has the biggest effect on properties, but rather the chemical makeup. However, particle size distribution can be controlled by this to some extent. [ 27 ]
They find use in coatings , adhesives , sealants and elastomers . Specific uses include industrial coatings, [ 28 ] UV coating resins, [ 29 ] [ 30 ] floor coatings, [ 31 ] hygiene coatings, [ 32 ] wood coatings, [ 33 ] adhesives, [ 34 ] concrete coatings, [ 35 ] automotive coatings, [ 36 ] [ 37 ] clear coatings [ 38 ] and anticorrosive applications. [ 39 ] They are also used in the design and manufacture of medical devices such as the polyurethane dressing, a liquid bandage based on polyurethane dispersion. [ 40 ] To improve their functionality in flame retardant applications, products are being developed which have this feature built into the polymer molecule. [ 41 ] They have also found use in general textile applications such as coating nonwovens. [ 42 ] Leather coatings with antibacterial properties have also been synthesized using PUDs and silver nanoparticles. [ 43 ] On a similar theme, recent (post 2020) innovations have included producing a waterborne polyurethane that has embedded silver particles to combat COVID . [ 44 ] On a similar theme, PUD with antimicrobial properties have been developed. [ 45 ]
Although they are perceived to have good environmental credentials [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] waterborne polyurethane dispersions tend to suffer from lower mechanical strength than other resins. The use of polycarbonate based polyols in the synthesis can help overcome this weakness. [ 59 ] The wear and corrosion resistance is also not as good and hence they are often hybridized. [ 60 ] [ 61 ] Other strategies used to overcome some of the weaknesses include molecular design and mixing/compounding with inorganic rather than polymeric materials. [ 62 ] The use of an anionic or cationic center or indeed a hydrophilic non-ionic manufacturing technique tends to result in a permanent inbuilt water resistance weakness. Research is being conducted and techniques developed to combat this weakness. [ 63 ] Simple blending has also been employed. This has the advantage in that if no new molecule has been formed but merely blending with existing registered raw materials, then that is a way around the work required to get registration of the material under various country regimes such as REACH in Europe and TSCA in the United States. Because of the surface tension of water being so high, pinholes and other problems of air-entrainment tend to be more common and need special additives to combat. [ 64 ] They also tend not to be manufactured with biobased polyols because vegetable based polyols don't have performance enhancing functional groups. Modification is possible to achieve this and enable even greener versions. [ 65 ]
Drying, curing and cross-linking is also not usually as good and hence research is proceeding in the area of post crosslinking to improve these features. [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ] [ 73 ] [ 74 ] [ 75 ] [ 76 ] [ 77 ]
The disadvantages of PUDs are being improved by research. [ 78 ] [ 79 ] [ 80 ] [ 81 ] Hybridization using other materials and techniques is one such area. PUDs that are waterborne and UV curable are being intensely researched with well over 100 research papers produced in the 2000-2020 time period. [ 29 ] [ 82 ] [ 83 ] [ 84 ] [ 85 ] [ 86 ] Waterborne PUD- Acrylates based on epoxidized soybean oil that is also UV curable have been produced and are feasible. [ 87 ] The nature of the acrylate affects the properties. [ 88 ] One use of hybrids is in textile finishes. [ 89 ]
As ionic centers are introduced with waterborne PUDs, the water resistance and uptake in the final film has been studied extensively. The nature of the polyol and the level of COOH groups and hydrophobic modification with other moieties can improve this property. Polyester polyols give the biggest improvements. [ 82 ] [ 90 ] Polycarbonate polyols also enhance properties, [ 91 ] especially if the polycarbonate is also fluorinated. [ 92 ] Reinforcing PUDs with nanomaterials also improves properties, [ 93 ] [ 94 ] as does silicone modification. [ 95 ] [ 96 ] [ 97 ]
To make PUDs more hydrophobic and water repellent and thus remove a weakness, a number of techniques have been researched. One way is to add hydroxyethyl acrylate to the polyol reacting with isocyanate. Once the PUD is made it will have terminal double bond functionality from the acrylate. This may now be copolymerized with a very hydrophobic acrylate such as stearyl acrylate using free radical techniques. This long alkyl chain introduced confers hydrophobicity. [ 98 ]
Another method of hybridization is to make a PUD that is both anionic but with a very substantial nonionic modification utilizing a polyether polyol based on ethylene oxide. In addition, a silicone diol maybe incorporated. [ 99 ]
As epoxy resins have some outstanding properties, research using epoxy to modify PUD is taking place. [ 100 ]
PUDs that are based on thiol rather than hydroxyl and also modified with both acrylate as well as epoxy functionality have been produced and researched. [ 101 ]
As PUDs are resin dispersed in water, when cast as a film and dried they are inherently high gloss. They can be designed to be matte/flat by incorporating siloxane functionality. [ 102 ]
Since PUDs are usually considered green and environmentally friendly, techniques being researched also include capturing carbon dioxide from the atmosphere to make the raw materials and then further synthesis. [ 103 ] | https://en.wikipedia.org/wiki/Polyurethane_dispersion |
Polyurethane foam is a solid polymeric foam based on polyurethane chemistry. As a specialist synthetic material with highly diverse applications, polyurethane foams are primarily used for thermal insulation and as a cushioning material in mattresses, upholstered furniture or as seating in vehicles. Its low density and thermal conductivity combined with its mechanical properties make them excellent thermal and sound insulators, as well as structural and comfort materials.
Polyurethane foams are thermosetting polymers. They cannot be melted and reshaped after initially formed, because the chemical bonds between the molecules in the material are very strong and are not broken down by heating. Once cured and cooled, the material maintains its shape and properties. [ 1 ]
Polyurethane foams are the most widely used representatives of thermoset foams. Depending on their cellular structure, they can be classified as open or closed-cell foams. Looking at mechanical properties, there are two main types of polyurethane foam; flexible (soft) and rigid (hard) foams. [ 2 ] Generally speaking, flexible polyurethane foams have an open-cell structure where the pores are interconnected, smaller in size and irregularly shaped; contrary to rigid polyurethane foams that have a closed-cell structure, where the pores are not interconnected. [ 3 ] The market share between these two types is largely equal. [ 4 ]
There are various processing technologies in the production of polyurethane foams. Depending on the properties of the end application, the two most often used at large scale production are moulding and slabstock (block) foaming. [ 5 ] Next to these, other prominent types include cavity-filling foam (e.g. car fillings used for acoustic insulation); and spray foam (e.g. roof thermal insulation). These are known as semi-flexible foams behind appropriate overlays. [ 6 ]
The flexible polyurethane foam (FPUF) is produced from the reaction of polyols and isocyanates , a process pioneered in 1937. [ 7 ] Depending on the application the foam will be used for, a series of additives are necessary to produce high-quality PU foam products. FPUF is a versatile material that can be tailored to exhibit different properties. It allows for superior compression, load-bearing and resilience that provides a cushioning effect. Because of this property, lightweightness, and efficient production process, it is often used in furniture, bedding, automotive seating, athletic equipment, packaging, footwear, and carpets. [ 7 ]
Flexible polyurethane foams with a high volume of open pores have been greatly regarded as an effective noise absorption material and are widely used as acoustic insulation in various sectors, from construction to transportation. [ 8 ] It is also a very resilient material that does not deteriorate over time and its lifetime is typically linked to the lifetime of the application it is used in. [ 9 ]
Flexible polyurethane foams can be manufactured through a continuous (slabstock) production or moulding process. In the continuous process, the mixed ingredients are poured on the conveyor belt. The chemical reaction occurs instantly, causing the foam to rise within seconds and then solidify. In theory, foam blocks of several kilometres in length could be produced this way. In reality, the foam blocks are typically cut at a length of between 15 and 120m, cured and stored for further processing. [ 10 ]
Contrary to slabstock foam, moulded foam production is a discontinuous process. Moulded foam articles are made one at a time by injecting the foam mixture into moulds. When the foam rises and expands, it occupies the whole space in the mould. It solidifies almost instantly and the produced part can then be removed from the mould, either mechanically or manually. [ 11 ] This is the biggest advantage of moulded PU foams – they can be moulded into specific desired shapes, eliminating the need for cutting and reducing waste fractions. They can be produced with multiple zones of hardness and with reinforcements for further easier assembly. [ 12 ] This is why moulded foam technology is widely used in the production of seat cushions used in the transport industries.
Based on the production process, other types of flexible polyurethane foams may include rebonded (or recycled), reticulated and auxetic PU foams.
Since the invention of polyurethane chemistry there have been constant innovations in the industry, driven by the need to decrease the toxicity of chemical substances used in production processes. Some examples include reducing Volatile Organic Compounds emissions or using blowing agents with a lower global warming potential (GWP) as well as ozone-depleting potential (ODP). [ 13 ]
In the last decades, the main focus of the FPUF industry has been improving the environmental impact of its products and processes. A cradle-to-gate analysis of flexible (TDI slabstock) PU foam shows that (by far) the largest effect on the life cycle of the PU foams is due to raw materials extraction and production. Depending on the parameters, these account for about 90% of the total Greenhouse Gas (GHG) emissions. [ 14 ]
Traditionally nearly all raw materials used for flexible PU foam production have been of fossil origin. Today, it is possible to make flexible PU foams from alternative, non-fossil sources, thus significantly improving its environmental footprint. [ 15 ] These include bio-polyols, recycled polyols and CO 2 -based polyols.
As a thermosetting polymer PU foam cannot just be melted at the end of its useful life to make new products. For PU foam-containing products, there are various recycling technologies available and in broad use today:
Globally today the most often used waste management methods are landfilling and energy recovery . These should only be used when recycling methods are not available or cost-effective. Energy recovery processes include combustion, incineration and thermal degradation of PU. [ 16 ]
Rigid polyurethane foam has many desirable properties which has enabled increased use in various applications, some of which are quite demanding. [ 22 ] [ 23 ] These properties include low thermal conduction making it useful as an insulator. It also has low density compared to metals and other materials and also good dimensional stability. [ 24 ] A metal will expand on heating whereas rigid PU foam does not. They have excellent strength to weight ratios. [ 25 ] Like many applications, there has been a trend to make rigid PU foam from renewable raw materials in place of the usual polyols. [ 26 ] [ 27 ] [ 28 ]
They are used in vehicles, planes and buildings in structural applications. [ 29 ] They have also been used in fire-retardant applications. [ 30 ]
Polyurethane foam has been widely used to insulate fuel tanks on Space Shuttles . However, it requires a perfect application, as any air pocket, dirt or an uncovered tiny spot can knock it off due to extreme conditions of liftoff . [ 31 ] Those conditions include violent vibrations, air friction and abrupt changes in temperature and pressure. For a perfect application of the foam there have been two obstacles: limitations related to wearing protective suits and masks by workers and inability to test for cracks before launch, such testing is done only by naked eye. [ 31 ] The loss of foam caused the Space Shuttle Columbia disaster . According to the Columbia accident report, NASA officials found foam loss in over 80% of the 79 missions for which they have pictures. [ 31 ]
By 2009 researchers created a superior polyimide foam to insulate the reusable cryogenic propellant tanks of Space Shuttles. [ 32 ] | https://en.wikipedia.org/wiki/Polyurethane_foam |
In chemistry , polyvalency (or polyvalence , multivalency ) is the property of molecules and larger species, such as antibodies , medical drugs, and even nanoparticles surface-functionalized with ligands, like spherical nucleic acids , that exhibit more than one supramolecular interaction . [ 1 ] [ 2 ] [ 3 ] For the number of chemical bonds of atoms , the term " valence " is used (Fig. 1). For both atoms and larger species, the number of bonds may be specified: divalent species can form two bonds; a trivalent species can form three bonds; and so on. [ 4 ]
Species that have polyvalency usually show enhanced or cooperative binding compared to their monovalent counterparts. [ 5 ] [ 6 ] [ 7 ] [ 8 ] Nanoparticles with multiple nucleic acid strands on their surfaces (e.g., DNA ) can form multiple bonds with one another by DNA hybridization to form hierarchical assemblies, some of which are highly crystalline in nature. [ 9 ] | https://en.wikipedia.org/wiki/Polyvalency_(chemistry) |
Polyvinyl alcohol ( PVOH , PVA , or PVAl ) is a water - soluble synthetic polymer . It has the idealized formula [CH 2 CH(OH)] n . It is used in papermaking , textile warp sizing , as a thickener and emulsion stabilizer in polyvinyl acetate (PVAc) adhesive formulations, in a variety of coatings, and 3D printing . It is colourless (white) and odorless. It is commonly supplied as beads or as solutions in water. [ 3 ] [ 4 ] Without an externally added crosslinking agent, PVA solution can be gelled through repeated freezing-thawing, yielding highly strong, ultrapure, biocompatible hydrogels which have been used for a variety of applications such as vascular stents , cartilages , contact lenses , etc. [ 5 ]
Although polyvinyl alcohol is often referred to by the acronym PVA, more generally PVA refers to polyvinyl acetate , which is commonly used as a wood adhesive and sealer.
PVA is used in a variety of medical applications because of its biocompatibility, low tendency for protein adhesion, and low toxicity. Specific uses include cartilage replacements, contact lenses , laundry detergent pods and eye drops . [ 6 ] Polyvinyl alcohol is used as an aid in suspension polymerizations . Its largest application in China is its use as a protective colloid to make PVAc dispersions. In Japan its major use is the production of Vinylon fiber. [ 7 ] This fiber is also manufactured in North Korea for self-sufficiency reasons, because no oil is required to produce it. Another application is photographic film. [ 8 ]
PVA-based polymers are used widely in additive manufacturing. For example, 3D printed oral dosage forms demonstrate great potential in the pharmaceutical industry. It is possible to create drug-loaded tablets with modified drug-release characteristics where PVA is used as a binder substance. [ 9 ]
Medically, PVA-based microparticles have received FDA 510(k) approval to be used as embolisation particles to be used for peripheral hypervascular tumors. [ 10 ] It may also used as the embolic agent in a Uterine Fibroid Embolectomy (UFE). [ 11 ] In biomedical engineering research, PVA has also been studied for cartilage , orthopaedic applications, [ 12 ] and potential materials for vascular graft . [ 13 ]
PVA is commonly used in household sponges that absorb more water than polyurethane sponges. [ citation needed ]
PVA may be used as an adhesive during preparation of stool samples for microscopic examination in pathology . [ 14 ]
Polyvinyl acetals are prepared by treating PVA with aldehydes . Butyraldehyde and formaldehyde afford polyvinyl butyral (PVB) and polyvinyl formal (PVF), respectively. Preparation of polyvinyl butyral is the largest use for polyvinyl alcohol in the US and Western Europe.
Unlike most vinyl polymers , PVA is not prepared by polymerization of the corresponding monomer , since the monomer, vinyl alcohol , is thermodynamically unstable with respect to its tautomerization to acetaldehyde . Instead, PVA is prepared by hydrolysis of polyvinyl acetate, [ 3 ] or sometimes other vinyl ester-derived polymers with formate or chloroacetate groups instead of acetate. The conversion of the polyvinyl esters is usually conducted by base-catalysed transesterification with ethanol:
The properties of the polymer are affected by the degree of transesterification.
Worldwide consumption of polyvinyl alcohol was over one million metric tons in 2006. [ 7 ]
PVA is an atactic material that exhibits crystallinity . In terms of microstructure, it is composed mainly of 1,3-diol linkages [−CH 2 −CH(OH)−CH 2 −CH(OH)−], but a few percent of 1,2-diols [−CH 2 −CH(OH)−CH(OH)−CH 2 −] occur, depending on the conditions for the polymerization of the vinyl ester precursor. [ 3 ]
Polyvinyl alcohol has excellent film-forming, emulsifying and adhesive properties. It is also resistant to oil, grease and solvents . It has high tensile strength and flexibility, as well as high oxygen and aroma barrier properties. However, these properties are dependent on humidity : water absorbed at higher humidity levels acts as a plasticiser , which reduces the polymer's tensile strength, but increases its elongation and tear strength.
Polyvinyl alcohol is widely used, thus its toxicity and biodegradation are of interest. Tests showed that fish (guppies) are not harmed, even at a poly(vinyl alcohol) concentration of 500 mg/L of water. [ 3 ]
The biodegradability of PVA is affected by the molecular weight of the sample. [ 3 ] Aqueous solutions of PVA degrade faster, which is why PVA grades that are highly water-soluble tend to have a faster biodegradation. [ 15 ] Not all PVA grades are readily biodegradable, but studies show that high water-soluble PVA grades such as the ones used in detergents can be readily biodegradable according to OECD
screening test conditions. [ 16 ]
Orally administered PVA is relatively harmless. [ 17 ] The safety of polyvinyl alcohol is based on some of the following observations: [ 17 ] | https://en.wikipedia.org/wiki/Polyvinyl_alcohol |
Polyvinyl nitrate (abbreviated: PVN) is a high-energy polymer with the idealized formula of [CH 2 CH(ONO 2 )]. Polyvinyl nitrate is a long carbon chain (polymer) with nitrate groups ( − O − NO 2 ) {\displaystyle {\ce {(-O-NO2)}}} bonded randomly along the chain. PVN is a white, fibrous solid, and is soluble in polar organic solvents such as acetone . PVN can be prepared by nitrating polyvinyl alcohol with an excess of nitric acid . Because PVN is also a nitrate ester such as nitroglycerin (a common explosive ), it exhibits energetic properties and is commonly used in explosives and propellants .
Polyvinyl nitrate was first synthesized by submersing polyvinyl alcohol (PVA) in a solution of concentrated sulfuric and nitric acids. This causes the PVA to lose a hydrogen atom from its hydroxy group ( deprotonation ), and the nitric acid (HNO 3 ) to lose a NO 2 + when in sulfuric acid. The NO 2 + attaches to the oxygen in the PVA and creates a nitrate group, producing polyvinyl nitrate. This method results in a low nitrogen content of 10% and an overall yield of 80%. This method is inferior, as PVA has a low solubility in sulfuric acid and a slow rate of nitration for PVA. This meant that a lot of sulfuric acid was needed relative to PVA and did not produce a high nitrogen PVN, which is desirable for its energetic properties. [ 1 ]
An improved method is where PVA is nitrated without sulfuric acid; however, when this solution is exposed to air, the PVA combusts . In this new method, either the PVA nitration is done in an inert gas ( carbon dioxide or nitrogen ) or the PVA powder is clumped into larger particles and submerged underneath the nitric acid to limit the amount of air exposure. [ 1 ]
Currently, the most common method is when PVA powder is dissolved in acetic anhydride at -10°C. Then cooled nitric acid is slowly added. [ 2 ] This produces a high nitrogen content PVN within about 5-7 hours. [ 3 ] Because acetic anhydride was used as the solvent instead of sulfuric acid, the PVA will not combust when exposed to air. [ 4 ]
PVN is a white thermoplastic with a softening point of 40-50°C. [ 5 ] The theoretical maximum nitrogen content of PVN is 15.73%. PVN is a polymer that has an atactic configuration , meaning the nitrate groups are randomly distributed along the main chain. Fibrous PVN increases in crystallinity as the nitrogen content increases, showing that the PVN molecules organize themselves more orderly as nitrogen percent increases. [ 3 ] Intramolecularly, the geometry of the polymer is planar zigzag . [ 6 ] The porous PVN can be gelatinized when added to acetone at room temperature. This creates a viscous slurry and loses its fibrous and porous nature; however, it retains most of its energetic properties. [ 3 ]
Source: [ 3 ]
Polyvinyl nitrate is a high-energy polymer due to the significant presence of O − NO 2 {\displaystyle {\ce {O - NO2}}} groups, similar to nitrocellulose and nitroglycerin. These nitrate groups have an activation energy of 53 kcal/mol are the primary cause of PVN's high chemical potential energy . The complete combustion reaction of PVN assuming full nitration is:
When burned, PVN samples with less nitrogen had a significantly higher heat of combustion because there were more hydrogen molecules and more heat was generated when oxygen was present. The heat of combustion was about 3,000 cal/g for 15.71% N and 3,700 cal/g for 11.76% N. Alternatively, PVN samples with a higher nitrogen content had a significantly higher heat of explosion as it had more O − NO 2 {\displaystyle {\ce {O - NO2}}} groups as it had more oxygen leading to more complete combustion. This leads to a more complete combustion and more heat generated when burned in inert or low oxygen environments.
Nitrate esters, in general, are unstable because of the weak N − O {\displaystyle {\ce {N - O}}} bond and tend to decompose at higher temperatures. Fibrous PVN is relatively stable at 80°C and is less stable as the nitrogen content increases. [ 3 ] [ 5 ] Gelatinized PVN is less stable than fibrous PVN. [ 3 ]
Source: [ 3 ]
Ignition temperature is the temperature at which a substance combusts spontaneously and requires no other additional energy (other than the temperature)/ This temperature can be used to determine the activation energy. For samples of varying nitrogen content, the ignition temperature decreases as nitrogen percentage increases, showing that PVN is more ignitable as nitrogen content increases. Using the Semenov equation :
where D is the ignition delay (the time it takes for a substance to ignite), E is the activation energy, R is the universal gas constant , T is absolute temperature, and C is a constant, dependent on the material.
The activation energy is greater than 13 kcal/mol and reaches 16 kcal/mol (at 15.71% nitrogen, near theoretical maximum) and varies greatly between different nitrogen concentrations and has no linear pattern between activation energy and the degree of nitration.
The height at which a mass is dropped on PVN and causes an explosion shows the sensitivity of PVN to impacts. As nitrogen content increases, fibrous PVN is more sensitive to impacts. Gelatinous PVN is similar to fibrous PVN in impact sensitivity. [ 3 ]
Because of the nitrate groups of PVN, polyvinyl nitrate is mainly used for its explosive and energetic capabilities. Structurally, PVN is similar to nitrocellulose in that it is a polymer with several nitrate groups off the main branch, differing only in their main chain (carbon and cellulose respectively). [ 7 ] Because of this similarity, PVN is typically used in explosives and propellants as a binder. In explosives, a binder is used to form an explosive where the explosive materials are difficult to mold (see Polymer-bonded explosive (PBX)) . A common binder polymer is hydroxyl-terminated polybutadiene (HTPB) or glycidyl azide polymer (GAP). Moreover, the binder needs a plasticizer such as dioctyl adipate (DOP) or 2-nitrodiphenylamine (2-NDPA) to make the explosive more flexible. [ 5 ] Polyvinyl nitrate combines the traits of both a binder and a plasticizer, as this polymer binds the explosive ingredients together and is flexible at is softening point (40-50°C). Moreover, PVN adds to the explosive's overall energetic potential due to its nitrate groups.
An example composition including polyvinyl nitrate is PVN, nitrocellulose and/or polyvinyl acetate, and 2-nitrodiphenylamine. This creates a moldable thermoplastic that can be combined with a powder containing nitrocellulose to create a cartridge case where the PVN composition acts as a propellant and assists as an explosive material. [ 8 ] | https://en.wikipedia.org/wiki/Polyvinyl_nitrate |
Polyvinyl siloxane ( PVS ), also called poly-vinyl siloxane , vinyl polysiloxane ( VPS ), or vinylpolysiloxane , is an addition-reaction silicone elastomer (an addition silicone). It is a viscous liquid that cures (solidifies) quickly into a rubber-like solid, taking the shape of whatever surface it was lying against while curing. As with two-part epoxy , its package keeps its two component liquids in separate tubes until the moment they are mixed and applied, because once mixed, they cure (harden) rapidly. Polyvinyl siloxane is widely used in dentistry as an impression material. [ 1 ] It is also used in other contexts where an impression similar to a dental impression is needed, such as in audiology (to take ear impressions for fitting custom hearing protection or hearing aids [ 2 ] ) or in industrial applications (such as to aid in the inspection of interior features of machined parts, for example, internal grooves inside bores ). Polyvinyl siloxane was commercially introduced in the 1970s.
To create the material, the user simply mixes a colored putty (often blue or pink) with a white putty, and the chemical reaction begins. PVS with a wide variety of working and setting times is available commercially. [ 3 ] Final set is noted when the product rebounds upon touching with a blunt or sharp instrument.
This reaction also gives off hydrogen gas and it is therefore advisable to wait up to an hour before pouring the ensuing cast. [ 4 ] [ 5 ]
In dentistry, this material is commonly referred to as having light or heavy body depending on specific usage. | https://en.wikipedia.org/wiki/Polyvinyl_siloxane |
Polyvinylcarbazole ( PVK ) is a temperature-resistant [ 2 ] thermoplastic polymer produced by radical polymerization from the monomer N -vinylcarbazole . It is a photoconductive polymer and thus the basis for photorefractive polymers and organic light-emitting diodes . [ 3 ]
Polyvinylcarbazole was discovered by the chemists Walter Reppe (1892-1969), Ernst Keyssner and Eugen Dorrer and patented by I.G. Farben in the USA in 1937. [ 4 ] [ 1 ] PVK was the first polymer whose photoconductivity was known. Starting in the 1960s, further polymers of this kind were sought. [ 3 ]
Polyvinylcarbazole is obtained from N -vinylcarbazole by radical polymerization in various ways. It can be produced by suspension polymerization at 180 °C with sodium chloride and potassium chromate as catalyst. [ 2 ] Alternatively, AIBN can also be used as a radical starter or a Ziegler-Natta catalyst . [ 1 ]
PVK can be used at temperatures of up to 160 - 170 °C and is therefore a temperature-resistant thermoplastic. The electrical conductivity changes depending on the illumination. For this reason, PVK is classified as a semiconductor or photoconductor . The polymer is extremely brittle, but the brittleness can be reduced by copolymerization with a little isoprene . [ 5 ]
Polyvinylcarbazole is soluble in aromatic hydrocarbons , halogenated hydrocarbons and ketones . [ 1 ] It is resistant to acids, alkalis, polar solvents and aliphatic hydrocarbons. [ 2 ] The addition of PVK to other plastic masses increases their temperature resistance.
Due to its high price and special properties, the use of PVK is limited to special areas. [ 2 ] It is used in insulation technology, [ 2 ] electrophotography (e.g. in copiers and laser printers), [ 3 ] for the fabrication of polymer photonic crystals, [ 6 ] for organic light-emitting diodes and photovoltaic devices. [ 1 ] In addition, PVK is a well researched component in photorefractive polymers and therefore plays an important role in holography. Another application is the production of cooking-proof copolymers with styrene . | https://en.wikipedia.org/wiki/Polyvinylcarbazole |
Polywater was a hypothesized polymerized form of water that was the subject of much scientific controversy during the late 1960s, first described by Soviet scientist Nikolai Fedyakin. By 1969 the popular press had taken notice of Western attempts to recreate the substance and sparked fears of a "polywater gap" between the United States and Soviet Union. Increased press attention also brought with it increased scientific attention, and as early as 1970 doubts about its authenticity were being circulated. [ 1 ] [ 2 ] [ 3 ] By 1973 it was found to be illusory, being just water with any number of common compounds contaminating it. [ 4 ] Today, polywater is best known as an example of pathological science . [ 5 ]
In 1961, the Soviet physicist Nikolai Fedyakin, working at the Technological Institute of Kostroma , Russia , performed measurements on the properties of water which had been condensed in, or repeatedly forced through, narrow quartz capillary tubes . Some of these experiments resulted in what was seemingly a new form of water with a higher boiling point , lower freezing point , and much higher viscosity than ordinary water – about that of a syrup . [ 6 ] [ 7 ]
Boris Derjaguin , director of the laboratory for surface physics at the Institute for Physical Chemistry in Moscow , heard about Fedyakin's experiments. He improved on the method to produce the new water, and though he still produced very small quantities of this mysterious material, he did so substantially faster than Fedyakin did. Investigations of the material properties showed a substantially lower freezing point of −40 °C or less, a boiling point of 150 °C or greater, a density of approx. 1.1 to 1.2 g/cm 3 , and increased expansion with increasing temperature. The results were published in Soviet science journals, [ 8 ] and short summaries were published in Chemical Abstracts in English, but Western scientists took no notice of the work.
In 1966, Derjaguin travelled to England for the "Discussions of the Faraday Society " in Nottingham . There, he presented the work again, and this time English scientists took note of what he referred to as anomalous water . English scientists then started researching the effect as well, and by 1968 it was also under study in the United States.
By 1969, the concept had spread to newspapers and magazines . [ 1 ] [ 2 ] There was fear [ failed verification ] by the United States military that there was a so-called "polywater gap" with the Soviet Union , a popular media term indicating a possible capability "gap", or discrepancy, between the US and the USSR, popularized by media hype of the " bomber gap " and the " missile gap ", during periods when the USSR appeared to be outstripping the US in numbers of these various weapons. [ 9 ]
A scientific furore followed. Some experiments carried out were able to reproduce Derjaguin's findings, while others failed. Several theories were advanced to explain the phenomenon. Some proposed it was the cause for increasing resistance on trans-Atlantic phone cables , while others predicted that if polywater were to contact ordinary water, it would convert that water into polywater, echoing the doomsday scenario in Kurt Vonnegut 's novel Cat's Cradle . By the 1970s, polywater was well known in the general population. [ 10 ]
During this time, several people questioned the authenticity of what had come to be known in the West as polywater. The main concern was contamination of the water, but the papers went to great lengths to note the care taken to avoid this. Denis Rousseau and Sergio Porto of Bell Labs carried out infrared spectrum analysis, which showed polywater to be mostly chlorine and sodium. [ 11 ]
Denis Rousseau undertook an experiment with his own sweat after playing a handball game at the lab and found it had identical properties. He then published a paper suggesting polywater was nothing more than water with small amounts of biological impurities. [ 12 ]
Another wave of research followed, this time more tightly controlled. Invariably, polywater could no longer be made. Chemical analysis found the samples of polywater to be contaminated with other substances (explaining the changes in melting and boiling points due to colligative properties ), and examination of polywater by electron microscopy showed it also contained small particles of various solids – from silica to phospholipids , explaining its greater viscosity.
When the experiments which had initially produced polywater were repeated with thoroughly cleaned glassware , the anomalous properties of the resulting water vanished, and even the scientists who had originally advanced the case for polywater agreed it did not exist.
In August 1973, Derjaguin and N. V. Churaev published a letter in the journal Nature in which they wrote; "these [anomalous] properties should be attributed to impurities rather than to the existence of polymeric water molecules". [ 13 ]
Denis Rousseau used polywater as a classic example of pathological science and has since written on other examples as well. [ 14 ]
It has been suggested that polywater should have been dismissed on theoretical grounds. The laws of thermodynamics predicted that, since polywater had a higher boiling point than ordinary water, it meant it was more stable, and thus all of Earth's water should have turned spontaneously into polywater, instead of just part of it. [ 15 ] Richard Feynman remarked that if such a material existed, then an animal would exist that would ingest water and excrete polywater, using the energy released from the process to survive. [ 15 ]
The episodes " The Naked Time " ( Star Trek , 1966) and its sequel, " The Naked Now " ( Star Trek: The Next Generation , 1987) involve forms of polywater intoxication . In the original episode, a scientific research outpost falls victim to polywater, which causes the crew to become so incapacitated that they all died after shutting off environmental controls in the compound. In the sequel, a Starfleet vessel is discovered adrift, its crew frozen in various states due to polywater intoxication. The Star Trek: Lower Decks episode " I, Excretus " briefly features a simulated version of the USS Cerritos plagued by polywater intoxication, leading to a shipwide orgy , as part of a holodeck drill. Beckett Mariner attempts the simulation, but is unable to stomach the scenario and chooses to eject herself from an airlock.
The story "Polywater Doodle" by Howard L. Myers appeared in the February 1971 issue of Analog Science Fiction and Fact . It features an animal composed entirely of polywater, with the metabolism described by Richard Feynman. (The title of the story is a pun on " Polly Wolly Doodle ".)
Polywater is the central idea of the 1972 espionage/thriller novel A Report from Group 17 by Robert C. O'Brien . The story revolves around the use of a type of polywater to make people controllable and incapable of independent thought or action.
There is a company named American Polywater Corporation, which is unrelated to the hypothesized form of water. The company is based in Stillwater, Minnesota . [ 16 ] [ 17 ] [ 18 ] | https://en.wikipedia.org/wiki/Polywater |
Polyworld is a cross-platform ( Linux , Mac OS X ) program written by Larry Yaeger to evolve Artificial Intelligence through natural selection and evolutionary algorithms .
It uses the Qt graphics toolkit and OpenGL to display a graphical environment in which a population of trapezoid agents search for food, mate, have offspring, and prey on each other. The population is typically only in the hundreds, as each individual is rather complex and the environment consumes considerable computer resources. The graphical environment is necessary since the individuals actually move around the 2-D plane and must be able to "see." Since some basic abilities, like eating carcasses or randomly generated food, seeing other individuals, mating or fighting with them, etc., are possible, a number of interesting behaviours have been observed to spontaneously arise after prolonged evolution, such as cannibalism, predators and prey, and mimicry.
Each individual makes decisions based on a neural net using Hebbian learning ; the neural net is derived from each individual's genome. The genome does not merely specify the wiring of the neural nets, but also determines their size, speed, color, mutation rate and a number of other factors. The genome is randomly mutated at a set probability, which are also changed in descendant organisms. [ 1 ]
This scientific software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Polyworld |
A polyyne is any organic compound with alternating single and triple bonds ; that is, a series of consecutive alkynes , (−C≡C−) n with n greater than 1. These compounds are also called polyacetylenes , especially in the natural products and chemical ecology literature, [ 1 ] even though this nomenclature more properly refers to acetylene polymers composed of alternating single and double bonds (−CR=CR′−) n with n greater than 1. They are also sometimes referred to as oligoynes , [ 2 ] [ needs IPA ] or carbinoids after " carbyne " (−C≡C−) ∞ , the hypothetical allotrope of carbon that would be the ultimate member of the series. [ 3 ] [ 4 ] The synthesis of this substance has been claimed several times since the 1960s, but those reports have been disputed. [ 5 ] Indeed, the substances identified as short chains of "carbyne" in many early organic synthesis attempts [ 6 ] would be called polyynes today.
The simplest polyyne is diacetylene or butadiyne, H−C≡C−C≡C−H . Along with cumulenes , polyynes are distinguished from other organic chains by their rigidity and high conductivity, [ 7 ] both of which make them promising as wires in molecular nanotechnology . Polyynes have been detected in interstellar molecular clouds where hydrogen is scarce. [ citation needed ]
The first reported synthesis of a polyyne was performed in 1869 by Carl Andreas Glaser [ de ] , who observed that copper phenylacetylide ( CuC≡C−C 6 H 5 ) undergoes oxidative dimerization in the presence of air to produce diphenylbutadiyne ( C 6 H 5 −C≡C−C≡C−C 6 H 5 ). [ 4 ]
Interest in these compounds has stimulated research into their preparation by organic synthesis by several general routes. As a main synthetic tool usually acetylene homocoupling reactions like the Glaser coupling or its associated Elinton and Hay protocols are used. [ 8 ] [ 4 ] Moreover, many of such procedures involve a Cadiot–Chodkiewicz coupling or similar reactions to unite two separate alkyne building-blocks or by alkylation of a pre-formed polyyne unit. [ 9 ] In addition to that, Fritsch–Buttenberg–Wiechell rearrangement was used as crucial step during the synthesis of the longest known polyyne ( C 44 ). [ 10 ] An elimination of chlorovinylsilanes was used as a final step in the synthesis of the longest known phenyl end-capped polyynes. [ 11 ]
Using various techniques, polyynes H(−C≡C−) n H with n up to 4 or 5 were synthesized during the 1950s. [ 12 ] Around 1971, T. R. Johnson and D. R. M. Walton developed the use of end-caps of the form – SiR 3 , where R was usually an ethyl group , to protect the polyyne chain during the chain-doubling reaction using Hay's catalyst (a copper(I) – TMEDA complex ). [ 12 ] [ 13 ] With that technique they were able to obtain polyynes like (CH 3 CH 2 ) 3 Si(−C≡C−) n Si(CH 2 CH 3 ) 3 with n up to 8 in pure state, and with n up to 16 in solution.
Later Tykwinski and co-workers were able to obtain ((CH 3 ) 2 CH) 3 Si(−C≡C−) n Si(CH(CH 3 ) 2 ) 3 polyynes with chain length up to C 20 . [ 14 ]
A polyyne compound with 10 acetylenic units (20 atoms), with the ends capped by Fréchet-type aromatic polyether dendrimers , was isolated and characterized in 2002. [ 2 ] Moreover, the synthesis of dicyanopolyynes with up to 8 acetylenic units was reported. [ 15 ] The longest phenyl end-capped polyynes were reported by Cox and co-workers in 2007. [ 11 ] As of 2010, the polyyne with the longest chain yet isolated had 22 acetylenic units (44 carbon atoms), end-capped with tris(3,5-di-t-butylphenyl)methyl groups. [ 10 ]
Alkynes with the formula H(−C≡C−) n H and n from 2 to 6 can be detected in the decomposition products of partially oxidized copper(I) acetylide ( (Cu + ) 2 ( − C≡C − ) (an acetylene derivative known since 1856 or earlier) by hydrochloric acid . A "carbonaceous" residue left by the decomposition also has the spectral signature of (−C≡C−) n chains. [ 16 ]
Organometallic polyynes capped with metal complexes are well characterized. As of the mid-2010s, the most intense research has concerned rhenium ( Re(−C≡C−) n Re , n = 3–10), [ 17 ] ruthenium ( RuRu(−C≡C−) n RuRu , n = 4–10), [ 18 ] iron ( Fe(−C≡C−) 6 Fe ), [ 19 ] platinum ( Pt(−C≡C−) n Pt , n = 8–14), [ 20 ] palladium ( Ar(−C≡C−) n Pd , n = 3–5, Ar = aryl ), [ 21 ] and cobalt ( Co 3 C(−C≡C−) n CCo 3 , n = 7–13) [ 22 ] complexes.
Long polyyne chains are said to be inherently unstable in bulk because they can cross-link with each other exothermically. [ 5 ] Explosions are a real hazard in this area of research. [ 23 ] They can be fairly stable, even against moisture and oxygen , if the end hydrogen atoms are replaced with a suitably inert end-group , such as tert -butyl or trifluoromethyl . [ 24 ] Bulky end-groups, that can keep the chains apart, work especially well at stabilizing polyynes. [ 2 ] In 1995 the preparation of carbyne chains with over 300 carbon atoms was reported using this technique. [ 24 ] However the report has been contested by a claim that the detected molecules were fullerene -like structures rather than long polyynes. [ 5 ]
Polyyne chains have also been stabilised to heating by co-deposition with silver nanoparticles , [ 25 ] and by complexation with a mercury -containing tridentate Lewis acid to form layered adducts . [ 26 ] Long polyyne chains encapsulated in double-walled carbon nanotubes or in the form of rotaxanes [ 27 ] have also been shown to be stable. [ 28 ] Despite rather low stability of longer polyynes there are some examples of their use as synthetic precursors in organic and organometallic synthesis. [ 29 ]
Synthetic polyynes of the form R(−C≡C−) n R , with n about 8 or more, often have a smoothly curved or helical backbone in the crystalline solid state, presumably due to crystal packing effects. [ 30 ] For example, when the cap R is triisopropylsilyl and n is 8, X-ray crystallography of the substance (a crystalline orange/yellow solid) shows the backbone bent by about 25–30 degrees in a broad arch, so that each C−C≡C angle deviates by 3.1 degrees from a straight line. This geometry affords a denser packing, with the bulky cap of an adjacent molecule nested into the concave side of the backbone. As a result, the distance between backbones of neighboring molecules is reduced to about 0.35 to 0.5 nm, near the range at which one expects spontaneous cross-linking. The compound is stable indefinitely at low temperature, but decomposes before melting. In contrast, the homologous molecules with n = 4 or n = 5 have nearly straight backbones that stay at least 0.5 to 0.7 nm apart, and melt without decomposing. [ 14 ]
A wide range of organisms synthesize polyynes. [ 1 ] [ 31 ] These chemicals have various biological activities, including as flavorings and pigments, chemical repellents and toxins, and potential application to biomedical research and pharmaceuticals. In plants, polyynes are found mainly in Asterids clade, especially in the sunflower , carrot , ginseng and bellflower families. However, they can also be found in some members of the tomato , olax , and sandalwood families. [ 32 ] The earliest polyyne to be isolated was dehydromatricaria ester (DME) in 1826; however, it was not fully characterized until later. [ 1 ] [ 33 ]
The simple fatty acid 8,10-octadecadiynoic acid is isolated from the root bark of the legume Paramacrolobium coeruleum of the family Caesalpiniaceae and has been investigated as a photopolymerizable unit in synthetic phospholipids . [ 9 ]
Thiarubrine B is the most prevalent among several related light-sensitive pigments that have been isolated from the Giant Ragweed ( Ambrosia trifida ), a plant used in herbal medicine. The thiarubrines have antibiotic, antiviral, and nematocidal activity, and activity against HIV-1 that is mediated by exposure to light. [ 34 ]
Polyynes such as falcarindiol can be found in Apiaceae vegetables like carrot , celery , fennel , parsley and parsnip where they show cytotoxic activities. [ 35 ] Aliphatic C 17 -polyynes of the falcarinol type were described to act as metabolic modulators [ 36 ] [ 37 ] and are studied as potential health-promoting nutraceuticals . [ 38 ] Falcarindiol is the main compound responsible for bitterness in carrots , and is the most active among several polyynes with potential anticancer activity found in Devil's club ( Oplopanax horridus ). Other polyynes from plants include oenanthotoxin and cicutoxin , which are poisons found in water dropwort ( Oenanthe spp. ) and water hemlock ( Cicuta spp. ).
Ichthyothere is a genus of plants whose active constituent is a polyyne called ichthyothereol . This compound is highly toxic to fish and mammals . [ 39 ] Ichthyothere terminalis leaves have traditionally been used to make poisoned bait by indigenous peoples of the lower Amazon basin . [ 39 ]
Dihydromatricaria acid is a polyyne produced and secreted by soldier beetles as a chemical defense. [ 40 ]
The octatetraynyl radicals and hexatriynyl radicals together with their ions are detected in space where hydrogen is rare. [ 41 ] Moreover, there have been claims [ 42 ] that polyynes have been found in astronomical impact sites on Earth as part of the mineral chaoite , but this interpretation has been contested. [ 43 ] See Astrochemistry . | https://en.wikipedia.org/wiki/Polyyne |
In the theory of dynamical systems (or turbulent flow ), the Pomeau –Manneville scenario is the transition to chaos (turbulence) due to intermittency . [ 1 ] [ 2 ] Named after Yves Pomeau and Paul Manneville . The aforementioned scenario is realized using the Pomeau–Manneville map. The Pomeau–Manneville map is a polynomial mapping (equivalently, recurrence relation), often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. Unlike other maps, the Pomeau–Manneville map exhibits intermittency , characterized by periods of low and high amplitude fluctuations. Recent research suggests that this bursting behavior might lead to anomalous diffusion.
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it .
This chaos theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pomeau–Manneville_scenario |
The Pomeranz–Fritsch reaction , also named Pomeranz–Fritsch cyclization , is a named reaction in organic chemistry. It is named after Paul Fritsch (1859–1913) and Cäsar Pomeranz (1860–1926). [ 1 ] [ 2 ] In general it is a synthesis of isoquinoline . [ 2 ] [ 3 ] [ 4 ]
The reaction below shows the acid-promoted synthesis of isoquinoline from benzaldehyde and a 2,2-dialkoxyethylamine. [ 5 ]
Various alkyl groups , e.g. methyl and ethyl groups, can be used as substituent R.
In the archetypical reaction sulfuric acid was used as proton donor, but Lewis acids such as trifluoroacetic anhydride and lanthanide triflates have been used occasionally. [ 1 ] [ 2 ] [ 4 ] Later, a wide range of diverse isoquinolines were successfully prepared. [ 4 ]
A possible mechanism is depicted below: [ 5 ]
First the benzalaminoacetal 1 is built by the condensation of benzaldehyde and a 2,2-dialkoxyethylamine. After the condensation a hydrogen -atom is added to one of the alkoxy groups. Subsequently, an alcohol is removed. Next, the compound 2 is built. After that a second hydrogen-atom is added to the compound. In the last step a second alcohol is removed and the bicyclic system becomes aromatic .
The Pomeranz–Fritsch reaction has general application in the preparation of isoquinoline derivatives. Isoquinolines find many applications, including: [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Pomeranz–Fritsch_reaction |
Pomology (from Latin pomum , " fruit ", + -logy , "study") is a branch of botany that studies fruits and their cultivation . Someone who researches and practices the science of pomology is called a pomologist . The term fruticulture (from Latin fructus , "fruit", + cultura , "care") is also used to describe the agricultural practice of growing fruits in orchards .
Pomological research is mainly focused on the development, enhancement, cultivation, and physiological studies of fruit trees . The goals of fruit tree improvement include enhancement of fruit quality, regulation of production periods, and reduction of production costs .
In ancient Mesopotamia, pomology was practiced by the Sumerians , who are known to have grown various types of fruit, including dates , grapes, apples, melons, and figs. [ 1 ] [ 2 ] While the first fruits cultivated by the Egyptians were likely indigenous , such as the palm date and sorghum , more fruits were introduced as other cultural influences were introduced. Grapes and watermelon were found throughout predynastic Egyptian sites, as were the sycamore fig , dom palm, and Christ's thorn . The carob , olive , apple , and pomegranate were introduced to Egyptians during the New Kingdom . Later, during the Greco-Roman period peaches and pears were also introduced. [ 3 ]
The ancient Greeks and Romans also had a healthy tradition of pomology, and they cultivated a wide range of fruits, including apples , pears , figs , grapes , quinces , citron, strawberries , blackberries , elderberries, currants , damson plums , dates, melons , rose hips , and pomegranates . [ 4 ] Less common fruits were the more exotic azeroles and medlars . Cherries and apricots , both introduced in the 1st century BC, were popular. Peaches were introduced in the 1st century AD from Persia. Oranges and lemons were known but used more for medicinal purposes than in cookery. The Romans, in particular, were known for their advanced methods of fruit cultivation and storage, and they developed many of the approaches that are still used in modern pomology. [ 4 ]
During the mid-19th century in the United States , farmers were expanding fruit orchard programs in response to growing markets. At the same time, horticulturists from the USDA and agricultural colleges were bringing new varieties to the US from foreign expeditions, and developing experimental lots for these fruits. In response to this increased interest and activity, the USDA established the Division of Pomology in 1886 and named Henry E. Van Deman as chief pomologist. An important focus of the division was to publish illustrated accounts of new varieties and to disseminate research findings to fruit growers and breeders through special publications and annual reports. During this period Andrew Jackson Downing and his brother Charles were prominent in pomology and horticulture , producing The Fruits and Fruit Trees of America (1845). [ 5 ]
The introduction of new varieties required an exact portrait of the fruit so that plant breeders could accurately document and disseminate their research results. Since the use of scientific photography was not widespread in the late 19th century, the USDA commissioned artists to create watercolor illustrations of newly introduced cultivars . Many of the watercolors were used for lithographic reproductions in USDA publications, such as the Report of the Pomologist and the Yearbook of Agriculture . [ citation needed ] Today, the collection of approximately 7,700 watercolors is preserved in the National Agricultural Library 's Special Collections, [ 6 ] where it serves as a major historic and botanic resource to a variety of researchers, including horticulturists , historians, artists, and publishers. [ citation needed ] | https://en.wikipedia.org/wiki/Pomology |
Pompeiu's theorem is a result of plane geometry , discovered by the Romanian mathematician Dimitrie Pompeiu . The theorem is simple, but not classical. It states the following:
The proof is quick. Consider a rotation of 60° about the point B . Assume A maps to C , and P maps to P '. Then P B = P ′ B {\displaystyle \scriptstyle PB\ =\ P'B} , and ∠ P B P ′ = 60 ∘ {\displaystyle \scriptstyle \angle PBP'\ =\ 60^{\circ }} . Hence triangle PBP ' is equilateral and P P ′ = P B {\displaystyle \scriptstyle PP'\ =\ PB} . Then P A = P ′ C {\displaystyle \scriptstyle PA\ =\ P'C} . Thus, triangle PCP ' has sides equal to PA , PB , and PC and the proof by construction is complete (see drawing). [ 1 ]
Further investigations reveal that if P is not in the interior of the triangle, but rather on the circumcircle , then PA , PB , PC form a degenerate triangle, with the largest being equal to the sum of the others; this observation is also known as Van Schooten's theorem . [ 1 ]
Generally, by the point P and the lengths to the vertices of the equilateral triangle - PA , PB , and PC two equilateral triangles ( the larger and the smaller) with sides a 1 {\displaystyle a_{1}} and a 2 {\displaystyle a_{2}} are defined:
The symbol △ denotes the area of the triangle whose sides have lengths PA , PB , PC . [ 3 ]
Pompeiu published the theorem in 1936; however August Ferdinand Möbius had already published a more general theorem about four points in the Euclidean plane in 1852. In this paper Möbius also derived the statement of Pompeiu's theorem explicitly as a special case of his more general theorem. For this reason, the theorem is also known as the Möbius-Pompeiu theorem . [ 4 ] | https://en.wikipedia.org/wiki/Pompeiu's_theorem |
In mathematics , the Pompeiu problem is a conjecture in integral geometry , named for Dimitrie Pompeiu , who posed the problem in 1929,
as follows. Suppose f is a nonzero continuous function defined on a Euclidean space, and K is a simply connected Lipschitz domain , so that the integral of f vanishes on every congruent copy of K . Then the domain is a ball .
A special case is Schiffer's conjecture .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pompeiu_problem |
Ponceau S , Acid Red 112 , or C.I. 27195 ( systematic name : 3-hydroxy-4-(2-sulfo-4-[4-sulfophenylazo]phenylazo)-2,7-naphthalenedisulfonic acid sodium salt [ 1 ] ) is a sodium salt of a diazo dye of a light red color, that may be used to prepare a stain for rapid reversible detection of protein bands on nitrocellulose or polyvinylidene fluoride (PVDF) membranes ( western blotting ), as well as on cellulose acetate membranes. [ 2 ] A Ponceau S stain is useful because it does not appear to have a deleterious effect on the sequencing of blotted polypeptides and is therefore one method of choice for locating polypeptides on western blots for blot-sequencing. [ 2 ] It is also easily reversed with water washes, facilitating subsequent immunological detection. [ 2 ] The stain can be completely removed from the protein bands by continued washing. [ 2 ] Common stain formulations include 0.1% (w/v) Ponceau S in 5% acetic acid or 2% (w/v) Ponceau S in 30% trichloroacetic acid and 30% sulfosalicylic acid . [ 3 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ponceau_S |
In civil engineering , ponding is the (typically) unwanted pooling of water, typically on a flat roof or roadway. Ponding water accelerates the deterioration of many materials, including seam adhesives in single-ply roof systems, steel equipment supports, and particularly roofing asphalt . On low-slope asphalt roofs, ponding water allows the oil solvent components of the asphalt to leach out and evaporate, leaving the roof membrane brittle and susceptible to cracking and leaking in the ponding location. [ 1 ] The time taken for water to saturate a zone , usually from rainfall , causing a pond to form, is referred to as the "ponding time". [ 2 ] [ 3 ] [ 4 ]
Most flat roof systems (properly called "low-slope roof systems") are designed with a slight pitch to shed water off the sides, usually into gutters, scuppers , internal drains, or a combination of these. [ 5 ] When a scupper or drain is clogged or fails for other reasons, storm water tends to pool around that low area. Over time, with each passing storm, the weight of the storm water will deflect the structural system beyond the structure's bending point, thus allowing a bigger puddle to form. As a bigger puddle forms more weight is applied to the structural system causing more bending, allowing an even bigger puddle, then more weight, until the structure fails. [ 6 ]
In the construction industry, the National Roofing Contractors Association (NRCA) defines roof ponding as "water that remains on a roof surface longer than 48 hours after the termination of the most recent rain event". [ 7 ] [ 8 ]
According to the 2009 International Building Code Chapter 15 "Roof Assemblies and Roof Top Structures" & Chapter 16 "Structural Design";
When scuppers are used for secondary (emergency overflow) roof drainage, the quantity, size, location and inlet elevation of the scuppers shall be sized to prevent the depth of ponding water from exceeding that for which the roof was designed ... Ponding instability. For roofs with a slope less than 1/4 inch per foot [1.19 degrees (0.0208 rad)], the design calculations shall include verification of adequate stiffness to preclude progressive deflection in accordance with Section 8.4 of ASCE 7. [ 9 ]
When water is diverted into a lower area that has no outlet or is not suitable for drainage, water will begin to pool, and over time the weight of the water will create a deeper pool, allowing more water to sit, eventually creating a permanent water feature. Some municipalities recognize this as an issue on private land, such as the City of Indianapolis . [ 10 ]
A municipality in New Zealand has noted that "groundwater ponding is a chronic problem, that results in damp housing and waterlogged sections. The damage that it causes is less apparent than the damaging events associated with floods, but the duration of groundwater ponding, which can last for several months, makes it a serious issue for those affected". [ 11 ]
Ponding that forms on paved surfaces, like streets or parking lots that are not properly pitched, will cause issues such as deep puddles and crocodile cracking . | https://en.wikipedia.org/wiki/Ponding |
Ponsse Plc ( Finnish : Ponsse Oyj ) [ 2 ] is a company domiciled in Finland that manufactures and markets a range of forestry vehicles and machinery such as forwarders and harvesters . The Ponsse company was established by the forest machine entrepreneur Einari Vidgrén [ fi ] in 1970. As of 2019 [update] , Ponsse's machines are used at logging sites in approximately 40 countries, and 80 per cent of the company's net sales come from exports. [ 3 ] [ page needed ] All machines are manufactured in the company's birthplace in Vieremä . Ponsse Group employs more than 1,800 people in 10 countries, and the company's shares are quoted on the NASDAQ OMX Nordic List .
Entrepreneur Einari Vidgrén [ fi ] receives encouraging feedback on machines he has built. He decides to set up a forest machine factory in Vieremä . However, help is required by the municipality of Vieremä in order to finance the project. A meeting is held by the municipal council, and they vote on the matter. The council approves the proposal with a majority of a single vote. The work is completed by the end of 1970, and Ponsse Plc is established as a result. [ 4 ]
In 1971, Vidgrén places an ad in the Helsingin Sanomat news paper in order to recruit an engineer for the factory. An application by Jouko Kelppe, a young engineer from Salo , attracts the most attention. Kelppe is hired to be the first ever engineer in the history of Ponsse. The manufacturing of the first machine is started in the spring of 1971. A forest machine contractor Eero Vainikainen is in the process of purchasing a Volvo or Valmet machine. However, after strong persuasion and visiting the Ponsse factory, he decides to buy the first ever Ponsse machine. The machine is driven out of the factory by Vidgrén in the autumn of 1971. [ 5 ]
Ponsse premieres in the international markets in 1974. A massive storm hits Germany, and a large number of foreign equipment is needed for harvesting the trees felled by the storm. Vidgrén hears that the job is well compensated, and sets out to Germany, accompanied by Finnish loggers and a Ponsse machine. [ 5 ]
Mechanized harvesting is increasing worldwide, and heavy machinery is becoming a talking point. The public demands lighter and more eco-friendly machines. Ponsse releases a new model S 15 forwarder in 1983. The machine is highly advanced at the time, as it is lighter but is still able to carry heavy loads, as well as function on soil with poor bearing capacity. [ 6 ]
Vidgrén is not satisfied with the grapples , or harvester heads , used in Ponsse machines. He wants Ponsse to make their own harvester heads. The first product, H520 is not completely trouble-free, and causes many problems for the company. Learning from these mistakes, a new model called H60 is released at the end of 1985. This marks an important step in the expansion of the product family. [ 3 ]
On 16 December 1988, Ponsse's entire share capital is transferred to the industrial company called Interpolator Oy, a part of SKOP Group. This makes Ponsse a part of Norcar Group, along with some earlier acquisitions. Vidgrén becomes a board member of Norcar Group, and his brother, Esa Vidgrén, is appointed as the managing director of Ponsse Plc. [ 7 ]
The computerized Kajaani 2000 loader control system represents the latest trend in the product development of forest machine control systems. In 1992, Ponsse releases two new machines, the HS10 harvester and the S10 forwarder. Einari Vidgrén receives the Finnish National Inventor Prize awarded by the Ministry of Trade and Industry , in recognition of his persistent work in the forest machine development. [ 7 ]
A group of investors led by Vidgrén purchase Ponsse back from SKOP Group in February 1993. Kajaanin Automatiikka Ky, a company manufacturing information systems in Kajaani , is merged with Ponsse. As a result, Ponsse Opti is launched. Ponsse becomes the first forest machine manufacturer in the world to introduce a PC-based measuring device system in their machines. As a result, Ponsse is rewarded with an ISO 9000 certification, the first forest machine manufacturer to do so. [ 4 ]
The expansion continues, as the first subsidiary , Ponsse AB, is established in Västerås , Sweden, in 1994. As the globalization increases, and Ponsse is getting attention from the international markets, subsidiaries are established also in the United States, France, and United Kingdom. A corporate development also happens, when the public quotation of Ponsse Plc shares on the Helsinki Stock Exchange begins in 1995. Two new harvester models are released in 1996, Ergo HS16 and Cobra HS10. [ 8 ]
Ponsse's 30th anniversary party is organized in 2000, and the occasion is used to announce a brand new product family with Mercedes-Benz engines. The new Beaver harvester is launched, as well as a new digital control system, called OptiControl. New retailer is established in New Brunswick and Quebec , Canada. The Finnish Forest Association grants Einari Vidgrén a golden medal for his special and long-term contribution to the forest industry in Finland in 2001. The following reasons are given for the selection: "Einari Vidgrén is awarded for his unique entrepreneurship, which led to one of the world's leading manufacturing companies of forest machinery being established in Finland. When Vidgrén noticed that the machines manufactured by others were not satisfactory, he decided to build one himself". [ 5 ]
Ponsse Road Show is organized as Vidgrén's 60th year celebration tour in 2003. The tour travels through ten locations in Finland, presenting machines and meeting customers across the country. The 3,000th manufactured Ponsse machine is handed out during the tour. New product line is launched in 2004, including Remote Service, the first ever real-time remote service connection in the forest machine industry. Ponsse establishes a subsidiary in Russia, as well as a retail agreement in Quebec, Canada. Ponsse becomes the main owner of Epec Oy, a control system manufacturer in Seinäjoki . Ponsse Ladies is founded.
Vidgrén creates a foundation bearing his name is 2005. The purpose of the foundation is to make the entrepreneurship related to wood harvesting better known, and increase the awareness of the mechanized harvesting industry, especially among the younger generation. The factory in Vieremä is expanded, and a new service center is established in Iisalmi . Several sponsorship deals are announced, including the javelin thrower Tero Pitkämäki , WRC -driver Mikko Hirvonen , and ice hockey team Kalpa . Another subsidiary, Ponsse Latin America, is established in Brazil, and a retail agreement in South Africa. New Bear harvester and Elephant forwarder are introduced in 2006. [ 5 ]
International Road Show tour is organized in 2007. The tour travels through various locations across Europe. Ponsse begins cooperation with the Moscow State University . The goal is to offer extensive training in the cut-to-length logging method. A subsidiary is established in China. Almost 30,000 visitors from all over the world are gathered in Metko exhibition, the biggest forestry event in Finland, in September 2008. The Great Recession and the 2007–2008 financial crisis put a heavy strain on the forest industry. Due to weakened demand and the future prospects for the forest machine industry, Ponsse gives summons for employee cooperation negotiations. [ 5 ]
Einari Vidgrén suddenly passed away at the age of 67 on 26 October 2010. The Board of Directors at Ponsse were forced to reorganize due to the sudden loss of their Chairman. Vidgrén's four sons became the primary shareowners of the company, and Juha Vidgrén was unanimously selected as the new Chairman of the Board. [ 5 ]
Epec Oy, a forest machine application and product development firm based in Kajaani , is transferred to Ponsse in 2011. This enables for a stronger development in the information systems for the forest machines. [ 4 ] In 2012, the President of Finland, Sauli Niinistö visits the Ponsse factory.
The 10,000th Ponsse machine is manufactured in 2015. The following year, Ponsse announces 32 million euro investments on their factory in Vieremä . [ 5 ] In 2018, Ponsse is named the most reputable company in Finland, according to the survey conducted by T-Media. In 2019, Ponsse employs about 1,800 people worldwide, and its machines operate in over 40 different countries. The company's exports account for 80% of revenue. Total revenue in 2019 was 667.4 million euros, and operating profit 67.3 million euros. [ 4 ]
Ponsse manufactures and sells a variety of forestry equipment, such as harvesters , forwarders , and harvester heads . Every product is manufactured at the company's headquarters in Vieremä , Finland. [ 4 ]
[ 4 ] | https://en.wikipedia.org/wiki/Ponsse |
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology ), and the additive group of the integers (also with the discrete topology), the real numbers, and every finite-dimensional vector space over the reals or a p -adic field .
The Pontryagin dual of a locally compact abelian group is the locally compact abelian topological group, consisting of the continuous group homomorphisms from the group to the circle group, with the operation of pointwise multiplication and the topology of uniform convergence on compact sets. The Pontryagin duality theorem establishes Pontryagin duality by stating that any locally compact abelian group is naturally isomorphic with its bidual (the dual of its dual). The Fourier inversion theorem is a special case of this theorem.
The subject is named after Lev Pontryagin who laid down the foundations for the theory of locally compact abelian groups and their duality during his early mathematical works in 1934. Pontryagin's treatment relied on the groups being second-countable and either compact or discrete. This was improved to cover the general locally compact abelian groups by Egbert van Kampen in 1935 and André Weil in 1940.
Pontryagin duality places in a unified context a number of observations about functions on the real line or on finite abelian groups:
The theory, introduced by Lev Pontryagin and combined with the Haar measure introduced by John von Neumann , André Weil and others depends on the theory of the dual group of a locally compact abelian group.
It is analogous to the dual vector space of a vector space: a finite-dimensional vector space V {\displaystyle V} and its dual vector space V ∗ {\displaystyle V^{*}} are not naturally isomorphic, but the endomorphism algebra (matrix algebra) of one is isomorphic to the opposite of the endomorphism algebra of the other: End ( V ) ≅ End ( V ∗ ) op , {\displaystyle {\text{End}}(V)\cong {{\text{End}}(V^{*})}^{\text{op}},} via the transpose. Similarly, a group G {\displaystyle G} and its dual group G ^ {\displaystyle {\widehat {G}}} are not in general isomorphic, but their endomorphism rings are opposite to each other: End ( G ) ≅ End ( G ^ ) op {\displaystyle {\text{End}}(G)\cong {\text{End}}({\widehat {G}})^{\text{op}}} . More categorically, this is not just an isomorphism of endomorphism algebras, but a contravariant equivalence of categories – see § Categorical considerations .
A topological group is a locally compact group if the underlying topological space is locally compact and Hausdorff ; a topological group is abelian if the underlying group is abelian .
Examples of locally compact abelian groups include finite abelian groups, the integers (both for the discrete topology , which is also induced by the usual metric), the real numbers, the circle group T (both with their usual metric topology), and also the p -adic numbers (with their usual p -adic topology).
For a locally compact abelian group G {\displaystyle G} , the Pontryagin dual is the group G ^ {\displaystyle {\widehat {G}}} of continuous group homomorphisms from G {\displaystyle G} to the circle group T {\displaystyle T} . That is, G ^ := Hom ( G , T ) . {\displaystyle {\widehat {G}}:=\operatorname {Hom} (G,T).} The Pontryagin dual G ^ {\displaystyle {\widehat {G}}} is usually endowed with the topology given by uniform convergence on compact sets (that is, the topology induced by the compact-open topology on the space of all continuous functions from G {\displaystyle G} to T {\displaystyle T} ).
For example, Z / n Z ^ = Z / n Z , Z ^ = T , R ^ = R , T ^ = Z . {\displaystyle {\widehat {\mathbb {Z} /n\mathbb {Z} }}=\mathbb {Z} /n\mathbb {Z} ,\ {\widehat {\mathbb {Z} }}=T,\ {\widehat {\mathbb {R} }}=\mathbb {R} ,\ {\widehat {T}}=\mathbb {Z} .}
Theorem [ 1 ] [ 2 ] — There is a canonical isomorphism G ≅ G ^ ^ {\displaystyle G\cong {\widehat {\widehat {G}}}} between any locally compact abelian group G {\displaystyle G} and its double dual.
Canonical means that there is a naturally defined map ev G : G → G ^ ^ {\displaystyle \operatorname {ev} _{G}\colon G\to {\widehat {\widehat {G}}}} ; more importantly, the map should be functorial in G {\displaystyle G} . For the multiplicative character χ {\displaystyle \chi } of the group G {\displaystyle G} , the canonical isomorphism ev G {\displaystyle \operatorname {ev} _{G}} is defined on x ∈ G {\displaystyle x\in G} as follows: ev G ( x ) ( χ ) = χ ( x ) ∈ T . {\displaystyle \operatorname {ev} _{G}(x)(\chi )=\chi (x)\in \mathbb {T} .} That is, ev G ( x ) : ( χ ↦ χ ( x ) ) . {\displaystyle \operatorname {ev} _{G}(x):(\chi \mapsto \chi (x)).}
In other words, each group element x {\displaystyle x} is identified to the evaluation character on the dual. This is strongly analogous to the canonical isomorphism between a finite-dimensional vector space and its double dual , V ≅ V ∗ ∗ {\displaystyle V\cong V^{**}} , and it is worth mentioning that any vector space V {\displaystyle V} is an abelian group . If G {\displaystyle G} is a finite abelian group, then G ≅ G ^ {\displaystyle G\cong {\widehat {G}}} but this isomorphism is not canonical. Making this statement precise (in general) requires thinking about dualizing not only on groups, but also on maps between the groups, in order to treat dualization as a functor and prove the identity functor and the dualization functor are not naturally equivalent. Also the duality theorem implies that for any group (not necessarily finite) the dualization functor is an exact functor .
One of the most remarkable facts about a locally compact group G {\displaystyle G} is that it carries an essentially unique natural measure , the Haar measure , which allows one to consistently measure the "size" of sufficiently regular subsets of G {\displaystyle G} . "Sufficiently regular subset" here means a Borel set ; that is, an element of the σ-algebra generated by the compact sets . More precisely, a right Haar measure on a locally compact group G {\displaystyle G} is a countably additive measure μ defined on the Borel sets of G {\displaystyle G} which is right invariant in the sense that μ ( A x ) = μ ( A ) {\displaystyle \mu (Ax)=\mu (A)} for x {\displaystyle x} an element of G {\displaystyle G} and A {\displaystyle A} a Borel subset of G {\displaystyle G} and also satisfies some regularity conditions (spelled out in detail in the article on Haar measure ). Except for positive scaling factors, a Haar measure on G {\displaystyle G} is unique.
The Haar measure on G {\displaystyle G} allows us to define the notion of integral for ( complex -valued) Borel functions defined on the group. In particular, one may consider various L p spaces associated to the Haar measure μ {\displaystyle \mu } . Specifically, L μ p ( G ) = { ( f : G → C ) | ∫ G | f ( x ) | p d μ ( x ) < ∞ } . {\displaystyle {\mathcal {L}}_{\mu }^{p}(G)=\left\{(f:G\to \mathbb {C} )\ {\Big |}\ \int _{G}|f(x)|^{p}\ d\mu (x)<\infty \right\}.}
Note that, since any two Haar measures on G {\displaystyle G} are equal up to a scaling factor, this L p {\displaystyle L^{p}} -space is independent of the choice of Haar measure and thus perhaps could be written as L p ( G ) {\displaystyle L^{p}(G)} . However, the L p {\displaystyle L^{p}} -norm on this space depends on the choice of Haar measure, so if one wants to talk about isometries it is important to keep track of the Haar measure being used.
The dual group of a locally compact abelian group is used as the underlying space for an abstract version of the Fourier transform . If f ∈ L 1 ( G ) {\displaystyle f\in L^{1}(G)} , then the Fourier transform is the function f ^ {\displaystyle {\widehat {f}}} on G ^ {\displaystyle {\widehat {G}}} defined by f ^ ( χ ) = ∫ G f ( x ) χ ( x ) ¯ d μ ( x ) , {\displaystyle {\widehat {f}}(\chi )=\int _{G}f(x){\overline {\chi (x)}}\ d\mu (x),} where the integral is relative to Haar measure μ {\displaystyle \mu } on G {\displaystyle G} . This is also denoted ( F f ) ( χ ) {\displaystyle ({\mathcal {F}}f)(\chi )} . Note the Fourier transform depends on the choice of Haar measure. It is not too difficult to show that the Fourier transform of an L 1 {\displaystyle L^{1}} function on G {\displaystyle G} is a bounded continuous function on G ^ {\displaystyle {\widehat {G}}} which vanishes at infinity .
Fourier Inversion Formula for L 1 {\displaystyle L^{1}} -Functions — For each Haar measure μ {\displaystyle \mu } on G {\displaystyle G} there is a unique Haar measure ν {\displaystyle \nu } on G ^ {\displaystyle {\widehat {G}}} such that whenever f ∈ L 1 ( G ) {\displaystyle f\in L^{1}(G)} and f ^ ∈ L 1 ( G ^ ) {\displaystyle {\widehat {f}}\in L^{1}\left({\widehat {G}}\right)} , we have f ( x ) = ∫ G ^ f ^ ( χ ) χ ( x ) d ν ( χ ) μ -almost everywhere {\displaystyle f(x)=\int _{\widehat {G}}{\widehat {f}}(\chi )\chi (x)\ d\nu (\chi )\qquad \mu {\text{-almost everywhere}}} If f {\displaystyle f} is continuous then this identity holds for all x {\displaystyle x} .
The inverse Fourier transform of an integrable function on G ^ {\displaystyle {\widehat {G}}} is given by g ˇ ( x ) = ∫ G ^ g ( χ ) χ ( x ) d ν ( χ ) , {\displaystyle {\check {g}}(x)=\int _{\widehat {G}}g(\chi )\chi (x)\ d\nu (\chi ),} where the integral is relative to the Haar measure ν {\displaystyle \nu } on the dual group G ^ {\displaystyle {\widehat {G}}} . The measure ν {\displaystyle \nu } on G ^ {\displaystyle {\widehat {G}}} that appears in the Fourier inversion formula is called the dual measure to μ {\displaystyle \mu } and may be denoted μ ^ {\displaystyle {\widehat {\mu }}} .
The various Fourier transforms can be classified in terms of their domain and transform domain (the group and dual group) as follows (note that T {\displaystyle \mathbb {T} } is Circle group ):
As an example, suppose G = R n {\displaystyle G=\mathbb {R} ^{n}} , so we can think about G ^ {\displaystyle {\widehat {G}}} as R n {\displaystyle \mathbb {R} ^{n}} by the pairing ( v , w ) ↦ e i v ⋅ w . {\displaystyle (\mathbf {v} ,\mathbf {w} )\mapsto e^{i\mathbf {v} \cdot \mathbf {w} }.} If μ {\displaystyle \mu } is the Lebesgue measure on Euclidean space, we obtain the ordinary Fourier transform on R n {\displaystyle \mathbb {R} ^{n}} and the dual measure needed for the Fourier inversion formula is μ ^ = ( 2 π ) − n μ {\displaystyle {\widehat {\mu }}=(2\pi )^{-n}\mu } . If we want to get a Fourier inversion formula with the same measure on both sides (that is, since we can think about R n {\displaystyle \mathbb {R} ^{n}} as its own dual space we can ask for μ ^ {\displaystyle {\widehat {\mu }}} to equal μ {\displaystyle \mu } ) then we need to use μ = ( 2 π ) − n 2 × Lebesgue measure μ ^ = ( 2 π ) − n 2 × Lebesgue measure {\displaystyle {\begin{aligned}\mu &=(2\pi )^{-{\frac {n}{2}}}\times {\text{Lebesgue measure}}\\{\widehat {\mu }}&=(2\pi )^{-{\frac {n}{2}}}\times {\text{Lebesgue measure}}\end{aligned}}}
However, if we change the way we identify R n {\displaystyle \mathbb {R} ^{n}} with its dual group, by using the pairing ( v , w ) ↦ e 2 π i v ⋅ w , {\displaystyle (\mathbf {v} ,\mathbf {w} )\mapsto e^{2\pi i\mathbf {v} \cdot \mathbf {w} },} then Lebesgue measure on R n {\displaystyle \mathbb {R} ^{n}} is equal to its own dual measure . This convention minimizes the number of factors of 2 π {\displaystyle 2\pi } that show up in various places when computing Fourier transforms or inverse Fourier transforms on Euclidean space. (In effect it limits the 2 π {\displaystyle 2\pi } only to the exponent rather than as a pre-factor outside the integral sign.) Note that the choice of how to identify R n {\displaystyle \mathbb {R} ^{n}} with its dual group affects the meaning of the term "self-dual function", which is a function on R n {\displaystyle \mathbb {R} ^{n}} equal to its own Fourier transform: using the classical pairing ( v , w ) ↦ e i v ⋅ w {\displaystyle (\mathbf {v} ,\mathbf {w} )\mapsto e^{i\mathbf {v} \cdot \mathbf {w} }} the function e − 1 2 x 2 {\displaystyle e^{-{\frac {1}{2}}x^{2}}} is self-dual. But using the pairing, which keeps the pre-factor as unity, ( v , w ) ↦ e 2 π i v ⋅ w {\displaystyle (\mathbf {v} ,\mathbf {w} )\mapsto e^{2\pi i\mathbf {v} \cdot \mathbf {w} }} makes e − π x 2 {\displaystyle e^{-\pi x^{2}}} self-dual instead. This second definition for the Fourier transform has the advantage that it maps the multiplicative identity to the convolution identity, which is useful as L 1 {\displaystyle L^{1}} is a convolution algebra. See the next section on the group algebra . In addition, this form is also necessarily isometric on L 2 {\displaystyle L^{2}} spaces. See below at Plancherel and L 2 Fourier inversion theorems .
The space of integrable functions on a locally compact abelian group G {\displaystyle G} is an algebra , where multiplication is convolution: the convolution of two integrable functions f {\displaystyle f} and g {\displaystyle g} is defined as ( f ∗ g ) ( x ) = ∫ G f ( x − y ) g ( y ) d μ ( y ) . {\displaystyle (f*g)(x)=\int _{G}f(x-y)g(y)\ d\mu (y).}
Theorem — The Banach space L 1 ( G ) {\displaystyle L^{1}(G)} is an associative and commutative algebra under convolution.
This algebra is referred to as the Group Algebra of G {\displaystyle G} . By the Fubini–Tonelli theorem , the convolution is submultiplicative with respect to the L 1 {\displaystyle L^{1}} norm, making L 1 ( G ) {\displaystyle L^{1}(G)} a Banach algebra . The Banach algebra L 1 ( G ) {\displaystyle L^{1}(G)} has a multiplicative identity element if and only if G {\displaystyle G} is a discrete group, namely the function that is 1 at the identity and zero elsewhere. In general, however, it has an approximate identity which is a net (or generalized sequence) { e i } i ∈ I {\displaystyle \{e_{i}\}_{i\in I}} indexed on a directed set I {\displaystyle I} such that f ∗ e i → f . {\displaystyle f*e_{i}\to f.}
The Fourier transform takes convolution to multiplication, i.e. it is a homomorphism of abelian Banach algebras L 1 ( G ) → C 0 ( G ^ ) {\displaystyle L^{1}(G)\to C_{0}\left({\widehat {G}}\right)} (of norm ≤ 1): F ( f ∗ g ) ( χ ) = F ( f ) ( χ ) ⋅ F ( g ) ( χ ) . {\displaystyle {\mathcal {F}}(f*g)(\chi )={\mathcal {F}}(f)(\chi )\cdot {\mathcal {F}}(g)(\chi ).}
In particular, to every group character on G {\displaystyle G} corresponds a unique multiplicative linear functional on the group algebra defined by f ↦ f ^ ( χ ) . {\displaystyle f\mapsto {\widehat {f}}(\chi ).}
It is an important property of the group algebra that these exhaust the set of non-trivial (that is, not identically zero) multiplicative linear functionals on the group algebra; see section 34 of ( Loomis 1953 ). This means the Fourier transform is a special case of the Gelfand transform .
As we have stated, the dual group of a locally compact abelian group is a locally compact abelian group in its own right and thus has a Haar measure, or more precisely a whole family of scale-related Haar measures.
Theorem — Choose a Haar measure μ {\displaystyle \mu } on G {\displaystyle G} and let ν {\displaystyle \nu } be the dual measure on G ^ {\displaystyle {\widehat {G}}} as defined above. If f : G → C {\displaystyle f:G\to \mathbb {C} } is continuous with compact support then f ^ ∈ L 2 ( G ^ ) {\displaystyle {\widehat {f}}\in L^{2}\left({\widehat {G}}\right)} and ∫ G | f ( x ) | 2 d μ ( x ) = ∫ G ^ | f ^ ( χ ) | 2 d ν ( χ ) . {\displaystyle \int _{G}|f(x)|^{2}\ d\mu (x)=\int _{\widehat {G}}\left|{\widehat {f}}(\chi )\right|^{2}\ d\nu (\chi ).} In particular, the Fourier transform is an L 2 {\displaystyle L^{2}} isometry from the complex-valued continuous functions of compact support on G {\displaystyle G} to the L 2 {\displaystyle L^{2}} -functions on G ^ {\displaystyle {\widehat {G}}} (using the L 2 {\displaystyle L^{2}} -norm with respect to μ {\displaystyle \mu } for functions on G {\displaystyle G} and the L 2 {\displaystyle L^{2}} -norm with respect to ν {\displaystyle \nu } for functions on G ^ {\displaystyle {\widehat {G}}} ).
Since the complex-valued continuous functions of compact support on G {\displaystyle G} are L 2 {\displaystyle L^{2}} -dense, there is a unique extension of the Fourier transform from that space to a unitary operator F : L μ 2 ( G ) → L ν 2 ( G ^ ) . {\displaystyle {\mathcal {F}}:L_{\mu }^{2}(G)\to L_{\nu }^{2}\left({\widehat {G}}\right).} and we have the formula ∀ f ∈ L 2 ( G ) : ∫ G | f ( x ) | 2 d μ ( x ) = ∫ G ^ | f ^ ( χ ) | 2 d ν ( χ ) . {\displaystyle \forall f\in L^{2}(G):\quad \int _{G}|f(x)|^{2}\ d\mu (x)=\int _{\widehat {G}}\left|{\widehat {f}}(\chi )\right|^{2}\ d\nu (\chi ).}
Note that for non-compact locally compact groups G {\displaystyle G} the space L 1 ( G ) {\displaystyle L^{1}(G)} does not contain L 2 ( G ) {\displaystyle L^{2}(G)} , so the Fourier transform of general L 2 {\displaystyle L^{2}} -functions on G {\displaystyle G} is "not" given by any kind of integration formula (or really any explicit formula). To define the L 2 {\displaystyle L^{2}} Fourier transform one has to resort to some technical trick such as starting on a dense subspace like the continuous functions with compact support and then extending the isometry by continuity to the whole space. This unitary extension of the Fourier transform is what we mean by the Fourier transform on the space of square integrable functions.
The dual group also has an inverse Fourier transform in its own right; it can be characterized as the inverse (or adjoint, since it is unitary) of the L 2 {\displaystyle L^{2}} Fourier transform. This is the content of the L 2 {\displaystyle L^{2}} Fourier inversion formula which follows.
Theorem — The adjoint of the Fourier transform restricted to continuous functions of compact support is the inverse Fourier transform L ν 2 ( G ^ ) → L μ 2 ( G ) {\displaystyle L_{\nu }^{2}\left({\widehat {G}}\right)\to L_{\mu }^{2}(G)} where ν {\displaystyle \nu } is the dual measure to μ {\displaystyle \mu } .
In the case G = T {\displaystyle G=\mathbb {T} } the dual group G ^ {\displaystyle {\widehat {G}}} is naturally isomorphic to the group of integers Z {\displaystyle \mathbb {Z} } and the Fourier transform specializes to the computation of coefficients of Fourier series of periodic functions.
If G {\displaystyle G} is a finite group, we recover the discrete Fourier transform . Note that this case is very easy to prove directly.
One important application of Pontryagin duality is the following characterization of compact abelian topological groups:
Theorem — A locally compact abelian group G {\displaystyle G} is compact if and only if the dual group G ^ {\displaystyle {\widehat {G}}} is discrete. Conversely, G {\displaystyle G} is discrete if and only if G ^ {\displaystyle {\widehat {G}}} is compact.
That G {\displaystyle G} being compact implies G ^ {\displaystyle {\widehat {G}}} is discrete or that G {\displaystyle G} being discrete implies that G ^ {\displaystyle {\widehat {G}}} is compact is an elementary consequence of the definition of the compact-open topology on G ^ {\displaystyle {\widehat {G}}} and does not need Pontryagin duality. One uses Pontryagin duality to prove the converses.
The Bohr compactification is defined for any topological group G {\displaystyle G} , regardless of whether G {\displaystyle G} is locally compact or abelian. One use made of Pontryagin duality between compact abelian groups and discrete abelian groups is to characterize the Bohr compactification of an arbitrary abelian locally compact topological group. The Bohr compactification B ( G ) {\displaystyle B(G)} of G {\displaystyle G} is H ^ {\displaystyle {\widehat {H}}} , where H has the group structure G ^ {\displaystyle {\widehat {G}}} , but given the discrete topology . Since the inclusion map ι : H → G ^ {\displaystyle \iota :H\to {\widehat {G}}} is continuous and a homomorphism, the dual morphism G ∼ G ^ ^ → H ^ {\displaystyle G\sim {\widehat {\widehat {G}}}\to {\widehat {H}}} is a morphism into a compact group which is easily shown to satisfy the requisite universal property .
Pontryagin duality can also profitably be considered functorially . In what follows, LCA is the category of locally compact abelian groups and continuous group homomorphisms. The dual group construction of G ^ {\displaystyle {\widehat {G}}} is a contravariant functor LCA → LCA , represented (in the sense of representable functors ) by the circle group T {\displaystyle \mathbb {T} } as G ^ = Hom ( G , T ) . {\displaystyle {\widehat {G}}={\text{Hom}}(G,\mathbb {T} ).} In particular, the double dual functor G → G ^ ^ {\displaystyle G\to {\widehat {\widehat {G}}}} is covariant .
A categorical formulation of Pontryagin duality then states that the natural transformation between the identity functor on LCA and the double dual functor is an isomorphism. [ 3 ] Unwinding the notion of a natural transformation, this means that the maps G → Hom ( Hom ( G , T ) , T ) {\displaystyle G\to \operatorname {Hom} (\operatorname {Hom} (G,T),T)} are isomorphisms for any locally compact abelian group G {\displaystyle G} , and these isomorphisms are functorial in G {\displaystyle G} . This isomorphism is analogous to the double dual of finite-dimensional vector spaces (a special case, for real and complex vector spaces).
An immediate consequence of this formulation is another common categorical formulation of Pontryagin duality: the dual group functor is an equivalence of categories from LCA to LCA op .
The duality interchanges the subcategories of discrete groups and compact groups . If R {\displaystyle R} is a ring and G {\displaystyle G} is a left R {\displaystyle R} – module , the dual group G ^ {\displaystyle {\widehat {G}}} will become a right R {\displaystyle R} –module; in this way we can also see that discrete left R {\displaystyle R} –modules will be Pontryagin dual to compact right R {\displaystyle R} –modules. The ring End ( G ) {\displaystyle {\text{End}}(G)} of endomorphisms in LCA is changed by duality into its opposite ring (change the multiplication to the other order). For example, if G {\displaystyle G} is an infinite cyclic discrete group, G ^ {\displaystyle {\widehat {G}}} is a circle group: the former has End ( G ) = Z {\displaystyle {\text{End}}(G)=\mathbb {Z} } so this is true also of the latter.
Generalizations of Pontryagin duality are constructed in two main directions: for commutative topological groups that are not locally compact , and for noncommutative topological groups. The theories in these two cases are very different.
When G {\displaystyle G} is a Hausdorff abelian topological group, the group G ^ {\displaystyle {\widehat {G}}} with the compact-open topology is a Hausdorff abelian topological group and the natural mapping from G {\displaystyle G} to its double-dual G ^ ^ {\displaystyle {\widehat {\widehat {G}}}} makes sense. If this mapping is an isomorphism, it is said that G {\displaystyle G} satisfies Pontryagin duality (or that G {\displaystyle G} is a reflexive group , [ 4 ] or a reflective group [ 5 ] ). This has been extended in a number of directions beyond the case that G {\displaystyle G} is locally compact. [ 6 ]
In particular, Samuel Kaplan [ 7 ] [ 8 ] showed in 1948 and 1950 that arbitrary products and countable inverse limits of locally compact (Hausdorff) abelian groups satisfy Pontryagin duality. Note that an infinite product of locally compact non-compact spaces is not locally compact.
Later, in 1975, Rangachari Venkataraman [ 9 ] showed, among other facts, that every open subgroup of an abelian topological group which satisfies Pontryagin duality itself satisfies Pontryagin duality.
More recently, Sergio Ardanza-Trevijano and María Jesús Chasco [ 10 ] have extended the results of Kaplan mentioned above. They showed that direct and inverse limits of sequences of abelian groups satisfying Pontryagin duality also satisfy Pontryagin duality if the groups are metrizable or k ω {\displaystyle k_{\omega }} -spaces but not necessarily locally compact, provided some extra conditions are satisfied by the sequences.
However, there is a fundamental aspect that changes if we want to consider Pontryagin duality beyond the locally compact case. Elena Martín-Peinador [ 11 ] proved in 1995 that if G {\displaystyle G} is a Hausdorff abelian topological group that satisfies Pontryagin duality, and the natural evaluation pairing { G × G ^ → T ( x , χ ) ↦ χ ( x ) {\displaystyle {\begin{cases}G\times {\widehat {G}}\to \mathbb {T} \\(x,\chi )\mapsto \chi (x)\end{cases}}} is (jointly) continuous, [ a ] then G {\displaystyle G} is locally compact. As a corollary, all non-locally compact examples of Pontryagin duality are groups where the pairing G × G ^ → T {\displaystyle G\times {\widehat {G}}\to \mathbb {T} } is not (jointly) continuous.
Another way to generalize Pontryagin duality to wider classes of commutative topological groups is to endow the dual group G ^ {\displaystyle {\widehat {G}}} with a bit different topology, namely the topology of uniform convergence on totally bounded sets . The groups satisfying the identity G ≅ G ^ ^ {\displaystyle G\cong {\widehat {\widehat {G}}}} under this assumption [ b ] are called stereotype groups . [ 5 ] This class is also very wide (and it contains locally compact abelian groups), but it is narrower than the class of reflective groups. [ 5 ]
In 1952 Marianne F. Smith [ 12 ] noticed that Banach spaces and reflexive spaces , being considered as topological groups (with the additive group operation), satisfy Pontryagin duality. Later B. S. Brudovskiĭ, [ 13 ] William C. Waterhouse [ 14 ] and K. Brauner [ 15 ] showed that this result can be extended to the class of all quasi-complete barreled spaces (in particular, to all Fréchet spaces ). In the 1990s Sergei Akbarov [ 16 ] gave a description of the class of the topological vector spaces that satisfy a stronger property than the classical Pontryagin reflexivity, namely, the identity ( X ⋆ ) ⋆ ≅ X {\displaystyle (X^{\star })^{\star }\cong X} where X ⋆ {\displaystyle X^{\star }} means the space of all linear continuous functionals f : X → C {\displaystyle f\colon X\to \mathbb {C} } endowed with the topology of uniform convergence on totally bounded sets in X {\displaystyle X} (and ( X ⋆ ) ⋆ {\displaystyle (X^{\star })^{\star }} means the dual to X ⋆ {\displaystyle X^{\star }} in the same sense). The spaces of this class are called stereotype spaces , and the corresponding theory found a series of applications in Functional analysis and Geometry, including the generalization of Pontryagin duality for non-commutative topological groups.
For non-commutative locally compact groups G {\displaystyle G} the classical Pontryagin construction stops working for various reasons, in particular, because the characters don't always separate the points of G {\displaystyle G} , and the irreducible representations of G {\displaystyle G} are not always one-dimensional. At the same time it is not clear how to introduce multiplication on the set of irreducible unitary representations of G {\displaystyle G} , and it is even not clear whether this set is a good choice for the role of the dual object for G {\displaystyle G} . So the problem of constructing duality in this situation requires complete rethinking.
Theories built to date are divided into two main groups: the theories where the dual object has the same nature as the source one (like in the Pontryagin duality itself), and the theories where the source object and its dual differ from each other so radically that it is impossible to count them as objects of one class.
The second type theories were historically the first: soon after Pontryagin's work Tadao Tannaka (1938) and Mark Krein (1949) constructed a duality theory for arbitrary compact groups known now as the Tannaka–Krein duality . [ 17 ] [ 18 ] In this theory the dual object for a group G {\displaystyle G} is not a group but a category of its representations Π ( G ) {\displaystyle \Pi (G)} .
The theories of first type appeared later and the key example for them was the duality theory for finite groups. [ 19 ] [ 20 ] In this theory the category of finite groups is embedded by the operation G ↦ C G {\displaystyle G\mapsto \mathbb {C} _{G}} of taking group algebra C G {\displaystyle \mathbb {C} _{G}} (over C {\displaystyle \mathbb {C} } ) into the category of finite dimensional Hopf algebras , so that the Pontryagin duality functor G ↦ G ^ {\displaystyle G\mapsto {\widehat {G}}} turns into the operation H ↦ H ∗ {\displaystyle H\mapsto H^{*}} of taking the dual vector space (which is a duality functor in the category of finite dimensional Hopf algebras). [ 20 ]
In 1973 Leonid I. Vainerman , George I. Kac , Michel Enock , and Jean-Marie Schwartz built a general theory of this type for all locally compact groups. [ 21 ] From the 1980s the research in this area was resumed after the discovery of quantum groups , to which the constructed theories began to be actively transferred. [ 22 ] These theories are formulated in the language of C*-algebras , or Von Neumann algebras , and one of its variants is the recent theory of locally compact quantum groups . [ 23 ] [ 22 ]
One of the drawbacks of these general theories, however, is that in them the objects generalizing the concept of a group are not Hopf algebras in the usual algebraic sense. [ 20 ] This deficiency can be corrected (for some classes of groups) within the framework of duality theories constructed on the basis of the notion of envelope of topological algebra. [ 24 ] | https://en.wikipedia.org/wiki/Pontryagin_duality |
A pony wall is a short wall.
In different circumstances, it may refer to:
This architectural element –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pony_wall |
In solid-state physics , the Poole–Frenkel effect (also known as Frenkel–Poole emission [ 1 ] ) is a model describing the mechanism of trap-assisted electron transport in an electrical insulator . It is named after Yakov Frenkel , who published on it in 1938, [ 2 ] extending the theory previously developed by H. H. Poole.
Electrons can move slowly through an insulator by the following process. The electrons are generally trapped in localized states (loosely speaking, they are "stuck" to a single atom, and not free to move around the crystal). Occasionally, random thermal fluctuations will give an electron enough energy to leave its localized state, and move to the conduction band . Once there, the electron can move through the crystal, for a brief amount of time, before relaxing into another localized state (in other words, "sticking" to a different atom). The Poole–Frenkel effect describes how, in a large electric field , the electron doesn't need as much thermal energy to be promoted into the conduction band (because part of this energy comes from being pulled by the electric field), so it does not need as large a thermal fluctuation and will be able to move more frequently.
On theoretical grounds, the Poole–Frenkel effect is comparable to the Schottky effect , which is the lowering of the metal-insulator energy barrier due to the electrostatic interaction with the electric field at a metal-insulator interface. However, the conductivity arising from the Poole–Frenkel effect is detected in presence of bulk-limited conduction (when the limiting conduction process occurs in the bulk of a material), while the Schottky current is observed when the conductivity is contact-limited (when the limiting conduction mechanism occurs at the metal-insulator interface). [ 3 ]
The electrical conductivity σ {\displaystyle \sigma } of dielectrics and semiconductors in presence of high electric fields (more than 10 5 V / c m {\displaystyle 10^{5}V/cm} for insulators and up to 10 3 V / c m {\displaystyle 10^{3}V/cm} for semiconductors) increases approximately as described by the Poole's law [ 2 ] (eventually leading to electrical breakdown ):
where
In this model the conduction is supposed to be carried by a free electron system moving in a self-consistent periodic potential.
On the contrary, Frenkel derived his formula describing the dielectric (or the semiconductor) as simply composed by neutral atoms acting as positively charged trap states (when empty, i.e. when the atoms are ionized).
For localized trap states with Coulomb potentials , the barrier height that an electron must cross to move from one atom to another is the depth of the trap potential well. Without any externally applied electric field, the maximum value of the potential is zero and is located at infinite distance from the trap center. [ 5 ] When an external electric field is applied, the height of the potential barrier is reduced on one side of the trap by the amount [ 2 ]
where:
The first contribution is due to the applied electric field, the second is due to the electrostatic attraction between the ionic trap site and the conduction electron.
The potential has now a maximum at a distance r 0 {\displaystyle r_{0}} from the Coulomb trap center, given by q 2 / ( 4 π ϵ r 0 2 ) = q E {\displaystyle q^{2}/(4\pi \epsilon r_{0}^{2})=qE} . [ 2 ] Therefore r 0 = q / ( 4 π ϵ E ) {\displaystyle r_{0}={\sqrt {q/(4\pi \epsilon E)}}} and [ 2 ]
This expression is similar to that obtained for the Schottky effect .
The factor 2 in the exponent, that makes the barrier reduction in the Poole–Frenkel effect twice larger than that experienced in the Schottky effect, is due to the interaction of the thermally excited electron with the immobile positive charge of the ion acting as a trap center, rather than with its mobile image charge induced in the metal at the Schottky interface. [ 6 ] Now if, without any applied electric field, the number of thermally ionized electrons is proportional to [ 2 ]
where:
then, in presence of an external electric field the electrical conductivity will be proportional to [ 2 ]
thus obtaining [ 2 ]
differing from Poole's law in the dependence on E {\displaystyle E} .
Taking everything into account (both the frequency with which electrons are excited into the conduction band, and their motion once they're there), and assuming a field-independent mobility of electrons, the standard quantitative expression for the Poole–Frenkel current is: [ 1 ] [ 7 ] [ 8 ]
where J is the current density .
Making the dependences from the applied voltage and the temperature explicit, the expression reads: [ 1 ]
where d is the dielectric thickness.
For a given dielectric, different conduction processes may dominate in different voltage and temperature ranges.
For materials such as Si 3 N 4 , Al 2 O 3 , and SiO 2 , at high temperature and high field regimes, the current J is likely due to Poole–Frenkel emission. [ 1 ] The detection of Poole–Frenkel emission as the limiting conduction process in a dielectric is usually made studying the slope in the so-called Poole–Frenkel plot, where the logarithm of the current density divided by the field ( l n ( J / E ) {\displaystyle ln(J/E)} ) versus the square root of the field ( E {\displaystyle {\sqrt {E}}} ) is depicted. The idea of such a plot originates from the expression of the Poole–Frenkel current density, which contains this proportionality ( l n ( J / E ) {\displaystyle ln(J/E)} vs E {\displaystyle {\sqrt {E}}} ), and would thus result in a straight line in this plot. For a fixed value of the voltage barrier in absence of any applied electric field, the slope is influenced by just one parameter: the dielectric permittivity. [ 9 ] Despite the same functional dependence of the current density upon the electric field intensity, one could differentiate between Poole–Frenkel conduction upon Schottky conduction as they would result in straight lines with different slopes in a Poole–Frenkel plot. The theoretical slopes can be evaluated knowing the high frequency dielectric constant of the material ( κ = ϵ / ϵ 0 {\displaystyle \kappa =\epsilon /\epsilon _{0}} , where ϵ 0 {\displaystyle \epsilon _{0}} is the vacuum permittivity ), and comparing these with the slopes detected experimentally. As an alternative, one can evaluate the value for κ {\displaystyle \kappa } equating the theoretical slopes to the experimental detected ones, provided that it is known if the conductivity is electrode-limited or bulk-limited. Such a value of the high frequency dielectric constant should then conform the relation κ = n 2 {\displaystyle \kappa =n^{2}} , where n {\displaystyle n} is the refractive index of the material. [ 3 ]
Although many progresses have been made on the topic since the classical work of Frenkel,
the Poole–Frenkel formula has been spreadly used to interpret several non-ohmic experimental currents observed in dielectrics and also semiconductors. [ 10 ] [ 11 ] The debate about the underlying assumptions of the classical Poole–Frenkel model has given life to several improved Poole–Frenkel models.
These hypotheses are presented in the following. [ 10 ]
Only electron (single-carrier) conduction is considered, assuming the existence of ohmic contacts capable to refill detrapped electrons at the electrodes, and space charge effects are neglected, supposing that the field is uniform. A revisitation of this latter assumption can be found, for example, in the “theory of space charge limited current enhanced by Frenkel effect” developed by Murgatroyd. [ 5 ]
The carriers mobility is assumed to be field-independent. Neglecting every kind of diffusion process for the de-trapped carriers, [ 5 ] the pre-exponential factor in the Poole–Frenkel formula is thus proportional to E {\displaystyle E} . This depiction would be suitable for the description of the conduction either in dielectrics or semiconductors. However, Poole–Frenkel effect is likely to be observed only in materials characterized by low mobility values, for, in high mobility solids, the re-trapping of carriers would be gradually inhibited by carrier depletion. [ 12 ] Still, different dependences of the pre-exponential factor from the field can be found: assuming that the carriers could be re-trapped, proportionality to E − 1 / 2 {\displaystyle E^{-1/2}} or E 1 / 2 {\displaystyle E^{1/2}} is obtained, depending on the electron retrapping occurring by the nearest neighbouring trap or after a drift. [ 12 ] Moreover, a pre-exponential factor proportional to E 1 / 2 {\displaystyle E^{1/2}} is found to be the result of random diffusion processes, [ 13 ] while dependencies on E − 3 / 2 {\displaystyle E^{-3/2}} and E − 3 / 4 {\displaystyle E^{-3/4}} are found to be the result of hopping and diffusion transport processes respectively. [ 14 ]
In the classical Poole–Frenkel theory a Coulombic trap potential is assumed, but steeper potentials belonging to multipolar defects or screened hydrogenic potentials are considered as well. [ 10 ]
Regarding the typology of traps, the Poole–Frenkel effect is described to occur for positively charged trap sites, i.e. for traps that are positive when empty and neutral when filled, in order for the electron to experience a Coulombic potential barrier due to the interaction with the positively charged trap. Donors or acceptors sites and electrons in the valence band will also exhibit the Poole–Frenkel effect as well. On the contrary, a neutral trap site, i.e. a site that is neutral when empty and charged (negatively for electrons) when filled, will not exhibit Poole–Frenkel effect.
Among the others, Simmons has proposed an alternative to the classical model with shallow neutral traps and deep donors, capable to exhibit a bulk-limited conduction with a Schottky electric field dependence, even in presence of a Poole–Frenkel conduction mechanism, thus explaining the "anomalous Poole–Frenkel effect" revealed by Ta 2 O 5 and SiO films. [ 3 ] Models there exist that consider the presence of both donor and acceptor trap sites, in a situation called compensation of traps .
The model of Yeargan and Taylor, for example, extends the classical Poole–Frenkel theory including diverse degrees of compensations: when only one kind of trap is considered, the slope of the curve in a Poole–Frenkel plot reproduces that obtained from Schottky emission, in spite of the barrier lowering being twice that for Schottky effect; the slope is twice larger in presence of compensation. [ 15 ]
As a further assumption a single energy level for the traps is assumed. However, the existence of further donor levels is discussed, even if they are supposed to be entirely filled for every field and temperature regime, and thus to not furnish any conduction carrier (this is equivalent to state that the additional donor levels are placed well below the Fermi level ). [ 10 ]
The calculation made for the trap depth reduction is a one-dimensional calculation, resulting in an overestimation of the effective barrier lowering.
In fact, only in the direction of the external electric field the potential well height is lowered as much estimated accordingly to the Poole–Frenkel expression. More accurate calculation, performed by Hartke [ 6 ] making an average of the electron emission probabilities with respect to any direction, shows that the growth of the free carriers concentration is about an order of magnitude less than that predicted by Poole–Frenkel equation. [ 5 ] The Hartke equation is equivalent to [ 5 ]
where
From a theoretical point of view, Hartke's expression has to be preferred to Poole–Frenkel equation on the grounds that the threedimensionality of the problem of the trap barrier lowering is considered. [ 5 ] Additional three-dimensional models have been developed, differing by the treatment they do of the emission process in the upwind direction. [ 10 ] Ieda, Sawa, and Kato, for example, have proposed a model that includes the barrier variation in directions both forward and opposite to the electric field. [ 16 ]
Poole–Frenkel saturation occurs when all the trap sites become ionized, resulting in a maximum of the number of conduction carriers.
The corresponding saturation field is obtained from the expression describing the vanishing of the barrier: [ 10 ]
where E s {\displaystyle E_{s}} is the saturation field. Thus [ 10 ]
The trap sites are now necessarily empty, being at the edge of the conduction band .
The fact that the Poole–Frenkel effect is described by an expression for the conductivity (and for the current) that diverges with increasing fields and does not experience a saturation, is attributable to the simplifying assumption that the trap population follows the Maxwell-Boltzmann statistics. An enhanced Poole–Frenkel model, comprehensive of a more accurate description of the trap statistics with the Fermi-Dirac formula, and capable to quantitatively represent the saturation, has been devised by Ongaro and Pillonnet. [ 10 ]
In charge trap flash memories, charge is stored in a trapping material, typically a silicon-nitride layer, as current flows through a dielectric. In the programming process, electrons are emitted from the substrate towards the trapping layer due to a large positive bias applied to the gate. The current transport is the result of two different conduction mechanisms, to be considered in series: the current through the oxide is by tunneling, the conduction mechanism through the nitride is a Poole–Frenkel transport. The tunneling current is described by a modified Fowler-Nordheim tunneling equation, i.e. a tunneling equation that takes into account that the shape of the tunneling barrier is not triangular (as assumed for the Fowler-Nordheim formula derivation), but composed of the series of a trapezoidal barrier in the oxide, and a triangular barrier in the nitride. The Poole–Frenkel process is the limiting mechanism of conduction at the beginning of the memory programming regime due to the higher current provided by tunneling. As the trapped electron charge raises, beginning to screen the field, the modified Fowler-Nordheim tunneling becomes the limiting process. The trapped charge density at the oxide-nitride interface is proportional to the integral of the Poole–Frenkel current flowed across it. [ 1 ] With an increasing number of memory write and erase cycles, retention characteristics worsen due to the increasing bulk conductivity in the nitride. [ 8 ] | https://en.wikipedia.org/wiki/Poole–Frenkel_effect |
Pop-up satellite archival tags ( PSATs ) are used to track movements of (usually large, migratory) marine animals. A PSAT (also commonly referred to as a PAT tag) is an archival tag (or data logger ) that is equipped with a means to transmit the collected data via the Argos satellite system . Though the data are physically stored on the tag, its major advantage is that it does not have to be physically retrieved like an archival tag for the data to be available making it a viable, fishery independent tool for animal behavior and migration studies. They have been used to track movements of ocean sunfish , [ 1 ] marlin , blue sharks , bluefin tuna , swordfish and sea turtles to name a few species. Location, depth, temperature, oxygen levels, and body movement data are used to answer questions about migratory patterns, seasonal feeding movements, daily habits, and survival after catch and release, for examples. [ 2 ]
A satellite tag is generally constructed of several components: a data-logging section, a release section, a float, and an antenna . The release sections include an energetically popped off release section or a corrosive pin that is actively corroded on a preset date or after a specified period of time. Some limitations of using satellite tags are their depth limitations (2000m), their costs ($499–$4000+), their vulnerability to loss by environmental issues ( biofouling ), or premature release through ingestion by a predator .
There are two methods of underwater geolocation that PSATs employ. The first method is through light based geolocation which uses the length of the day and a noon time calculation to estimate the tags location while underwater. This method has a functional depth limitation of light penetration which can be as shallow as a few meters to upwards of hundreds of meters. Geolocation estimates based on light are usually coupled with additional satellite data like sea surface temperature or other available data input such as bathymetry, land avoidance, and physical limitations of the tagged animal. The other method available is through measuring ambient light and the Earth's magnetic field . This method has a functional depth limitation equivalent of the maximum depth limitation, generally 1800m. Magnetic based geolocation is generally not coupled with additional satellite data or other inputs, and relies on the Earth magnetic field for latitude estimations and light (noon time) for longitude estimations.
Pop-up satellite tags range in length from about 125–215 mm (4.9–8.5 in) and weigh 36-108 grams in air. A tag must be small compared to the size of the animal, anywhere from 3-5% of the total fish weight, so that it does not interfere with normal behavior.
These tags record information such as temperature, magnetics, acceleration, light level, oxygen levels and pressure at set intervals of a few seconds to several hours. [ 3 ] Data are often collected for several weeks or months, but with new advances in memory technology microSD cards tags can store data for centuries. PSATs record data in non-volatile memory so that data are retained even if the power source fails.
When the PSAT releases from the animal on which it was attached, it floats to the surface, and begins to transmit data to the Argos satellites at a frequency of 401.65 MHz +/-. Therefore, the tag does not have to be physically recovered for the data to be obtained. Summarized data illustrating where the fish's migration started and ended is usually recovered from the tag within about seven days; however, tags can transmit significant amounts of oceanic data for months after they release from the fish.
Limitations of PSAT technology are that it is subject to loss by malfunction of the power source, environmental effects such as biofouling, ingestion by a predator , its depth limitation and cost. Most PSATS have internal software designed to detect damaging or sub-optimal conditions that will trigger an early release and transmission of data. For example, PSATs can withstand pressures to depths of 2,000 to 2,500 metres (6,600 to 8,200 ft) depending on the model. If data indicate no change in pressure (depth) for a period of time, this could trigger an early release due to premature release (a tag pulling out of the fish early) or death of the animal to which it was attached. Such internal checks can alert researchers to unexpected or undesirable events. Ingestion by a predator is more difficult to detect in the sense of forcing a tag to report; however, in data processing it is indicated by an immediate loss of light and an increase in temperature that stabilizes while it is inside the predator. [ 4 ]
The most popular method of determining an animal's location underwater requires the tag to acquire light levels throughout the day. Observing the length of the day, from when the tag observed the first light until the last light, the tag can determine its latitudinal location (with accuracy exceeding 1 degree). From the length of day the tag computes the noon time which is converted to a longitude location (with accuracy averaging about 0.5 degree or 30–50 nautical miles). This method of geolocation is suitable for animals that inhabit clear waters near the surface. At depths or in turbid waters, light based geolocation does not work as well due to light attenuation. It also does not work well during the equinoxes when the length of day is globally uniform. Manufacturers of this technology include Wildlife Computers, Microwave Telemetry, and Lotek Wireless. Star-Oddi is in the development phase of a pop-up satellite tag as well.
Another approach to geolocation couples light and magnetics. This method measures the total Earth's magnetic field for latitude estimations while using light based noon time detection for longitude. These tags measure the Earth's magnetic field on their built-in magnetometers throughout the day and then take the average value as the tag's daily location. Average accuracy of this method is approximately 35 nautical miles. Manufacturers of this technology include Desert Star Systems. | https://en.wikipedia.org/wiki/Pop-up_satellite_archival_tag |
A pop filter , pop shield or pop screen is a noise protection filter for microphones , typically used in a recording studio . It serves to reduce or eliminate popping sounds caused by the mechanical impact of fast-moving air on the microphone from plosives during recorded speech and singing. Pop filters can also keep saliva off the microphone during recording.
Popping sounds occur particularly in the pronunciation of aspirated plosives (such as the first p in the English word popping ). Other plosives can be t , k , d , b , and g sounds. The popping sound recorded by a microphone has two components: the high-frequency component, caused by air moving past the grille or other parts of the microphone body; and the low-frequency component, caused by air impacting the diaphragm. [ 1 ] Mechanical and electrical saturation (e.g. clipping ) can also play a role depending on the amount of headroom designed into these systems.
A typical pop filter is composed of one or more layers of acoustically semi-transparent material such as woven nylon stretched over a circular frame and often includes a clamp and a flexible mounting bracket. Metal pop filters use a fine mesh metal screen in place of the nylon. Some studio condenser microphones have an integral pop filter built into their design.
Metal pop filters are durable and designed with wider holes having less effect on high frequencies.
An improvised pop shield, functionally identical to the professional units, can be made with material from tights or stockings stretched over a kitchen sieve , embroidery hoop or a loop of wire such as a bent clothes hanger . It is important that the pop shield not be attached directly to the microphone as vibrations will be transmitted from the shield to the microphone.
Pop filters are designed to attenuate the energy of the plosive, which otherwise might exceed the design input capacity of the microphone, leading to clipping . In effect, the plosive's discrete envelope of sound energy is intercepted and broken up by the strands of the filter material before it can impinge on, and momentarily distort, the sensitive diaphragm of the microphone. Pop filters do not appreciably affect hissing sounds or sibilance , for which de-essing is used.
Additionally, a pop filter can protect against the accumulation of saliva on the microphone element. Salts in human saliva are corrosive, so the use of a pop filter may improve the lifespan of the microphone. [ 2 ]
A pop filter differs from a microphone windscreen . Pop filters are generally used in a studio environment to help improve the sound quality of the recorded voice, while windscreens are typically used outdoors and get rid of any low distortion. Windscreens are also used by vocalists on stage to reduce plosives and saliva, though they may not be as acoustically transparent as a studio pop filter.
The position of the pop filter depends on the amount of power the artist is going to communicate while recording. The position of the pop filter is different in different recording situations, with a further position from the microphone causing fewer pop sounds. More distance means increasing the microphone gain and gaining more room noise. Normally, to get good quality, the pop filter should be placed about 2–6 inches (5–15 cm) away from the microphone. [ 3 ] | https://en.wikipedia.org/wiki/Pop_filter |
A Pople diagram or Pople's Diagram is a diagram which describes the relationship between various calculation methods in computational chemistry . It was initially introduced in January 1965 by Sir John Pople , KBE FRS , during the Symposium of Atomic and Molecular Quantum Theory in Florida . [ 1 ] The Pople Diagram can be either 2-dimensional or 3-dimensional , with the axes representing ab initio methods , basis sets and treatment of relativity. [ 2 ] The diagram attempts to balance calculations by giving all aspects of a computation equal weight.
John Pople first introduced the Pople Diagram during the Symposium on Atomic and Molecular Quantum Theory held on Sanibel Island, Florida, in January 1965. He called it a "hyperbola of quantum chemistry", which illustrates the inverse relationship between the sophistication of a calculational method and the number of electrons in a molecule that can be studied by that method. [ 1 ] Alternative (reverse) arrangement of the vertical axis or interchange of the two axes are also possible. [ 3 ] [ 4 ]
The 2-dimensional Pople diagram describes the convergence of the quantum-mechanical nonrelativistic electronic energy with the size of the basis set and the level of electron correlation included in the wavefunction. [ 5 ] In order to reproduce accurate experimental thermochemical properties, secondary energetic contributions have to be considered. The third dimension of the Pople diagram consists of such energetic contributions. These contributions may include: spin–orbit interaction , scalar relativistic, zero-point vibrational energy, and deviations from the Born–Oppenheimer approximation . The three-dimensional Pople diagram (also known as the Csaszar cube. [ 6 ] ) describes the energy contributions involved in quantum chemistry composite methods . [ 7 ] | https://en.wikipedia.org/wiki/Pople_diagram |
The Pople notation is named after the Nobel laureate John Pople and is a simple method of presenting second-order spin coupling systems in NMR . [ 1 ]
The notation labels each (NMR active) nucleus with a letter of the alphabet. The difference in chemical shift , δ, relative to the J-coupling between nuclei mirrors the separation of the letter labels in the Latin alphabet . The letters used tend to be limited to A,B,M,N,X,Y.
For example, AB indicates two nuclei which have similar chemical shifts (Δδ similar to or smaller than J), whereas AX indicates two which lie further apart on the spectrum (Δδ significantly larger than J). A 2 B would similarly indicate a spin system containing two equivalent nuclei (A) and a third, inequivalent one (B). Nuclei which are in equivalent chemical environments (that is, symmetry-related), but inequivalent magnetic environments are distinguished with a prime; e.g. AA' . This key aspect of the notation, i.e., using a prime to differentiate between chemical equivalence only compared to full magnetic equivalence, was introduced by Richards and Schaefer in 1958. [ 2 ]
The notation can be used to represent systems of more than two nuclei, for example AMX represents three nuclei, each moderately separated from the others, and ABX represents two nuclei whose peaks are closely spaced and one other nucleus which is more distant.
Examples:
PHCl 2 is an AX system whereas
CH 3 CH 2 F is an A 3 M 2 X system,
This nuclear magnetic resonance –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pople_notation |
In convex analysis , Popoviciu's inequality is an inequality about convex functions . It is similar to Jensen's inequality and was found in 1965 by Tiberiu Popoviciu , [ 1 ] [ 2 ] a Romanian mathematician.
Let f be a function from an interval I ⊆ R {\displaystyle I\subseteq \mathbb {R} } to R {\displaystyle \mathbb {R} } . If f is convex , then for any three points x , y , z in I ,
If a function f is continuous , then it is convex if and only if the above inequality holds for all x , y , z from I {\displaystyle I} . When f is strictly convex, the inequality is strict except for x = y = z . [ 3 ]
It can be generalized to any finite number n of points instead of 3, taken on the right-hand side k at a time instead of 2 at a time: [ 4 ]
Let f be a continuous function from an interval I ⊆ R {\displaystyle I\subseteq \mathbb {R} } to R {\displaystyle \mathbb {R} } . Then f is convex if and only if, for any integers n and k where n ≥ 3 and 2 ≤ k ≤ n − 1 {\displaystyle 2\leq k\leq n-1} , and any n points x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} from I ,
[ 5 ] [ 6 ] [ 7 ] [ 8 ]
Popoviciu's inequality can also be generalized to a weighted inequality. [ 9 ]
Let f be a continuous function from an interval I ⊆ R {\displaystyle I\subseteq \mathbb {R} } to R {\displaystyle \mathbb {R} } . Let x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} be three points from I {\displaystyle I} , and let w 1 , w 2 , w 3 {\displaystyle w_{1},w_{2},w_{3}} be three nonnegative reals such that w 2 + w 3 ≠ 0 , w 3 + w 1 ≠ 0 {\displaystyle w_{2}+w_{3}\neq 0,w_{3}+w_{1}\neq 0} and w 1 + w 2 ≠ 0 {\displaystyle w_{1}+w_{2}\neq 0} . Then, | https://en.wikipedia.org/wiki/Popoviciu's_inequality |
Structural Assessment
Seismic Retrofit Design
Geotechnical Design
Site Monitoring
Project Management
Popp & Asociații is a professional services company based in Bucharest , Romania . It provides structural design & assessment, consultancy, retrofitting design, and project management services for all aspects of the built environment either existing or new, including infrastructure works design.
The company was founded in 2002 [ 1 ] by prof. Traian Popp, a preeminent Romanian senior structural engineer, [ 2 ] along with fellow engineering professionals Dragoș Marcu and Mădălin Coman.
Popp & Asociații had its breakthrough projects in 2004, with the structural design of the Charles de Gaulle Plaza office tower [ 3 ] and the seismic structural retrofitting of the 110 year old Bucharest Palace of Justice . The Charles de Gaulle Plaza tower site conditions imposed a top-down [ 4 ] infrastructure approach for the building's 5 underground levels, the first of its kind in Romania. Equivalent ground-breaking techniques had to be used for the Palace of Justice retrofitting and strengthening as the palace was listed in the 1980s to be demolished in 1990 [ 5 ] due to irreparable seismic damage following the 1977 earthquake .
The company has continuously evolved thereafter, progressively broadening its expertise and range of services. The Popp & Asociații Group now provides geotechnical engineering services, along with building and site monitoring, on site and laboratory material testing services, research and development and structural design consultancy services. [ 6 ]
The Popp & Asociații portfolio spans over a large range of projects, including high-rise office and residential buildings, large-scale commercial centres, deep excavations and historical monuments of national and international importance. Further business includes international consulting contracts for the evaluation of existing buildings to seismic actions, along with research activities for the development of design codes and guides. [ 7 ] | https://en.wikipedia.org/wiki/Popp_&_Asociații |
A poppy is a flowering plant in the subfamily Papaveroideae of the family Papaveraceae . Poppies are herbaceous plants , often grown for their colourful flowers. One species of poppy, Papaver somniferum , is the source of the narcotic drug mixture opium , which contains powerful medicinal alkaloids such as morphine and has been used since ancient times as an analgesic and narcotic medicinal and recreational drug . It also produces edible seeds . Following the trench warfare in the poppy fields of Flanders , Belgium, during World War I , poppies have become a symbol of remembrance of soldiers who have died during wartime, especially in the UK, Canada, Australia, New Zealand and other Commonwealth realms .
Poppies are herbaceous annual , biennial or short-lived perennial plants. Some species are monocarpic , dying after flowering.
Poppies can be over 1 metre (3.3 ft) tall with flowers up to 15 centimetres (5.9 in) across. Flowers of species (not cultivars) have 4 or 6 petals, many stamens forming a conspicuous whorl in the center of the flower and an ovary composed of 2 or more fused carpels. The petals are showy, may be of almost any colour and may have markings. The petals are crumpled in the bud and as blooming finishes, the petals often lie flat before falling away.
In the temperate zones, poppies bloom from spring into early summer. [ 1 ] Most species secrete latex when injured. Bees use poppies as a pollen source . The pollen of the oriental poppy, Papaver orientale , is dark blue, that of the field or corn poppy ( Papaver rhoeas ) is grey to dark green. [ 2 ] The opium poppy, Papaver somniferum , grows wild in Southeast Europe and Southeast Asia . It is believed that it originated in the Mediterranean region. [ 3 ]
Poppies belong to the subfamily Papaveroideae of the family Papaveraceae , which includes the following genera:
The flowers of most poppy species are attractive and are widely cultivated as annual or perennial ornamental plants . This has resulted in a number of commercially important cultivars, such as the Shirley poppy, a cultivar of Papaver rhoeas and semi-double or double (flore plena) forms of the opium poppy Papaver somniferum and oriental poppy ( Papaver orientale ). Poppies of several other genera are also cultivated in gardens. [ citation needed ]
Poppy seeds are rich in oil, carbohydrates , calcium and protein . Poppy oil is often used as cooking oil, salad dressing oil, or in products such as margarine. Poppy oil can also be added to spices for cakes or breads. Poppy products are also used in different paints, varnishes, and some cosmetics. [ 4 ]
A few species have other uses, principally as sources of drugs and foods. The opium poppy is widely cultivated and its worldwide production is monitored by international agencies. It is used for production of dried latex and opium , the principal precursor of narcotic and analgesic opiates such as morphine , heroin , and codeine .
Poppy seeds contain small quantities of both morphine and codeine , [ 5 ] which are pain-relieving drugs. Poppy seeds and fixed oils can also be nonnarcotic because when they are harvested about twenty days after the flower has opened, the morphine is no longer present. [ 4 ] Poppy cultivation is strictly regulated worldwide, with the exception of India where opium gum, which also contains the analgesic thebaine , is legally produced. [ 6 ]
Papaver somniferum was domesticated by the indigenous people of Western and Central Europe between 6000 and 3500 BC. [ 7 ] However, it is believed that its origins may come from the Sumerian people , where the first use of opium was recognized. [ 8 ] Poppies and opium made their way around the world along the silk road . [ 9 ] Juglets resembling poppy seed pods have been discovered with trace amounts of opium and the flower appeared in jewelry and on art pieces in Ancient Egypt, dated 1550–1292 BC. [ 10 ] [ 11 ]
The eradication of poppy cultivation came about in the early 1900s through international conferences due to safety concerns associated with the production of opium. In the 1970s the American war on drugs targeted Turkish production of the plant, leading to a more negative popular opinion of the U.S. [ 12 ]
The girl's given name "Poppy" is taken from the name of the flower. [ 13 ]
A poppy flower is depicted on the reverse of the Macedonian 500- denar banknote, issued in 1996 and 2003. [ 14 ] The poppy is also part of the coat of arms of North Macedonia .
Canada has issued special quarters (25-cent coins) with a red poppy on the reverse in 2004, 2008, 2010, and 2015. The 2004 Canadian "poppy" quarter was the world's first coloured circulation coin. [ 15 ]
Poppies have long been used as a symbol of sleep, peace, and death : Sleep because the opium extracted from them is a sedative , and death because of the common blood-red colour of the red poppy in particular. [ 16 ] In Greek and Roman myths, poppies were used as offerings to the dead. [ 17 ] Poppies used as emblems on tombstones symbolize eternal sleep. This symbolism was evoked in L. Frank Baum 's 1900 children's novel The Wonderful Wizard of Oz , in which a magical poppy field threatened to make the protagonists sleep forever. [ 17 ] A second interpretation of poppies in Classical mythology is that the bright scarlet colour signifies a promise of resurrection after death. [ 18 ]
Red-flowered poppy is unofficially considered the national flower of the Albanians in Albania , Kosovo and elsewhere. This is due to its red and black colours, the same as the colours of the flag of Albania. Red poppies are also the national flower of Poland . The California poppy, Eschscholzia californica , is the state flower of California. [ 19 ]
The powerful symbolism of Papaver rhoeas has been borrowed by various advocacy campaigns, such as the White Poppy and Simon Topping 's black poppy.
The poppy of wartime remembrance is Papaver rhoeas , the red-flowered corn poppy. This poppy is a common plant of disturbed ground in Europe and is found in many locations, including Flanders , which is the setting of the famous poem " In Flanders Fields " by the Canadian surgeon and soldier John McCrae . In Canada, the United Kingdom, Australia, South Africa and New Zealand, artificial poppies (plastic in Canada, paper in the UK, Australia, South Africa, Malta and New Zealand) are worn to commemorate those who died in war. This form of commemoration is associated with Remembrance Day , which falls on 11 November. In Canada, Australia and the UK, poppies are often worn from the beginning of November through to the 11th, or Remembrance Sunday if that falls on a later date. In New Zealand and Australia, soldiers are also commemorated on ANZAC day (25 April), [ 20 ] although the poppy is still commonly worn around Remembrance Day. Wearing of poppies has been a custom since 1924 in the United States. [ 21 ] Moina Michael of Georgia is credited as the founder of the Memorial Poppy in the United States. [ 22 ] [ 23 ] [ 24 ]
Artificial poppies (called "Buddy Poppies") are used in the veterans' aid campaign by the Veterans of Foreign Wars , which provides money to the veterans who assemble the poppies and various aid programs to veterans and their families. [ 25 ] | https://en.wikipedia.org/wiki/Poppy |
In physics , the poppy-seed bagel theorem concerns interacting particles (e.g., electrons ) confined to a bounded surface (or body) A {\displaystyle A} when the particles repel each other pairwise with a magnitude that is proportional to the inverse distance between them raised to some positive power s {\displaystyle s} . In particular, this includes the Coulomb law observed in electrostatics and Riesz potentials extensively studied in potential theory . Other classes of potentials, which not necessarily involve the Riesz kernel, for example nearest neighbor interactions, are also described by this theorem in the macroscopic regime. [ 1 ] [ 2 ] For N {\displaystyle N} such particles, a stable equilibrium state, which depends on the parameter s {\displaystyle s} , is attained when the associated potential energy of the system is minimal (the so-called generalized Thomson problem ). For large numbers of points, these equilibrium configurations provide a discretization of A {\displaystyle A} which may or may not be nearly uniform with respect to the surface area (or volume ) of A {\displaystyle A} . The poppy-seed bagel theorem asserts that for a large class of sets A {\displaystyle A} , the uniformity property holds when the parameter s {\displaystyle s} is larger than or equal to the dimension of the set A {\displaystyle A} . [ 3 ] For example, when the points (" poppy seeds ") are confined to the 2-dimensional surface of a torus embedded in 3 dimensions (or "surface of a bagel "), one can create a large number of points that are nearly uniformly spread on the surface by imposing a repulsion proportional to the inverse square distance between the points, or any stronger repulsion ( s ≥ 2 {\displaystyle s\geq 2} ). From a culinary perspective, to create the nearly perfect poppy-seed bagel where bites of equal size anywhere on the bagel would contain essentially the same number of poppy seeds, impose at least an inverse square distance repelling force on the seeds.
For a parameter s > 0 {\displaystyle s>0} and an N {\displaystyle N} -point set ω N = { x 1 , … , x N } ⊂ R p {\displaystyle \omega _{N}=\{x_{1},\ldots ,x_{N}\}\subset \mathbb {R} ^{p}} , the s {\displaystyle s} -energy of ω N {\displaystyle \omega _{N}} is defined as follows: E s ( ω N ) := ∑ i ≠ j 1 ≤ i , j ≤ N 1 | x i − x j | s {\displaystyle E_{s}(\omega _{N}):=\sum _{\stackrel {1\leq i,j\leq N}{i\not =j}}{\frac {1}{|x_{i}-x_{j}|^{s}}}} For a compact set A {\displaystyle A} we define its minimal N {\displaystyle N} -point s {\displaystyle s} -energy as E s ( A , N ) := min E s ( ω N ) , {\displaystyle {\mathcal {E}}_{s}(A,N):=\min E_{s}(\omega _{N}),} where the minimum is taken over all N {\displaystyle N} -point subsets of A {\displaystyle A} ; i.e., ω N ⊂ A {\displaystyle \omega _{N}\subset A} . Configurations ω N {\displaystyle \omega _{N}} that attain this infimum are called N {\displaystyle N} -point s {\displaystyle s} -equilibrium configurations .
We consider compact sets A ⊂ R p {\displaystyle A\subset \mathbb {R} ^{p}} with the Lebesgue measure λ ( A ) > 0 {\displaystyle \lambda (A)>0} and s ⩾ p {\displaystyle s\geqslant p} . For every N ⩾ 2 {\displaystyle N\geqslant 2} fix an N {\displaystyle N} -point s {\displaystyle s} -equilibrium configuration ω N ∗ = { x 1 , N , … , x N , N } {\displaystyle \omega _{N}^{*}=\{x_{1,N},\ldots ,x_{N,N}\}} . Set μ N := 1 N ∑ i = 1 , … , N δ x i , N , {\displaystyle \mu _{N}:={\frac {1}{N}}\sum _{i=1,\ldots ,N}\delta _{x_{i,N}},} where δ x {\displaystyle \delta _{x}} is a unit point mass at point x {\displaystyle x} . Under these assumptions, in the sense of weak convergence of measures , μ N → ∗ μ , {\displaystyle \mu _{N}{\stackrel {*}{\rightarrow }}\mu ,} where μ {\displaystyle \mu } is the Lebesgue measure restricted to A {\displaystyle A} ; i.e., μ ( B ) = λ ( A ∩ B ) / λ ( A ) {\displaystyle \mu (B)=\lambda (A\cap B)/\lambda (A)} .
Furthermore, it is true that lim N → ∞ E s ( A , N ) N 1 + s / p = C s , p λ ( A ) s / p , {\displaystyle \lim _{N\to \infty }{\frac {{\mathcal {E}}_{s}(A,N)}{N^{1+s/p}}}={\frac {C_{s,p}}{\lambda (A)^{s/p}}},} where the constant C s , p {\displaystyle C_{s,p}} does not depend on the set A {\displaystyle A} and, therefore, C s , p = lim N → ∞ E s ( [ 0 , 1 ] p , N ) N 1 + s / p , {\displaystyle C_{s,p}=\lim _{N\to \infty }{\frac {{\mathcal {E}}_{s}([0,1]^{p},N)}{N^{1+s/p}}},} where [ 0 , 1 ] p {\displaystyle [0,1]^{p}} is the unit cube in R p {\displaystyle \mathbb {R} ^{p}} .
Consider a smooth d {\displaystyle d} -dimensional manifold A {\displaystyle A} embedded in R p {\displaystyle \mathbb {R} ^{p}} and denote its surface measure by σ {\displaystyle \sigma } . We assume σ ( A ) > 0 {\displaystyle \sigma (A)>0} . Assume s ⩾ d {\displaystyle s\geqslant d} As before, for every N ⩾ 2 {\displaystyle N\geqslant 2} fix an N {\displaystyle N} -point s {\displaystyle s} -equilibrium configuration ω N ∗ = { x 1 , N , … , x N , N } {\displaystyle \omega _{N}^{*}=\{x_{1,N},\ldots ,x_{N,N}\}} and set μ N := 1 N ∑ i = 1 , … , N δ x i , N . {\displaystyle \mu _{N}:={\frac {1}{N}}\sum _{i=1,\ldots ,N}\delta _{x_{i,N}}.} Then, [ 4 ] [ 5 ] in the sense of weak convergence of measures , μ N → ∗ μ , {\displaystyle \mu _{N}{\stackrel {*}{\rightarrow }}\mu ,} where μ ( B ) = σ ( A ∩ B ) / σ ( A ) {\displaystyle \mu (B)=\sigma (A\cap B)/\sigma (A)} . If H d {\displaystyle H^{d}} is the d {\displaystyle d} -dimensional Hausdorff measure normalized so that H d ( [ 0 , 1 ] d ) = 1 {\displaystyle H^{d}([0,1]^{d})=1} , then [ 4 ] [ 6 ] lim N → ∞ E s ( A , N ) N 1 + s / d = 2 s α d − s / d ⋅ C s , d ( H d ( A ) ) s / d , {\displaystyle \lim _{N\to \infty }{\frac {{\mathcal {E}}_{s}(A,N)}{N^{1+s/d}}}=2^{s}\alpha _{d}^{-s/d}\cdot {\frac {C_{s,d}}{(H^{d}(A))^{s/d}}},} where α d = π d / 2 / Γ ( 1 + d / 2 ) {\displaystyle \alpha _{d}=\pi ^{d/2}/\Gamma (1+d/2)} is the volume of a d-ball .
For p = 1 {\displaystyle p=1} , it is known [ 6 ] that C s , 1 = 2 ζ ( s ) {\displaystyle C_{s,1}=2\zeta (s)} , where ζ ( s ) {\displaystyle \zeta (s)} is the Riemann zeta function . Using a modular form approach to linear programming , Viazovska together with coauthors established in a 2022 paper that in dimensions p = 8 {\displaystyle p=8} and p = 24 {\displaystyle p=24} , the values of C s , p {\displaystyle C_{s,p}} , s > p {\displaystyle s>p} , are given by the Epstein zeta function [ 7 ] associated with the E 8 {\displaystyle E_{8}} lattice and Leech lattice , respectively. [ 8 ] It is conjectured that for p = 2 {\displaystyle p=2} , the value of C s , p {\displaystyle C_{s,p}} is similarly determined as the value of the Epstein zeta function for the hexagonal lattice . Finally, in every dimension p ≥ 1 {\displaystyle p\geq 1} it is known that when s = p {\displaystyle s=p} , the scaling of E s ( A , N ) {\displaystyle {\mathcal {E}}_{s}(A,N)} becomes N 2 log N {\displaystyle N^{2}\log N} rather than N 2 = N 1 + s / p {\displaystyle N^{2}=N^{1+s/p}} , and the value of C s , p {\displaystyle C_{s,p}} can be computed explicitly as the volume of the unit p {\displaystyle p} -dimensional ball : [ 4 ] C s , p = H p ( B p ) = π p / 2 Γ ( 1 + p / 2 ) . {\displaystyle C_{s,p}=H^{p}({\mathcal {B}}^{p})={\frac {\pi ^{p/2}}{\Gamma (1+p/2)}}.} The following connection between the constant C s , p {\displaystyle C_{s,p}} and the problem of sphere packing is known: [ 9 ] lim s → ∞ ( C s , p ) 1 / s = 1 s ( α p Δ p ) 1 / p , {\displaystyle \lim _{s\to \infty }(C_{s,p})^{1/s}={\frac {1}{s}}\left({\frac {\alpha _{p}}{\Delta _{p}}}\right)^{1/p},} where α p {\displaystyle \alpha _{p}} is the volume of a p-ball and Δ p = sup ρ ( P ) , {\displaystyle \Delta _{p}=\sup \rho ({\mathcal {P}}),} where the supremum is taken over all families P {\displaystyle {\mathcal {P}}} of non-overlapping unit balls such that the limit ρ ( P ) = lim r → ∞ λ ( [ − r , r ] p ∩ ⋃ B ∈ P B ) ( 2 r ) p {\displaystyle \rho ({\mathcal {P}})=\lim _{r\to \infty }{\frac {\lambda \left([-r,r]^{p}\cap \bigcup _{B\in {\mathcal {P}}}B\right)}{(2r)^{p}}}} exists. | https://en.wikipedia.org/wiki/Poppy-seed_bagel_theorem |
Popular Astronomy is an American magazine published by John August Media, LLC and hosted at TechnicaCuriosa.com for amateur astronomers . Prior to its revival in 2009, the title was published between 1893 and 1951. [ 1 ] It was the successor to The Sidereal Messenger , which was published from March 1882 to 1892. [ 1 ] The first issue of Popular Astronomy appeared in September 1893. [ 2 ] Each yearly volume of Popular Astronomy contained 10 issues, [ 1 ] for a total of 59 volumes.
The first editor, from 1893 to 1909, was William W. Payne of Carleton College , [ 2 ] with Charlotte R. Willard as co-editor 1893–1905. Payne was followed by Herbert C. Wilson , who served in the post between 1909 and 1926. [ 2 ] Dr. Curvin Henry Gingrich, Professor of Mathematics and Astronomy at Carleton, served as the final editor for the initial publication run, which ended with his sudden death (by heart attack) in 1951. Dr. Gingrich received a six-page eulogy written by Dr. Frederick C. Leonard , in the August 1951 issue of the magazine.
The magazine played an important role in the development of amateur variable star observing in the United States. [ 3 ]
In 2017 Popular Astronomy has returned as part of TechnicaCuriosa.com, along with sister titles Popular Electronics and Mechanix Illustrated .
This science and technology magazine–related article is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about magazines . Further suggestions might be found on the article's talk page .
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Popular_Astronomy_(US_magazine) |
1800s: Martineau · Tocqueville · Marx · Spencer · Le Bon · Ward · Pareto · Tönnies · Veblen · Simmel · Durkheim · Addams · Mead · Weber · Du Bois · Mannheim · Elias
In sociology , popularity is how much a person, idea, place, item or other concept is either liked or accorded status [ 1 ] [ 2 ] [ 3 ] by other people. Liking can be due to reciprocal liking , interpersonal attraction , and similar factors. Social status can be due to dominance , superiority, and similar factors. For example, a kind person may be considered likable and therefore more popular than another person, and a wealthy person may be considered superior and therefore more popular than another person.
There are two primary types of interpersonal popularity: perceived and sociometric. Perceived popularity is measured by asking people who the most popular or socially important people in their social group [ 4 ] are. Sociometric popularity is measured by objectively measuring the number of connections a person has to others in the group. [ 5 ] A person can have high perceived popularity without having high sociometric popularity, and vice versa .
According to psychologist Tessa Lansu at the Radboud University Nijmegen , "Popularity [has] to do with being the middle point of a group and having influence on it." [ 6 ]
The term popularity is borrowed from the Latin term popularis , which originally meant "common." The current definition of the word popular, the "fact or condition of being well liked by the people", was first seen in 1601. [ 7 ]
While popularity is a trait often ascribed to an individual, it is an inherently social phenomenon and thus can only be understood in the context of groups of people. Popularity is a collective perception, and individuals report the consensus of a group's feelings towards an individual or object when rating popularity. It takes a group of people to like something, so the more that people advocate for something or claim that someone is best liked, the more attention it will get, and the more popular it will be deemed. [ 8 ]
Notwithstanding the above, popularity as a concept can be applied, assigned, or directed towards objects such as songs, movies, websites, activities, soaps, foods etc. Together, these objects collectively make up popular culture , or the consensus of mainstream preferences in society. In essence, anything, human or non-human, can be deemed popular.
For many years, popularity research focused on a definition of popularity that was based on being "well liked." Eventually, it was discovered that those who are perceived as popular are not necessarily the most well liked as originally assumed. When students are given the opportunity to freely elect those they like most and those they perceive as popular, a discrepancy often emerges. [ 9 ] This is evidence that there are two main forms of personal popularity that social psychology recognizes, sociometric popularity and perceived popularity. [ 10 ] Prinstein distinguishes between the two types as likeability vs. social status . [ 11 ]
Sociometric popularity can be defined by how liked an individual is. This liking is correlated with prosocial behaviours . Those who act in prosocial ways are likely to be deemed sociometrically popular. Often they are known for their interpersonal abilities, their empathy for others, and their willingness to cooperate non-aggressively. [ 12 ] This is a more private judgement, characterized by likability, that will not generally be shared in a group setting. Often, it is impossible to know whom individuals find popular on this scale unless confidentiality is ensured. [ 9 ]
Perceived popularity is used to describe those individuals who are known among their peers as being popular. Unlike sociometric popularity, perceived popularity is often associated with aggression and dominance and is not dependent on prosocial behaviors. This form of popularity is often explored by the popular media. Notable works dealing with perceived popularity include Mean Girls , Odd Girl Out , and Ferris Bueller's Day Off . Individuals who have perceived popularity are often highly socially visible and frequently emulated but rarely liked. [ 10 ] Since perceived popularity is a measure of visible reputation and emulation, this form of popularity is most openly discussed, agreed upon within a group, and what most people refer to when they call someone popular. [ 9 ]
To date, only one comprehensive theory of interpersonal popularity has been proposed: that of A. L. Freedman in the book Popularity Explained . The 3 Factor Model proposed attempts to reconcile the two concepts of sociometric and perceived popularity by combining them orthogonally and providing distinct definitions for each. In doing so, it reconciles the counter intuitive fact that liking does not guarantee perceived popularity nor does perceived popularity guarantee being well liked.
Popularity Explained was first published as a blog before being converted to a book and various versions have been available online since 2013.
There are four primary concepts that Popularity Explained relies on.
According to Freedman, an individual's place in the social landscape is determined by a combination of three factors: what they are; who they are; and the situation.
The Volume-Control Model offers analytical framework to understand how popularity is used to gain political and economic power. [ 15 ] This model explains the way information is organized and selected based on its popularity among users. It links between information popularization and the opposite mechanism, information personalization . Both popularization and personalization are employed together by tech companies, organizations, governments or individuals as complementing mechanisms to gain economic, political, and social power. Among the social implications of information popularization is the emergence of homogeneity, which often reflects dominant views. An example would be the bias of search engines . While Google Images uses PageRank to organize results based on their popularity, it presents mainly white young females as a result for the query "beauty". [ 15 ]
One of the most widely agreed upon theories about what leads to an increased level of popularity for an individual is the perceived value which that individual brings to the group. [ 16 ] This seems to be true for members of all groups, but is especially demonstrable in groups that exist for a specific purpose. For example, sports teams exist with the goal of being successful in competitions against other sports teams. Study groups exist so that the members of the group can mutually benefit from one another's academic knowledge. In these situations, leaders often emerge because other members of the group perceive them as adding a lot of value to the group as a whole. On a sports team, this means that the best players are usually elected captain and in study groups people might be more inclined to like an individual who has a lot of knowledge to share. [ 12 ] It has been argued that this may be a result of our evolutionary tendencies to favor individuals who are most likely to aid in our own survival. [ 17 ]
The actual value which an individual brings to a group is not of consequence in determining his or her popularity; the only thing that is important is his or her value as perceived by the other members of the group. While perceived value and actual value may often overlap, this is not a requisite and it has been shown that there are instances in which an individual's actual value is relatively low, but they are perceived as highly valuable nevertheless. [ 18 ]
Attractiveness, specifically physical attractiveness , has been shown to have very profound effects on popularity. [ 19 ] People who are physically attractive are more likely to be thought of as possessing positive traits. People who are attractive are expected to perform better on tasks and are more likely to be trusted. [ 18 ] Additionally, they are judged to possess many other positive traits such as mental health, intelligence, social awareness, and dominance. [ 20 ]
Additionally, people who are of above average attractiveness are assumed to also be of above average value to the group. Research shows that attractive people are often perceived to have many positive traits based on nothing other than their looks, regardless of how accurate these perceptions are. [ 21 ] This phenomenon is known as the Halo effect [ 18 ] This means that, in addition to being more well-liked, attractive people are more likely to be seen as bringing actual value to the group, even when they may be of little or no value at all. In essence, physically attractive people are given the benefit of the doubt while less attractive individuals must prove that they are bringing value to the group. [ 12 ] It has been shown empirically that being physically attractive is correlated with both sociometric and perceived popularity. Some possible explanations for this include increased social visibility and an increased level of tolerance for aggressive, social interactions that may increase perceived popularity. [ 12 ]
The degree to which an individual is perceived as popular is often highly correlated with the level of aggression with which that individual interacts with his or her peers. There are two main categories of aggression, relational and overt, both of which have varying consequences for popularity depending on several factors, such as the gender and attractiveness of the aggressor. [ 22 ]
The relationship also depends on culture. Prinstein notes that studies have found that increased aggression tends to correlate with higher social status in the United States, but lower social status in China. [ 11 ]
Relational aggression is nonviolent aggression that is emotionally damaging to another individual. Examples of relationally aggressive activities include ignoring or excluding an individual from a group, delivering personal insults to another person, and the spreading of rumors. Relational aggression is more frequently used by females than males. [ 12 ]
It has been found that relational aggression almost always has a strongly negative relationship with sociometric popularity but can have a positive relationship with perceived popularity depending on the perceived level of attractiveness of the aggressor. For an aggressor who is perceived as unattractive, relational aggression, by both males and females, leads to less perceived popularity. For an attractive aggressor however, relational aggression has been found to actually have a positive relationship with perceived popularity. [ 12 ]
The relationship between attractiveness and aggression is further intertwined by the finding that increased levels of physical attractiveness actually further decreased the sociometric popularity of relationally aggressive individuals. [ 12 ]
In short, the more physically attractive an individual is, the more likely they are to experience decreased levels of sociometric popularity but increased levels of perceived popularity for engaging in relationally aggressive activities.
Overt aggression is aggression that involves individuals physically interacting with each other in acts such as pushing, hitting, kicking or otherwise causing physical harm or submission in the other person. This includes threats of violence and physical intimidation as well.
It has been shown that overt aggression directly leads to perceived popularity when the aggressor is attractive. [ 10 ] Experiments that are controlled for levels of physical attractiveness show that individuals who are attractive and overtly aggressive have a higher degree of perceived popularity than attractive non-overtly aggressive individuals. This was found to be true to a small degree for females and a large degree for males. [ 12 ]
Attractive individuals who are overtly aggressive barely suffer any consequences in terms of sociometric popularity. This is a key difference between overt and relational aggression because relational aggression has a strongly negative relationship on sociometric popularity, especially for attractive individuals. For unattractive individuals, there is again a strongly negative relationship between overt aggression and sociometric popularity. [ 12 ] This means that attractive individuals stand to gain a lot of perceived popularity at the cost of very little sociometric popularity by being overtly aggressive while unattractive individuals stand to gain very little perceived popularity from acts of overt aggression but will be heavily penalized with regards to sociometric popularity.
According to Talcott Parsons, as rewritten by Fons Trompenaars, there are four main types of culture, [ 23 ] marked by:
Only the responsiveness/rejection culture results in teenagers actively trying to become popular. There is no effort for popularity in Northern or Southern Europe, Latin America or Asia. This emotional bonding is specific for the high schools in the United States . In the love/hate cultures, the family and close friends are more important than popularity. In the approval/criticism cultures, actions are more important than persons, so no strong links develop during school.
Popularity is gauged primarily through social status. Because of the importance of social status, peers play the primary role in social decision making so that individuals can increase the chances that others like them. However, as children, individuals tend to do this through friendship, academics, and interpersonal conduct. [ 24 ] [ 25 ] By adulthood, work and romantic relationships become much more important. This peer functioning and gaining popularity is a key player in increasing interest in social networks and groups in the workplace. To succeed in such a work environment, adults then place popularity as a higher priority than any other goal, even romance. [ 9 ]
These two types of popularity, perceived popularity and sociometric popularity, are more correlated for girls than they are for boys. However, it is said that men can possess these qualities to a larger extent, making them more likely to be a leader, more powerful, and more central in a group, but also more likely than women to be socially excluded. [ 9 ] Boys tend to become popular based on athletic ability, coolness, toughness, and interpersonal skills; however, the more popular a boy gets, the worse he tends to do on his academic work. On the other hand, this negative view of academics is not seen at all in popular girls, who gain popularity based on family background (primarily socioeconomic status), physical appearance, and social ability. Boys are also known to be more competitive and rule focused, whereas girls have more emotional intimacy. [ 24 ]
In some instances, it has been found that in predominantly white high schools, attractive non-white students are on average significantly more sociometrically popular than equally attractive white students. One theory that has been put forth to explain this phenomenon is a high degree of group cohesiveness among minority students compared with the relative lack of cohesion amongst members of the majority. Since there is more cohesion, there is more availability for one person to be liked by many since they are all in contact. This acts like Zipf's Law , where the cohesion is a confounding factor that forces the greater links in the smaller minority, causing them to be more noticed and thus more popular. [ 26 ] When considering race as a predictor for perceived popularity by asking a class how popular and important each other person is, African American students were rated most popular by their peers. Popularity in race was found to be correlated with athleticism, and because African Americans have a stereotype of being better at sports than individuals of other races, they are viewed as more popular. Additionally, White and Hispanic children were rated as more popular the better they succeeded in school and came from a higher socioeconomic background. No single factor can explain popularity, but instead the interaction between many factors such as race and athleticism vs. academics. [ 27 ]
More tasks in the workplace are being done in teams, leading to a greater need of people to seek and feel social approval. [ 8 ] In academic settings, a high social standing among peers is associated with positive academic outcomes. [ 28 ] [ 29 ] Popularity also leads to students in academic environments to receive more help, have more positive relationships and stereotypes, and be more approached by peers. [ 8 ] While this is the research found in schools, it is likely to be generalized to a workplace.
Popularity is positively linked to job satisfaction, individual job performance, and group performance. [ 8 ] The popular worker, besides just feeling more satisfied with his job, feels more secure, believes he has better working conditions, trusts his supervisor, and possesses more positive opportunities for communication with both management and co-workers, causing a greater feeling of responsibility and belongingness at work. [ 30 ] Others prefer to work with popular individuals, most notably in manual labor jobs because, although they might not be the most knowledgeable for the job, they are approachable, willing to help, cooperative in group work, and are more likely to treat their coworkers as an equal. If an employee feels good-natured, genial, but not overly independent, more people will say that they most prefer to work with that employee. [ 31 ]
According to the mere-exposure effect , employees in more central positions that must relate to many others throughout the day, such as a manager, are more likely to be considered popular. [ 8 ] There are many characteristics that contribute to popularity: [ 32 ]
With a greater focus on groups in the workplace, it is essential that leaders effectively deal with and mediate groups to avoid clashing. Sometimes a leader does not need to be popular to be effective, but there are a few characteristics that can help a leader be more accepted and better liked by his group. Without group or team cohesiveness, there is no correlation between leadership and popularity; however, when a group is cohesive, the higher up someone is in the leadership hierarchy, the more popular they are for two reasons. [ 33 ] First, a cohesive group feels more personal responsibility for their work, thus placing more value on better performance. Cohesive members see leaders as taking a bulk of the work and investing a lot of personal time, so when they see a job's value they can ascribe its success to the leader. This greatest contribution principle is perceived as a great asset to the team, and members view the leader more favorably and he gains popularity. [ 33 ] Secondly, cohesive groups have well established group values. Leaders can become more popular in these groups by realizing and acting on dominant group values. Supporting group morals and standards leads to high positive valuation from the group, leading to popularity. [ 34 ]
Popularity is a term widely applicable to the modern era thanks primarily to social networking technology. Being "liked" has been taken to a completely different level on ubiquitous sites such as Facebook .
Popularity is a social phenomenon but it can also be ascribed to objects that people interact with. Collective attention is the only way to make something popular, and information cascades play a large role in rapid rises in something's popularity. [ 35 ] [ 36 ] Rankings for things in popular culture, like movies and music, often do not reflect the public's taste, but rather the taste of the first few buyers because social influence plays a large role in determining what is popular and what is not through an information cascade .
Information cascades have strong influence causing individuals to imitate the actions of others, whether or not they are in agreement. For example, when downloading music, people don't decide 100% independently which songs to buy. Often they are influenced by charts depicting which songs are already trending. Since people rely on what those before them do, one can manipulate what becomes popular among the public by manipulating a website's download rankings. [ 37 ] Experts paid to predict sales often fail but not because they are bad at their jobs; instead, it is because they cannot control the information cascade that ensues after first exposure by consumers. Music is again, an excellent example. Good songs rarely perform poorly on the charts and poor songs rarely perform very well, but there is tremendous variance that still makes predicting the popularity of any one song very difficult. [ 38 ]
Experts can determine if a product will sell in the top 50% of related products or not, but it is difficult to be more specific than that. Due to the strong impact that influence plays, this evidence emphasizes the need for marketers. They have a significant opportunity to show their products in the best light, with the most famous people, or being in the media most often. Such constant exposure is a way of gaining more product followers. Marketers can often make the difference between an average product and a popular product. However, since popularity is primarily constructed as a general consensus of a group's attitude towards something, word-of-mouth is a more effective way to attract new attention. Websites and blogs start by recommendations from one friend to another, as they move through social networking services. Eventually, when the fad is large enough, the media catches on to the craze. This spreading by word-of-mouth is the social information cascade that allows something to grow in usage and attention throughout a social group until everyone is telling everyone else about it, at which point it is deemed popular. [ 39 ]
Individuals also rely on what others say when they know that the information they are given could be completely incorrect. This is known as groupthink . Relying on others to influence one's own decisions is a very powerful social influence, but can have negative impacts. [ 40 ]
The popularity of many different things can be described by Zipf's powerlaw , which posits that there is a low frequency of very large quantities and a high frequency of low quantities. This illustrates popularity of many different objects.
For example, there are few very popular websites, but many websites have small followings. This is the result of interest; as many people use e-mail, it is common for sites like Yahoo! to be accessed by large numbers of people; however, a small subset of people would be interested in a blog on a particular video game . In this situation, only Yahoo! would be deemed a popular site by the public. [ 41 ] This can additionally be seen in social networking services , such as Facebook . The average number of friends on Facebook is 130, while very few people have large social networks. However, some individuals do have more than 5,000 friends. This reflects that very few people can be extremely well-connected, but many people are somewhat connected. The number of friends a person has, has been a way to determine how popular an individual is, so the small number of people who have an extremely high number of friends is a way of using social networking services, like Facebook, to illustrate how only a few people are deemed popular. [ 42 ]
Popular people may not be those who are best liked interpersonally by their peers, but they do receive most of the positive behavior from coworkers when compared to nonpopular workers. [ 8 ] This is a result of the differences between sociometric and perceived popularity. When asked who is most popular, employees typically respond based on perceived popularity; however, they really prefer the social interactions with those who are more sociometrically popular. For each individual to ensure that they are consistent with the group's popularity consensus, those who are high in perceived popularity are treated with the same positive behaviors as those who are more interpersonally, but privately, liked by specific individuals. Well-liked workers are most likely to get salary increases and promotions, while disliked (unpopular) workers are the first to get their salary cut back or laid off during recessions. [ citation needed ]
During interactions with others in the work environment, more popular individuals receive more organizational citizenship behavior (helping and courteousness from others) and less counter productive work behavior (rude reactions and withheld information) than those who are considered less popular in the workplace. [ 8 ] Coworkers agree with each other on who is and who is not popular and, as a group, treat popular coworkers more favorably. While popularity has proven to be a big determiner of getting more positive feedback and interactions from coworkers, such a quality matters less in organizations where workloads and interdependence is high, such as the medical field. [ 8 ]
In many instances, physical appearance has been used as one indicator of popularity. Attractiveness plays a large role in the workplace and physical appearance influences hiring, whether or not the job might benefit from it. For example, some jobs, such as salesperson, benefit from attractiveness when it comes down to the bottom line, but there have been many studies which have shown that, in general, attractiveness is not at all a valid predictor of on-the-job performance. [ 43 ] Many individuals have previously thought this was only a phenomenon in the more individualistic cultures of the Western world, but research has shown that attractiveness also plays a role in hiring in collectivist cultures as well. Because of the prevalence of this problem during the hiring process in all cultures, researchers have recommended training a group to ignore such influencers, just like legislation has worked to control for differences in sex, race, and disabilities. [ 43 ] | https://en.wikipedia.org/wiki/Popularity |
The term population biology has been used with different meanings.
In 1971, Edward O. Wilson et al . used the term in the sense of applying mathematical models to population genetics , community ecology , and population dynamics . [ 1 ] Alan Hastings used the term in 1997 as the title of his book on the mathematics used in population dynamics. [ 2 ] The name was also used for a course given at UC Davis in the late 2010s, which describes it as an interdisciplinary field combining the areas of ecology and evolutionary biology . The course includes mathematics , statistics , ecology, genetics , and systematics . Numerous types of organisms are studied. [ 3 ]
The journal Theoretical Population Biology is published.
This biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Population_biology |
Population equivalent (PE) or unit per capita loading , or equivalent person (EP) , is a parameter for characterizing industrial wastewaters . It essentially compares the polluting potential of an industry (in terms of biodegradable organic matter) with a population (or certain number of people), which would produce the same polluting load. [ 1 ] : 65 In other words, it is the number expressing the ratio of the sum of the pollution load produced during 24 hours by industrial facilities and services to the individual pollution load in household sewage produced by one person in the same time. This refers to the amount of oxygen-demanding substances in wastewater which will consume oxygen as it bio-degrades , usually as a result of bacterial activity. [ 2 ]
A value frequently used in the international literature for PE, which was based on a German publication, is 54 gram of BOD (Biochemical oxygen demand) per person (or per capita or per inhabitant) per day. [ 1 ] : 65 [ 2 ] This has been adopted by many countries for design purposes but other values are also in use. For example, a commonly used definition used in Europe is: 1 PE equates to 60 gram of BOD per person per day, and it also equals 200 liters of sewage per day. [ 3 ] [ 4 ] [ 5 ] In the United States, a figure of 80 grams BOD per day is normally used. [ 6 ] : 171
If the base value is taken as 60 grams of BOD per person per day, then the equation to calculate PE from an industrial wastewater is:
[inhab/(unit/d)] | https://en.wikipedia.org/wiki/Population_equivalent |
Population genetics is a subfield of genetics that deals with genetic differences within and among populations , and is a part of evolutionary biology . Studies in this branch of biology examine such phenomena as adaptation , speciation , and population structure . [ 1 ]
Population genetics was a vital ingredient in the emergence of the modern evolutionary synthesis . Its primary founders were Sewall Wright , J. B. S. Haldane and Ronald Fisher , who also laid the foundations for the related discipline of quantitative genetics . Traditionally a highly mathematical discipline, modern population genetics encompasses theoretical, laboratory, and field work. Population genetic models are used both for statistical inference from DNA sequence data and for proof/disproof of concept. [ 2 ]
What sets population genetics apart from newer, more phenotypic approaches to modelling evolution, such as evolutionary game theory and adaptive dynamics , is its emphasis on such genetic phenomena as dominance , epistasis , the degree to which genetic recombination breaks linkage disequilibrium , and the random phenomena of mutation and genetic drift . This makes it appropriate for comparison to population genomics data.
Population genetics began as a reconciliation of Mendelian inheritance and biostatistics models. Natural selection will only cause evolution if there is enough genetic variation in a population. Before the discovery of Mendelian genetics , one common hypothesis was blending inheritance . But with blending inheritance, genetic variance would be rapidly lost, making evolution by natural or sexual selection implausible. The Hardy–Weinberg principle provides the solution to how variation is maintained in a population with Mendelian inheritance. According to this principle, the frequencies of alleles (variations in a gene) will remain constant in the absence of selection, mutation, migration and genetic drift. [ 3 ]
The next key step was the work of the British biologist and statistician Ronald Fisher . In a series of papers starting in 1918 and culminating in his 1930 book The Genetical Theory of Natural Selection , Fisher showed that the continuous variation measured by the biometricians could be produced by the combined action of many discrete genes, and that natural selection could change allele frequencies in a population, resulting in evolution. In a series of papers beginning in 1924, another British geneticist, J. B. S. Haldane , worked out the mathematics of allele frequency change at a single gene locus under a broad range of conditions. Haldane also applied statistical analysis to real-world examples of natural selection, such as peppered moth evolution and industrial melanism , and showed that selection coefficients could be larger than Fisher assumed, leading to more rapid adaptive evolution as a camouflage strategy following increased pollution. [ 4 ] [ 5 ]
The American biologist Sewall Wright , who had a background in animal breeding experiments, focused on combinations of interacting genes, and the effects of inbreeding on small, relatively isolated populations that exhibited genetic drift. In 1932 Wright introduced the concept of an adaptive landscape and argued that genetic drift and inbreeding could drive a small, isolated sub-population away from an adaptive peak, allowing natural selection to drive it towards different adaptive peaks. [ citation needed ]
The work of Fisher, Haldane and Wright founded the discipline of population genetics. This integrated natural selection with Mendelian genetics, which was the critical first step in developing a unified theory of how evolution worked. [ 4 ] [ 5 ] John Maynard Smith was Haldane's pupil, whilst W. D. Hamilton was influenced by the writings of Fisher. The American George R. Price worked with both Hamilton and Maynard Smith. American Richard Lewontin and Japanese Motoo Kimura were influenced by Wright and Haldane. [ citation needed ]
The mathematics of population genetics were originally developed as the beginning of the modern synthesis . Authors such as Beatty [ 6 ] have asserted that population genetics defines the core of the modern synthesis. For the first few decades of the 20th century, most field naturalists continued to believe that Lamarckism and orthogenesis provided the best explanation for the complexity they observed in the living world. [ 7 ] During the modern synthesis, these ideas were purged, and only evolutionary causes that could be expressed in the mathematical framework of population genetics were retained. [ 8 ] Consensus was reached as to which evolutionary factors might influence evolution, but not as to the relative importance of the various factors. [ 8 ]
Theodosius Dobzhansky , a postdoctoral worker in T. H. Morgan 's lab, had been influenced by the work on genetic diversity by Russian geneticists such as Sergei Chetverikov . He helped to bridge the divide between the foundations of microevolution developed by the population geneticists and the patterns of macroevolution observed by field biologists, with his 1937 book Genetics and the Origin of Species . Dobzhansky examined the genetic diversity of wild populations and showed that, contrary to the assumptions of the population geneticists, these populations had large amounts of genetic diversity, with marked differences between sub-populations. The book also took the highly mathematical work of the population geneticists and put it into a more accessible form. Many more biologists were influenced by population genetics via Dobzhansky than were able to read the highly mathematical works in the original. [ 9 ]
In Great Britain E. B. Ford , the pioneer of ecological genetics , [ 10 ] continued throughout the 1930s and 1940s to empirically demonstrate the power of selection due to ecological factors including the ability to maintain genetic diversity through genetic polymorphisms such as human blood types . Ford's work, in collaboration with Fisher, contributed to a shift in emphasis during the modern synthesis towards natural selection as the dominant force. [ 4 ] [ 5 ] [ 11 ] [ 12 ]
The original, modern synthesis view of population genetics assumes that mutations provide ample raw material, and focuses only on the change in frequency of alleles within populations . [ 13 ] The main processes influencing allele frequencies are natural selection , genetic drift , gene flow and recurrent mutation . Fisher and Wright had some fundamental disagreements about the relative roles of selection and drift. [ 14 ] The availability of molecular data on all genetic differences led to the neutral theory of molecular evolution . In this view, many mutations are deleterious and so never observed, and most of the remainder are neutral, i.e. are not under selection. With the fate of each neutral mutation left to chance (genetic drift), the direction of evolutionary change is driven by which mutations occur, and so cannot be captured by models of change in the frequency of (existing) alleles alone. [ 13 ] [ 15 ]
The origin-fixation view of population genetics generalizes this approach beyond strictly neutral mutations, and sees the rate at which a particular change happens as the product of the mutation rate and the fixation probability . [ 13 ]
Natural selection , which includes sexual selection , is the fact that some traits make it more likely for an organism to survive and reproduce . Population genetics describes natural selection by defining fitness as a propensity or probability of survival and reproduction in a particular environment. The fitness is normally given by the symbol w =1- s where s is the selection coefficient . Natural selection acts on phenotypes , so population genetic models assume relatively simple relationships to predict the phenotype and hence fitness from the allele at one or a small number of loci. In this way, natural selection converts differences in the fitness of individuals with different phenotypes into changes in allele frequency in a population over successive generations. [ citation needed ]
Before the advent of population genetics, many biologists doubted that small differences in fitness were sufficient to make a large difference to evolution. [ 9 ] Population geneticists addressed this concern in part by comparing selection to genetic drift . Selection can overcome genetic drift when s is greater than 1 divided by the effective population size . When this criterion is met, the probability that a new advantageous mutant becomes fixed is approximately equal to 2s . [ 16 ] [ 17 ] The time until fixation of such an allele is approximately ( 2 l o g ( s N ) + γ ) / s {\displaystyle (2log(sN)+\gamma )/s} . [ 18 ]
Dominance means that the phenotypic and/or fitness effect of one allele at a locus depends on which allele is present in the second copy for that locus. Consider three genotypes at one locus, with the following fitness values [ 19 ]
s is the selection coefficient and h is the dominance coefficient. The value of h yields the following information:
Epistasis means that the phenotypic and/or fitness effect of an allele at one locus depends on which alleles are present at other loci. Selection does not act on a single locus, but on a phenotype that arises through development from a complete genotype. [ 20 ] However, many population genetics models of sexual species are "single locus" models, where the fitness of an individual is calculated as the product of the contributions from each of its loci—effectively assuming no epistasis.
In fact, the genotype to fitness landscape is more complex. Population genetics must either model this complexity in detail, or capture it by some simpler average rule. Empirically, beneficial mutations tend to have a smaller fitness benefit when added to a genetic background that already has high fitness: this is known as diminishing returns epistasis. [ 21 ] When deleterious mutations also have a smaller fitness effect on high fitness backgrounds, this is known as "synergistic epistasis". However, the effect of deleterious mutations tends on average to be very close to multiplicative, or can even show the opposite pattern, known as "antagonistic epistasis". [ 22 ]
Synergistic epistasis is central to some theories of the purging of mutation load [ 23 ] and to the evolution of sexual reproduction .
The genetic process of mutation takes place within an individual, resulting in heritable changes to the genetic material. This process is often characterized by a description of the starting and ending states, or the kind of change that has happened at the level of DNA (e.g,. a T-to-C mutation, a 1-bp deletion), of genes or proteins (e.g., a null mutation, a loss-of-function mutation), or at a higher phenotypic level (e.g., red-eye mutation). Single-nucleotide changes are frequently the most common type of mutation, but many other types of mutation are possible, and they occur at widely varying rates that may show systematic asymmetries or biases ( mutation bias ).
Mutations can involve large sections of DNA becoming duplicated , usually through genetic recombination . [ 24 ] This leads to copy-number variation within a population. Duplications are a major source of raw material for evolving new genes. [ 25 ] Other types of mutation occasionally create new genes from previously noncoding DNA. [ 26 ] [ 27 ]
In the distribution of fitness effects (DFE) for new mutations, only a minority of mutations are beneficial. Mutations with gross effects are typically deleterious. Studies in the fly Drosophila melanogaster suggest that if a mutation changes a protein produced by a gene, this will probably be harmful, with about 70 percent of these mutations having damaging effects, and the remainder being either neutral or weakly beneficial. [ 28 ]
This biological process of mutation is represented in population-genetic models in one of two ways, either as a deterministic pressure of recurrent mutation on allele frequencies, or a source of variation. In deterministic theory, evolution begins with a predetermined set of alleles and proceeds by shifts in continuous frequencies, as if the population is infinite. The occurrence of mutations in individuals is represented by a population-level "force" or "pressure" of mutation, i.e., the force of innumerable events of mutation with a scaled magnitude u applied to shifting frequencies f(A1) to f(A2). For instance, in the classic mutation–selection balance model, [ 29 ] the force of mutation pressure pushes the frequency of an allele upward, and selection against its deleterious effects pushes the frequency downward, so that a balance is reached at equilibrium, given (in the simplest case) by f = u/s.
This concept of mutation pressure is mostly useful for considering the implications of deleterious mutation, such as the mutation load and its implications for the evolution of the mutation rate. [ 30 ] Transformation of populations by mutation pressure is unlikely. Haldane [ 31 ] argued that it would require high mutation rates unopposed by selection, and Kimura [ 32 ] concluded even more pessimistically that even this was unlikely, as the process would take too long (see evolution by mutation pressure ).
However, evolution by mutation pressure is possible under some circumstances and has long been suggested as a possible cause for the loss of unused traits. [ 33 ] For example, pigments are no longer useful when animals live in the darkness of caves, and tend to be lost. [ 34 ] An experimental example involves the loss of sporulation in experimental populations of B. subtilis . Sporulation is a complex trait encoded by many loci, such that the mutation rate for loss of the trait was estimated as an unusually high value, μ = 0.003 {\displaystyle \mu =0.003} . [ 35 ] Loss of sporulation in this case can occur by recurrent mutation, without requiring selection for the loss of sporulation ability. When there is no selection for loss of function, the speed at which loss evolves depends more on the mutation rate than it does on the effective population size , [ 36 ] indicating that it is driven more by mutation than by genetic drift.
The role of mutation as a source of novelty is different from these classical models of mutation pressure.
When population-genetic models include a rate-dependent process of mutational introduction or origination, i.e., a process that introduces new alleles including neutral and beneficial ones, then the properties of mutation may have a more direct impact on the rate and direction of evolution, even if the rate of mutation is very low. [ 37 ] [ 38 ] That is, the spectrum of mutation may become very important, particularly mutation biases , predictable differences in the rates of occurrence for different types of mutations, because bias in the introduction of variation can impose biases on the course of evolution. [ 39 ]
Mutation plays a key role in other classical and recent theories including Muller's ratchet , subfunctionalization , Eigen's concept of an error catastrophe and Lynch's mutational hazard hypothesis .
Genetic drift is a change in allele frequencies caused by random sampling . [ 40 ] That is, the alleles in the offspring are a random sample of those in the parents. [ 41 ] Genetic drift may cause gene variants to disappear completely, and thereby reduce genetic variability. In contrast to natural selection, which makes gene variants more common or less common depending on their reproductive success, [ 42 ] the changes due to genetic drift are not driven by environmental or adaptive pressures, and are equally likely to make an allele more common as less common.
The effect of genetic drift is larger for alleles present in few copies than when an allele is present in many copies. The population genetics of genetic drift are described using either branching processes or a diffusion equation describing changes in allele frequency. [ 43 ] These approaches are usually applied to the Wright-Fisher and Moran models of population genetics. Assuming genetic drift is the only evolutionary force acting on an allele, after t generations in many replicated populations, starting with allele frequencies of p and q, the variance in allele frequency across those populations is
Ronald Fisher held the view that genetic drift plays at the most a minor role in evolution, and this remained the dominant view for several decades. No population genetics perspective have ever given genetic drift a central role by itself, but some have made genetic drift important in combination with another non-selective force. The shifting balance theory of Sewall Wright held that the combination of population structure and genetic drift was important. Motoo Kimura 's neutral theory of molecular evolution claims that most genetic differences within and between populations are caused by the combination of neutral mutations and genetic drift. [ 45 ]
The role of genetic drift by means of sampling error in evolution has been criticized by John H Gillespie [ 46 ] and Will Provine , [ 47 ] who argue that selection on linked sites is a more important stochastic force, doing the work traditionally ascribed to genetic drift by means of sampling error. The mathematical properties of genetic draft are different from those of genetic drift. [ 48 ] The direction of the random change in allele frequency is autocorrelated across generations. [ 40 ]
Because of physical barriers to migration, along with the limited tendency for individuals to move or spread ( vagility ), and tendency to remain or come back to natal place ( philopatry ), natural populations rarely all interbreed as may be assumed in theoretical random models ( panmixy ). [ 49 ] There is usually a geographic range within which individuals are more closely related to one another than those randomly selected from the general population. This is described as the extent to which a population is genetically structured. [ 50 ]
Genetic structuring can be caused by migration due to historical climate change , species range expansion or current availability of habitat . Gene flow is hindered by mountain ranges, oceans and deserts or even human-made structures such as the Great Wall of China , which has hindered the flow of plant genes. [ 51 ]
Gene flow is the exchange of genes between populations or species, breaking down the structure. Examples of gene flow within a species include the migration and then breeding of organisms, or the exchange of pollen . Gene transfer between species includes the formation of hybrid organisms and horizontal gene transfer . Population genetic models can be used to identify which populations show significant genetic isolation from one another, and to reconstruct their history. [ 52 ]
Subjecting a population to isolation leads to inbreeding depression . Migration into a population can introduce new genetic variants, [ 53 ] potentially contributing to evolutionary rescue . If a significant proportion of individuals or gametes migrate, it can also change allele frequencies, e.g. giving rise to migration load . [ 54 ]
In the presence of gene flow, other barriers to hybridization between two diverging populations of an outcrossing species are required for the populations to become new species .
Horizontal gene transfer is the transfer of genetic material from one organism to another organism that is not its offspring; this is most common among prokaryotes . [ 55 ] In medicine, this contributes to the spread of antibiotic resistance , as when one bacteria acquires resistance genes it can rapidly transfer them to other species. [ 56 ] Horizontal transfer of genes from bacteria to eukaryotes such as the yeast Saccharomyces cerevisiae and the adzuki bean beetle Callosobruchus chinensis may also have occurred. [ 57 ] [ 58 ] An example of larger-scale transfers are the eukaryotic bdelloid rotifers , which appear to have received a range of genes from bacteria, fungi, and plants. [ 59 ] Viruses can also carry DNA between organisms, allowing transfer of genes even across biological domains . [ 60 ] Large-scale gene transfer has also occurred between the ancestors of eukaryotic cells and prokaryotes, during the acquisition of chloroplasts and mitochondria . [ 61 ]
If all genes are in linkage equilibrium , the effect of an allele at one locus can be averaged across the gene pool at other loci. In reality, one allele is frequently found in linkage disequilibrium with genes at other loci, especially with genes located nearby on the same chromosome. Recombination breaks up this linkage disequilibrium too slowly to avoid genetic hitchhiking , where an allele at one locus rises to high frequency because it is linked to an allele under selection at a nearby locus. Linkage also slows down the rate of adaptation, even in sexual populations. [ 62 ] [ 63 ] [ 64 ] The effect of linkage disequilibrium in slowing down the rate of adaptive evolution arises from a combination of the Hill–Robertson effect (delays in bringing beneficial mutations together) and background selection (delays in separating beneficial mutations from deleterious hitchhikers ).
Linkage is a problem for population genetic models that treat one gene locus at a time. It can, however, be exploited as a method for detecting the action of natural selection via selective sweeps .
In the extreme case of an asexual population , linkage is complete, and population genetic equations can be derived and solved in terms of a travelling wave of genotype frequencies along a simple fitness landscape . [ 65 ] Most microbes , such as bacteria , are asexual. The population genetics of their adaptation have two contrasting regimes. When the product of the beneficial mutation rate and population size is small, asexual populations follow a "successional regime" of origin-fixation dynamics, with adaptation rate strongly dependent on this product. When the product is much larger, asexual populations follow a "concurrent mutations" regime with adaptation rate less dependent on the product, characterized by clonal interference and the appearance of a new beneficial mutation before the last one has fixed .
Neutral theory predicts that the level of nucleotide diversity in a population will be proportional to the product of the population size and the neutral mutation rate. The fact that levels of genetic diversity vary much less than population sizes do is known as the "paradox of variation". [ 66 ] While high levels of genetic diversity were one of the original arguments in favor of neutral theory, the paradox of variation has been one of the strongest arguments against neutral theory.
It is clear that levels of genetic diversity vary greatly within a species as a function of local recombination rate, due to both genetic hitchhiking and background selection . Most current solutions to the paradox of variation invoke some level of selection at linked sites. [ 67 ] For example, one analysis suggests that larger populations have more selective sweeps, which remove more neutral genetic diversity. [ 68 ] A negative correlation between mutation rate and population size may also contribute. [ 69 ]
Life history affects genetic diversity more than population history does, e.g. r-strategists have more genetic diversity. [ 67 ]
Population genetics models are used to infer which genes are undergoing selection. One common approach is to look for regions of high linkage disequilibrium and low genetic variance along the chromosome, to detect recent selective sweeps .
A second common approach is the McDonald–Kreitman test which compares the amount of variation within a species ( polymorphism ) to the divergence between species (substitutions) at two types of sites; one assumed to be neutral. Typically, synonymous sites are assumed to be neutral. [ 70 ] Genes undergoing positive selection have an excess of divergent sites relative to polymorphic sites. The test can also be used to obtain a genome-wide estimate of the proportion of substitutions that are fixed by positive selection, α. [ 71 ] [ 72 ] According to the neutral theory of molecular evolution , this number should be near zero. High numbers have therefore been interpreted as a genome-wide falsification of neutral theory. [ 73 ]
The simplest test for population structure in a sexually reproducing, diploid species, is to see whether genotype frequencies follow Hardy-Weinberg proportions as a function of allele frequencies. For example, in the simplest case of a single locus with two alleles denoted A and a at frequencies p and q , random mating predicts freq( AA ) = p 2 for the AA homozygotes , freq( aa ) = q 2 for the aa homozygotes, and freq( Aa ) = 2 pq for the heterozygotes . In the absence of population structure, Hardy-Weinberg proportions are reached within 1–2 generations of random mating. More typically, there is an excess of homozygotes, indicative of population structure. The extent of this excess can be quantified as the inbreeding coefficient, F .
Individuals can be clustered into K subpopulations. [ 74 ] [ 75 ] The degree of population structure can then be calculated using F ST , which is a measure of the proportion of genetic variance that can be explained by population structure. Genetic population structure can then be related to geographic structure, and genetic admixture can be detected.
Coalescent theory relates genetic diversity in a sample to demographic history of the population from which it was taken. It normally assumes neutrality , and so sequences from more neutrally evolving portions of genomes are therefore selected for such analyses. It can be used to infer the relationships between species ( phylogenetics ), as well as the population structure, demographic history (e.g. population bottlenecks , population growth ), biological dispersal , source–sink dynamics [ 76 ] and introgression within a species.
Another approach to demographic inference relies on the allele frequency spectrum . [ 77 ]
By assuming that there are loci that control the genetic system itself, population genetic models are created to describe the evolution of dominance and other forms of robustness , the evolution of sexual reproduction and recombination rates, the evolution of mutation rates , the evolution of evolutionary capacitors , the evolution of costly signalling traits , the evolution of ageing , and the evolution of co-operation . For example, most mutations are deleterious, so the optimal mutation rate for a species may be a trade-off between the damage from a high deleterious mutation rate and the metabolic costs of maintaining systems to reduce the mutation rate, such as DNA repair enzymes. [ 78 ]
One important aspect of such models is that selection is only strong enough to purge deleterious mutations and hence overpower mutational bias towards degradation if the selection coefficient s is greater than the inverse of the effective population size . This is known as the drift barrier and is related to the nearly neutral theory of molecular evolution . Drift barrier theory predicts that species with large effective population sizes will have highly streamlined, efficient genetic systems, while those with small population sizes will have bloated and complex genomes containing for example introns and transposable elements . [ 79 ] However, somewhat paradoxically, species with large population sizes might be so tolerant to the consequences of certain types of errors that they evolve higher error rates, e.g. in transcription and translation , than small populations. [ 80 ] | https://en.wikipedia.org/wiki/Population_genetics |
The population index , or r-value, indicates the magnitude distribution of a meteor shower . Values below 2.5 correspond to distributions where bright meteors are more frequent than average, while values above 3.0 mean that the share of faint meteors is larger than usual. [ 1 ] Population indices are not solely associated with meteor showers.
This meteoroid-, meteor-, or meteorite-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Population_index |
The field of population informatics is the systematic study of populations via secondary analysis of massive data collections (termed " big data ") about people. Scientists in the field refer to this massive data collection as the social genome , denoting the collective digital footprint of our society. Population informatics applies data science to social genome data to answer fundamental questions about human society and population health much like bioinformatics applies data science to human genome data to answer questions about individual health. It is an emerging research area at the intersection of SBEH (Social, Behavioral, Economic, & Health) sciences, computer science, and statistics in which quantitative methods and computational tools are used to answer fundamental questions about our society.
The term was first used in August 2012 when the Population Informatics Lab was founded at the University of North Carolina at Chapel Hill by Dr. Hye-Cung Kum. The term was first defined in a peer reviewed article in 2013 [ 1 ] and further elaborated on in another article in 2014. [ 2 ] The first Workshop on Population Informatics for Big Data was held at the ACM SIGKDD conference in Sydney, Australia, in August 2015.
To study social, behavioral, economic, and health sciences using the massive data collections, aka social genome data, about people. The primary goal of population informatics is to increase the understanding of social processes by developing and applying computationally intensive techniques to the social genome data. [ citation needed ]
Some of the important sub-disciplines are : [ citation needed ]
Record Linkage , the task of finding records in a dataset that refer to the same entity across different data sources, is a major activity in the population informatics field because most of the digital traces about people are fragmented in many heterogeneous databases that need to be linked before analysis can be done. [ citation needed ]
Once relevant datasets are linked, the next task is usually to develop valid meaningful measures to answer the research question. Often developing measures involves iterating between inductive and deductive approaches with the data and research question until usable measures are developed because the data were collected for other purposes with no intended use to answer the question at hand. Developing meaningful and useful measures from existing data is a major challenge in many research projects. In computation fields, these measures are often called features. [ citation needed ]
Finally, with the datasets linked and required measures developed, the analytic dataset is ready for analysis. Common analysis methods include traditional hypothesis driven research as well more inductive approaches such as data science and predictive analytics .
Computational social science refers to the academic sub-disciplines concerned with computational approaches to the social sciences. This means that computers are used to model, simulate, and analyze social phenomena. Fields include computational economics and computational sociology . The seminal article on computational social science is by Lazer et al. 2009 [ 3 ] which was a summary of a workshop held at Harvard with the same title. However, the article does not define the term computational social science precisely.
In general, computational social science is a broader field and encompasses population informatics. Besides population informatics, it also includes complex simulations of social phenomena. Often complex simulation models use results from population informatics to configure with real world parameters. [ citation needed ]
Data Science for Social Good (DSSG) is another similar field coming about. But again, DSSG is a bigger field applying data science to any social problem that includes study of human populations but also many problems that do not use any data about people. [ citation needed ]
Population reconstruction is the multi-disciplinary field to reconstruct specific (historical) populations by linking data from diverse sources, leading to rich novel resources for study by social scientists. [ 4 ]
The firstWorkshop on Population Informatics for Big Data was held at the ACM SIGKDD conference in Sydney, Australia, in 2015. The workshop brought together computer science researchers, as well as public health practitioners and researchers. This Wikipedia page started at the workshop.
The International Population Data Linkage Network (IPDLN) facilitates communication between centres that specialize in data linkage and users of the linked data. The producers and users alike are committed to the systematic application of data linkage to produce community benefit in the population and health-related domains.
Three major challenges specific to population informatics are: | https://en.wikipedia.org/wiki/Population_informatics |
In physics , specifically statistical mechanics , a population inversion occurs when a system (such as a group of atoms or molecules ) exists in a state in which more members of the system are in higher, excited states than in lower, unexcited energy states . It is called an "inversion" because in many familiar and commonly encountered physical systems in thermal equilibrium , this is not possible. This concept is of fundamental importance in laser science because the production of a population inversion is a necessary step in the workings of a standard laser .
To understand the concept of a population inversion, it is necessary to understand some thermodynamics and the way that light interacts with matter . To do so, it is useful to consider a very simple assembly of atoms forming a laser medium .
Assume there is a group of N atoms, each of which is capable of being in one of two energy states : either
The number of these atoms which are in the ground state is given by N 1 , and the number in the excited state N 2 . Since there are N atoms in total,
The energy difference between the two states, given by
determines the characteristic frequency ν 12 {\textstyle \nu _{12}} of light which will interact with the atoms; This is given by the relation
h being the Planck constant .
If the group of atoms is in thermal equilibrium , it can be shown from Maxwell–Boltzmann statistics that the ratio of the number of atoms in each state is given by the ratio of two Boltzmann distributions , the Boltzmann factor:
where T is the thermodynamic temperature of the group of atoms, k is the Boltzmann constant and g 1 and g 2 are the degeneracies of each state.
Calculable is the ratio of the populations of the two states at room temperature ( T ≈ 300 K ) for an energy difference Δ E that corresponds to light of a frequency corresponding to visible light ( ν ≈ 5 × 10 14 Hz ). In this case Δ E = E 2 − E 1 ≈ 2.07 eV, and kT ≈ 0.026 eV. Since E 2 − E 1 ≫ kT , it follows that the argument of the exponential in the equation above is a large negative number, and as such N 2 / N 1 is vanishingly small; i.e., there are almost no atoms in the excited state. When in thermal equilibrium, then, it is seen that the lower energy state is more populated than the higher energy state, and this is the normal state of the system. As T increases, the number of electrons in the high-energy state ( N 2 ) increases, but N 2 never exceeds N 1 for a system at thermal equilibrium; rather, at infinite temperature, the populations N 2 and N 1 become equal. In other words, a population inversion ( N 2 / N 1 > 1 ) can never exist for a system at thermal equilibrium. To achieve population inversion therefore requires pushing the system into a non-equilibrated state.
There are three types of possible interactions between a system of atoms and light that are of interest:
If light ( photons ) of frequency ν 12 passes through the group of atoms, there is a possibility of the light being absorbed by electrons which are in the ground state, which will cause them to be excited to the higher energy state. The rate of absorption is proportional to the radiation density of the light, and also to the number of atoms currently in the ground state, N 1 .
If atoms are in the excited state, spontaneous decay events to the ground state will occur at a rate proportional to N 2 , the number of atoms in the excited state. The energy difference between the two states Δ E 21 is emitted from the atom as a photon of frequency ν 21 as given by the frequency-energy relation above.
The photons are emitted stochastically , and there is no fixed phase relationship between photons emitted from a group of excited atoms; in other words, spontaneous emission is incoherent . In the absence of other processes, the number of atoms in the excited state at time t , is given by
where N 2 (0) is the number of excited atoms at time t = 0, and τ 21 is the mean lifetime of the transition between the two states.
If an atom is already in the excited state, it may be agitated by the passage of a photon that has a frequency ν 21 corresponding to the energy gap Δ E of the excited state to ground state transition. In this case, the excited atom relaxes to the ground state, and it produces a second photon of frequency ν 21 . The original photon is not absorbed by the atom, and so the result is two photons of the same frequency. This process is known as stimulated emission .
Specifically, an excited atom will act like a small electric dipole which will oscillate with the external field provided. One of the consequences of this oscillation is that it encourages electrons to decay to the lowest energy state. When this happens due to the presence of the electromagnetic field from a photon, a photon is released in the same phase and direction as the "stimulating" photon, and is called stimulated emission.
The rate at which stimulated emission occurs is proportional to the number of atoms N 2 in the excited state, and the radiation density of the light. The base probability of a photon causing stimulated emission in a single excited atom was shown by Albert Einstein to be exactly equal to the probability of a photon being absorbed by an atom in the ground state. Therefore, when the numbers of atoms in the ground and excited states are equal, the rate of stimulated emission is equal to the rate of absorption for a given radiation density.
The critical detail of stimulated emission is that the induced photon has the same frequency and phase as the incident photon. In other words, the two photons are coherent . It is this property that allows optical amplification , and the production of a laser system. During the operation of a laser, all three light-matter interactions described above are taking place. Initially, atoms are energized from the ground state to the excited state by a process called pumping , described below. Some of these atoms decay via spontaneous emission, releasing incoherent light as photons of frequency, ν . These photons are fed back into the laser medium, usually by an optical resonator . Some of these photons are absorbed by the atoms in the ground state, and the photons are lost to the laser process. However, some photons cause stimulated emission in excited-state atoms, releasing another coherent photon. In effect, this results in optical amplification .
If the number of photons being amplified per unit time is greater than the number of photons being absorbed, then the net result is a continuously increasing number of photons being produced; the laser medium is said to have a gain of greater than unity.
Recall from the descriptions of absorption and stimulated emission above that the rates of these two processes are proportional to the number of atoms in the ground and excited states, N 1 and N 2 , respectively. If the ground state has a higher population than the excited state ( N 1 > N 2 ), then the absorption process dominates, and there is a net attenuation of photons. If the populations of the two states are the same ( N 1 = N 2 ), the rate of absorption of light exactly balances the rate of emission; the medium is then said to be optically transparent .
If the higher energy state has a greater population than the lower energy state ( N 1 < N 2 ), then the emission process dominates, and light in the system undergoes a net increase in intensity. It is thus clear that to produce a faster rate of stimulated emissions than absorptions, it is required that the ratio of the populations of the two states is such that N 2 / N 1 > 1; In other words, a population inversion is required for laser operation.
Many transitions involving electromagnetic radiation are strictly forbidden under quantum mechanics. The allowed transitions are described by so-called selection rules , which describe the conditions under which a radiative transition is allowed. For instance, transitions are only allowed if Δ S = 0, S being the total spin angular momentum of the system. In real materials, other effects, such as interactions with the crystal lattice, intervene to circumvent the formal rules by providing alternate mechanisms. In these systems, the forbidden transitions can occur, but usually at slower rates than allowed transitions. A classic example is phosphorescence where a material has a ground state with S = 0, an excited state with S = 0, and an intermediate state with S = 1. The transition from the intermediate state to the ground state by emission of light is slow because of the selection rules. Thus emission may continue after the external illumination is removed. In contrast fluorescence in materials is characterized by emission which ceases when the external illumination is removed.
Transitions that do not involve the absorption or emission of radiation are not affected by selection rules. The radiationless transition between levels, such as between the excited S = 0 and S = 1 states, may proceed quickly enough to siphon off a portion of the S = 0 population before it spontaneously returns to the ground state.
The existence of intermediate states in materials is essential to the technique of optical pumping of lasers (see below).
A population inversion is required for laser operation, but cannot be achieved in the above theoretical group of atoms with two energy-levels when they are in thermal equilibrium. In fact, any method by which the atoms are directly and continuously excited from the ground state to the excited state (such as optical absorption) will eventually reach equilibrium with the de-exciting processes of spontaneous and stimulated emission. At best, an equal population of the two states, N 1 = N 2 = N /2, can be achieved, resulting in optical transparency but no net optical gain.
To achieve lasting non-equilibrium conditions, an indirect method of populating the excited state must be used. To understand how this is done, consider a slightly more realistic model, that of a three-level laser . Again consider a group of N atoms, this time with each atom able to exist in any of three energy states, levels 1, 2 and 3, with energies E 1 , E 2 , and E 3 , and populations N 1 , N 2 , and N 3 , respectively.
Assume E 1 < E 2 < E 3 ; that is, the energy of level 2 lies between that of the ground state and level 3.
Initially, the system of atoms is at thermal equilibrium, and the majority of the atoms will be in the ground state, i.e., N 1 ≈ N , N 2 ≈ N 3 ≈ 0 . If the atoms are subjected to light of a frequency ν 13 = 1 h ( E 3 − E 1 ) {\displaystyle \scriptstyle \nu _{13}\,=\,{\frac {1}{h}}\left(E_{3}-E_{1}\right)} , the process of optical absorption will excite electrons from the ground state to level 3. This process is called pumping , and does not necessarily always directly involve light absorption; other methods of exciting the laser medium, such as electrical discharge or chemical reactions, may be used. The level 3 is sometimes referred to as the pump level or pump band , and the energy transition E 1 → E 3 as the pump transition , which is shown as the arrow marked P in the diagram on the right.
Upon pumping the medium, an appreciable number of atoms will transition to level 3, such that N 3 > 0 . To have a medium suitable for laser operation, it is necessary that these excited atoms quickly decay to level 2. The energy released in this transition may be emitted as a photon (spontaneous emission), however in practice the 3 → 2 transition called the Auger effect (labeled R in the diagram) is usually radiationless , with the energy being transferred to vibrational motion ( heat ) of the host material surrounding the atoms, without the generation of a photon.
An electron in level 2 may decay by spontaneous emission to the ground state, releasing a photon of frequency ν 12 (given by E 2 − E 1 = hν 12 ), which is shown as the transition L , called the laser transition in the diagram. If the lifetime of this transition, τ 21 is much longer than the lifetime of the radiationless 3 → 2 transition τ 32 (if τ 21 ≫ τ 32 , known as a favourable lifetime ratio ), the population of the E 3 will be essentially zero ( N 3 ≈ 0 ) and a population of excited state atoms will accumulate in level 2 ( N 2 > 0 ). If over half the N atoms can be accumulated in this state, this will exceed the population of the ground state N 1 . A population inversion ( N 2 > N 1 ) has thus been achieved between level 1 and 2, and optical amplification at the frequency ν 21 can be obtained.
Because at least half the population of atoms must be excited from the ground state to obtain a population inversion, the laser medium must be very strongly pumped. This makes three-level lasers rather inefficient, despite being the first type of laser to be discovered (based on a ruby laser medium, by Theodore Maiman in 1960). A three-level system could also have a radiative transition between level 3 and 2, and a non-radiative transition between 2 and 1. In this case, the pumping requirements are weaker. In practice, most lasers are four-level lasers , described below.
Here, there are four energy levels, energies E 1 , E 2 , E 3 , E 4 , and populations N 1 , N 2 , N 3 , N 4 , respectively. The energies of each level are such that E 1 < E 2 < E 3 < E 4 .
In this system, the pumping transition P excites the atoms in the ground state (level 1) into the pump band (level 4). From level 4, the atoms again decay by a fast, non-radiative transition Ra into the level 3. Since the lifetime of the laser transition L is long compared to that of Ra ( τ 32 ≫ τ 43 ), a population accumulates in level 3 (the upper laser level ), which may relax by spontaneous or stimulated emission into level 2 (the lower laser level ). This level likewise has a fast, non-radiative decay Rb into the ground state.
As before, the presence of a fast, radiationless decay transition results in the population of the pump band being quickly depleted ( N 4 ≈ 0). In a four-level system, any atom in the lower laser level E 2 is also quickly de-excited, leading to a negligible population in that state ( N 2 ≈ 0). This is important, since any appreciable population accumulating in level 3, the upper laser level, will form a population inversion with respect to level 2. That is, as long as N 3 > 0, then N 3 > N 2 , and a population inversion is achieved. Thus optical amplification, and laser operation, can take place at a frequency of ν 32 ( E 3 − E 2 = hν 32 ).
Since only a few atoms must be excited into the upper laser level to form a population inversion, a four-level laser is much more efficient than a three-level one, and most practical lasers are of this type. In reality, many more than four energy levels may be involved in the laser process, with complex excitation and relaxation processes involved between these levels. In particular, the pump band may consist of several distinct energy levels, or a continuum of levels, which allow optical pumping of the medium over a wide range of wavelengths.
Note that in both three- and four-level lasers, the energy of the pumping transition is greater than that of the laser transition. This means that, if the laser is optically pumped, the frequency of the pumping light must be greater than that of the resulting laser light. In other words, the pump wavelength is shorter than the laser wavelength. It is possible in some media to use multiple photon absorptions between multiple lower-energy transitions to reach the pump level; such lasers are called up-conversion lasers.
While in many lasers the laser process involves the transition of atoms between different electronic energy states, as described in the model above, this is not the only mechanism that can result in laser action. For example, there are many common lasers (e.g., dye lasers , carbon dioxide lasers ) where the laser medium consists of complete molecules, and energy states correspond to vibrational and rotational modes of oscillation of the molecules. This is the case with water masers , that occur in nature .
In some media it is possible, by imposing an additional optical or microwave field, to use quantum coherence effects to reduce the likelihood of a ground-state to excited-state transition. This technique, known as lasing without inversion , allows optical amplification to take place without producing a population inversion between the two states.
Stimulated emission was first observed in the microwave region of the electromagnetic spectrum, giving rise to the acronym MASER for Microwave Amplification by Stimulated Emission of Radiation. In the microwave region, the Boltzmann distribution of molecules among energy states is such that, at room temperature, all states are populated almost equally.
To create a population inversion under these conditions, it is necessary to selectively remove some atoms or molecules from the system based on differences in properties. For instance, in a hydrogen maser , the well-known 21cm wave transition in atomic hydrogen , where the lone electron flips its spin state from parallel to the nuclear spin to antiparallel, can be used to create a population inversion because the parallel state has a magnetic moment and the antiparallel state does not. A strong inhomogeneous magnetic field will separate atoms in the higher energy state from a beam of mixed-state atoms. The separated population represents a population inversion that can exhibit stimulated emissions. | https://en.wikipedia.org/wiki/Population_inversion |
In statistics a population proportion , generally denoted by P {\displaystyle P} or the Greek letter π {\displaystyle \pi } , [ 1 ] is a parameter that describes a percentage value associated with a population . A census can be conducted to determine the actual value of a population parameter, but often a census is not practical due to its costs and time consumption. For example, the 2010 United States Census showed that 83.7% of the American population was identified as not being Hispanic or Latino; the value of .837 is a population proportion. In general, the population proportion and other population parameters are unknown.
A population proportion is usually estimated through an unbiased sample statistic obtained from an observational study or experiment , resulting in a sample proportion , generally denoted by p ^ {\displaystyle {\hat {p}}} and in some textbooks by p {\displaystyle p} . [ 2 ] [ 3 ] For example, the National Technological Literacy Conference conducted a national survey of 2,000 adults to determine the percentage of adults who are economically illiterate; the study showed that 1,440 out of the 2,000 adults sampled did not understand what a gross domestic product is. [ 4 ] The value of 72% (or 1440/2000) is a sample proportion.
A proportion is mathematically defined as being the ratio of the quantity of elements (a countable quantity ) in a subset S {\displaystyle S} to the size of a set R {\displaystyle R} :
where X {\displaystyle X} is the count of successes in the population, and N {\displaystyle N} is the size of the population.
This mathematical definition can be generalized to provide the definition for the sample proportion:
where x {\displaystyle x} is the count of successes in the sample, and n {\displaystyle n} is the size of the sample obtained from the population. [ 5 ] [ 2 ]
One of the main focuses of study in inferential statistics is determining the "true" value of a parameter. Generally the actual value for a parameter will never be found, unless a census is conducted on the population of study. However, there are statistical methods that can be used to get a reasonable estimation for a parameter. These methods include confidence intervals and hypothesis testing .
Estimating the value of a population proportion can be of great implication in the areas of agriculture, business, economics, education, engineering, environmental studies, medicine, law, political science, psychology, and sociology.
A population proportion can be estimated through the usage of a confidence interval known as a one-sample proportion in the Z-interval whose formula is given below:
where p ^ {\displaystyle {\hat {p}}} is the sample proportion, n {\displaystyle n} is the sample size, and z ∗ {\displaystyle z^{*}} is the upper 1 − C 2 {\displaystyle {\frac {1-C}{2}}} critical value of the standard normal distribution for a level of confidence C {\displaystyle C} . [ 6 ]
To derive the formula for the one-sample proportion in the Z-interval , a sampling distribution of sample proportions needs to be taken into consideration. The mean of the sampling distribution of sample proportions is usually denoted as μ p ^ = P {\displaystyle \mu _{\hat {p}}=P} and its standard deviation is denoted as: [ 2 ]
Since the value of P {\displaystyle P} is unknown, an unbiased statistic p ^ {\displaystyle {\hat {p}}} will be used for P {\displaystyle P} . The mean and standard deviation are rewritten respectively as:
Invoking the central limit theorem , the sampling distribution of sample proportions is approximately normal —provided that the sample is reasonably large and unskewed.
Suppose the following probability is calculated:
where 0 < C < 1 {\displaystyle 0<C<1} and ± z ∗ {\displaystyle \pm z^{*}} are the standard critical values.
The inequality
can be algebraically re-written as follows:
From the algebraic work done above, it is evident from a level of certainty C {\displaystyle C} that P {\displaystyle P} could fall in between the values of:
In general the formula used for estimating a population proportion requires substitutions of known numerical values. However, these numerical values cannot be "blindly" substituted into the formula because statistical inference requires that the estimation of an unknown parameter be justifiable. For a parameter's estimation to be justifiable, there are three conditions that need to be verified:
The conditions for SRS, normality, and independence are sometimes referred to as the conditions for the inference tool box in most statistical textbooks. For a more detailed look into regions where this simplification is not used look to ( https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Jeffreys_interval )
Suppose a presidential election is taking place in a democracy. A random sample of 400 eligible voters in the democracy's voter population shows that 272 voters support candidate B. A political scientist wants to determine what percentage of the voter population support candidate B.
To answer the political scientist's question, a one-sample proportion in the Z-interval with a confidence level of 95% can be constructed in order to determine the population proportion of eligible voters in this democracy that support candidate B.
It is known from the random sample that p ^ = 272 400 = 0.68 {\displaystyle {\hat {p}}={\frac {272}{400}}=0.68} with sample size n = 400 {\displaystyle n=400} . Before a confidence interval is constructed, the conditions for inference will be verified.
With the conditions for inference verified, it is permissible to construct a confidence interval.
Let p ^ = 0.68 , n = 400 , {\displaystyle {\hat {p}}=0.68,n=400,} and C = 0.95 {\displaystyle C=0.95}
To solve for z ∗ {\displaystyle z^{*}} , the expression 1 − C 2 {\displaystyle {\frac {1-C}{2}}} is used.
1 − C 2 = 1 − 0.95 2 = 0.05 2 = 0.0250 {\displaystyle {\frac {1-C}{2}}={\frac {1-0.95}{2}}={\frac {0.05}{2}}=0.0250}
By examining a standard normal bell curve, the value for z ∗ {\displaystyle z^{*}} can be determined by identifying which standard score gives the standard normal curve an upper tail area of 0.0250 or an area of 1 – 0.0250 = 0.9750. The value for z ∗ {\displaystyle z^{*}} can also be found through a table of standard normal probabilities.
From a table of standard normal probabilities, the value of Z {\displaystyle Z} that gives an area of 0.9750 is 1.96. Hence, the value for z ∗ {\displaystyle z^{*}} is 1.96.
The values for p ^ = 0.68 {\displaystyle {\hat {p}}=0.68} , n = 400 {\displaystyle n=400} , z ∗ = 1.96 {\displaystyle z^{*}=1.96} can now be substituted into the formula for one-sample proportion in the Z-interval:
p ^ ± z ∗ p ^ ( 1 − p ^ ) n ⇒ ( 0.68 ) ± ( 1.96 ) ( 0.68 ) ( 1 − 0.68 ) ( 400 ) ⇒ 0.68 ± 1.96 0.000544 {\displaystyle {\hat {p}}\pm z^{*}{\sqrt {\frac {{\hat {p}}(1-{\hat {p}})}{n}}}\Rightarrow (0.68)\pm (1.96){\sqrt {\frac {(0.68)(1-0.68)}{(400)}}}\Rightarrow 0.68\pm 1.96{\sqrt {0.000544}}} ⇒ ( 0.63429 , 0.72571 ) {\displaystyle \Rightarrow {\bigl (}0.63429,0.72571{\bigr )}}
Based on the conditions of inference and the formula for the one-sample proportion in the Z-interval, it can be concluded with a 95% confidence level that the percentage of the voter population in this democracy supporting candidate B is between 63.429% and 72.571%.
A commonly asked question in inferential statistics is whether the parameter is included within a confidence interval. The only way to answer this question is for a census to be conducted. Referring to the example given above, the probability that the population proportion is in the range of the confidence interval is either 1 or 0. That is, the parameter is included in the interval range or it is not. The main purpose of a confidence interval is to better illustrate what the ideal value for a parameter could possibly be.
A very common error that arises from the construction of a confidence interval is the belief that the level of confidence, such as C = 95 % {\displaystyle C=95\%} , means 95% chance. This is incorrect. The level of confidence is based on a measure of certainty, not probability. Hence, the values of C {\displaystyle C} fall between 0 and 1, exclusively.
A more precise estimate of P can be obtained by choosing ranked set sampling instead of simple random sampling [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Population_proportion |
Population viability analysis ( PVA ) is a species -specific method of risk assessment frequently used in conservation biology .
It is traditionally defined as the process that determines the probability that a population will go extinct within a given number of years.
More recently, PVA has been described as a marriage of ecology and statistics that brings together species characteristics and environmental variability to forecast population health and extinction risk. Each PVA is individually developed for a target population or species, and consequently, each PVA is unique. The larger goal in mind when conducting a PVA is to ensure that the population of a species is self-sustaining over the long term. [ 1 ]
Population viability analysis (PVA) is used to estimate the likelihood of a population’s extinction and indicate the urgency of recovery efforts, and identify key life stages or processes that should be the focus of recovery efforts. PVA is also used to identify factors that drive population dynamics, compare proposed management options and assess existing recovery efforts. [ 2 ] PVA is frequently used in endangered species management to develop a plan of action, rank the pros and cons of different management scenarios, and assess the potential impacts of habitat loss. [ 3 ]
In the 1970s, Yellowstone National Park was the centre of a heated debate over different proposals to manage the park’s problem grizzly bears ( Ursus arctos ). In 1978, Mark Shaffer proposed a model for the grizzlies that incorporated random variability, and calculated extinction probabilities and minimum viable population size. [ 4 ] The first PVA is credited to Shaffer. [ 4 ]
PVA gained popularity in the United States as federal agencies and ecologists required methods to evaluate the risk of extinction and possible outcomes of management decisions, particularly in accordance with the Endangered Species Act of 1973, and the National Forest Management Act of 1976.
In 1986, Gilpin and Soulé broadened the PVA definition to include the interactive forces that affect the viability of a population, including genetics.
The use of PVA increased dramatically in the late 1980s and early 1990s following advances in personal computers and software packages.
The endangered Fender's blue butterfly ( Icaricia icarioides ) was recently assessed with a goal of providing additional information to the United States Fish and Wildlife Service , which was developing a recovery plan for the species. The PVA concluded that the species was more at risk of extinction than previously thought and identified key sites where recovery efforts should be focused. The PVA also indicated that because the butterfly populations fluctuate widely from year to year, to prevent the populations from going extinct the minimum annual population growth rate must be kept much higher than at levels typically considered acceptable for other species. [ 5 ]
Following a recent outbreak of canine distemper virus, a PVA was performed for the critically endangered island fox ( Urocyon littoralis ) of Santa Catalina Island, California . The Santa Catalina island fox population is uniquely composed of two subpopulations that are separated by an isthmus , with the eastern subpopulation at greater risk of extinction than the western subpopulation. PVA was conducted with the goals of 1) evaluating the island fox’s extinction risk, 2) estimating the island fox’s sensitivity to catastrophic events, and 3) evaluating recent recovery efforts which include release of captive-bred foxes and transport of wild juvenile foxes from the west to the east side. Results of the PVA concluded that the island fox is still at significant risk of extinction, and is highly susceptible to catastrophes that occur more than once every 20 years. Furthermore, extinction risks and future population sizes on both sides of the island were significantly dependent on the number of foxes released and transported each year. [ 6 ]
PVAs in combination with sensitivity analysis can also be used to identify which vital rates has the relative greatest effect on population growth and other measures of population viability. For example, a study by Manlik et al. (2016) forecast the viability of two bottlenose dolphin populations in Western Australia and identified reproduction as having the greatest influence on the forecast of these populations. One of the two populations was forecast to be stable, whereas the other population was forecast to decline, if it isolated from other populations and low reproductive rates persist. The difference in viability between the two studies was primarily due to differences in reproduction and not survival. The study also showed that temporal variation in reproduction had a greater effect on population growth than temporal variation in survival. [ 7 ]
Debates exist and remain unresolved over the appropriate uses of PVA in conservation biology and PVA’s ability to accurately assess extinction risks.
A large quantity of field data is desirable for PVA; some conservatively estimate that for a precise extinction probability assessment extending T years into the future, five-to-ten times T years of data are needed. Datasets of such magnitude are typically unavailable for rare species; it has been estimated that suitable data for PVA is available for only 2% of threatened bird species. PVA for threatened and endangered species is particularly a problem as the predictive power of PVA plummets dramatically with minimal datasets. Ellner et al. (2002) argued that PVA has little value in such circumstances and is best replaced by other methods. Others argue that PVA remains the best tool available for estimations of extinction risk, especially with the use of sensitivity model runs.
Even with an adequate dataset, it is possible that a PVA can still have large errors in extinction rate predictions. It is impossible to incorporate all future possibilities into a PVA: habitats may change, catastrophes may occur, new diseases may be introduced. PVA utility can be enhanced by multiple model runs with varying sets of assumptions including the forecast future date. Some prefer to use PVA always in a relative analysis of benefits of alternative management schemes, such as comparing proposed resource management plans.
Accuracy of PVAs has been tested in a few retrospective studies. For example, a study comparing PVA model forecasts with the actual fate of 21 well-studied taxa, showed that growth rate projections are accurate, if input variables are based on sound data, but highlighted the importance of understanding density-dependence (Brook et al. 2000). [ 8 ] Also, McCarthey et al. (2003) [ 9 ] showed that PVA predictions are relatively accurate, when they are based on long-term data. Still, the usefulness of PVA lies more in its capacity to identify and assess potential threats, than in making long-term, categorical predictions (Akçakaya & Sjögren-Gulve 2000). [ 10 ]
Improvements to PVA likely to occur in the near future include: 1) creating a fixed definition of PVA and scientific standards of quality by which all PVA are judged and 2) incorporating recent genetic advances into PVA. [ citation needed ] | https://en.wikipedia.org/wiki/Population_viability_analysis |
Pore-C is a genomic technique [ 1 ] [ 2 ] [ 3 ] which utilizes chromatin conformation capture (3C) and Oxford Nanopore Technologies ' (ONT) long-read sequencing to characterize three-dimensional (3D) chromatin structure. To characterize concatemers , the originators of Pore-C developed an algorithm to identify alignments that are assigned to a restriction fragment ; concatemers with greater than two associated fragments are deemed high order. [ 2 ] Pore-C attempts to improve on previous 3C technologies, such as Hi-C and SPRITE, by not requiring DNA amplification prior to sequencing. [ 2 ] This technology was developed as a simpler and more easily scalable method of capturing higher-order chromatin structure and mapping regions of chromatin contact. In addition, Pore-C can be used to visualize epigenomic interactions due to the capability of ONT long-read sequencing to detect DNA methylation . Applications of this technology include analysis of combinatorial chromatin interactions, the generation of de novo chromosome scale assemblies, visualization of regions associated with multi-locus histone bodies, and detection and resolution of structural variants . [ 2 ]
Although the DNA within eukaryotic cells is linear, it is also intricately folded and packaged to fit within each cell’s nucleus . [ 4 ] [ 5 ] Thus, specific parts of the genome may be closer in physical space than would otherwise appear to be based on DNA sequence alone. The 3D genome refers to how DNA is spatially organized within cells. [ 4 ] [ 5 ] The 3D structures found in the genome include active and inactive chromatin, chromatin loops, and topologically associated domains (TADs). These structures function to regulate gene expression . In genomic and epigenomic research, chromatin structure is most often visualized by 3C techniques, [ 5 ] which quantify interactions between loci to construct a 3D map. The fundamental 3C technique is used to quantify interactions between pairs of genomic loci. Methods that are derived from this technique, such as 4C, 5C, and Hi-C assays, allow quantification of pairwise interactions between multiple loci. [ 6 ] Other variations, such as ChIP -loop [ 6 ] and ChIA-PET , [ 7 ] combine 3C with immunoprecipitation assays to detect interactions mediated by a protein of interest. These techniques all involve an amplification step, most often using polymerase chain reaction (PCR). A limitation of most current 3D chromatin assays is that they are less useful to categorize interactions between more than two loci, and Pore-C was developed to fill this gap in technology. [ 2 ] Additionally, not requiring PCR amplification simplifies the workflow, therefore Pore-C is intended to be simpler and more easily scalable than previous techniques. Pore-C can also be used in populations of cells to characterize topology polymorphisms at specific loci. [ 2 ]
Many methods to characterize the 3D genome are variations on 3C technology. [ 5 ] Like other 3C-based technologies, [ 5 ] Pore-C seeks to characterize the architecture of the 3D genome by determining which genomic loci are in close spatial proximity (within ~200 nm). [ 2 ] Similar to previous 3C-based methods, [ 5 ] Pore-C relies on crosslinking, restriction enzyme digestion, proximity ligation, reverse cross-linking, and protein degradation steps. [ 2 ] However, Pore-C is distinct from many previous methods in its subsequent utilization of ONT long-read sequencing, which facilitates the resolution of multi-way chromosome contacts and simultaneous detection of DNA methylation [ 2 ] [ 3 ]
First, in order to preserve the 3D structure of the genome from degradation in subsequent steps, DNA is cross-linked to DNA-associated proteins, such as histones . [ 2 ] Formaldehyde is used for cross-linking, as it joins DNA to proteins with covalent bonds, thus temporarily locking the 3D genome in place. [ 8 ] Specifically, after a series of washes with phosphate-buffered saline (PBS), cells are pelletted with centrifugation, and then resuspended in a formaldehyde and PBS solution. Following a short incubation period, glycine is added to stop the cross-linking reaction. [ 8 ] [ 2 ] By quenching the excess formaldehyde, glycine prevents the reaction from going to completion, thereby maximizing the efficiency of later steps and ensuring the cross-linking reaction is reversible. [ 8 ]
Cross-linking generates loops of DNA, with each loop arising from a separate locus. [ 5 ] To capture long-range interactions between distant loci, potentially from different chromosomes, these loops are first cut and then re-joined back together based on proximity. Although fragments deriving from the same loop may reanneal back together, sometimes fragments from separate loops will ligate together, thus creating chimeric sequences. [ 5 ] The cutting and rejoining of DNA is achieved by the in situ restriction enzyme digestion and proximity ligation steps respectively. Specifically, a restriction endonuclease cuts the DNA to create free ends, whereas T4 ligase is used to join fragments together. [ 5 ] Ultimately, these steps result in genomic loci close together in physical space being linked together on contiguous DNA segments referred to as concatemers. [ 2 ]
Next, in order to isolate DNA for sequencing, proteins bound to the DNA have to be detached and degraded. [ 5 ] First, Proteinase K, sodium dodecyl sulfate (SDS; a detergent), Tween-20, and nuclease-free water are added. [ 2 ] Subsequently, the reaction is heated to 56 °C in a thermocycler for optimal reaction kinetics. Proteinase K degrades proteins, and SDS acts a denaturing agent that disrupts protein structure. [ 9 ] [ 10 ] This reaction results in the breakage of covalent bonds between DNA and protein and removes potential protein contamination. [ 5 ] DNA is then isolated and purified, typically using phenol-chloroform extraction followed by ethanol precipitation. [ 2 ]
Pore-C concatemers undergo size selection prior to library preparation and ONT long-read sequencing. [ 2 ] Via size selection, Pore-C is able to detect high-order interactions, which are defined as concatemers containing greater than two DNA fragments. Specifically, Pore-C size selection enriches for DNA sequences greater than 1.5 kb, thereby filtering out shorter concatemers unlikely to contain greater than two fragments. [ 2 ] Many size selection methods have been developed for ONT long-read sequencing. [ 11 ] For example, Solid Phase Reversible Immobilisation (SPRI) size selection has been used in the Pore-C literature. [ 2 ] [ 3 ] Following size selection, library preparation for ONT long-read sequencing is performed, usually with a ligation sequencing kit provided by ONT. Key steps include DNA repair and adaptor ligation. [ 2 ] [ 3 ] Subsequently, DNA is loaded onto flow cells for sequencing, where each concatemer is fed through a pore, aided by a motor protein. [ 2 ] [ 11 ] Nitrogenous DNA bases are read out by their characteristic disruption of an electric current [ 11 ]
Overall, bioinformatic approaches applied to Pore-C data allow for the inference of pairwise and multi-way contacts between loci. [ 2 ] Since concatemers in Pore-C contain DNA sequences that come from different regions of the genome, aligning sequencing reads to a reference genome is challenging. One solution to this problem involves a bioinformatic pipeline using a greedy piece-wise algorithm. [ 2 ] Further analysis of Pore-C results depends on the study and what other data types are available. [ 3 ]
Pore-C is a relatively new method, so its applications have not yet been fully appreciated. [ 2 ] A strength of Pore-C over previous methods is its ability to detect interactions between more than two genomic loci. Such high-order interactions enable the study of cellular processes, such as gene expression regulation at a more system-level scale. [ 2 ] [ 3 ] With statistical methods, Pore-C data can be used to identify cooperative interactions, wherein high-order interactions are observed at a frequency greater than the sum of their expected pairwise contacts. [ 2 ] In addition, using ONT long reads, Pore-C can detect DNA methylation, thereby providing an additional layer of epigenetic information to analyze. [ 2 ] In the future, Pore-C may be applied to study how the 3D genome changes during developmental processes, such as cellular differentiation. [ 3 ] Additionally, Pore-C may be applied to the study of cancer, where the 3D genome is often structurally rearranged, which can result in aberrant gene transcription via processes such as enhancer hijacking. [ 2 ] | https://en.wikipedia.org/wiki/Pore-C |
Pore pressure gradient is a dimensional petrophysical term used by drilling engineers and mud engineers during the design of drilling programs for drilling (constructing) oil and gas wells into the earth. It is the pressure gradient inside the pore space of the rock column from the surface of the ground down to the total depth (TD), as compared to the pressure gradient of seawater in deep water.
In drilling engineering, the pore pressure gradient is usually expressed in API-type International Association of Drilling Contractors (IADC) physical units of measurement, namely "psi per foot", whereas in " pure math ," the gradient of a scalar function expressed by the math notation grad( f ) may not have physical units associated with it.
In the well-known formula
taught in almost all petroleum engineering courses worldwide, the mud weight (MW) is expressed in pounds per U.S. gallon, and the true vertical depth (TVD) is expressed in feet, and 0.052 is a commonly used conversion constant that can be derived by dimensional analysis:
1 p s i f t × 1 f t 12 i n × 1 l b / i n 2 1 p s i × 231 i n 3 1 U S G a l = 19.25000000 l b / g a l {\displaystyle \mathrm {{\frac {1\;psi}{ft}}\times {\frac {1\;ft}{12\;in}}\times {\frac {1\;lb/in^{2}}{1\;psi}}\times {\frac {231\;in^{3}}{1\;US\;Gal}}=19.25000000\;lb/gal} }
It would be more accurate to divide a value in lb/gal by 19.25 than to multiply that value by 0.052. The magnitude of the error caused by multiplying by 0.052 is approximately 0.1%.
Example: For a column of fresh water of 8.33 pounds per gallon (lb/U.S. gal) standing still hydrostatically in a 21,000 feet vertical cased wellbore from top to bottom (vertical hole), the pressure gradient would be
and the hydrostatic bottom hole pressure (BHP) is then
However, the formation fluid pressure (pore pressure) is usually much greater than a column of fresh water, and can be as much as 19 lb/U.S. gal (e.g., in Iran). For an onshore vertical wellbore with an exposed open hole interval at 21,000 feet with a pore pressure gradient of 19 lb/U.S. gal, the BHP would be
The calculation of a bottom hole pressure and the pressure induced by a static column of fluid are the most important and basic calculations in all well control courses taught worldwide for the prevention of oil and gas well blowouts.
Using the figures above, we can calculate the maximum pressure at various depths in an offshore oil well.
A well with 5,000 feet of seawater and 15,000 feet of rock could have an overburden pressures at the bottom as high as 17,220 psi (5000 * 0.444 + 15000 * 1.0). That pressure is reduced at the surface by the weight of oil and gas the riser pipe, but this is only a small percentage of the total. It takes heavy mud (drilling fluid) inserted at the bottom to control the well when pressures are this high. | https://en.wikipedia.org/wiki/Pore_pressure_gradient |
The pore space of soil contains the liquid and gas phases of soil , i.e., everything but the solid phase that contains mainly minerals of varying sizes as well as organic compounds .
In order to understand porosity better a series of equations have been used to express the quantitative interactions between the three phases of soil.
Macropores or fractures play a major role in infiltration rates in many soils as well as preferential flow patterns, hydraulic conductivity and evapotranspiration. Cracks are also very influential in gas exchange, influencing respiration within soils. Modeling cracks therefore helps understand how these processes work and what the effects of changes in soil cracking such as compaction, can have on these processes.
The pore space of soil may contain the habitat of plants ( rhizosphere ) and microorganisms .
The dry bulk density of a soil greatly depends on the mineral assemblage making up the soil and on its degree of compaction . The density of quartz is around 2.65 g/cm 3 but the dry bulk density of a soil can be less than half that value.
Most soils have a dry bulk density between 1.0 and 1.6 g/cm 3 but organic soil and some porous clays may have a dry bulk density well below 1 g/cm 3 .
Core samples are taken by pushing a metallic cutting edge into the soil at the desired depth or soil horizon .
The soil samples are then oven dried (often at 105 °C) until constant weight.
The dry bulk density of a soil is inversely proportional to its porosity . The more pore space in a soil, the lower its dry bulk density.
or, more generally, for an unsaturated soil in which the pores are filled by two fluids, air and water:
The porosity η {\displaystyle \eta } is a measure of the total pore space in the soil. This is defined as a fraction of volume often given in percent . The amount of porosity in a soil depends on the minerals that make up the soil and on the amount of sorting occurring within the soil structure . For example, a sandy soil will have a larger porosity than a silty sand, because the silt will fill the gaps in between the sand particles.
Hydraulic conductivity (K) is a property of soil that describes the ease with which water can move through pore spaces. It depends on the permeability of the material (pores, compaction) and on the degree of saturation. Saturated hydraulic conductivity, K sat , describes water movement through saturated media. Where hydraulic conductivity has the capability to be measured at any state. It can be estimated by numerous kinds of equipment. To calculate hydraulic conductivity, Darcy's law is used. The manipulation of the law depends on the soil saturation and instrument used.
Infiltration is the process by which water on the ground surface enters the soil. The water enters the soil through the pores by the forces of gravity and capillary action . The largest cracks and pores offer a great reservoir for the initial flush of water. This allows a rapid infiltration . The smaller pores take longer to fill and rely on capillary forces as well as gravity. The smaller pores have a slower infiltration as the soil becomes more saturated .
A pore is not simply a void in the solid structure of soil. The various pore size categories have different characteristics and contribute different attributes to soils depending on the number and frequency of each type. A widely used classification of pore size is that of Brewer (1964): [ 1 ] [ 2 ] [ 3 ]
The pores that are too large to have any significant capillary force. Unless impeded, water will drain from these pores, and they are generally air-filled at field capacity . Macropores can be caused by cracking, division of peds and aggregates , as well as plant roots, and zoological exploration. [ 3 ] Size >75 μm. [ 4 ]
The largest pores filled with water at field capacity . Also known as storage pores because of the ability to store water useful to plants. They do not have capillary forces too great so that the water does not become limiting to the plants. The properties of mesopores are highly studied by soil scientists because of their impact on agriculture and irrigation . [ 3 ] Size 30–75 μm. [ 4 ]
These are "pores that are sufficiently small that water within these pores is considered immobile, but available for plant extraction." [ 3 ] Because there is little movement of water in these pores, solute movement is mainly by the process of diffusion. Size 5–30 μm. [ 4 ]
These pores are suitable for habitation by microorganisms. Their distribution is determined by soil texture and soil organic matter , and they are not greatly affected by compaction. [ 5 ] [ 3 ] Size 0.1–5 μm. [ 4 ]
Pores that are too small to be penetrated by most microorganisms. Organic matter in these pores is therefore protected from microbial decomposition. They are filled with water unless the soil is very dry, but little of this water is available to plants, and water movement is very slow. [ 5 ] [ 3 ] Size <0.1 μm. [ 4 ]
Basic crack modeling has been undertaken for many years by simple observations and measurements of crack size, distribution, continuity and depth. These observations have either been surface observation or done on profiles in pits. Hand tracing and measurement of crack patterns on paper was one method used prior to advances in modern technology. Another field method was with the use of string and a semicircle of wire. [ 6 ] The semi circle was moved along alternating sides of a string line. The cracks within the semicircle were measured for width, length and depth using a ruler. The crack distribution was calculated using the principle of Buffon's needle .
This method relies on the fact that crack sizes have a range of different water potentials. At zero water potential at the soil surface an estimate of saturated hydraulic conductivity is produced, with all pores filled with water. As the potential is decreased progressively larger cracks drain. By measuring at the hydraulic conductivity at a range of negative potentials, the pore size distribution can be determined. While this is not a physical model of the cracks, it does give an indication to the sizes of pores within the soil.
Horgan and Young (2000) produced a computer model to create a two-dimensional prediction of surface crack formation. It used the fact that once cracks come within a certain distance of one another they tend to be attracted to each other. Cracks also tend to turn within a particular range of angles and at some stage a surface aggregate gets to a size that no more cracking will occur. These are often characteristic of a soil and can therefore be measured in the field and used in the model. However it was not able to predict the points at which cracking starts and although random in the formation of crack pattern, in many ways, cracking of soil is often not random, but follows lines of weaknesses. [ 7 ]
A large core sample is collected. This is then impregnated with araldite and a fluorescent resin . The core is then cut back using a grinding implement, very gradually (~1 mm per time), and at every interval the surface of the core sample is digitally imaged. The images are then loaded into a computer where they can be analysed. Depth, continuity, surface area and a number of other measurements can then be made on the cracks within the soil.
Using the infinite resistivity of air, the air spaces within a soil can be mapped. A specially designed resistivity meter had improved the meter-soil contact and therefore the area of the reading. [ 8 ] This technology can be used to produce images that can be analysed for a range of cracking properties. | https://en.wikipedia.org/wiki/Pore_space_in_soil |
Pore structure is a common term employed to characterize the porosity , pore size, pore size distribution, and pore morphology (such as pore shape, surface roughness, and tortuosity of pore channels) of a porous medium . [ 1 ] [ 2 ] Pores are the openings in the surfaces impermeable porous matrix which gases, liquids, or even foreign microscopic particles can inhabit them. [ 3 ] The pore structure and fluid flow in porous media are intimately related.
With micro nanoscale pore radii, complex connectivity, and significant heterogeneity, [ 4 ] the complexity of the pore structure affects the hydraulic conductivity and retention capacity of these fluids. [ 5 ] The intrinsic permeability is the attribute primarily influenced by the pore structure, and the fundamental physical factors governing fluid flow and distribution are the grain surface-to-volume ratio and grain shape. [ 6 ]
The idea that the pore space is made up of a network of channels through which fluid can flow is particularly helpful. Pore openings are the comparatively thin sections that divide the relatively large portions known as pore bodies. Other anatomical analogies include "belly" or "waist" for the broad region of a pore and "neck" or "throat" for the constrictive part. Pore bodies are the intergranular gaps with dimensions that are generally significantly smaller than those of the surrounding particles in a medium where textural pore space predominates, such as sand. On the other hand, a wormhole [ 7 ] can be regarded as a single pore if its diameter is practically constant over its length.
Such pores can have one of three types of boundaries: (1) constriction, which is a plane across the locally narrowest part of the pore space; (2) interface with another pore (such as a wormhole or crack); or (3) interface with solid. [ 8 ]
The proportion of empty space in a porous media is called porosity . [ 9 ] It is determined by dividing the volume of the pores or voids by the overall volume. It is expressed as a percentage or as a decimal fraction between 0 and 1. Porosity for the majority of rocks ranges from less than 1% to 40%.
Porosity influences fluid storage in geothermal systems, oil and gas fields, and aquifers , making it evident that it plays a significant role in geology . Fluid movement and transport across geological formations, as well as the link between the bulk properties of the rock and the characteristics of particular minerals, are controlled by the size and connectivity of the porous structure. [ 10 ]
The samples' total volume and pore space volume were measured in order to calculate the porosities.
Measuring pore space volume
A helium pyrometer was used to calculate the volume of the pores and relied on Boyle's law . (P 1 V 1 =P 2 V 2 ) and helium gas, which easily passes through tiny holes and is inert, to identify the solid fraction of a sample. A sample chamber with a known volume is where the core is put. Pressure is applied to a reference chamber with a known volume. The helium gas may now go from the reference chamber to the sample chamber thanks to the connection between the two rooms. The volume of the sample solid is calculated using the ratio between the starting and final pressures. The pore volume, as calculated by the helium pycnometer, is the difference between the total volume and the solid volume. [ 11 ]
Typically, the effective radius of the pore body or neck is used to define the size of pores. [ 8 ] The position, shape, and connection of pores in solids are only a few of their numerous attributes and the most straightforward aspect of a pore to visualize is likely its size, or its extent in a single spatial dimension .
In comparison to other factors like pore shape, it is arguable that pore size has the biggest or broadest impact on the characteristics of solids. Therefore, using pore size or pore size distribution to describe and contrast various porous substances is definitely convenient and valuable. [ 12 ]
The three main pore size ranges (The current classification of pore size recommended by the International Union of Pure and Applied Chemistry) are as following: [ 12 ]
The relative abundance of each pore size in a typical volume of soil is represented by the pore size distribution. It is represented by the function f(r), whose value is proportional to the total volume of all pores whose effective radius is within an infinitesimal range centered on r. And f(r) can be thought to have textural and structural components. [ 8 ]
Mercury intrusion porosimetry [ 13 ] and gas adsorption [ 14 ] are common techniques for determining the pore size distribution of materials and power sources.
When studying the pore size distribution using the gas adsorption technique utilizing the nitrogen or argon adsorption isotherm at their boiling temperatures, it is possible to determine the pore size from the molecular level to a few hundred nm. The pressure sensor 's precise constraints and the coolant's temperature stability result in a maximum observed pore size of just a little bit more than 100 nm in a realistic environment. [ 15 ]
Mercury porosimetry determines the pore size distribution and quantifies the associated incursion amount by applying pressure to the non-wetting mercury. The pore size may be readily estimated using this method and ranges from a few nm to 1000 m. The material must be robust enough to withstand the pressure since mercury intrusion requires 140 MPa of pressure for pores smaller than 10 nm. Additionally, it utilizes the idea to determine the pore size of the inkbottle neck. [ 15 ]
The relationship between pore size and pore size distribution in a randomly constructed porous system, is expected to be monotone: bigger pores are connected to larger particles. The relationship between pore size and particle size is complicated by the nonrandom nature of most soils. Big pores may be found in both large and tiny particles, including clays, which promote aggregation and therefore the development of large interaggregate pores. Subdivisions of a pore size distribution in randomly structured media can express more specific characteristics of soils with more complex conceptualizations, such as the hysteresis of soil water retention. [ 8 ]
The pore morphology is the shape, surface roughness, and tortuosity of pore channels representing the liquid and gaseous phases. [ 16 ]
Tortuosity of pore channels is a unique geometric quantity that is utilized not only to measure the transport characteristics of porous system, but also to express the sinuosity and complexity of internal percolation routes. [ 17 ] [ 18 ] [ 19 ]
Toruosity is intimately connected to the transport behavior of electrical conductivity , fluid permeation, [ 20 ] molecular diffusion, and heat transfer in geoscience , impacting petrophysical parameters such as permeability, effective diffusivity , thermal conductivity , and formation resistivity factor. [ 18 ] [ 21 ]
The standard definition of surface roughness for porous medium is based on the average measured vertical coordinate value in comparison to a relative surface height, such as root-mean-square roughness or arithmetic roughness. However, the lack of fractal topology consideration led to the relative surface height definition being deemed inadequate in reality. [ 22 ] [ 23 ]
The ratio of "real surface area" to "geometric smooth-surface area" was used as the second definition of surface roughness. This definition has been applied in several research to alter flow equations or measure the fluid-fluid interfacial area. [ 24 ] [ 25 ]
The fundamental idea of fractal geometry is where the third definition of surface roughness comes from, [ 26 ] in which either modifies the pore surfaces (two-dimensional) or the whole porous medium (three-dimensional) using fractal dimension adjustments, resulting in larger surface dimensions or reduced media dimensions. [ 27 ] The hurst roughness exponent, a similar definition, is occasionally used. This quantity, which spans from 0 to 1, is connected to the fractal dimension. | https://en.wikipedia.org/wiki/Pore_structure |
Poribacteria are a candidate phylum of bacteria originally discovered [ 1 ] in the microbiome of marine sponges ( Porifera ). Poribacteria are Gram-negative primarily aerobic mixotrophs with the ability for oxidative phosphorylation , glycolysis , and autotrophic carbon fixation via the Wood – Ljungdahl pathway . [ 2 ] [ 3 ] Poribacterial heterotrophy is characterised by an enriched set of glycoside hydrolases, uronic acid degradation, as well as several specific sulfatases. This heterotrophic repertoire of poribacteria was suggested to be involved in the degradation of the extracellular sponge host matrix. [ 3 ]
Single-cell genomics and metagenomic shotgun sequencing approaches reveal a poribacterial genome size range between about 4.2 and 6.5 megabases [ 2 ] [ 3 ] [ 4 ] [ 5 ] encoding 4,254 protein -coding genes, of which an unusually high 24% have no homology to known genes . Among the genes of identifiable homology, reconstructed pathways suggest that the poribacterial central metabolism is capable of glycolysis , tricarboxylic acid cycle , pentose phosphate pathways , oxidative phosphorylation , the Entner-Doudoroff pathway, and autotrophic carbon fixation via Wood–Ljungdahl pathway. Further, Poribacteria seem to engage in assimilatory denitrification and ammonia scavenging with potential relevance in nitrogen re-cycling within the sponge holobiont. The poribacterial genome is also reported to contain an unusually high number of phage defence systems including CRISPR-CAS and restriction modification systems . [ 6 ]
Cell compartmentalization into distinct membrane-bound organelles is a universal and defining property of eukaryotes, but had not been observed in prokaryotes other than the Planctomycetota . Poribacteria were previously thought to be distinguished from other microorganisms associated with marine sponges by such a distinctive morphology featuring a large membrane-bound cellular compartment that was suggested to contain DNA. [ 1 ] The distinctive poribacterial compartments were originally identified using fluorescence in situ hybridization and electron microscopy . [ 1 ] Genomic evidence suggests the presence of protein-bound organelles, but not for membrane-bound organelles. [ 6 ] More recently, correlative light-electron microscopy , confirmed two elements of poribacterial subcellular compartmentation: [ 7 ] Firstly, Bacterial microcompartments , atypically localized at the cell membrane. Secondly, spherical bipolar compartments which are discussed to be most likely carbon rich storage polymers such as Polyhydroxybutyrate .
Genomic analyses of poribacteria reveal several families of cell-surface repeat proteins that resemble those found in eukaryotes, and are infrequently found in prokaryotes. Examples include ankyrin and leucine-rich repeat domains, [ 2 ] as well as tetratricopeptides . [ 6 ] Unusual low-density lipoprotein receptor repeat proteins are also found, of unknown function. Most of these protein families are thought to be involved in surface interactions with the sponge host. [ 6 ] In addition, genetic infrastructure for sterol biosynthesis is observed in poribacterial genomes, otherwise found almost exclusively in eukaryotes and the planctomycete Gemmata obscuriglobus . [ 2 ]
Poribacteria are symbionts of marine sponges , among the most abundant microorganisms in the highly diverse microbiome of the sponge mesohyl . [ 2 ] They have been found in a large variety of sponge species from diverse geographic origins. [ 8 ] The composition of microorganisms in the sponge microbiome can be vertically inherited, with adult sponges transmitting their distinctive microbial communities to offspring. [ 9 ] | https://en.wikipedia.org/wiki/Poribacteria |
A porism is a mathematical proposition or corollary . It has been used to refer to a direct consequence of a proof , analogous to how a corollary refers to a direct consequence of a theorem . In modern usage, it is a relationship that holds for an infinite range of values but only if a certain condition is assumed, such as Steiner's porism . [ 1 ] The term originates from three books of Euclid that have been lost. A proposition may not have been proven, so a porism may not be a theorem or true.
The book that talks about porisms first is Euclid 's Porisms . What is known of it is in Pappus of Alexandria 's Collection , who mentions it along with other geometrical treatises, and gives several lemmas necessary for understanding it. [ 2 ] Pappus states:
Pappus said that the last definition was changed by certain later geometers, who defined a porism as an accidental characteristic as τὸ λεῖπον ὑποθέσει τοπικοῦ θεωρήματος ( to leîpon hypothései topikoû theōrḗmatos ), that which falls short of a locus-theorem by a (or in its) hypothesis. Proclus pointed out that the word porism was used in two senses: one sense is that of "corollary", as a result unsought but seen to follow from a theorem. In the other sense, he added nothing to the definition of "the older geometers", except to say that the finding of the center of a circle and the finding of the greatest common measure are porisms. [ 3 ] [ 2 ]
Pappus rejected Euclid's definition of porism . A porism, expressed in modern language, asserts that given four straight lines, of which three turn about the points in which they meet the fourth if two of the points of intersection of these lines lie each on a fixed straight line, the remaining point of intersection will also lie on another straight line. The general definition applies to any number, n , of straight lines, of which n can turn about as many points fixed on the ( n + 1)th. These n straight lines cut two and two into 1 ⁄ 2 n ( n − 1) points, 1 ⁄ 2 n ( n − 1) being a triangular number whose side is n − 1. If they are made to turn about the n fixed points so that any n − 1 of their 1 ⁄ 2 n ( n − 1) points of intersection, chosen subject to a certain limitation, lie on n − 1 given fixed straight lines, then each of the remaining points of intersection, 1 ⁄ 2 n ( n − 1)( n − 2) in number, describes a straight line. [ 2 ]
The above can be expressed as: If about two fixed points, P and Q, one makes the turn two straight lines meeting on a given straight line, L, and if one of them cuts off a segment, AM, from a fixed straight line, AX, given in position, another fixed straight line BY, and a point B fixed on it can be determined, such that the segment BM' made by the second moving line on this second fixed-line measured from B has a given ratio X to AM. The lemmas which Pappus gives in connection with the porisms are:
Robert Simson explained the only three propositions which Pappus indicates with any completeness, which was published in the Philosophical Transactions in 1723. Later he investigated the subject of porisms generally in a work entitled De porismatibus traclatus; quo doctrinam porisrnatum satis explicatam, et in posterum ab oblivion tutam fore sperat auctor , and published after his death in a volume, Roberti Simson opera quaedam reliqua (Glasgow, 1776). [ 4 ]
Simson's treatise, De porismatibus , begins with the definitions for theorem, problem, datum, porism, and locus. Simon wrote that Pappus's definition is too general, and that he substituted it as:
Porisma est propositio in qua proponitur demonstrare rem aliquam, vel plures datas esse, cui, vel quibus, ut et cuilibet ex rebus innumeris, non quidem datis, sed quae ad ea quae data sunt eandem habent rationem, convenire ostendendum est affectionem quandam communem in propositione descriptam. Porisma etiam in forma problematis enuntiari potest, si nimirum ex quibus data demonstranda sunt, invenienda proponantur. [ clarification needed ]
Simson said that a locus is a species of porism. Then follows a Latin translation of Pappus's note on the porisms, and the propositions which form the bulk of the treatise. [ 4 ]
John Playfair 's memoir ( Trans. Roy. Soc. Edin. , 1794, vol. iii.), a sort of sequel to Simson's treatise, explored the probable origin of porisms, or the steps that led ancient geometers to discover them. Playfair remarked that the careful investigation of all possible particular cases of a proposition would show that
These cases could be defined separately, were in a manner intermediate between theorems and problems, and were called "porisms." Playfair defined a porism as "[a] proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions." [ 4 ]
Although Playfair's definition of a porism appears to be most favoured in England, Simson's view has been most generally accepted abroad, and had the support of Michel Chasles . However, in Liouville 's Journal de mathematiques pures et appliquées (vol. xx., July, 1855), P. Breton published Recherches nouvelles sur les porismes d'Euclide , in which he gave a new translation of the text of Pappus, and sought to base a view of the nature of a porism that conforms more closely to Pappus's definition. This was followed in the same journal and in La Science by a controversy between Breton and A. J. H. Vincent, who disputed the interpretation given by the former of Pappus's text, and declared himself in favour of Frans van Schooten 's idea, put forward in his Mathematicae exercitationes (1657). According to Schooten, if the various relations between straight lines in a figure are written down in the form of equations or proportions, then the combination of these equations in all possible ways, and of new equations thus derived from them leads to the discovery of innumerable new properties of the figure. [ 4 ]
The discussions between Breton and Vincent, which C. Housel joined, did not carry forward the work of restoring Euclid's Porisms , which was left for Chasles. His work ( Les Trois livres de porismes d'Euclide , Paris, 1860) makes full use of all the material found in Pappus. [ 4 ]
An interesting hypothesis about porisms was put forward by H. G. Zeuthen ( Die Lehre von den Kegelschnitten im Altertum , 1886, ch. viii.). Zeuthen observed, for example the intercept-porism is still true if the two fixed points are points on a conic, and the straight lines drawn through them intersect on the conic instead of on a fixed straight line. He conjectured that the porisms were a by-product of a fully developed projective geometry of conics. [ 4 ]
Attribution: | https://en.wikipedia.org/wiki/Porism |
Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow, pressure and bulk solid deformation within a linear porous medium and it is an extension of elasticity and porous medium flow (diffusion equation). [ 1 ] The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot (1935, 1941) [ 2 ] as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils.
The theory of poroelasticity has been widely applied in geomechanics , [ 3 ] hydrology , [ 4 ] biomechanics , [ 5 ] tissue mechanics, [ 6 ] cell mechanics , [ 7 ] and micromechanics. [ 8 ]
An intuitive sense of the response of a saturated elastic porous medium to mechanical loading can be developed by thinking about, or experimenting with, a fluid-saturated sponge. If a fluid-saturated sponge is compressed, fluid will flow from the sponge. If the sponge is in a fluid reservoir and compressive pressure is subsequently removed, the sponge will reimbibe the fluid and expand. The volume of the sponge will also increase if its exterior openings are sealed and the pore fluid pressure is increased. The basic ideas underlying the theory of poroelastic materials are that the pore fluid pressure contributes to the total stress in the porous matrix medium and that the pore fluid pressure alone can strain the porous matrix medium. There is fluid movement in a porous medium due to differences in pore fluid pressure created by different pore volume strains associated with mechanical loading of the porous medium. [ 9 ] In unconventional reservoir and source rocks for natural gas like coal and shales, there can be strain due to sorption of gases like methane and carbon dioxide on the porous rock surfaces. [ 10 ] Depending on the gas pressure the induced sorption-based strain can be poroelastic or poroinelastic in nature. [ 11 ]
The theories of poroelasticity can be divided into two categories: static (or quasi-static) and dynamic theories, [ 12 ] just like mechanics can be divided into statics and dynamics. The static poroelasticity considers processes in which the fluid movement and solid skeleton deformation occur simultaneously and affect each other. The static poroelasticity is predominant in the literature for poroelasticity; as a result, this term is used interchangeably with poroelasticity in many publications. This static poroelasticity theory is a generalization of the one-dimensional consolidation theory in soil mechanics . This theory was developed from Biot's work in 1941. [ 2 ] The dynamic poroelasticity is proposed for understanding the wave propagation in both the liquid and solid phases of saturated porous materials. The inertial and associated kinetic energy, which are not considered in static poroelasticity, are included. This is especially necessary when the speed of the movement of the phases in the porous material is considerable, e.g., when vibration or stress waves is present. [ 13 ] The dynamic poroelasticity was developed attributed to Biot's work on the propagation of elastic waves in fluid-saturated media. [ 14 ] [ 15 ]
References for the theory of poroelasticity: | https://en.wikipedia.org/wiki/Poroelasticity |
Poromechanics is a branch of physics and specifically continuum mechanics that studies the behavior of fluid-saturated porous media . [ 1 ] A porous medium or a porous material is a solid (referred to as matrix) permeated by an interconnected network of pores or voids filled with a fluid . In general, the fluid may be composed of liquid or gas phases or both. In the simplest case, both the solid matrix and the pore space occupy two separate, continuously connected domains, such as in a kitchen sponge. Some porous media has a more complex microstructure in which, for example, the pore space is disconnected. Pore space that is unable to exchange fluid with the exterior is termed occluded pore space. Alternatively, in the case of granular porous media , the solid phase may constitute disconnected domains, termed the "grains", which are load-bearing under compression, though can flow when sheared.
Natural substances including rocks , [ 2 ] soils , [ 3 ] biological tissues including plants, [ 4 ] heart , [ 5 ] and cancellous bone , [ 6 ] and man-made materials such as foams , [ 7 ] gels , [ 8 ] ceramics , and concrete [ 9 ] can be considered as porous media. Porous materials share common coupled processes such as diffusion and consolidation, hydration and swelling, drying and shrinkage, heating and build-up of pore pressure, freezing and spalling, capillarity and cracking. [ 1 ] Porous media whose solid matrix is elastic and the fluid is viscous are called poroelastic. The structural properties of a porous medium is characterized by its porosity , pore size and shape, connectivity, and specific surface area. The physical (mechanical, hydraulic, thermal) properties of a porous media are determined by its microstructure as well as the properties of its constituents (solid matrix and fluid). The distribution of pores across multiple scales as well as the pressure of the fluid with which they are filled give rise to distinct poromechanical behavior of the bulk. [ 10 ] Porous media whose pore space is filled with a single fluid phase, typically a liquid, is considered to be saturated. Porous media whose pore space is only partially fluid is a fluid is known to be unsaturated.
Poromechanics relates the loading of solid and fluid phases within a porous body to the deformation of the solid skeleton and pore space. A representative elementary volume (REV) of a porous medium and the superposition of the domains of the skeleton and connected pores is shown in Fig. 1. In tracking the material deformation, one must be careful to properly apportion sub-volumes that correspond to the solid matrix and pore space. To do this, it is often convenient to introduce a porosity , which measures the fraction of the REV that constitutes pore space. To keep track of the porosity in a deforming material volume, mechanicians consider two descriptions, namely: [ 1 ]
The Eulerian and Lagrangian descriptions of porosity are readily related by noting that
where J = det ( F ) {\displaystyle J=\det(\mathbf {F} )} is the Jacobian of the deformation with F {\displaystyle \mathbf {F} } being the deformation gradient . In a small-strain, linearized theory of deformation, the volume ratio is approximated by J ≃ ( 1 + ϵ v ) {\displaystyle J\simeq (1+\epsilon _{\mathrm {v} })} , where ϵ v {\displaystyle \epsilon _{\mathrm {v} }} is the infinitesimal volume strain . Another useful descriptor of the REV's pore space is the void ratio , which compares the current volume of the pores to the current volume of the solid matrix. As such, the void ratio takes definition in an Eulerian frame of reference and is calculated as
where 1 − n {\displaystyle 1-n} measures the fraction of the volume occupied by the solid skeleton.
When a material element of a porous medium undergoes a deformation, the porosity changes due to i) the material's observable macroscopic dilation and ii) the volume dilation of the material's solid skeleton. The latter cannot be assess from experiments on the material's bulk structure. The volume of the solid skeleton in an infinitesimal material element, which is denoted by d V t s {\displaystyle \mathrm {d} V_{t}^{\mathrm {s} }} , is related to the deformed and undeformed total material volumes by
where the definition of the Lagrangian porosity further requires 1 − ϕ 0 = d V 0 s / d V 0 {\displaystyle 1-\phi _{0}=\mathrm {d} V_{0}^{\mathrm {s} }/\mathrm {d} V_{0}} . Thus, under the assumption of infinitesimal strain theory, the total volumetric strain of a material element can be separated into strain contributions of the solid matrix and pore space as follows:
where ϵ s = d V t s / d V 0 s − 1 {\displaystyle \epsilon _{\mathrm {s} }=\mathrm {d} V_{t}^{\mathrm {s} }/\mathrm {d} V_{0}^{\mathrm {s} }-1} is recognized as the linearized volume strain acting in the solid.
Considering a fluid saturated, deformable porous solid, we follow an observation frame that moves together with the solid skeleton but allows pore fluid exchange with the surroundings (i.e., an open system). There is no chemical reaction (i.e., mass exchange) between the solid and the fluid phases. Summoning mass balance, momentum balance, the First and the Second laws of thermodynamics of individual phases, one can arrive at the energy balance and entropy imbalance of the overall mixture. By separately discussing the energy dissipation due to mechanical deformation and mass/heat transport, it is possible to arrive at the following free energy imbalance for the porous skeleton
Φ s = S i j d E i j + p d ϕ − S s d T − d Ψ s ≥ 0 {\displaystyle {\Phi ^{s}}={S_{ij}}d{E_{ij}}+pd\phi -{S^{s}}dT-d{\Psi ^{s}}\geq 0}
where S i j {\displaystyle {S_{ij}}} is the Second Piola-Kirchoff stress; E i j {\displaystyle E_{ij}} is the Green-Lagrangian strain; p {\displaystyle p} the pore fluid pressure; ϕ {\displaystyle \phi } the Lagrangian porosity; T {\displaystyle T} is temperature; S s {\displaystyle S^{s}} and Ψ s {\displaystyle \Psi ^{s}} are the entropy and the elastic stored energy ( Helmholtz free energy ) of the solid skeleton; Φ s {\displaystyle \Phi ^{s}} is the rate of energy dissipation. Assuming small deformation, [ 11 ] elastic solid, and isothermal condition, the previous equation simplifies to:
d Ψ s = σ i j d ε i j + p d ϕ {\displaystyle d{\Psi _{s}}={\sigma _{ij}}d{\varepsilon _{ij}}+pd\phi }
where ε i j = 1 2 ( ∂ u i ∂ x j + ∂ u j ∂ x i ) {\displaystyle {\varepsilon _{ij}}={\frac {1}{2}}\left({{\frac {\partial {u_{i}}}{\partial {x_{j}}}}+{\frac {\partial {u_{j}}}{\partial {x_{i}}}}}\right)} is the infinitesimal strain; u i {\displaystyle u_{i}} and x i {\displaystyle x_{i}} are the displacement and position vectors, respectively; σ i j {\displaystyle \sigma _{ij}} is Cauchy stress. The constitutive equation for an elastic porous media can thus be generally stated as:
σ i j = ∂ Ψ s ∂ ε i j ; p = ∂ Ψ s ∂ ϕ {\displaystyle {\sigma _{ij}}={\frac {\partial {\Psi _{s}}}{\partial {\varepsilon _{ij}}}};p={\frac {\partial {\Psi _{s}}}{\partial \phi }}}
Let us specify the following quadratic form of Ψ s ( ε i j , ϕ ) {\displaystyle {\Psi _{s}}\left({{\varepsilon _{ij}},\phi }\right)} :
Ψ s ( ε i j , ϕ ) = 1 2 ( K − 2 3 G + α 2 N ) ε k k 2 + G ε i j ε i j − α N ε k k ( ϕ − ϕ 0 ) + 1 2 N ( ϕ − ϕ 0 ) 2 {\displaystyle {\Psi _{s}}\left({{\varepsilon _{ij}},\phi }\right)={\frac {1}{2}}\left({K-{\frac {2}{3}}G+{\alpha ^{2}}N}\right){\varepsilon _{kk}}^{2}+G{\varepsilon _{ij}}{\varepsilon _{ij}}-\alpha N{\varepsilon _{kk}}\left({\phi -{\phi _{0}}}\right)+{\frac {1}{2}}N{\left({\phi -{\phi _{0}}}\right)^{2}}}
where e i j = ε i j − δ i j ε k k / 3 {\displaystyle {e_{ij}}={\varepsilon _{ij}}-{\delta _{ij}}{\varepsilon _{kk}}/3} is the strain deviator; ϕ 0 {\displaystyle {\phi _{0}}} is the initial porosity of the undeformed porous medium; K {\displaystyle K} , G {\displaystyle G} , α {\displaystyle \alpha } , N {\displaystyle N} are material constants. We can immediately obtain Biot’s linear isotropic poroelasticity in terms of ϕ {\displaystyle {\phi }} :
{ σ i j = ∂ Ψ s ∂ ε i j = ( K + α 2 N − 2 3 G ) δ i j ε k k + 2 G ε i j − α N δ i j ( ϕ − ϕ 0 ) p = ∂ Ψ s ∂ ϕ = − α N ε k k + N ( ϕ − ϕ 0 ) {\displaystyle \left\{{\begin{array}{l}{\sigma _{ij}}={\frac {\partial {\Psi _{s}}}{\partial {\varepsilon _{ij}}}}=\left({K+{\alpha ^{2}}N-{\frac {2}{3}}G}\right){\delta _{ij}}{\varepsilon _{kk}}+2G{\varepsilon _{ij}}-\alpha N{\delta _{ij}}\left({\phi -{\phi _{0}}}\right)\\p={\frac {\partial {\Psi _{s}}}{\partial \phi }}=-\alpha N{\varepsilon _{kk}}+N\left({\phi -{\phi _{0}}}\right)\end{array}}\right.}
or more commonly in incremental form:
{ d σ i j = ( K − 2 3 G ) δ i j d ε k k + 2 G d ε i j − α δ i j d p d ϕ = 1 N d p + α d ε k k {\displaystyle \left\{{\begin{array}{l}d{\sigma _{ij}}=\left({K-{\frac {2}{3}}G}\right){\delta _{ij}}d{\varepsilon _{kk}}+2Gd{\varepsilon _{ij}}-\alpha {\delta _{ij}}dp\\d\phi ={\frac {1}{N}}dp+\alpha d{\varepsilon _{kk}}\end{array}}\right.}
Comparing with the usual linear elasticity equations, one can identify that K {\displaystyle K} and G {\displaystyle G} are the bulk and shear modulus of the porous material under drained ( d p = 0 {\displaystyle dp=0} ) conditions; α {\displaystyle \alpha } , named the Biot’s coefficient, is a new property for porous media that relates the change of porosity to the strain variation under drained condition; N {\displaystyle N} is a tangent modulus linking the pressure variation and porosity variation under constant volumetric strain ( d ε k k = 0 {\displaystyle d\varepsilon _{kk}=0} ).
The first equation can be rewritten in such a way that the right-hand side is exactly the same as the linear elasticity equation:
σ i j ″ = σ i j + α p δ i j = ( K − 2 3 G ) δ i j ε k k + 2 G ε i j {\displaystyle {\sigma ''_{ij}}={\sigma _{ij}}+\alpha p{\delta _{ij}}=\left({K-{\frac {2}{3}}G}\right){\delta _{ij}}{\varepsilon _{kk}}+2G{\varepsilon _{ij}}}
Term σ i j ″ {\displaystyle {\sigma ''_{ij}}} is called the Biot’s effective stress that represents the stress transmitted solely through the solid skeleton. Terzaghi’s effective stress which is widely used in soil mechanics can be retrieved by setting α = 1 {\displaystyle \alpha =1} .
Although the ϕ {\displaystyle {\phi }} -based formulation is rooted in the free energy balance of the porous skeleton, it is typically difficult to track porosity changes during experiments, making the model calibration/validation inconvenient. In rock mechanics testing, the usual controlled/monitored variables are stress, strain, pore fluid pressure, and the net flux of pore fluid of the test sample. A better external variable in replace of ϕ {\displaystyle {\phi }} is therefore the variation of fluid content, ζ {\displaystyle \zeta } , defined as the amount of fluid volume entering the solid frame per unit volume of solid frame. [ 12 ] [ 13 ] Its increment can be written as
d ζ = d m f ρ f = d ( ρ f ϕ ) ρ f = d ϕ + ϕ d ρ f ρ f {\displaystyle d\zeta ={\frac {dm_{f}}{\rho _{f}}}={\frac {d\left({{\rho _{f}}\phi }\right)}{\rho _{f}}}=d\phi +\phi {\frac {d{\rho _{f}}}{\rho _{f}}}}
where m f {\displaystyle m_{f}} is the fluid mass content; ρ f {\displaystyle \rho _{f}} is the fluid density. By replacing d ϕ {\displaystyle d\phi } with d ζ {\displaystyle d\zeta } , and considering fluid state equation d ρ f / ρ f = d p / K f {\displaystyle d{\rho _{f}}/{\rho _{f}}=dp/K_{f}} , Biot’s theory can be also written in the following ζ {\displaystyle \zeta } -based form:
{ d σ i j = ( K − 2 3 G ) δ i j d ε k k + 2 G d ε i j − α δ i j d p d ζ = 1 M d p + α d ε k k {\displaystyle \left\{{\begin{array}{l}d{\sigma _{ij}}=\left({K-{\frac {2}{3}}G}\right){\delta _{ij}}d{\varepsilon _{kk}}+2Gd{\varepsilon _{ij}}-\alpha {\delta _{ij}}dp\\d\zeta ={\frac {1}{M}}dp+\alpha d{\varepsilon _{kk}}\end{array}}\right.}
or
{ d σ i j = ( K u − 2 3 G ) δ i j d ε k k + 2 G d ε i j − α M δ i j d ζ d p = M ( d ζ − α d ε k k ) {\displaystyle \left\{{\begin{array}{l}d{\sigma _{ij}}=\left({{K_{u}}-{\frac {2}{3}}G}\right){\delta _{ij}}d{\varepsilon _{kk}}+2Gd{\varepsilon _{ij}}-\alpha M{\delta _{ij}}d\zeta \\dp=M\left({d\zeta -\alpha d{\varepsilon _{kk}}}\right)\end{array}}\right.}
where K f {\displaystyle K_{f}} is the fluid tangent bulk modulus; M = K f N / ( K f + N ϕ ) {\displaystyle M={K_{f}}N/\left({{K_{f}}+N\phi }\right)} is Biot modulus; K u = K + b 2 M {\displaystyle {K_{u}}=K+{b^{2}}M} is the undrained bulk modulus. Note that both M {\displaystyle M} and N {\displaystyle N} have been called Biot modulus in different literatures. [ 1 ] [ 13 ] It is expected that M {\displaystyle M} would be dependent on the property of the fluid while N {\displaystyle N} is a sole property of the porous skeleton. Indeed, in-depth micromechanical analysis permits one to quantitatively connect the macroscopic poroelastic parameters with the intrinsic properties of the constituents of the porous media such as matrix bulk modulus and fluid bulk modulus. [ 14 ] [ 15 ]
When measuring the linear elastic properties of porous solids, laboratory experiments are typically performed under one of two limit cases:
The constitutive equation above describes the response of a local porous material in response to stress and fluid pressure changes. The full description of coupled hydromechanical processes relevant for practical applications also requires the complete governing equations and compatible initial and boundary conditions. The governing equations are summarized below:
Balance of linear momentum:
σ i j , j + ρ b i = 0 {\displaystyle {\sigma _{ij,j}}+\rho {b_{i}}=0} (static) or σ i j , j + ρ b i = ρ u ¨ i s + ρ f w ¨ i {\displaystyle {\sigma _{ij,j}}+\rho {b_{i}}=\rho {{\ddot {u}}_{i}^{s}}+{\rho _{f}}{{\ddot {w}}_{i}}} (dynamic)
Balance of mass (of the pore fluid):
ζ ˙ + q i , i = 0 {\displaystyle {\dot {\zeta }}+{q_{i,i}}=0}
Darcy’s law
q i = − K ∂ ∂ x i ( p ρ f g + z ) {\displaystyle {q_{i}}=-K{\frac {\partial }{\partial {x_{i}}}}\left({{\frac {p}{{\rho _{f}}g}}+z}\right)}
Compatibility of infinitesimal strains
ε i j = 1 2 ( u i , j s + u j , i s ) {\displaystyle {\varepsilon _{ij}}={\frac {1}{2}}\left({{u_{i,j}^{s}}+{u_{j,i}^{s}}}\right)}
where ρ = ( 1 − ϕ ) ρ s + ϕ ρ f {\displaystyle \rho =\left({1-\phi }\right){\rho _{s}}+\phi {\rho _{f}}} is the total density of the porous medium; b i {\displaystyle b_{i}} is the body force; w i = ϕ ( u i f − u i s ) {\displaystyle {w_{i}}=\phi \left({{u_{i}^{f}}-{u_{i}^{s}}}\right)} is the relative fluid to solid displacement; u i s {\displaystyle u_{i}^{s}} and u i f {\displaystyle u_{i}^{f}} denote solid and fluid displacements, respectively; an overdot denotes a derivative with respect to time; q i {\displaystyle q_{i}} is specific discharge vector; K {\displaystyle K} is hydraulic conductivity; g {\displaystyle g} is gravitational acceleration. The governing equations (13) combined with the constitutive equations (7) given the previous section provide a total of 20 equations, which correspond to a total of 20 unknowns ( u i , ε i j , σ i j , q i , p , ζ {\displaystyle {u_{i}},{\varepsilon _{ij}},{\sigma _{ij}},{q_{i}},p,\zeta } ). The system is closed and can be solved when supplied with proper initial and boundary conditions.
Solutions to poromechanical problems can be sought analytically or numerically. Numerical techniques including finite difference and finite element methods are frequently invoked in industrial applications. Closed-form analytical solutions have been also developed for many practically relevant problems and are well-documented in textbooks. [ 3 ] [ 13 ] [ 16 ] Analytical solutions are useful for verification of computational codes and developing qualitative intuitions about poromechanical problems.
Reinhard Woltman (1757-1837), a German hydraulic and geotechnical engineer, first introduced the concepts of volume fractions and angles of internal friction within porous media in his study on the connection between soil moisture and its apparent cohesion. [ 17 ] His work addressed the calculation of earth pressure against retaining walls. Achille Delesse (1817-1881), a French geologist and mineralogist, reasoned that the volume fraction of voids – otherwise termed the volumetric porosity – equals the surface fraction of voids – otherwise termed the areal porosity – when the size, shape, and orientation of the pores are randomly distributed. [ 18 ] Henry Darcy (1803-1858), a French hydraulic engineer, observed the proportionality between the rate of discharge and the loss of water pressure in tests with natural sand, now known as Darcy’s law. [ 19 ] The first important concept related to saturated, deformable porous solids might be considered the principle of effective stress introduced by Karl von Terzaghi (1883-1963), an Austrian engineer. Terzaghi postulated that the mean effective stress experienced by the solid skeleton of a porous medium with incompressible constituents, σ ′ = σ − p {\displaystyle \sigma '=\sigma -p} , is the total stress acting on the volume element, σ {\displaystyle \sigma } , subtracted by the pressure of the fluid acting in the pore space, p {\displaystyle p} . [ 20 ] Terzaghi combined his effective stress concept with Darcy’s law for fluid flow and derived a one-dimensional consolidation theory explaining the time-dependent deformation of soils as the pore fluid drains, [ 21 ] which might be the first mathematical treatise on coupled hydromechanical problems in porous media.
A more general and formal introduction of poroelasticity and poromechanics is attributed to Maurice Anthony Biot (1905–1985), a Belgian-American applied physicist. In a series of papers published between 1935 and 1962, Biot developed the theory of linear isotropic poroelasticity (now known as Biot theory) which gives a complete description of the mechanical behavior of a poroelastic medium. [ 12 ] [ 22 ] [ 23 ] [ 14 ] [ 24 ] The generality of Biot theory lies in its three-dimensional formulation in the framework of continuum mechanics, [ 12 ] its accountant for the compressibility of solid and fluid phases, [ 14 ] [ 15 ] its consistency with micromechanical analyses which explicitly considers the inclusions and heterogeneities of porous media, [ 25 ] and its compatibility with thermodynamics. [ 1 ] Different from Terzaghi’s, Biot’s effective stress accounts for the compressibility of the solid and applies generally for deeper rocks and other compliant porous materials.
It is worth mentioning that, parallel to Biot’s developments, another lesser-known path towards a theory of porous media follows the formulation of mixture theory (see [ 26 ] ). One may consider Biot theory as a phenomenological, macroscopic approach to poromechanics as it is grounded on experimentally measurable quantities (stress, strain, pore fluid pressure, and variation in fluid content). The mixture theory of porous media, on the other hand, takes a different route by focusing on the fundamental balance laws of spatially superposed and interacting constituents (solid, fluid). [ 27 ] [ 28 ] The constitutive relations of each constituent are separately derived first, and the macroscopic behavior of the mixture is a result of averaging. The mixture theory can account for arbitrary number of constituents that can be miscible or immiscible and inert or active. [ 29 ] However, it usually comes with excessive number of material parameters that may be difficult to calibrate experimentally. Coussy [ 30 ] showed that it is possible to derive Biot’s theory from mixture theory, revealing the profound connection between the two. Controversy exists between Terzaghi, father of soil mechanics, and Paul Fillunger (1883-1937), father of mixture theory, on the correct form of the effectives stress in the early developments of poromechanics. [ 31 ]
Since Biot’s pioneering works, the linear isotropic poroelasticity theory have been reinterpreted and reformulated, [ 15 ] [ 32 ] generalized to material anisotropy, [ 33 ] [ 34 ] large deformation, and inelasticity, [ 35 ] and coupled with multiphysical (thermal, chemical, electromagnetic) fields. [ 36 ] [ 37 ] [ 38 ] Poromechanics theories for partially saturated porous materials, [ 39 ] microporous materials, [ 40 ] and surface-active materials [ 41 ] [ 42 ] have also been developed.
By introducing inertia terms in the set of governing equations shown above, the resulting solutions can capture fast dynamic effects such as wave propagation through porous medium, and thus the system is referred to as the theory of poroelastodynamics. One of the key findings is that there exist three types of elastic waves in poroelastic media: a shear or transverse wave, and two types of longitudinal or compressional waves, which Biot called type I and type II waves. [ 22 ] [ 23 ] The transverse and type I (or fast) longitudinal wave are similar to the transverse and longitudinal waves in an elastic solid, respectively. The slow compressional wave (also known as Biot’s slow wave), is unique to poroelastic materials and is characterized by the out-of-phase movement between solid and fluid. The prediction of the Biot’s slow wave generated some controversy, until it was experimentally observed by Thomas Plona in 1980. [ 43 ] Conversion of energy from fast compressional and shear waves into the highly attenuating slow compressional wave is a significant cause of elastic wave attenuation in porous media. [ 2 ]
Other important early contributors to the theory of poroelastodynamics were Yakov Frenkel and Fritz Gassmann. [ 44 ] [ 45 ] [ 46 ] Further reading about the dynamics and acoustics of porous media. [ 47 ] [ 48 ] [ 49 ]
Recent applications of poroelasticity to biology, such as modeling blood flows through the beating myocardium, have also required an extension of the equations to nonlinear (large deformation) elasticity and the inclusion of inertia forces. | https://en.wikipedia.org/wiki/Poromechanics |
Porosimetry is an analytical technique used to determine various quantifiable aspects of a material's porous structure, such as pore diameter , total pore volume , surface area , and bulk and absolute densities .
The technique involves the intrusion of a non-wetting liquid (often mercury ) at high pressure into a material through the use of a porosimeter . The pore size can be determined based on the external pressure needed to force the liquid into a pore against the opposing force of the liquid's surface tension .
A force balance equation known as Washburn's equation for the above material having cylindrical pores is given as: [ 1 ]
Since the technique is usually performed within a vacuum , the initial gas pressure is zero. The contact angle of mercury with most solids is between 135° and 142°, so an average of 140° can be taken without much error. The surface tension of mercury at 20 °C under vacuum is 480 mN / m . With the various substitutions, the equation becomes:
As pressure increases, so does the cumulative pore volume. From the cumulative pore volume, one can find the pressure and pore diameter where 50% of the total volume has been added to give the median pore diameter.
This article about materials science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Porosimetry |
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material , and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface (cf. closed-cell foam ).
There are many ways to test porosity in a substance or part, such as industrial CT scanning .
The term porosity is used in multiple fields including pharmaceutics , ceramics , metallurgy , materials , manufacturing , petrophysics , hydrology , earth sciences , soil mechanics , rock mechanics , and engineering . [ 1 ]
In gas-liquid two-phase flow , the void fraction is defined as the fraction of the flow-channel volume that is occupied by the gas phase or, alternatively, as the fraction of the cross-sectional area of the channel that is occupied by the gas phase. [ 2 ]
Void fraction usually varies from location to location in the flow channel (depending on the two-phase flow pattern). It fluctuates with time and its value is usually time averaged. In separated (i.e., non- homogeneous ) flow, it is related to volumetric flow rates of the gas and the liquid phase, and to the ratio of the velocity of the two phases (called slip ratio ).
Used in geology , hydrogeology , soil science , and building science , the porosity of a porous medium (such as rock or sediment ) describes the fraction of void space in the material, where the void may contain, for example, air or water. It is defined by the ratio :
where V V is the volume of void-space (such as fluids) and V T is the total or bulk volume of material, including the solid and void components. Both the mathematical symbols ϕ {\displaystyle \phi } and n {\displaystyle n} are used to denote porosity.
Porosity is a fraction between 0 and 1, typically ranging from less than 0.005 for solid granite to more than 0.5 for peat and clay .
The porosity of a rock, or sedimentary layer, is an important consideration when attempting to evaluate the potential volume of water or hydrocarbons it may contain. Sedimentary porosity is a complicated function of many factors, including but not limited to: rate of burial, depth of burial, the nature of the connate fluids , the nature of overlying sediments (which may impede fluid expulsion). One commonly used relationship between porosity and depth is the decreasing exponential function given by the Athy (1930) equation: [ 3 ]
where, ϕ ( z ) {\displaystyle \phi (z)} is the porosity of the sediment at a given depth ( z {\displaystyle z} ) (m), ϕ 0 {\displaystyle \phi _{0}} is the initial porosity of the sediment at the surface of soil (before its burial), and k {\displaystyle k} is the compaction coefficient (m −1 ). The letter e {\displaystyle e} with a negative exponent denotes the decreasing exponential function. The porosity of the sediment exponentially decreases with depth, as a function of its compaction.
A value for porosity can alternatively be calculated from the bulk density ρ bulk {\displaystyle \rho _{\text{bulk}}} , saturating fluid density ρ fluid {\displaystyle \rho _{\text{fluid}}} and particle density ρ particle {\displaystyle \rho _{\text{particle}}} :
If the void space is filled with air, the following simpler form may be used:
A mean normal particle density can be taken as approximately 2.65 g/cm 3 ( silica , siliceous sediments or aggregates), or 2.70 g/cm 3 ( calcite , carbonate sediments or aggregates), although a better estimation can be obtained by examining the lithology of the particles.
Porosity can be proportional to hydraulic conductivity ; for two similar sandy aquifers , the one with a higher porosity will typically have a higher hydraulic conductivity (more open area for the flow of water), but there are many complications to this relationship. The principal complication is that there is not a direct proportionality between porosity and hydraulic conductivity but rather an inferred proportionality. There is a clear proportionality between pore throat radii and hydraulic conductivity. Also, there tends to be a proportionality between pore throat radii and pore volume. If the proportionality between pore throat radii and porosity exists then a proportionality between porosity and hydraulic conductivity may exist. However, as grain size or sorting decreases the proportionality between pore throat radii and porosity begins to fail and therefore so does the proportionality between porosity and hydraulic conductivity. For example: clays typically have very low hydraulic conductivity (due to their small pore throat radii) but also have very high porosities (due to the structured nature of clay minerals ), which means clays can hold a large volume of water per volume of bulk material, but they do not release water rapidly and therefore have low hydraulic conductivity.
Well sorted (grains of approximately all one size) materials have higher porosity than similarly sized poorly sorted materials (where smaller particles fill the gaps between larger particles). The graphic illustrates how some smaller grains can effectively fill the pores (where all water flow takes place), drastically reducing porosity and hydraulic conductivity, while only being a small fraction of the total volume of the material. For tables of common porosity values for earth materials , see the "further reading" section in the Hydrogeology article.
Consolidated rocks (e.g., sandstone , shale , granite or limestone ) potentially have more complex "dual" porosities, as compared with alluvial sediment . This can be split into connected and unconnected porosity. Connected porosity is more easily measured through the volume of gas or liquid that can flow into the rock, whereas fluids cannot access unconnected pores.
Porosity is the ratio of pore volume to its total volume. Porosity is controlled by: rock type, pore distribution, cementation, diagenetic history and composition. Porosity is not controlled by grain size, as the volume of between-grain space is related only to the method of grain packing.
Rocks normally decrease in porosity with age and depth of burial. Tertiary age Gulf Coast sandstones are in general more porous than Cambrian age sandstones. There are exceptions to this rule, usually because of the depth of burial and thermal history.
Porosity of surface soil typically decreases as particle size increases. This is due to soil aggregate formation in finer textured surface soils when subject to soil biological processes. Aggregation involves particulate adhesion and higher resistance to compaction. Typical bulk density of sandy soil is between 1.5 and 1.7 g/cm 3 . This calculates to a porosity between 0.43 and 0.36. Typical bulk density of clay soil is between 1.1 and 1.3 g/cm 3 . This calculates to a porosity between 0.58 and 0.51. This seems counterintuitive because clay soils are termed heavy , implying lower porosity. Heavy apparently refers to a gravitational moisture content effect in combination with terminology that harkens back to the relative force required to pull a tillage implement through the clayey soil at field moisture content as compared to sand.
Porosity of subsurface soil is lower than in surface soil due to compaction by gravity. Porosity of 0.20 is considered normal for unsorted gravel size material at depths below the biomantle . Porosity in finer material below the aggregating influence of pedogenesis can be expected to approximate this value.
Soil porosity is complex. Traditional models regard porosity as continuous. This fails to account for anomalous features and produces only approximate results. Furthermore, it cannot help model the influence of environmental factors which affect pore geometry. A number of more complex models have been proposed, including fractals , bubble theory, cracking theory, Boolean grain process, packed sphere, and numerous other models. The characterisation of pore space in soil is an associated concept.
The ratio of holes to solid that the wind "sees". Aerodynamic porosity is less than visual porosity, by an amount that depends on the constriction of holes.
Casting porosity is a consequence of one or more of the following: gasification of contaminants at molten-metal temperatures; shrinkage that takes place as molten metal solidifies; and unexpected or uncontrolled changes in temperature or humidity.
While porosity is inherent in die casting manufacturing, its presence may lead to component failure where pressure integrity is a critical characteristic. Porosity may take on several forms from interconnected micro-porosity, folds, and inclusions to macro porosity visible on the part surface. The end result of porosity is the creation of a leak path through the walls of a casting that prevents the part from holding pressure. Porosity may also lead to out-gassing during the painting process, leaching of plating acids and tool chatter in machining pressed metal components. [ 5 ]
Several methods can be employed to measure porosity:
where | https://en.wikipedia.org/wiki/Porosity |
Porous carbons (PCs) are versatile materials with a wide range of applications, including sensors, actuators , thermal insulation , and energy conversion and supercapacitors. [ 1 ] [ 2 ] Some examples of PCs are graphene and carbon nanotube -based aerogel . Physical properties that make PCs unique are their low density, high conductivity, mechanical flexibility, and stability in extreme environments. [ 3 ]
To ensure durability of PCs, mechanical properties are important to study. Elaborate efforts have been made for studying compressive brittleness of porous carbon materials. In 1999, Iizuka, et al. studied the mechanical properties of wood ceramics , a type of porous carbon material. [ 4 ] Stable medium-density fiber was used as the base material of wood ceramics and phenol resin was impregnated into the board. [ 4 ] Starting at 300 °C, Young's modulus and the compressive strength first decreased with increasing temperature, but at 500 °C the strength increases sharply until it reaches 800 °C and plateaus. [ 4 ] The effects of temperature were due to microstructural changes in the resin during carbonization. Effects of impregnates phenol resin at 800 °C were also investigated. Results showed that Young's modulus increased with phenol resin impregnation (Figure 1). The maximum Young's modulus was 5 MPa and the maximum compressive strength was 80 MPa. [ 4 ] Wall-bending mechanical test were also performed and it was found that cell wall is breakage was correlated to relative density on compressive strength and Young's modulus.
Another type of compressive porous carbon consisting of cellulose and graphene aerogels was studied by Mi, et al . Modified cellulose/graphene aerogels (MCGA) was synthesized via bidirectional freeze drying and grafting of long carbon chains through chemical vapor deposition (Figure 2). [ 5 ] [ 3 ] The final product had a bulk density of 5.9 mg/cm 3 and surface area of 47.3 m 2 /g with flexible cellulose nanofibril and stiff graphene components. [ 3 ] After optimizing the concentration of graphene oxide concentration and anisotropic porous structure, tensile tests were performed. It was found that MGCA could recover 99.8% and 96.3% when compressed to 60% and 90% strain, respectively. [ 3 ] SEM images showed that due to its unique structure, MCGA pore walls were able to wrinkle and fold during compression. Another unique characteristic of this material is its absorption capacity of 80-197 times its weight towards hydrophobic compounds, such as oils and chemical solvents. [ 3 ]
On the contrary, less effort has been made to study the stretchability of porous carbons. Gao, et al . synthesized a long-range lamellar scaffold composed of chitosan and graphene oxide via bidirectional freezing, freeze drying , and annealing . [ 6 ] The result is a material with density of 11 mg cm −3 and porosity of about 99.4%. Various tensile tests were conducted, and it was found that carbon spring could revert to its original shape upon 80% compression strain and -60% stretching strain with a Poisson's ratio between 0.05 and 0.1. [ 6 ] The narrow hysteresis loop of the stress-strain curve indicates a low energy dissipation (energy loss coefficient of about 0.2) because of its negligible interior friction, localized buckling, or cracks during deformation processes. [ 6 ] The stretchable mechanical properties of this material allow for great candidates for vibrational and magnetism sensors . | https://en.wikipedia.org/wiki/Porous_carbon |
Porous glass is glass that includes pores, usually in the nanometre - or micrometre -range, commonly prepared by one of the following processes: through metastable phase separation in borosilicate glasses (such as in their system SiO 2 -B 2 O 3 -Na 2 O), followed by liquid extraction of one of the formed phases; [ 1 ] [ 2 ] through the sol-gel process ; or simply by sintering glass powder .
The specific properties and commercial availability of porous glass make it one of the most extensively researched and characterized amorphous solids . Due to the possibility of modeling the microstructure , porous glasses have a high potential as a model system. They show a high chemical, thermal and mechanical resistance, which results from a rigid and incompressible silica network. They can be produced in high quality and with pore sizes ranging from 1 nm up to any desired value. An easy functionalization of the inner surface opens a wide field of applications for porous glasses.
A further special advantage of porous glasses compared to other porous materials, is that they can be made not only as powder or granulate, but also as larger pieces in almost any user defined shape and texture.
In the first half of the 20th century, Turner and Winks discovered that borosilicate glasses can be leached by acids. Their investigations showed that not only the chemical stability can be influenced by thermal treatment but also density , refractive index , thermal expansion and viscosity . In 1934, Nordberg and Hood [ clarification needed ] discovered that alkali borosilicate glasses separate in soluble (sodium borate rich) and insoluble (silica rich) phases if the glass is thermally treated. By extraction using mineral acids the soluble phase can be removed and a porous silica network remains. During a sintering process after extraction, a silica glass is generated, which has properties approaching those of quartz glass . The manufacturing of such high-silica glasses has been published as the VYCOR -process.
In scientific literature, porous glass is a porous material containing approximately 96% silica , which is produced by an acidic extraction or a combined acidic and alkaline extraction respectively, of phase separated alkali borosilicate glasses , and features a three-dimensional interconnected porous microstructure. For commercially available porous glasses, the terms porous VYCOR-Glass (PVG) and Controlled Pore Glass (CPG) are used. The pore structure is formed by a syndetic channel system and has a specific surface from 10 to 300 m 2 /g. Porous glasses can be generated by an acidic extraction of phase separated alkaliborosilica glasses, or by a sol-gel-process. By regulating the manufacturing parameters, it is possible to produce a porous glass with a pore size of between 0.4 and 1000 nm in a very narrow pore size distribution. You can generate various moulds, for example, irregular particles (powder, granulate), spheres, plates, sticks, fibers, ultra thin membranes, tubes and rings.
Precondition for repetitious manufacturing of porous glass is the knowledge about structure determining and structure controlling parameters. The composition of the initial glass is a structure controlling parameter. The manufacturing of the initial glass, mainly the cooling process, the temperature and time of thermal treatment, and the after treatment are structure determining parameters. The phase diagram for sodiumborosilica glass shows a miscibility gap for certain glass compositions.
The upper critical temperature lies at about 760 °C and the lower one at about 500 °C. O.S. Moltschanova was the first person who exactly described the definition of the exsolution. For a phase separation the initial glass composition must lie in the miscibility gap of the ternary Na 2 O - B 2 O 3 - SiO 2 glass system. By a thermal treatment, an interpenetration structure is generated, which results from a spinodal decomposition of the sodium-rich borate phase and the silica phase. This procedure is called primary decomposition . Using an initial glass composition, which lies on the line of anomaly, it is possible to attain a maximum decomposition, which is almost strainless.
As both phases have a different resistances to water, mineral acids, and inorganic salt solutions, the sodium-rich borate phase in these mediums can be removed by extraction. Optimal extraction is possible only if the initial glass composition and thermal treatment are chosen such that combine structures form, and not droplet structures. The texture is influenced by the composition of the initial glass, which directs size and type of decomposition areas. In the context of porous glasses, "texture" implies properties like specific pore volume, specific surface, pore size, and porosity. Furthermore, the texture of porous glasses is influenced by the concentration of the extraction medium and the ratio of fluid to solid. The emerging areas of decomposition depend on time and temperature of the thermal treatment.
Also, colloidal silica is solving in the sodium-rich borate phase, when time and temperature of thermal treatment are increased. This process is called secondary decomposition. The colloidal silica deposit in the macro pores during extraction and obscure the real pore structure. The solubility of colloidal silica in alkaline solutions is higher than network silica, and thus can be removed by an alkaline after-treatment.
Because of their high mechanical, thermal and chemical stability, variable manufacturing of pore sizes with a small pore size distribution and variety of surface modifications, a wide array of applications are possible. The fact that porous glasses can be produced in many different shapes is another advantage for application in industry, medicine, pharmacy research, biotechnology and sensor technology.
Porous glasses are ideal for material separation, because of the small pore size distribution. This is why they are used in gas chromatography, thin layer chromatography and affinity chromatography. An adaptation of stationary phase for a separation problem is possible by a specific modification of the surface of the porous glass.
In biotechnology, porous glasses have benefits for the cleaning of DNA and the immobilization of enzymes or microorganisms. Controlled pore glass (CPG) with pore sizes between 50 and 300 nm is also excellently suited for the synthesis of oligonucleotides . In this application, a linker, a nucleoside or a non-nucleosidic compound, is first attached to the surface of CPG. The chain length of produced oligonucleotides is dependent on the pore size of CPG.
In addition, porous glasses are used for manufacturing implants, especially dental implants, for which porous glass powder is processed with plastics to form a composite. The particle size and the pore size influence the elasticity of the composite so as to fit the optical and mechanical properties to surrounding tissue, for example, the appearance and hardness of dental enamel.
With the ability to form porous glasses as platelets, membrane technology is another important area of application. Hyper filtration of sea – and brackish water and ultra filtration in "downstream process" are but two. Additionally, they are often appropriate as a carrier for catalysts. For example, the olefin – metathesis was realized on the system metal – metal oxide/porous glass.
Porous glasses can be used as membrane reactors as well, again because of their high mechanical, thermal and chemical stability. Membrane reactors can improve conversion of limited balance reactions, while one reaction product is removed by a selective membrane. For example, in the decomposition of hydrogen sulfide on a catalyst in a glass capillary, the conversion by reaction was higher with glass capillary than without. | https://en.wikipedia.org/wiki/Porous_glass |
In materials science , a porous medium or a porous material is a material containing pores (voids). [ 1 ] The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid ( liquid or gas ). The skeletal material is usually a solid , but structures like foams are often also usefully analyzed using concept of porous media.
A porous medium is most often characterised by its porosity . Other properties of the medium (e.g. permeability , tensile strength , electrical conductivity , tortuosity ) can sometimes be derived from the respective properties of its constituents (solid matrix and fluid) and the media porosity and pores structure, but such a derivation is usually complex. Even the concept of porosity is only straightforward for a poroelastic medium.
Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a sponge . However, there is also a concept of closed porosity and effective porosity , i.e. the pore space accessible to flow.
Many natural substances such as rocks and soil (e.g. aquifers , petroleum reservoirs ), zeolites , biological tissues (e.g. bones, wood, cork ), and man made materials such as cements and ceramics can be considered as porous media. Many of their important properties can only be rationalized by considering them to be porous media.
The concept of porous media is used in many areas of applied science and engineering: filtration , mechanics ( acoustics , geomechanics , soil mechanics , rock mechanics ), engineering ( petroleum engineering , bioremediation , construction engineering ), geosciences ( hydrogeology , petroleum geology , geophysics ), biology and biophysics , material science . Two important current fields of application for porous materials are energy conversion and energy storage , where porous materials are essential for superpacitors, (photo-) catalysis , [ 2 ] fuel cells , [ 3 ] and batteries .
At the microscopic and macroscopic levels, porous media can be classified.
At the microscopic scale, the structure is represented statistically by the distribution of pore sizes, the degree of pore interconnection and orientation, the proportion of dead pores, etc. [ 4 ] The macroscopic technique makes use of bulk properties that have been averaged at scales far bigger than pore size. [ 4 ] [ 5 ]
Depending on the goal, these two techniques are frequently employed since they are complimentary. It is obvious that the microscopic description is required to comprehend surface phenomena like the adsorption of macromolecules from polymer solutions and the blocking of pores, whereas the macroscopic approach is frequently quite sufficient for process design where fluid flow , heat, and mass transfer are of highest concern. and the molecular dimensions are significantly smaller than pore size of the porous system. [ 4 ] [ 6 ]
Fluid flow through porous media is a subject of common interest and has emerged a separate field of study. The study of more general behaviour of porous media involving deformation of the solid frame is called poromechanics .
The theory of porous flows has applications in inkjet printing [ 7 ] and nuclear waste disposal [ 8 ] technologies, among others.
Numerous factors influence fluid flow in porous media, and its fundamental function is to expend energy and create fluid via the wellbore. In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes this connection is Darcy's law , [ 9 ] particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media. [ 10 ]
A representation of the void phase that exists inside porous materials using a set or network of pores. It serves as a structural foundation for the prediction of transport parameters and is employed in the context of pore structure characterisation. [ 11 ]
There are many idealized models of pore structures. They can be broadly divided into three categories:
Porous materials often have a fractal -like structure, having a pore surface area that seems to grow indefinitely when viewed with progressively increasing resolution. [ 12 ] Mathematically, this is described by assigning the pore surface a Hausdorff dimension greater than 2. [ 13 ] Experimental methods for the investigation of pore structures include confocal microscopy [ 14 ] and x-ray tomography . [ 15 ] Porous materials have found some applications in many engineering fields including automotive sectors. [ 16 ]
One of the Laws for porous materials is the generalized Murray's law . The generalized Murray's law is based on optimizing mass transfer by minimizing transport resistance in pores with a given volume, and can be applicable for optimizing mass transfer involving mass variations and chemical reactions involving flow processes, molecule or ion diffusion. [ 17 ]
For connecting a parent pipe with radius of r 0 to many children pipes with radius of r i , the formula of generalized Murray's law is: r o a = 1 1 − X ∑ i = 1 N r i a {\displaystyle r_{o}^{a}={1 \over 1-X}\sum _{i=1}^{N}r_{i}^{a}} , where the X is the ratio of mass variation during mass transfer in the parent pore, the exponent α is dependent on the type of the transfer. For laminar flow α =3; for turbulent flow α =7/3; for molecule or ionic diffusion α =2; etc. | https://en.wikipedia.org/wiki/Porous_medium |
The porous medium equation , also called the nonlinear heat equation , is a nonlinear partial differential equation taking the form: [ 1 ]
∂ u ∂ t = Δ ( u m ) , m > 1 {\displaystyle {\frac {\partial u}{\partial t}}=\Delta \left(u^{m}\right),\quad m>1}
where Δ {\displaystyle \Delta } is the Laplace operator . It may also be put into its equivalent divergence form: ∂ u ∂ t = ∇ ⋅ [ D ( u ) ∇ u ] {\displaystyle {\partial u \over {\partial t}}=\nabla \cdot \left[D(u)\nabla u\right]} where D ( u ) = m u m − 1 {\displaystyle D(u)=mu^{m-1}} may be interpreted as a diffusion coefficient and ∇ ⋅ ( ⋅ ) {\displaystyle \nabla \cdot (\cdot )} is the divergence operator.
Despite being a nonlinear equation, the porous medium equation may be solved exactly using separation of variables or a similarity solution . However, the separation of variables solution is known to blow up to infinity at a finite time. [ 2 ]
The similarity approach to solving the porous medium equation was taken by Barenblatt [ 3 ] and Kompaneets/ Zeldovich , [ 4 ] which for x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} was to find a solution satisfying: u ( t , x ) = 1 t α v ( x t β ) , t > 0 {\displaystyle u(t,x)={1 \over {t^{\alpha }}}v\left({x \over {t^{\beta }}}\right),\quad t>0} for some unknown function v {\displaystyle v} and unknown constants α , β {\displaystyle \alpha ,\beta } . The final solution to the porous medium equation under these scalings is: u ( t , x ) = 1 t α ( b − m − 1 2 m β ‖ x ‖ 2 t 2 β ) + 1 m − 1 {\displaystyle u(t,x)={1 \over {t^{\alpha }}}\left(b-{m-1 \over {2m}}\beta {\|x\|^{2} \over {t^{2\beta }}}\right)_{+}^{1 \over {m-1}}} where ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|^{2}} is the ℓ 2 {\displaystyle \ell ^{2}} - norm , ( ⋅ ) + {\displaystyle (\cdot )_{+}} is the positive part , and the coefficients are given by: α = n n ( m − 1 ) + 2 , β = 1 n ( m − 1 ) + 2 {\displaystyle \alpha ={n \over {n(m-1)+2}},\quad \beta ={1 \over {n(m-1)+2}}}
The porous medium equation has been found to have a number of applications in gas flow, heat transfer, and groundwater flow. [ 5 ]
The porous medium equation name originates from its use in describing the flow of an ideal gas in a homogeneous porous medium. [ 6 ] We require three equations to completely specify the medium's density ρ {\displaystyle \rho } , flow velocity field v {\displaystyle {\bf {v}}} , and pressure p {\displaystyle p} : the continuity equation for conservation of mass ; Darcy's law for flow in a porous medium; and the ideal gas equation of state . These equations are summarized below: ε ∂ ρ ∂ t = − ∇ ⋅ ( ρ v ) ( Conservation of mass ) v = − k μ ∇ p ( Darcy's law ) p = p 0 ρ γ ( Equation of state ) {\displaystyle {\begin{aligned}\varepsilon {\partial \rho \over {\partial t}}&=-\nabla \cdot (\rho {\bf {v}})&({\text{Conservation of mass}})\\{\bf {v}}&=-{k \over {\mu }}\nabla p&({\text{Darcy's law}})\\p&=p_{0}\rho ^{\gamma }&({\text{Equation of state}})\end{aligned}}} where ε {\displaystyle \varepsilon } is the porosity , k {\displaystyle k} is the permeability of the medium, μ {\displaystyle \mu } is the dynamic viscosity , and γ {\displaystyle \gamma } is the polytropic exponent (equal to the heat capacity ratio for isentropic processes ). Assuming constant porosity, permeability, and dynamic viscosity, the partial differential equation for the density is: ∂ ρ ∂ t = c Δ ( ρ m ) {\displaystyle {\partial \rho \over {\partial t}}=c\Delta \left(\rho ^{m}\right)} where m = γ + 1 {\displaystyle m=\gamma +1} and c = γ k p 0 / ( γ + 1 ) ε μ {\displaystyle c=\gamma kp_{0}/(\gamma +1)\varepsilon \mu } .
Using Fourier's law of heat conduction , the general equation for temperature change in a medium through conduction is: ρ c p ∂ T ∂ t = ∇ ⋅ ( κ ∇ T ) {\displaystyle \rho c_{p}{\partial T \over {\partial t}}=\nabla \cdot (\kappa \nabla T)} where ρ {\displaystyle \rho } is the medium's density, c p {\displaystyle c_{p}} is the heat capacity at constant pressure , and κ {\displaystyle \kappa } is the thermal conductivity . If the thermal conductivity depends on temperature according to the power law: κ = α T n {\displaystyle \kappa =\alpha T^{n}} Then the heat transfer equation may be written as the porous medium equation: ∂ T ∂ t = λ Δ ( T m ) {\displaystyle {\partial T \over {\partial t}}=\lambda \Delta \left(T^{m}\right)} with m = n + 1 {\displaystyle m=n+1} and λ = α / ρ c p m {\displaystyle \lambda =\alpha /\rho c_{p}m} . The thermal conductivity of high-temperature plasmas seems to follow a power law. [ 7 ] | https://en.wikipedia.org/wiki/Porous_medium_equation |
Porous polymers are a class of porous media materials in which monomers form 2D and 3D polymers containing angstrom- to nanometer-scale pores formed by the arrangement of the monomers. They may be either crystalline or amorphous. Subclasses include covalent organic frameworks (COFs), hydrogen-bonded organic frameworks (HOFs), metal-organic frameworks (MOFs), and porous organic polymers (POPs). The subfield of chemistry specializing in porous polymers is called reticular chemistry .
Covalent organic frameworks are crystalline porous polymers assembled from organic monomers linked through covalent bonds . [ 1 ]
Hydrogen-bonded organic frameworks are crystalline porous polymers assembled from organic monomers linked through hydrogen bonds . [ 2 ]
Metal-organic frameworks are crystalline porous polymers assembled from organic monomers connected by coordination to metal atom centers. [ 3 ] | https://en.wikipedia.org/wiki/Porous_polymer |
Porphine or porphin is an organic compound of empirical formula C 20 H 14 N 4 . It is heterocyclic and aromatic . The molecule is a flat macrocycle , consisting of four pyrrole -like rings joined by four methine bridges, which makes it the simplest of the tetrapyrroles . [ 2 ]
The nonpolar tetrapyrrolic ring structure of porphine means it is poorly soluble in most organic solvents and hardly water soluble. [ 3 ] As a result, porphine is mostly of theoretical interest. It has been detected in GC-MS of certain fractions of Piper betle . [ 4 ]
Substituted derivatives of porphine are called porphyrins. Many porphyrins are found in nature with the dominant example being protoporphyrin IX . [ 5 ] Many synthetic porphyrins are also known, including octaethylporphyrin [ 6 ] and tetraphenylporphyrin . [ 7 ] | https://en.wikipedia.org/wiki/Porphine |
Porphobilinogen ( PBG ) is an organic compound that occurs in living organisms as an intermediate in the biosynthesis of porphyrins , which include critical substances like hemoglobin and chlorophyll . [ 1 ]
The structure of the molecule can be described as molecule of pyrrole with sidechains substituted for hydrogen atoms at positions 2, 3 and 4 in the ring (1 being the nitrogen atom); respectively, an aminomethyl group −CH 2 −NH 2 , an acetic acid (carboxymethyl) group −CH 2 −COOH , and a propionic acid (carboxyethyl) group −CH 2 −CH 2 −COOH .
In the first step of the porphyrin biosynthesis pathway, porphobilinogen is generated from aminolevulinate (ALA) by the enzyme ALA dehydratase .
In the typical porphyrin biosynthesis pathway, four molecules of porphobilinogen are concatenated by carbons 2 and 5 of the pyrrole ring (adjacent to the nitrogen atom) into hydroxymethyl bilane by the enzyme porphobilinogen deaminase , also known as hydroxymethylbilane synthase .
Acute intermittent porphyria causes an increase in urinary porphobilinogen. [ 2 ] | https://en.wikipedia.org/wiki/Porphobilinogen |
In philosophy (particularly the theory of categories ), the Porphyrian tree or Tree of Porphyry is a classic device for illustrating a "scale of being" ( Latin : scala praedicamentalis ), attributed to the 3rd-century CE Greek neoplatonist philosopher and logician Porphyry , and revived through the translations of Boethius . [ 1 ]
Porphyry suggests the tree in his introduction (" Isagoge ") to Aristotle 's Categories . Porphyry presented Aristotle's classification of categories in a way that was later adopted into tree-like diagrams of two-way divisions, which indicate that a species is defined by a genus and a differentia and that this logical process continues until the lowest species is reached, which can no longer be so defined. No illustrations or diagrams occur in editions of Porphyry's original work; diagrams were eventually made, and became associated with the scheme that Porphyry describes, following Aristotle.
Porphyry's Isagoge was originally written in Greek, but was translated into Latin in the early 6th century CE by Boethius . Translations by Boethius became the standard philosophical logic textbook in the Middle Ages, [ 2 ] and theories of categories based on Porphyry's work were still being taught to students of logic until the late 19th century.
Philosopher James Franklin offers some history of the Porphyrian tree:
Thus, the notion of the Porphyrian tree as an actual diagram comes later than Porphyry himself. Still, scholars do speak of Porphyry's tree as in the Isagoge and they mean by this only that the idea of dividing genera into species via differentiae is found in the Isagoge . But, of course, Porphyry was only following what was already in Aristotle, and Aristotle was following what was already in his teacher, Plato . [ 6 ]
The following Porphyrian tree consists of three columns of words; the middlemost (in boldface) contains the series of genera and species , and we can take it as analogous to the trunk of a tree. The extremes (the terms that jut out to the left and right), containing the differentiae , we can take as analogous to the branches of a tree:
The diagram shows the highest genus to be substance. (Whether substance is a highest genus, really, is not in question here: right now we are only going to discuss what the diagram shows, not whether what it shows is true or false.) The technical term for a highest substance is summum genus . So, substance is the summum genus as far as this diagram goes. The diagram shows that the genus substance has two differentia, namely, "thinking" and "extended." This indicates that there are two species of the genus substance, thinking substance and extended substance. The diagram does not give a term for the species of thinking substance (this would be "mind"), but it does give the term for the species of extended substance, namely, body. That is, body is a species of the genus substance; body is that species of the genus substance that is extended.
Now that we have seen body as a species of substance, we treat body as a genus itself. As a genus, it has two differentia of its own, inanimate and animate. So, there are two species of body, inanimate body and animate body. The diagram does not tell us what the term for inanimate body is, but it indicates a term for animate body, namely, animal. Animal is an animate species of the genus body.
And, again, now that we have looked at animal as a species of the genus body, we look at animal now as a genus and consider its differentia, which are shown on the diagram to be irrational and rational. Thus, according to the diagram there are two species of the genus animal, irrational animal and rational animal. We are not told by the diagram what a term for irrational animal is, but the diagram indicates that a rational animal is a human. Thus, human is a rational species of the genus animal.
Beneath human, however, there are no further species. "This" and "that" if they are considered differentiae, are of a special kind that map the species human not onto a new species but onto particular humans. [ 7 ] The particular human Plato is named in the diagram. Plato is not a species (that is why his name is not in bold, unlike the species above). So, human is the lowest species in this diagram. The technical name for the lowest species in such a scheme is the infima species . So, for this diagram, human is the infima species .
This article incorporates text from a publication now in the public domain : Chambers, Ephraim , ed. (1728). "Arbor Porphyriana" . Cyclopædia, or an Universal Dictionary of Arts and Sciences (1st ed.). James and John Knapton, et al. p. 128. | https://en.wikipedia.org/wiki/Porphyrian_tree |
Porphyrins ( / ˈ p ɔːr f ər ɪ n s / POR -fər-ins ) are a group of heterocyclic , macrocyclic , organic compounds , composed of four modified pyrrole subunits interconnected at their α carbon atoms via methine bridges ( =CH− ). In vertebrates , an essential member of the porphyrin group is heme , which is a component of hemoproteins , whose functions include carrying oxygen in the bloodstream . In plants , an essential porphyrin derivative is chlorophyll , which is involved in light harvesting and electron transfer in photosynthesis .
The parent of porphyrins is porphine , a rare chemical compound of exclusively theoretical interest. Substituted porphines are called porphyrins. [ 1 ] With a total of 26 π-electrons the porphyrin ring structure is often described as aromatic . [ 2 ] One result of the large conjugated system is that porphyrins absorb strongly in the visible region of the electromagnetic spectrum, i.e. they are deeply colored. The name "porphyrin" derives from Greek πορφύρα (porphyra) ' purple ' . [ 3 ]
Porphyrin complexes consist of a square planar MN 4 core. The periphery of the porphyrins, consisting of sp 2 -hybridized carbons, generally display small deviations from planarity. "Ruffled" or saddle-shaped porphyrins is attributed to interactions of the system with its environment. [ 4 ] Additionally, the metal is often not centered in the N 4 plane. [ 5 ] For free porphyrins, the two pyrrole protons are mutually trans and project out of the N 4 plane. [ 6 ] These nonplanar distortions are associated with altered chemical and physical properties. Chlorophyll -rings are more distinctly nonplanar, but they are more saturated than porphyrins. [ 7 ]
Concomitant with the displacement of two N- H protons, porphyrins bind metal ions in the N4 "pocket". The metal ion usually has a charge of 2+ or 3+. A schematic equation for these syntheses is shown, where M = metal ion and L = a ligand :
A geoporphyrin, also known as a petroporphyrin, is a porphyrin of geologic origin. [ 8 ] They can occur in crude oil , oil shale , coal, or sedimentary rocks. [ 8 ] [ 9 ] Abelsonite is possibly the only geoporphyrin mineral, as it is rare for porphyrins to occur in isolation and form crystals. [ 10 ]
The field of organic geochemistry had its origins in the isolation of porphyrins from petroleum. These findings helped establish the biological origins of petroleum. [ 11 ] [ 12 ] Petroleum is sometimes "fingerprinted" by analysis of trace amounts of nickel and vanadyl porphyrins. Metalloporphyrins in general are highly stable organic compounds, and the detailed structures of the extracted derivatives made clear that they originated from chlorophyll.
In non-photosynthetic eukaryotes such as animals, insects, fungi, and protozoa , as well as the α-proteobacteria group of bacteria, the committed step for porphyrin biosynthesis is the formation of δ-aminolevulinic acid (δ-ALA, 5-ALA or dALA) by the reaction of the amino acid glycine with succinyl-CoA from the citric acid cycle . In plants , algae , bacteria (except for the α-proteobacteria group) and archaea , it is produced from glutamic acid via glutamyl-tRNA and glutamate-1-semialdehyde . The enzymes involved in this pathway are glutamyl-tRNA synthetase , glutamyl-tRNA reductase , and glutamate-1-semialdehyde 2,1-aminomutase . This pathway is known as the C5 or Beale pathway.
Two molecules of dALA are then combined by porphobilinogen synthase to give porphobilinogen (PBG), which contains a pyrrole ring. Four PBGs are then combined through deamination into hydroxymethyl bilane (HMB), which is hydrolysed to form the circular tetrapyrrole uroporphyrinogen III . This molecule undergoes a number of further modifications. Intermediates are used in different species to form particular substances, but, in humans, the main end-product protoporphyrin IX is combined with iron to form heme. Bile pigments are the breakdown products of heme.
The following scheme summarizes the biosynthesis of porphyrins, with references by EC number and the OMIM database. The porphyria associated with the deficiency of each enzyme is also shown:
A common synthesis for porphyrins is the Rothemund reaction , first reported in 1936, [ 13 ] [ 14 ] which is also the basis for more recent methods described by Adler and Longo. [ 15 ] The general scheme is a condensation and oxidation process starting with pyrrole and an aldehyde .
Porphyrins have been evaluated in the context of photodynamic therapy (PDT) since they strongly absorb light, which is then converted to heat in the illuminated areas. [ 16 ] This technique has been applied in macular degeneration using verteporfin . [ 17 ]
PDT is considered a noninvasive cancer treatment, involving the interaction between light of a determined frequency, a photo-sensitizer, and oxygen. This interaction produces the formation of a highly reactive oxygen species (ROS), usually singlet oxygen, as well as superoxide anion, free hydroxyl radical, or hydrogen peroxide. [ 18 ] These high reactive oxygen species react with susceptible cellular organic biomolecules such as; lipids, aromatic amino acids, and nucleic acid heterocyclic bases, to produce oxidative radicals that damage the cell, possibly inducing apoptosis or even necrosis. [ 19 ]
Porphyrin-based compounds are of interest as possible components of molecular electronics and photonics. [ 20 ] Synthetic porphyrin dyes have been incorporated in prototype dye-sensitized solar cells . [ 21 ] [ 22 ]
Porphyrins have been investigated as possible anti-inflammatory agents [ 23 ] and evaluated on their anti-cancer and anti-oxidant activity. [ 24 ] Several porphyrin-peptide conjugates were found to have antiviral activity against HIV in vitro . [ 25 ]
Heme biosynthesis is used as biomarker in environmental toxicology studies. While excess production of porphyrins indicate organochlorine exposure, lead inhibits ALA dehydratase enzyme. [ 26 ]
Several heterocycles related to porphyrins are found in nature, almost always bound to metal ions. These include
A benzoporphyrin is a porphyrin with a benzene ring fused to one of the pyrrole units. e.g. verteporfin is a benzoporphyrin derivative. [ 27 ]
The first synthetic porphyrin isomer was reported by Emanual Vogel and coworkers in 1986. [ 28 ] This isomer [18]porphyrin-(2.0.2.0) is named as porphycene , and the central N 4 Cavity forms a rectangle shape as shown in figure. [ 29 ] Porphycenes showed interesting photophysical behavior and found versatile compound towards the photodynamic therapy . [ 30 ] This result was followed by the preparation of [18]porphyrin-(2.1.0.1), named it as corrphycene or porphycerin . [ 31 ] Other non-natural porphyrins include [18]porphyrin-(2.1.1.0) and [18]porphyrin-(3.0.1.0) or isoporphycene . [ 32 ] The N-confused porphyrins feature one of the pyrrolic subunits with the nitrogen atoms facing outwards from the core of the macrocycle. [ 33 ] [ 34 ] | https://en.wikipedia.org/wiki/Porphyrin |
Port-Royal Logic , or Logique de Port-Royal , is the common name of La logique, ou l'art de penser , an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole , two prominent members of the Jansenist movement, centered on Port-Royal . Blaise Pascal likely contributed considerable portions of the text. Its linguistic companion piece is the Port-Royal Grammar (1660) by Arnauld and Lancelot.
Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting strong Cartesian elements in its metaphysics and epistemology (Arnauld having been one of the main philosophers whose objections were published, with replies, in Descartes ' Meditations on First Philosophy ). The Port-Royal Logic is sometimes cited as a paradigmatic example of traditional term logic .
The philosopher Louis Marin particularly studied it in the 20th century ( La Critique du discours , Éditions de Minuit, 1975), while Michel Foucault considered it, in The Order of Things , one of the bases of the classical épistémè .
Among the contributions of the Port-Royal Logic is the popularization of the distinction between comprehension and extension , which would later become a more refined distinction between intension and extension . [ 1 ] Roughly speaking: a definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa.
The main idea traces back through the scholastic philosophers to Aristotle 's ideas about genus and species , [ 2 ] and is fundamental in the philosophy of Leibniz . [ 3 ] More recently, it has been related to mathematical lattice theory in formal concept analysis , and independently formalized similarly by Yu. Schreider 's group in Moscow , [ 4 ] Jon Barwise & Jerry Seligman in Information Flow , [ 5 ] and others.
This logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Port-Royal_Logic |
Port and starboard are nautical terms for watercraft and spacecraft , referring respectively to the left and right sides of the vessel, when aboard and facing the bow (front).
Vessels with bilateral symmetry have left and right halves which are mirror images of each other. One asymmetric feature is where access to a boat, ship, or aircraft is at the side; it is usually only on the port side (hence the name).
Port side and starboard side respectively refer to the left and right sides of the vessel, when aboard and facing the bow. The port and starboard sides of the vessel always refer to the same portion of the vessel's structure, and do not depend on the position of someone aboard the vessel.
The port side is the side to the left of an observer aboard the vessel and facing the bow , towards the direction the vessel is heading when underway in the forward direction. The starboard side is to the right of such an observer. [ 1 ]
This convention allows orders and information to be communicated unambiguously, without needing to know which way any particular crew member is facing. [ 2 ] [ 3 ]
The term starboard derives from the Old English steorbord , steor meaning steer, and bord meaning side. Before ships had rudders , they were steered with a steering oar on the right hand side of the ship, because more people are right-handed . [ 2 ] The "steer-board" etymology is shared by the German Steuerbord, Dutch stuurboord and Swedish / Danish / Norwegian styrbord , which gave rise to the French tribord , Italian tribordo, [ a ] Catalan estribord , Portuguese estibordo , Spanish estribor and Estonian tüürpoord .
Since the steering oar was on the right side of the boat, it would dock on the left side. In Old English, this side was known as bæcbord. [ 6 ] An Anglo-Saxon record of a voyage by Ohthere of Hålogaland used the word "bæcbord" ("back-board") for the left side of a ship. With the steering rudder on the starboard side the man on the rudder had his back to the left side of ship. German Backbord , Dutch bakboord , Swedish babord , Spanish babor , Portuguese bombordo , Italian babordo , [ a ] French bâbord , and Estonian pakpoord , are all cognate .
From around 1300 it the term ladde-borde was used, from Middle English ladebord , lade meaning load, and bord meaning side. [ 3 ] Ladebord was changed to larboard in the 1500s, possibly by association with starboard. This side was also called port , since it was the docking side. [ 7 ] The Oxford English Dictionary cites this usage since 1543. [ 8 ]
Larboard sounds similar to starboard and in 1844 the Royal Navy ordered that port be used instead. [ 9 ] [ 10 ] The United States Navy followed suit in 1846. [ 11 ] Larboard continued to be used well into the 1850s by whalers . [ 12 ] In chapter 12 of Life on the Mississippi (1883) Mark Twain writes larboard to refer to the left side of the ship ( Mississippi River steamboat ) in his days on the river – circa 1857–1861. [ 13 ] Lewis Carroll rhymed larboard and starboard in "Fit the Second" of The Hunting of the Snark (1876). [ 14 ]
The navigational treaty convention, the International Regulations for Preventing Collisions at Sea —for instance, as appears in the UK's Merchant Shipping (Distress Signals and Prevention of Collisions) Regulations 1996 (and comparable US documents from the US Coast Guard ) [ 15 ] —sets forth requirements for maritime vessels to avoid collisions, whether by sail or powered, and whether a vessel is overtaking, approaching head-on, or crossing. [ 15 ] : 11–12 To set forth these navigational rules, the terms starboard and port are essential, and to aid in in situ decision-making, the two sides of each vessel are marked, dusk to dawn, by navigation lights , the vessel's starboard side by green and its port side by red. [ 15 ] : 15 Aircraft are lit in the same way.
Port and starboard are also commonly used when dividing crews; for example with a two watch system the teams supplying the personnel are often named Port and Starboard. This may extend to entire crews, such as the forward-deployed crews of the Royal Navy’s Gulf -based frigate, [ 16 ] or ballistic missile submarines . | https://en.wikipedia.org/wiki/Port_and_starboard |
PortableApps.com is a website that distributes free applications for Windows that have been packaged for portability. These portable applications are intended to be used from removable storage devices such as USB flash drives .
The site was founded by John T. Haller and includes contributions from over 100 people, including developers, designers, and translators. [ 1 ]
PortableApps.com started out as a Haller's personal website hosting a portable version of Mozilla Firefox in March 2004. [ 3 ] He then expanded the project to include Mozilla Thunderbird and OpenOffice.org . The open-source group of portable programs outgrew his personal website and he moved it to a community site, PortableApps.com. [ 4 ] The site currently hosts various projects created by forum members, and is also used for bug reporting and suggestions. [ 5 ] Some PortableApps distributions are hosted on SourceForge . [ 6 ]
Application installers designed for use with the PortableApps.com menu follow the convention of using filenames ending in a paf .exe extension, include HTML documentation, and store data in the Data directory. Installers intended for use with the PortableApps.com menu can be either NSIS installers that are generated with the PortableApps.com Installer, compressed archives with self extractors, or a custom Windows executable.
The majority of applications can run on most computers with Windows 2000 [update] or later. [ 7 ] Many apps will also run under Wine on Unix-like operating systems. Older versions of many apps support Windows 95/98/Me, but no new releases support these systems. [ 8 ]
The PortableApps.com Launcher (also known as PAL) is used to make applications portable by handling path redirection, environment variable changes, file and directory movement, configuration file path updates. and similar changes, as configured. [ 9 ] The PortableApps.com Launcher allows software to be made portable without any modification. All modern apps use PAL and the installers are made using the Nullsoft Scriptable Install System . | https://en.wikipedia.org/wiki/PortableApps.com |
The Portable Aqua Unit for Lifesaving (short PAUL ), also known as Water Backpack is a portable membrane water filter developed at the University of Kassel for humanitarian aid. It allows the decentralized supply of clean water in emergency and disaster situations.
The filter only needs water (e.g. from wells or rivers), to function. There are neither chemicals nor energy nor trained personnel required. The entire operation is shown in four pictograms, so that it can be operated without any prior knowledge, as a test with different population groups in India has shown.
The core of the device is a membrane filter unit. After it is set up at its destination, it is filled with about 100 litres of raw water from surface waters. After a waiting period of one to two minutes the filtered water flows out of the drain hose. During filtering raw water must be replenished continuously .
At about 1.15 metres of water pressure, the water is filtered through the membrane with a pore size of 20 to 100 nm . The device removes bacteria with an efficiency of 99.999% (measurement Institut Fresenius, E. coli and Coliform ) and viruses to 99.9% (measured Bonn University, coliphages ).
A system based on ultrafiltration system (unlike Reverse osmosis based units) is not able to filter out solutes like salts or liquids like mineral oils. They pass through the membrane. Water contaminated with such substances therefore can not be cleaned.
A device with an average supply of 1200 litres of raw water can, according to the Sphere standards (2011), [ 1 ] supply clean, drinkable water for 400 people per day.
The water filter is designed for use in emergency and disaster situations. As a backpack it can, if necessary, be brought by walking to the locations. It first came in March 2010 to use in Chile. Since September 2010, the spread increased significantly so that in April 2012, about 700 copies in over 30 countries worldwide.
As the lifespan of the membrane is around ten years, aid agencies can leave the device after a disaster on site. Regular servicing or cleaning of the filter every few months is recommended, and depending on the degree of contamination of the raw water necessary. To clean it the backpack is to be filled once completely and then emptied through the bottom outlet to flush the sediments out.
PAUL is beside the German Foreign Office [ 2 ] used by many organizations in humanitarian relief.
The device was developed in the Department of Urban Water Management in the Department of Civil Engineering at the University of Kassel under the "German Federal Environmental Foundation" funded projects. The current optimization project will run until mid-2013 in a research project.
The project "PAUL - Potable water at disasters" in 2011 at the German competition "365 Landmarks in the Land of Ideas" as the national winner in the Category Society Competition. [ 3 ] | https://en.wikipedia.org/wiki/Portable_Aqua_Unit_for_Lifesaving |
Portable Compiled Format (PCF) is a bitmap font format used by X Window System in its core font system, and has been used for decades. PCF fonts are usually installed, by default, on most Unix -based operating systems, and are used in terminals such as xterm . PCF fonts replaced Bitmap Distribution Format due to a slight efficiency increase, however most applications have moved on to scalable fonts . [ 1 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Portable_Compiled_Format |
In electrical safety testing , portable appliance testing ( PAT inspection or PAT testing ) is a process by which electrical appliances are routinely checked for safety, commonly used in the United Kingdom , Ireland , New Zealand and Australia . In Australia and New Zealand it is commonly known as Test and Tag . The formal term for the process is In-service Inspection & Testing of Electrical Equipment .
Testing involves a visual inspection of the equipment and verification that power cables are in good condition. Additionally, other tests may be done when required, such as a verification of earthing (grounding) continuity , a test of the soundness of insulation between the current -carrying parts, and a check for any exposed metal that could be touched. The formal limits for a pass/ fail of these electrical tests vary somewhat depending on the category of equipment being tested.
Other countries have similar procedures, for example, testing of equipment according to DGUV Vorschrift 3 in Germany .
Health and safety regulations require that electrical appliances are safe and well maintained to prevent harm to workers. Many equipment manufacturers recommend testing at regular intervals to ensure continual safety, with the interval between tests varying based on both the type of appliance and the environment in which it is to be used. The European Low Voltage Directive governs the manufacture or importation of electrical appliances. Compliance with these standards has to be declared and indicated by the display of the CE mark on the product. The responsibility for testing lies with the manufacturer or the importer and is policed by Trading Standards. [ 1 ]
In Australia and New Zealand the standard used is AS/NZS3760. [ 2 ]
Testing equipment has been specifically developed for PAT inspections, based on the testing equipment used by manufacturers to ensure compliance with the British Standard Code of Practice and European product standards relevant to that type of appliance. This in turn allows testing and the interpretation of results to be de-skilled to a large extent. [ citation needed ] The inspection of the appliances can largely be carried out in-house in many organisations. This can result in cost savings and more flexibility as to exactly when a PAT is carried out.
British law (the Electricity at Work Regulations 1989 ) requires that all electrical systems (including electrical appliances) are maintained (so far as it is reasonable and practicable) to prevent risk of injury or danger. [ 3 ] Domestic premises are not covered by this legislation, although occupiers' liability requires householders not to deliberately expose occupants or visitors to unreasonable risks. The HSE and the local authority are responsible for the policing of this legislation.
Guidance from the IET (published under the IEE brand) and the Health and Safety Executive (HSE) recommends that a competent person must inspect the installation regularly in any public building or a place that people work. They suggest initial intervals for combined inspection and testing that range from three months (for construction equipment) to one year, and in many cases, longer periods for re-testing (certain types of appliance in schools, hotels, offices and shops). [ 4 ]
Although the Electricity at Work Regulations 1989 is an obligation on UK businesses, there is no obligation to undertake PAT inspection. In reality neither act nor their corresponding regulations and associated statutory instruments detail PAT inspection as an obligation, but rather impose a requirement of maintenance of safety and evidence of routine maintenance for all hand-held, portable and plug-in equipment.
Today a great many private companies and other organizations do meet their legal obligations to protect their workers by an enforced PAT regime, but it is not the only route.
Recent [ when? ] HSE publications have relaxed their tone somewhat to acknowledge this, and now point out that in many situations an annual PAT test is disproportionate to the risks and is often not required. [ 5 ] In 2011, the HSE reviewed its approach to portable appliance maintenance in its own offices. Thinking about the type of equipment in use, and how it was used, the HSE looked back at the results from its annual testing of portable appliances across its estate over the last five years. Using the results of the previous tests, the HSE decided that further portable appliance tests are not needed within the foreseeable future or at all for certain types of portable equipment. Also, they decided to continue to monitor any faults reported as a result of user checks and visual inspections and review its maintenance system if evidence suggests that it needs revising. Electrical equipment will continue to be maintained by a series of user checks and visual inspections by staff that have had some training.
Annual portable appliance testing is not always necessary in low risk environments. You do not need to be qualified as an electrician to carry out visual inspections. Regular user checks and visual inspections can be a good method of maintaining portable electric equipment. For landlords maintaining legal requirements it is not compulsory for them to have all appliances tested, but they do need to show a "duty of care" and most letting agents recommend that a test certificate is obtained. [ 6 ]
In the UK there is no legal instrument that requires a sub-contractor to ensure that all tools and equipment are PAT inspected before bringing onto a site of work. Neither is there any legal instrument which obliges the site owner to ensure third-party equipment is PAT inspected either by themselves or the equipment owner.
The internal policies of many UK businesses and educational establishments make mistaken reference to PAT inspection being a legal requirement under the Electricity at Work Regulations, which is false. Having such a policy is legitimate for internal reasons, but it is not underwritten by law; it is only their interpretation. Therefore, it is not a legal requirement to have a PAT inspection sticker or certificate, rather the obligation is that equipment must be safe.
The HSE recommend policies use phrases such as "equipment that is brought onto site for an event must be in a safe condition" and refrain from overzealous statements such as "must be PAT inspected" which can be restrictive without improving safety.
The first official appliance-testing equipment in the UK was used for government housing estates. This was under the control of the Property Services Agency – prior to 1972 the Ministry of Public Building and Works . [ citation needed ] In some cases testing was conducted on a three-month (high-risk) and six-month (low-risk) cycle from the early 1960s onwards. Extensive record-keeping was made into log-books and generally the equipment used was an insulation resistance tester, simple hand tools and visual inspection. Evidence of testing was clearly visible to workers in the form of "passed," "tested for electrical safety," and "do not use after..." labels affixed to various parts of the electrical equipment used. This early testing and inspection was done under a planned maintenance scheme and pre-dated both the Health and Safety at Work Act 1974 and the Electricity at Work Act 1989.
PAT testing is not exclusively confined to formal testing but is rather a combination of inspection and testing processes. Most dangerous defects can be found simply by inspecting the appliances for obvious signs of damage such as frayed cables. According to the HSE, simple inspection can find more than 90% of defects. [ 7 ]
The tests an appliance is required to undergo will depend on the type of appliance, its electrical class and subject to a risk assessment by the technician. For example, it may not be safe to perform a leakage current test which powers up the appliance, if that appliance is something like a grinder, if it cannot be suitably secured.
The test equipment earth lead/probe is connected/touched to metal parts on both Class I and Class II appliances. For Class I an earth test is performed to prove good continuity between the earth pin of the appliance's plug and exposed metal parts on the appliance. For Class II an insulation test is performed which checks that voltage injected on the live supply wires (line and neutral) is sufficiently insulated from the appliance's case and any exposed metal parts (e.g. connectors).
The equipment shall have a measured resistance of the protective earth circuit or the earthing conductor of an extension cord or appliance cord set, which does not exceed 1Ω. [ 8 ]
Testing is performed using an ohmmeter or PAT tester
The choice of which of the tests to use is at the operator's discretion as there is merit in each test for given situations. Later model testers that are battery powered are limited to doing the "screen test". Older mains powered units can do all tests. The purpose of the high current test is to simulate a fault condition: if a live part contacts the earthed metalwork, the earth conductor should be able to carry sufficient current to blow the fuse and render the appliance safe, without the earth conductor itself burning out. On the other hand, some equipment (especially IT equipment) could be damaged by this test, as the earth connection is only for functional purposes and is not meant to be relied upon for safety.
An insulation resistance test is performed to check the condition of conductor and component insulation. Values should not be less than 1MΩ for Class I and Class II appliances at 500 V d.c., or at 250 V d.c. [ 9 ] to avoid the equipment apparently failing the test because the metal oxide varistors (MOVs) or electro-magnetic interference (EMI) suppression triggered, for equipment containing voltage limiting devices such as MOVs or EMI suppression.
This test is performed using an insulation resistance test meter, or PAT tester, by applying a nominal voltage to the live conductors (line and neutral) of an appliance, and placing 0 volt reference on the earthed parts of a Class I appliance or the external metal parts of a Class II appliance;
A leakage current test is an alternative to the insulation resistance test. A deficiency of the insulation resistance test is that the DC voltage will not activate electromagnetic switches or internal relays etc. that are common in many modern power tools, computers, and TVs, etc. and therefore it can only test the appliance up to those components. For such appliances an alternate leakage current test is available on some testing equipment which performs an AC based test (at reduced voltage), with values not exceeding 5mA for Class I appliances or 1mA for Class II appliances. [ 10 ]
AS/NZS 3760:2010 section 2.3.3.2 requires a leakage test to be carried out if equipment being tested must be energised to close the circuit or operate a switching device. Leakage testing does require the item being tested to be powered up thus meaning the item will switch on and operate.
In countries where the sockets are polarised, polarity testing is a simple test that can be carried out using a polarity tester to determine whether the line and neutral of the plug end are correctly connected to the corresponding terminals at the socket end. [ 11 ] [ 12 ]
Functional testing involves simply testing that functionality of the appliance actually works, and perhaps checking that the power consumption is normal.
The RCD functionality of a portable RCD , which provides RCD protection in the form of an adapter between an appliance and a socket, can be tested using the same techniques as for RCDs found in a building's fixed electrical installation. The testing functionality is included in some PAT testing equipment.
Specific microwave leakage testing was recommended for microwave ovens in the United Kingdom up until version 3 of the IET Code of Practice. [ 13 ] This included testing that the device immediately ceases production of microwave radiation when the door is opened (a functional test), and testing that any radiation leakage when operating is less than 5 mWcm −2 .
A piece of calibrated equipment is required for radiation leakage testing. This is usually a hand-held device with a sensing antenna that can be scanned over the areas where the door meets the casing to find any radiation hot-spots whilst the unit is operating. As microwave ovens are not normally designed to be operated without a load this will usually take the form of an open container containing a quantity of water which is used to absorb the energy and as it gets warmed gives an indication that a unit not previously examined by a tester is actually producing microwaves. After checking for leakage the door is required to be opened and the measurement device is not to record a level above the given limit. In some scenarios a known quantity of water is heated for a known period of time and the temperature rise over the period of operation is used to generate an indication of the effective power output of the magnetron (another functional test). This can be helpful to determine whether the oven is operating at the expected power levels indicated by labelling.
Microwave leakage testing was removed in version 4 of the IET Code of Practice, to revert microwave oven testing to the same as any other appliance, but with emphasis put on the visual inspection of the door seal. [ 13 ]
In the UK there is no requirement to have a formal qualification to carry out formal PAT Testing, nor a need to be a qualified electrician or have a background in the electrical industry. The Electricity at Work regulations of 1989 simply state that where required, inspection and testing must be carried out by a competent person, however it does not mention a benchmark for competency. It has become accepted practice however for individuals operating as PAT Testers to hold a nationally recognised City & Guilds 2377–22 qualification (or a later version such as 2377-77 Level 3 Award in the In-service Inspection and Testing of Electrical Equipment (603/6790/8) ). [ 14 ] Guidance is provided by the IET in the form of the Code of Practice for In-service Inspection and Testing of Electrical Equipment – 5th Edition published in October 2021. [ 15 ]
In Australia it is a legal requirement, per AS/NZS 3760 2010, that formal PAT testing ( Test and Tag ) is performed by a competent person, with suitable competence being gained through formal training, experience, or combination thereof. [ 16 ]
In New Zealand it is not a legal requirement to attend a training course, however persons undertaking PAT Testing must be deemed competent by a responsible person (being the owner of the premises' electrical equipment or someone with a legal responsibility for the safety of electrical equipment).
PAT testing can be conducted using either a collection of instruments that each perform a single specific type of test, such as an insulation resistance tester, or using an instrument in which all necessary test functionality is combined.
These are the simple-to-use, comparatively much cheaper, and often used by businesses who test in-house . These test instruments simply display PASS or FAIL when a test is carried out. Mains powered testers require AC power. Battery operated testers are self-contained and convenient to use. They usually come with rechargeable batteries.
Aside from pass and fail indication, the interface will also include an option for selecting between Class I and Class II appliances.
Advanced test instruments display much more detailed result information, such as the measurement in Ohms of an insulation resistance test. They may also provide more options giving greater control over how each test carried out, for example providing a choice of test voltages for an insulation resistance test. Detailed readings naturally require greater knowledge to understand and interpret.
Advanced PAT testers can be effective as facility management tools because they may record the location and test status of electrical equipment and appliances.
Some advanced PAT testers can transfer information to a computer. Bluetooth-enabled computerised PAT testers make the two way transfer of test data between the test instrument and PC-based record keeping systems much simpler, and can be used with other test accessories such as label printers.
As PAT test instruments are sophisticated devices and perform an important safety role. As such it is important to make sure that they are continuing to measure correctly. If an instrument is not periodically checked and calibrated, then the accuracy of tests performed since it was last checked are drawn into question, which could create a problem in the event of a claim. It is usually recommended that calibration is carried out annually.
When a PAT test instrument is calibrated, it is internally trimmed to match the original specification.
Dual purpose check boxes (which are essentially known resistances either side of the test limits) have also been introduced, which are capable of validating the accuracy of both electrical installation testers and portable appliance testers in the field, reducing the risk of a tester being used when not operating correctly - this also allows the re-calibration interval to be increased. | https://en.wikipedia.org/wiki/Portable_appliance_testing |
A portable collision avoidance system ( PCAS ) is a proprietary aircraft collision avoidance system similar in function to traffic collision avoidance system (TCAS). TCAS is the industry standard for commercial collision avoidance systems but PCAS is gaining recognition as an effective means of collision avoidance for general aviation and is in use the world over by independent pilots in personally owned or rented light aircraft as well as by flight schools and flying clubs. PCAS was manufactured by Zaon. [ 1 ] Its main competitor is FLARM .
PCAS allows pilots, particularly in single pilot VFR aircraft, an additional instrument to increase their situational awareness of other aircraft operating nearby. A basic system will notify pilots of the nearest transponder equipped aircraft, its relative height and distance, and importantly if the distance is decreasing or increasing. More advanced systems can integrate with EFIS , overlaying nearby aircraft on the GPS map with relative height information. This information reduces pilot work loads in busy airspace. It may also help pilots to hone their ability to spot nearby aircraft by alerting them when an aircraft is near.
The original PCAS technology was developed in 1999 by Zane Hovey, a pilot and flight instructor, who also patented a portable ADS-b version as well. [ 2 ] Through this technology, transponder-equipped aircraft are detected and ranged, and the altitude is decoded. PCAS G4 technology has advanced to the point that highly accurate range, relative altitude, and 45 degree direction can be accurately detected in a portable cockpit device. PCAS gained notoriety with the growing popular TV series The Aviators (TV series) as a sponsor, and specifically in episode 6 airing on both PBS and the Discovery Channel Network.
ATC ground stations and active TCAS systems transmit interrogation pulses on an uplink frequency of 1,030 MHz. Aircraft transponders reply on a downlink frequency of 1,090 MHz. PCAS devices detect these transponder responses, then analyze and display conflict information.
PCAS is passive and less expensive than active aircraft detection systems, such as TCAS. TCAS operates with more precision than PCAS but is also more expensive and usually requires 'permanent' in-aircraft installation (requiring, in the United States, an FAA-approved mechanic to install). Class 2 TCAS gives mandatory instructions (called Resolution Advisories) whereas PCAS only alerts the pilot and may give a suggestion as to how to act. [ 3 ] A very well known general aviation organization completed an evaluation of the PCAS XRX system to demonstrate the capabilities. [ 4 ]
An interrogation is sent out from ground-based RADAR stations and/or TCAS or other actively interrogating systems in your area. This signal is sent on 1,030 MHz. For TCAS, this interrogation range can have a radius of 40 miles from the interrogation source. The Ground RADAR range can be 200 miles or more.
The transponder on any aircraft within range of the interrogation replies on 1090 MHz with their squawk code (known as mode A) and altitude code (or mode C).
Mode S transponders also reply on this frequency, and encoded within the mode S transmission is the mode A (squawk) and mode C (altitude) information.
Military aircraft also respond on this frequency but use a different transmission protocol (see Step 3).
A PCAS-containing aircraft's own transponder should also reply. However, the XRX unit watches for this signal and will not report it as a threat aircraft. The unit may use this information to establish base altitude for use in step 4.
The PCAS unit computes range (maximum 6 miles) based on the amplitude of the received signal, the altitude code is decoded, and the signal angle-of-arrival is determined to a resolution of "quadrants" (ahead, behind, left, or right) using a directional antenna array. [ 5 ] XRX will recognize interrogations from TCAS, Skywatch, and any other "active" system, military protocols, and Mode S transmissions.
The altitude of the aircraft (in the example, 2,500 ft.) is compared to the altitude of the PCAS altitude (e.g., 1,500 ft.) and the relative altitude is calculated (e.g., 1,000 ft. above you). With relative direction, altitude and range determined, XRX displays this information and stores it in memory.
If additional aircraft are within detection range, the above process is repeated for each aircraft. The top threat is displayed on the left of the traffic screen and the second and third threats are displayed on the right.
The greatest threat is determined by looking at aircraft within the detection window and comparing primarily the vertical separation (± relative altitude), and secondarily the range to the aircraft currently being displayed. XRX uses algorithms to determine which of two or more aircraft is a greater threat. [ 6 ] | https://en.wikipedia.org/wiki/Portable_collision_avoidance_system |
A portable emissions measurement system ( PEMS ) is a vehicle emissions testing device that is small and light enough to be carried inside or moved with a motor vehicle that is being driven during testing, rather than on the stationary rollers of a dynamometer that only simulates real-world driving.
Early examples of mobile vehicle emissions equipment were developed and marketed in the early 1990s by Warren Spring Laboratory UK during the early 1990s, which was used to measure on-road emissions as part of the UK Environment Research Program. Governmental agencies like United States Environmental Protection Agency (USEPA) and various states and private entities have begun to use PEMS in order to reduce both the costs and time involved in making mobile emissions decisions.
The European Commission introduced PEMS as a mandatory requirement for light-duty vehicle type approval in 2016 by amending the regulation that was established in 2007. [ 1 ]
Leo Breton of the US EPA invented the Real-time On-road Vehicle Emissions Reporter (ROVER) in 1995. [ 2 ] [ 3 ] The first commercially available device was invented by Michal Vojtisek-Lom, [ 4 ] and developed by David Miller of Clean Air Technologies International (CATI) Inc. in Buffalo, New York in 1999. These early field devices used engine data from either an on-board diagnostics (OBD) port, or directly from an engine sensor array . The first unit was developed for, and sold to - Dr. H. Christopher Frey of North Carolina State University (NCSU) for the first on-road testing project, which was sponsored by the North Carolina Department of Transportation. [ 5 ] David W. Miller, who co-founded CATI, first coined the phrase "Portable Emissions Measurement System" and "PEMS" when working on a 2000
New York City Metropolitan Transportation Agency bus project with Dr. Thomas Lanni of the New York State Department of Environmental Conservation, [ 6 ] as a short-hand description of the new device. Other governmental groups and universities soon followed, and quickly began to use the equipment due to its balance of accuracy, low cost, light weight, and availability. From 1999 through 2004, research groups such as Virginia Tech, [ 7 ] Penn State, and Texas A&M Transportation Institute, [ 8 ] Texas Southern University and others began to use PEMS in border crossing projects, roadway evaluations, traffic control methods, before-and-after scenarios, [ clarification needed ] and ferries, planes, and off-road vehicles, to explore what was possible outside of a lab environment. [ 9 ] [ 10 ] [ 11 ] [ 12 ] A project performed in April 2002 by the California Air Resources Board (CARB) - using non-1065 PEMS equipment, [ 13 ] tested 40 trucks over a period of 2½ days; [ 14 ] of which, 22 trucks were tested on road in Tulare, California. During this time, a high-profile project performed with early PEMS equipment was the World Trade Center (WTC) Ground Zero Project in lower Manhattan, [ 15 ] testing concrete pumpers, bulldozers, graders, and later - diesel cranes on Building #7 - 40 stories high. Other early PEMS projects such as Dr. Chris Frey's field work was used by the USEPA in the development of the MOVES Model. [ 16 ] However, users such as regulators and vehicle manufacturers had to wait for ROVER to be commercialized to conduct actual measurements of mass emissions rather than depend on estimates of mass emissions using data the OBD port, or a direct engine measurement, in order to have a more defensible data set. This push led to a new 2005 standard known as CFR 40 Part 1065. [ 17 ]
Many governmental entities (such as the USEPA and the United Nations Framework Convention on Climate Change or UNFCCC ) have identified target mobile-source pollutants in various mobile standards as CO 2 , NO x , Particulate Matter (PM), Carbon Monoxide (CO), Hydrocarbons (HC), to ensure that emissions standards are being met. Further, these governing bodies have begun adopting in-use testing program for non-road diesel engines , as well as other types of internal combustion engines, and are requiring the use of PEMS testing. It is important to delineate the various classifications of the latest 'transferable' emissions testing equipment from-time PEMS equipment, in order to best understand the desire of portability in field-testing of emissions.
Because a PEMS unit is able to be carried easily by one person from jobsite to jobsite, and can be used without the requirement of 'team lifting', the required emissions testing projects are economically viable. Simply put, more testing can be done more quickly, by less workers, dramatically increasing the amount of testing done in a certain time period. This in turn, significantly reduces the 'cost per test', yet at the same time increases the overall accuracy required in a 'real-world' environment. [ 18 ] Because the law of large numbers will create a convergence of results, it means that repeatability, predictability, and accuracy are enhanced, while simultaneously reducing the overall cost of the testing.
Nearly all modern engines, when tested new and according to the accepted testing protocols in a laboratory, produce relatively low emissions well within the set standards. As all individual engines of the same series are supposed to be identical, only one or several engines of each series get tested. The tests have shown that:
These findings are consistent with published literature, and with the data from a myriad of subsequent studies. They are more applicable to spark-ignition engines and considerably less to diesels, but with the regulation-driven advances in diesel engine technology (comparable to the advances in spark-ignition engines since the 1970s) it can be expected that these findings are likely to be applicable to the new generation diesel engines. Since 2000, multiple entities have used PEMS data to measured in-use, on-road emissions on hundreds of diesel engines installed in school buses, transit buses, delivery trucks, plow trucks, over-the-road trucks, pickups, vans, forklifts, excavators, generators, loaders, compressors, locomotives, passenger ferries, and other on-road, off-road and non-road applications . All the previously listed findings were demonstrated; in addition, it was noticed that extended idling of engines can have a significant impact on the emissions during subsequent operation.
Also, PEMS testing identified several engine "anomalies" where fuel-specific NOx emissions were two to three times higher than expected during some modes of operation, suggesting deliberate alterations of the engine control unit (ECU) settings. Such data set can be readily used for developing emissions inventories, as well as to evaluate various improvements in engines, fuels, exhaust after-treatment and other areas. (Data collected on "conventional" fleets then serves as "baseline" data to which various improvements are compared.) This data set can also be examined for compliance with not-to-exceed (NTE) and in-use emissions standards , which are 'US-based' emission standards that require on-road testing.
It is often difficult for PEMS to offer the same accuracy and variety of species measured as is possible with top-of-the-line laboratory instrumentation because PEMS are typically limited in size, weight and power consumption. For this reason, objections were raised [ by whom? ] against using PEMS for compliance verification. But there is also the potential for inaccuracy in fleet emissions deduced from laboratory measurements. For this reason, European WLTP results from PEMS will be weighted with a conformity factor of 2.1 (1.5 after 2019), i.e. the emissions measured by the PEMS are allowed to be a factor 2.1 higher than the limit. [ 19 ]
It is expected [ 20 ] that a variety of on-board systems will be designed, ranging from bread-box sized [ 21 ] [ 22 ] PEMS to instrumented trailers towed behind the tested truck. [ 23 ] The benefits of each approach need to be considered in light of other sources of errors associated with emissions monitoring, notably vehicle-to-vehicle differences, and the emissions variability within the vehicle itself.
PEMS need to be safe enough to use on public roads. During testing, portable emissions systems could attach extensions of the tailpipe, add lines and cables outside the vehicle, carry lead-acid batteries in the passenger compartment, have hot components accessible to bystanders, block emergency exits, interfere with the driver, or have loose components that could be caught in moving parts. Modifications to or disassembly of the tested vehicle such as drilling into the exhaust or removing intake air system need to be examined for their acceptance by both fleet managers and drivers, especially on passenger-carrying vehicles. The test equipment can not draw excessive electrical load from the test vehicle. Instead, sealed lead-acid batteries, fuel cells and generators have been used as external power sources, though they may add other hazards during driving.
The more time and expertise installation of the equipment requires, the greater the cost of testing, limiting the number of vehicles that can be tested. More testing is also possible with equipment that is versatile enough to be used on more than one type of vehicle. The weight and size of the equipment and consumables like calibration gases might limit moving to a sufficient number locations. Any restrictions on transport of hazardous materials (i.e. Flame ionization detector (FID) fuel or calibration gases) need to be taken into the account. The ability of the test crew to repair PEMS in the field using locally available resources can also be essential.
Ultimately, it should be demonstrated to show that a PEMS is suitable to the desired application. If the ultimate goal is to verify the compliance with in-use emissions requirements, a fleet of vehicles with known characteristics – including engines with dual-mapping and otherwise non-compliant engines – should be made available for testing. It should be then up to the PEMS manufacturers to practically demonstrate how these non-compliant vehicles can be identified using their system.
In order to achieve the required amount of 'testing volume' needed to validate real-world testing, three points must be considered:
Once a particular portable emissions system has been identified and pronounced as accurate, the next step is to ensure that the worker(s) are properly protected from work hazards associated with the task(s) being performed in the use of the testing equipment. For example, typical functions for a worker may be to transport the equipment to the jobsite (i.e. car, truck, train, or plane), carry the equipment to the jobsite, and lift the equipment into position.
On-road vehicle emissions testing is very different from the laboratory testing, bringing both considerable benefits and challenges: As the testing can take place during the regular operation of the tested vehicles, a large number of vehicles can be tested within a relatively short period of time and at relatively low cost. Engines than cannot be easily tested otherwise (i.e., ferry boat propulsion engines) can be tested. True real-world emissions data can be obtained. The instruments have to be small, lightweight, withstand difficult environment, and must not pose a safety hazard. Emissions data is subject to considerable variances, as real-world conditions are often neither well defined nor repeatable, and significant variances in emissions can exist even among otherwise identical engines.
On-road emissions testing therefore requires a different mindset than the traditional approach of testing in the laboratory and using models to predict real-world performance. In the absence of established methods, use of PEMS requires careful, thoughtful, broad approach. This should be considered when designing, evaluating and selecting PEMS for the desired application.
A recent example of PEMS advantages over laboratory testing is the Volkswagen (VW) Scandal of 2015 . [ 24 ] [ 25 ] Under a small grant from the International Council on Clean Transportation (icct), Daniel K Carder of West Virginia University (WVU) uncovered on-board software "cheats" that VW had installed on some diesel passenger vehicles ( Dieselgate scandal). The only way the discovery could have been made was by a non-programmed, random, on-road evaluation - utilizing a PEMS device. VW is now liable for over US$14 billion in fines. In 2016, these latest developments led to a global resurgence of interest in smaller, lighter, integrated and cost-effective "non-1065" PEMS, similar to the demonstration on MythBusters 2011 Episode 171 of "Bikes and Bazookas", in which a non-1065 PEMS was used to establish the difference between car and motorcycle pollution.
Overview of integrated PEMS (iPEMS) development
In response to Dieselgate , the " Real Driving Emissions " (RDE) standard has been developed in the European Union (EU) which has, in turn, increased the demand for smaller, lighter, more portable, less expensive and integrated PEMS [ 26 ] equipment kits. iPEMS equipment is not presently able to be used as a "certification" device in the U.S.
Definition of iPEMS
The following features are common to the smaller and lighter class of iPEMS equipment:
Advantages of iPEMS over 1065 PEMS equipment
The advantage of iPEMS equipment is that they are designed to both complement 1065 PEMS in addition to providing expanded capabilities, which are being driven by the requirements for quicker decision-making compounded by the 2015 Volkswagen scandal. These devices are presently being pursued by both the European Union (EU) and China for their RDE Programs. [ 27 ] | https://en.wikipedia.org/wiki/Portable_emissions_measurement_system |
Portable water purification devices are self-contained, easily transported units used to purify water from untreated sources (such as rivers, lakes, and wells ) for drinking purposes. Their main function is to eliminate pathogens , and often also suspended solids and some unpalatable or toxic compounds .
These units provide an autonomous supply of drinking water to people without access to clean water supply services, including inhabitants of developing countries and disaster areas, military personnel, campers , hikers , and workers in wilderness , and survivalists . They are also called point-of-use water treatment systems and field water disinfection techniques.
Techniques include heat (including boiling), filtration, activated charcoal adsorption, chemical disinfection (e.g. chlorination , iodine, ozonation , etc.), ultraviolet purification (including sodis ), distillation (including solar distillation), and flocculation . Often these are used in combination.
Untreated water may contain potentially pathogenic agents, including protozoa , bacteria, viruses, and some larvae of higher-order parasites such as liver flukes and roundworms. Chemical pollutants such as pesticides , heavy metals and synthetic organics may be present. Other components may affect taste, odour and general aesthetic qualities, including turbidity from soil or clay, colour from humic acid or microscopic algae, odours from certain type of bacteria, particularly Actinomycetes which produce geosmin , [ 1 ] and saltiness from brackish or sea water.
Common metallic contaminants such as copper and lead can be treated by increasing the pH using soda ash or lime, which precipitates such metals. Careful decanting of the clear water after settlement or the use of filtration provides acceptably low levels of metals. Water contaminated by aluminium or zinc cannot be treated in this way using a strong alkali as higher pHs re-dissolve the metal salts. Salt is difficult to remove except by reverse osmosis or distillation .
Most portable treatment processes focus on mitigating human pathogens for safety and removing particulates matter, tastes and odours. Significant pathogens commonly present in the developed world include Giardia , Cryptosporidium , Shigella , hepatitis A virus , Escherichia coli , and enterovirus . [ 2 ] In less developed countries there may be risks from cholera and dysentery organisms and a range of tropical enteroparasites.
Giardia lamblia and Cryptosporidium spp. , both of which cause diarrhea (see giardiasis and cryptosporidiosis ) are common pathogens. In backcountry areas of the United States and Canada they are sometimes present in sufficient quantity that water treatment is justified for backpackers, [ 3 ] although this has created some controversy. [ 4 ] (See wilderness acquired diarrhea .) In Hawaii and other tropical areas, Leptospira spp. are another possible problem. [ 5 ]
Less commonly seen in developed countries are organisms such as Vibrio cholerae which causes cholera and various strains of Salmonella which cause typhoid and para-typhoid diseases. Pathogenic viruses may also be found in water. The larvae of flukes are particularly dangerous in area frequented by sheep , deer , or cattle . If such microscopic larvae are ingested, they can form potentially life-threatening cysts in the brain or liver . This risk extends to plants grown in or near water including the commonly eaten watercress .
In general, more human activity up stream (i.e. the larger the stream/river) the greater the potential for contamination from sewage effluent , surface runoff , or industrial pollutants . Groundwater pollution may occur from human activity (e.g. on-site sanitation systems or mining) or might be naturally occurring (e.g. from arsenic in some regions of India and Bangladesh). Water collected as far upstream as possible above all known or anticipated risks of pollution poses the lowest risk of contamination and is best suited to portable treatment methods.
Not all techniques by themselves will mitigate all hazards. Although flocculation followed by filtration has been suggested as best practice [ 6 ] this is rarely practicable without the ability to carefully control pH and settling conditions. Ill-advised use of alum as a flocculant can lead to unacceptable levels of aluminium in the water so treated. [ 7 ] If water is to be stored, halogens offer extended protection.
Heat kills disease-causing micro-organisms, with higher temperatures and/or duration required for some pathogens. Sterilization of water (killing all living contaminants) is not necessary to make water safe to drink; one only needs to render enteric (intestinal) pathogens harmless. Boiling does not remove most pollutants and does not leave any residual protection.
The World Health Organization (WHO) states bringing water to rolling boil then naturally cooling is sufficient to inactivate pathogenic bacteria, viruses and protozoa. [ 8 ]
The Centers for Disease Control and Prevention (CDC) recommends a rolling boil for 1 minute. At high elevations, though, the boiling point of water drops. At altitudes greater than 6,562 feet (2,000 meters) boiling should continue for 3 minutes. [ 9 ]
All bacterial pathogens are quickly killed above 60 °C (140 °F), therefore, although boiling is not necessary to make the water safe to drink, the time taken to heat the water to boiling is usually sufficient to reduce bacterial concentrations to safe levels. [ 10 ] Encysted protozoan pathogens may require higher temperatures to remove any risk. [ 11 ]
Boiling is not always necessary nor sometimes enough. Pasteurization where enough pathogens are killed typically occurs at 63 °C for 30 minutes or 72 °C for 15 seconds. Certain pathogens must be heated above boiling (e.g. botulism – Clostridium botulinum requires 118 °C (244 °F), most endospores require 120 °C (248 °F), [ 12 ] and prions even higher). Higher temperatures may be achieved with a pressure cooker . Heat combined with ultraviolet light (UV), such as sodis method, reduces the necessary temperature and duration.
Portable pump filters are commercially available with ceramic filters that filter 5,000 to 50,000 litres per cartridge, removing pathogens down to the 0.2–0.3 micrometer (μm) range. Some also utilize activated charcoal filtering. Most filters of this kind remove most bacteria and protozoa, such as Cryptosporidium and Giardia lamblia, but not viruses except for the very largest of 0.3 μm and larger diameters, so disinfection by chemicals or ultraviolet light is still required after filtration. It is worth noting that not all bacteria are removed by 0.2 μm pump filters; for example, strands of thread-like Leptospira spp. (which can cause leptospirosis) are thin enough to pass through a 0.2 μm filter. Effective chemical additives to address shortcomings in pump filters include chlorine, chlorine dioxide, iodine, and sodium hypochlorite (bleach). There have been polymer and ceramic filters on the market that incorporated iodine post-treatment in their filter elements to kill viruses and the smaller bacteria that cannot be filtered out, but most have disappeared due to the unpleasant taste imparted to the water, as well as possible adverse health effects when iodine is ingested over protracted periods.
While the filtration elements may do an excellent job of removing most bacteria and fungi contaminants from drinking water when new, the elements themselves can become colonization sites. In recent years some filters have been enhanced by bonding silver metal nanoparticles to the ceramic element and/or to the activated charcoal to suppress growth of pathogens.
Small, hand-pumped reverse osmosis filters were originally developed for the military in the late 1980s for use as survival equipment, for example, to be included with inflatable rafts on aircraft. Civilian versions are available. Instead of using the static pressure of a water supply line to force the water through the filter, pressure is provided by a hand-operated pump. These devices can generate drinkable water from seawater.
The Portable Aqua Unit for Lifesaving ("PAUL") is a portable ultrafiltration -based membrane water filter for humanitarian aid. It allows the decentralized supply of clean water in emergency and disaster situations for about 400 persons per unit per day. The filter is designed to function with neither chemicals nor energy nor trained personnel. [ citation needed ]
Granular activated carbon filtering utilizes a form of activated carbon with a high surface area, and adsorbs many compounds, including many toxic compounds. Water passing through activated carbon is commonly used in concert with hand pumped filters to address organic contamination , taste, or objectionable odors. Activated carbon filters aren't usually used as the primary purification techniques of portable water purification devices, but rather as secondary means to complement another purification technique. It is most commonly implemented for pre- or post-filtering, in a separate step than ceramic filtering, in either case being implemented prior to the addition of chemical disinfectants used to control bacteria or viruses that filters cannot remove. Activated charcoal can remove chlorine from treated water, removing any residual protection remaining in the water protecting against pathogens, and should not, in general, be used without careful thought after chemical disinfection treatments in portable water purification processing. Ceramic/Carbon Core filters with a 0.5 μm or smaller pore size are excellent for removing bacteria and cysts while also removing chemicals.
Chemical disinfection with halogens , chiefly chlorine and iodine , results from oxidation of essential cellular structures and enzymes . The primary factors that determine the rate and proportion of microorganisms killed are the residual or available halogen concentration and the exposure time. [ 13 ] Secondary factors are pathogen species, water temperature, pH, and organic contaminants. In field-water disinfection, use of concentrations of 1–16 mg/L for 10–60 min is generally effective. Of note, Cryptosporidium oocysts, likely Cyclospora species, Ascaris eggs are extremely resistant to halogens and field inactivation may not be practical with bleach and iodine.
Iodine used for water purification is commonly added to water as a solution, in crystallized form, or in tablets containing tetraglycine hydroperiodide that release 8 mg of iodine per tablet. The iodine kills many, but not all, of the most common pathogens present in natural fresh water sources. Carrying iodine for water purification is an imperfect but lightweight solution for those in need of field purification of drinking water. Kits are available in camping stores that include an iodine pill and a second pill (vitamin C or ascorbic acid ) that will remove the iodine taste from the water after it has been disinfected . The addition of vitamin C, in the form of a pill or in flavored drink powders, precipitates much of the iodine out of the solution, so it should not be added until the iodine has had sufficient time to work. This time is 30 minutes in relatively clear, warm water, but is considerably longer if the water is turbid or cold. If the iodine has precipitated out of the solution, then the drinking water has less available iodine in the solution. Tetraglycine hydroperiodide maintains its effectiveness indefinitely before the container is opened; although some manufacturers suggest not using the tablets more than three months after the container has initially been opened, the shelf life is in fact very long provided that the container is resealed immediately after each time it is opened. [ 14 ]
Similarly to potassium iodide (KI), sufficient consumption of tetraglycine hydroperiodide tablets may protect the thyroid against uptake of radioactive iodine. A 1995 study found that daily consumption of water treated with 4 tablets containing tetraglycine hydroperiodide reduced the uptake of radioactive iodine in human subjects to a mean of 1.1 percent, from a baseline mean of 16 percent, after a week of treatment. At 90 days of daily treatment, uptake was further reduced to a mean of 0.5 percent. [ 15 ] However, unlike KI, tetraglycine hydroperiodide is not recommended by the WHO for this purpose. [ 16 ]
Iodine should be allowed at least 30 minutes to kill Giardia . [ 17 ]
A potentially lower cost alternative to using iodine-based water purification tablets is the use of iodine crystals, although there are serious risks of acute iodine toxicity if preparation and dilution are not measured with some accuracy. [ 18 ] [ 19 ] This method may not be adequate in killing Giardia cysts in cold water. [ 20 ] An advantage of using iodine crystals is that only a small amount of iodine is dissolved from the iodine crystals at each use, giving this method of treating water a capability for treating very large volumes of water. Unlike tetraglycine hydroperiodide tablets, iodine crystals have an unlimited shelf life as long as they are not exposed to air for long periods of time or are kept under water. Iodine crystals will sublimate if exposed to air for long periods of time. The large quantity of water that can be purified with iodine crystals at low cost makes this technique especially cost effective for point of use or emergency water purification methods intended for use longer than the shelf life of tetraglycine hydroperiodide.
Chlorine-based halazone tablets were formerly popularly used for portable water purification. Chlorine in water is more than three times more effective as a disinfectant against Escherichia coli than iodine. [ 21 ] Halazone tablets were thus commonly used during World War II by U.S. soldiers for portable water purification, even being included in accessory packs for C-rations until 1945.
Sodium dichloroisocyanurate (NaDCC) has largely displaced halazone tablets for the few remaining chlorine-based water purification tablets available today.
Common bleach including calcium hypochlorite (Ca[OCl] 2 ) and sodium hypochlorite (NaOCl) are common, well-researched, low-cost oxidizers.
Chlorine bleach tablets give a more stable platform for disinfecting the water than liquid bleach as the liquid version tends to degrade with age and give unregulated results unless assays are carried out, which may be impractical in the field. Still, liquid bleach may nonetheless safely be used for short-term emergency water disinfection.
The United States Environmental Protection Agency (EPA) recommends two drops of 8.25% sodium hypochlorite solution (regular, unscented chlorine bleach) mixed per one quart/liter of water and leave to stand covered for 30 to 60 minutes. Two drops of 5% solution also suffices. Double the amount of bleach if the water is cloudy, colored, or very cold. Afterwards, the water should have a slight chlorine odor. If not repeat the dosage and let stand for another 15 minutes before use. After this treatment, the water may be left open to reduce the chlorine smell and taste. [ 22 ] [ 6 ]
The CDC and Population Services International (PSI) promote a similar product (a 0.5% - 1.5% sodium hypochlorite solution) as part of their Safe Water System (SWS) strategy. The product is sold in developing countries under local brand names specifically for the purpose of disinfecting drinking water. [ 9 ]
Neither chlorine (e.g., bleach) nor iodine alone is considered completely effective against Cryptosporidium , although they are partially effective against Giardia . Chlorine is considered slightly better against the latter. A more complete field solution that includes chemical disinfectants is to first filter the water, using a 0.2 μm ceramic cartridge pumped filter, followed by treatment with iodine or chlorine, thereby filtering out cryptosporidium, Giardia, and most bacteria, along with the larger viruses, while also using chemical disinfectant to address smaller viruses and bacteria that the filter cannot remove. This combination is also potentially more effective in some cases than even using portable electronic disinfection based on UV treatment.
Chlorine dioxide can come from tablets or be created by mixing two chemicals together. It is more effective than iodine or chlorine against giardia, and although it has only low to moderate effectiveness against cryptosporidium, iodine and chlorine are ineffective against this protozoan. [ 9 ] The cost of chlorine dioxide treatment is higher than the cost of iodine treatment. [ citation needed ]
A simple brine {salt + water} solution in an electrolytic reaction produces a powerful mixed oxidant disinfectant (mostly chlorine in the form of hypochlorous acid (HOCl) and some peroxide, ozone, chlorine dioxide). [ 23 ]
Sodium dichloroisocyanurate or troclosene sodium, more commonly shortened as NaDCC, is a form of chlorine used for disinfection. It is used by major non-governmental organizations such as UNICEF [ 24 ] to treat water in emergencies.
Sodium dichloroisocyanurate tablets are available in a range of concentrations to treat differing volumes of water [ 25 ] to give the World Health Organization's recommended 5ppm [ 26 ] available chlorine. They are effervescent tablets allowing the tablet to dissolve in a matter of minutes.
An alternative to iodine-based preparations in some usage scenarios are silver ion/ chlorine dioxide -based tablets or droplets. These solutions may disinfect water more effectively than iodine-based techniques while leaving hardly any noticeable taste in the water in some usage scenarios. [ citation needed ] Silver ion/chlorine dioxide-based disinfecting agents will kill Cryptosporidium and Giardia , if utilized correctly. The primary disadvantage of silver ion/chlorine dioxide-based techniques is the long purification times (generally 30 minutes to 4 hours, depending on the formulation used). Another concern is the possible deposition and accumulation of silver compounds in various body tissues leading to a rare condition called argyria that results in a permanent, disfiguring, bluish-gray pigmentation of the skin, eyes, and mucous membranes.
One recent study has found that the wild Salmonella which would reproduce quickly during subsequent dark storage of solar-disinfected water could be controlled by the addition of just 10 parts per million of hydrogen peroxide. [ 27 ]
Ultraviolet (UV) light induces the formation of covalent linkages on DNA and thereby prevents microbes from reproducing. Without reproduction, the microbes become far less dangerous. Germicidal UV-C light in the short wavelength range of 100–280 nm acts on thymine , one of the four base nucleotides in DNA. When a germicidal UV photon is absorbed by a thymine molecule that is adjacent to another thymine within the DNA strand, a covalent bond or dimer between the molecules is created. This thymine dimer prevents enzymes from "reading" the DNA and copying it, thus neutering the microbe. Prolonged exposure to ionizing radiation can cause single and double-stranded breaks in DNA, oxidation of membrane lipids, and denaturation of proteins, all of which are toxic to cells. Still, there are limits to this technology. Water turbidity (i.e., the amount of suspended & colloidal solids contained in the water to be treated) must be low, such that the water is clear, for UV purification to work well - thus a pre-filter step might be necessary.
A concern with UV portable water purification is that some pathogens are hundreds of times less sensitive to UV light than others. Protozoan cysts were once believed to be among the least sensitive, however recent studies have proved otherwise, demonstrating that both Cryptosporidium and Giardia are deactivated by a UV dose of just 6 mJ/cm 2 [ 28 ] However, EPA regulations and other studies show that it is viruses that are the limiting factor of UV treatment, requiring a 10-30 times greater dose of UV light than Giardia or Cryptosporidium . [ 29 ] [ 30 ] Studies have shown that UV doses at the levels provided by common portable UV units are effective at killing Giardia [ 31 ] and that there was no evidence of repair and reactivation of the cysts. [ 32 ]
Water treated with UV still has the microbes present in the water, only with their means for reproduction turned "off". In the event that such UV-treated water containing neutered microbes is exposed to visible light (specifically, wavelengths of light over 330-500 nm) for any significant period of time, a process known as photo reactivation can take place, where the possibility for repairing the damage in the bacteria's reproduction DNA arises, potentially rendering them once more capable of reproducing and causing disease. [ 33 ] UV-treated water must therefore not be exposed to visible light for any significant period of time after UV treatment, before consumption, to avoid ingesting reactivated and dangerous microbes.
Recent developments in semiconductor technology allows for the development of UV-C Light Emitting Diodes (LEDs). UV-C LED systems address disadvantages of mercury-based technology, namely: power-cycling penalties, high power needs, fragility, warm-up time, and mercury content.
In solar water disinfection (often shortened as "sodis"), microbes are destroyed by temperature and UVA radiation provided by the sun . Water is placed in a transparent plastic PET bottle or plastic bag, oxygenated by shaking partially filled capped bottles prior to filling the bottles all the way, and left in the sun for 6–24 hours atop a reflective surface.
Solar distillation relies on sunlight to warm and evaporate the water to be purified which then condenses and trickles into a container. In theory, a solar (condensation) still removes all pathogens, salts, metals, and most chemicals but in field practice the lack of clean components, easy contact with dirt, improvised construction, and disturbances result in cleaner, yet contaminated water.
Water filters can be made on-site using local materials such as sand and charcoal (e.g. from firewood burned in a special way). These filters are sometimes used by soldiers and outdoor enthusiasts. Due to their low cost they can be made and used by anyone. The reliability of such systems is highly variable. Such filters can do little, if anything, to mitigate germs and other harmful constituents and can give a false sense of security that the water so produced is potable. Water processed through an improvised filter should undergo secondary processing such as boiling to render it safe for consumption.
Human water-borne diseases usually come from other humans, thus human-derived materials ( feces , medical waste, wash water, lawn chemicals, gasoline engines, garbage, etc.) should be kept far away from water sources. For example, human excreta should be buried well away (>60 meters/200 feet) from water sources to reduce contamination. [ 9 ] In some wilderness areas it is recommended that all waste be packed up and carted out to a properly designated disposal point. | https://en.wikipedia.org/wiki/Portable_water_purification |
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Algae ( UK : / ˈ æ l ɡ iː / AL -ghee , US : / ˈ æ l dʒ iː / ⓘ AL -jee ; sg. : alga / ˈ æ l ɡ ə / ⓘ AL -gə ) is an informal term for any organisms of a large and diverse group of photosynthetic organisms that are not plants , and includes species from multiple distinct clades . Such organisms range from unicellular microalgae , such as cyanobacteria , Chlorella , and diatoms , to multicellular macroalgae such as kelp or brown algae which may grow up to 50 metres (160 ft) in length. Most algae are aquatic organisms and lack many of the distinct cell and tissue types, such as stomata , xylem , and phloem that are found in land plants . The largest and most complex marine algae are called seaweeds . In contrast, the most complex freshwater forms are the Charophyta , a division of green algae which includes, for example, Spirogyra and stoneworts . Algae that are carried passively by water are plankton , specifically phytoplankton .
Algae constitute a polyphyletic group because they do not include a common ancestor , and although eukaryotic algae with chlorophyll -bearing plastids seem to have a single origin (from symbiogenesis with cyanobacteria ), they were acquired in different ways. Green algae are a prominent example of algae that have primary chloroplasts derived from endosymbiont cyanobacteria. Diatoms and brown algae are examples of algae with secondary chloroplasts derived from endosymbiotic red algae , which they acquired via phagocytosis . Algae exhibit a wide range of reproductive strategies, from simple asexual cell division to complex forms of sexual reproduction via spores .
Algae lack the various structures that characterize plants (which evolved from freshwater green algae), such as the phyllids (leaf-like structures) and rhizoids of bryophytes ( non-vascular plants ), and the roots , leaves and other xylemic / phloemic organs found in tracheophytes ( vascular plants ). Most algae are autotrophic , although some are mixotrophic , deriving energy both from photosynthesis and uptake of organic carbon either by osmotrophy , myzotrophy or phagotrophy . Some unicellular species of green algae, many golden algae , euglenids , dinoflagellates , and other algae have become heterotrophs (also called colorless or apochlorotic algae), sometimes parasitic , relying entirely on external energy sources and have limited or no photosynthetic apparatus. Some other heterotrophic organisms, such as the apicomplexans , are also derived from cells whose ancestors possessed chlorophyllic plastids, but are not traditionally considered as algae. Algae have photosynthetic machinery ultimately derived from cyanobacteria that produce oxygen as a byproduct of splitting water molecules , unlike other organisms that conduct anoxygenic photosynthesis such as purple and green sulfur bacteria . Fossilized filamentous algae from the Vindhya basin have been dated to 1.6 to 1.7 billion years ago. ( Full article... )
A coenocyte ( / ˈ s iː n ə ˌ s aɪ t / ) is a multinucleate cell which can result from multiple nuclear divisions without their accompanying cytokinesis , in contrast to a syncytium , which results from cellular aggregation followed by dissolution of the cell membranes inside the mass. The word syncytium in animal embryology is used to refer to the coenocytic blastoderm of invertebrates . A coenocytic colony is referred to as a coenobium ( pl. : coenobia ), and most coenobia are composed of a distinct number of cells, often as a multiple of two (4, 8, etc.).
Research suggests that coenobium formation may be a defense against grazing in some species. ( Full article... )
Red algae , or Rhodophyta ( / r oʊ ˈ d ɒ f ɪ t ə / , / ˌ r oʊ d ə ˈ f aɪ t ə / ; from Ancient Greek ῥόδον ( rhódon ) ' rose ' and φυτόν ( phutón ) ' plant ' ), make up one of the oldest groups of eukaryotic algae . The Rhodophyta comprises one of the largest phyla of algae , containing over 7,000 recognized species within over 900 genera amidst ongoing taxonomic revisions. The majority of species (6,793) are Florideophyceae , and mostly consist of multicellular , marine algae, including many notable seaweeds . Red algae are abundant in marine habitats. Approximately 5% of red algae species occur in freshwater environments, with greater concentrations in warmer areas. Except for two coastal cave dwelling species in the asexual class Cyanidiophyceae , no terrestrial species exist, which may be due to an evolutionary bottleneck in which the last common ancestor lost about 25% of its core genes and much of its evolutionary plasticity.
Red algae form a distinct group characterized by eukaryotic cells without flagella and centrioles , chloroplasts without external endoplasmic reticulum or unstacked (stroma) thylakoids , and use phycobiliproteins as accessory pigments , which give them their red color. Despite their name, red algae can vary in color from bright green, soft pink, resembling brown algae, to shades of red and purple, and may be almost black at greater depths. Unlike green algae, red algae store sugars as food reserves outside the chloroplasts as floridean starch , a type of starch that consists of highly branched amylopectin without amylose . Most red algae are multicellular , macroscopic, and reproduce sexually . The life history of red algae is typically an alternation of generations that may have three generations rather than two. Coralline algae , which secrete calcium carbonate and play a major role in building coral reefs , belong there. ( Full article... )
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Animals are multicellular , eukaryotic organisms in the biological kingdom Animalia ( / ˌ æ n ɪ ˈ m eɪ l i ə / ). With few exceptions, animals consume organic material , breathe oxygen , have myocytes and are able to move , can reproduce sexually , and grow from a hollow sphere of cells , the blastula , during embryonic development . Animals form a clade , meaning that they arose from a single common ancestor . Over 1.5 million living animal species have been described , of which around 1.05 million are insects , over 85,000 are molluscs , and around 65,000 are vertebrates . It has been estimated there are as many as 7.77 million animal species on Earth. Animal body lengths range from 8.5 μm (0.00033 in) to 33.6 m (110 ft). They have complex ecologies and interactions with each other and their environments, forming intricate food webs . The scientific study of animals is known as zoology , and the study of animal behaviour is known as ethology .
The animal kingdom is divided into five major clades, namely Porifera , Ctenophora , Placozoa , Cnidaria and Bilateria . Most living animal species belong to the clade Bilateria, a highly proliferative clade whose members have a bilaterally symmetric and significantly cephalised body plan , and the vast majority of bilaterians belong to two large clades: the protostomes , which includes organisms such as arthropods , molluscs , flatworms , annelids and nematodes ; and the deuterostomes , which include echinoderms , hemichordates and chordates , the latter of which contains the vertebrates . The much smaller basal phylum Xenacoelomorpha have an uncertain position within Bilateria.
Animals first appeared in the fossil record in the late Cryogenian period and diversified in the subsequent Ediacaran period in what is known as the Avalon explosion . Earlier evidence of animals is still controversial; the sponge -like organism Otavia has been dated back to the Tonian period at the start of the Neoproterozoic , but its identity as an animal is heavily contested. Nearly all modern animal phyla first appeared in the fossil record as marine species during the Cambrian explosion , which began around 539 million years ago (Mya), and most classes during the Ordovician radiation 485.4 Mya. Common to all living animals, 6,331 groups of genes have been identified that may have arisen from a single common ancestor that lived about 650 Mya during the Cryogenian period. ( Full article... )
Zoology ( UK : / z u ˈ ɒ l ə dʒ i / zoo- OL -ə-jee , US : / z oʊ ˈ ɒ l ə dʒ i / zoh- OL -ə-jee ) is the scientific study of animals . Its studies include the structure , embryology , classification , habits , and distribution of all animals, both living and extinct , and how they interact with their ecosystems . Zoology is one of the primary branches of biology . The term is derived from Ancient Greek ζῷον , zōion ('animal'), and λόγος , logos ('knowledge', 'study'). ( Full article... )
Jellyfish , also known as sea jellies or simply jellies , are the medusa -phase of certain gelatinous members of the subphylum Medusozoa , which is a major part of the phylum Cnidaria .
Jellyfish are mainly free-swimming marine animals , although a few are anchored to the seabed by stalks rather than being motile. They are made of an umbrella-shaped main body made of mesoglea , known as the bell , and a collection of trailing tentacles on the underside. Via pulsating contractions, the bell can provide propulsion for locomotion through open water. The tentacles are armed with stinging cells and may be used to capture prey or to defend against predators. Jellyfish have a complex life cycle , and the medusa is normally the sexual phase, which produces planula larvae. These then disperse widely and enter a sedentary polyp phase which may include asexual budding before reaching sexual maturity. ( Full article... )
Dermotherium is a genus of fossil mammals closely related to the living colugos , a small group of gliding mammals from Southeast Asia. Two species are recognized: D. major from the Late Eocene of Thailand , based on a single fragment of the lower jaw, and D. chimaera from the Late Oligocene of Thailand, known from three fragments of the lower jaw and two isolated upper molars . In addition, a single isolated upper molar from the Early Oligocene of Pakistan has been tentatively assigned to D. chimaera . All sites where fossils of Dermotherium have been found were probably forested environments and the fossil species were probably forest dwellers like living colugos, but whether they had the gliding adaptations of the living species is unknown.
Some features of the teeth differentiate Dermotherium from both living colugo species, but other features are shared with only one of the two. The third lower incisor , lower canine , and third lower premolar at least are pectinate or comblike, bearing longitudinal rows of tines or cusps , an unusual feature of colugos (the first two lower incisors are unknown in Dermotherium ). The fourth lower premolar instead resembles the lower molars. The front part of these teeth, the trigonid , is broader in D. chimaera than in D. major , which is known only from the second and third lower molars. The two species also differ in the configuration of the inner back corner of the lower molars. The upper molars are triangular teeth bearing several distinct small cusps, particularly on the second upper molar, and with wrinkled enamel . ( Full article... )
The following table lists estimated numbers of described extant species for the animal groups with the largest numbers of species, [ 1 ] along with their principal habitats (terrestrial, fresh water, [ 2 ] and marine), [ 3 ] and free-living or parasitic ways of life. [ 4 ] Species estimates shown here are based on numbers described scientifically; much larger estimates have been calculated based on various means of prediction, and these can vary wildly. For instance, around 25,000–27,000 species of nematodes have been described, while published estimates of the total number of nematode species include 10,000–20,000; 500,000; 10 million; and 100 million. [ 5 ] Using patterns within the taxonomic hierarchy, the total number of animal species—including those not yet described—was calculated to be about 7.77 million in 2011. [ 6 ] [ 7 ] [ a ]
3,000–6,500 [ 15 ]
4,000–25,000 [ 15 ]
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Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning , designing , and constructing buildings or other structures . The term comes from Latin architectura ; from Ancient Greek ἀρχιτέκτων ( arkhitéktōn ) ' architect ' ; from ἀρχι- ( arkhi- ) ' chief ' and τέκτων ( téktōn ) ' creator ' . Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art . Historical civilizations are often identified with their surviving architectural achievements.
Architecture began as rural, oral vernacular architecture that developed from trial and error to successful replication. Ancient urban architecture was preoccupied with building religious structures and buildings symbolizing the political power of rulers until Greek and Roman architecture shifted focus to civic virtues. Indian and Chinese architecture influenced forms all over Asia and Buddhist architecture in particular took diverse local flavors. During the Middle Ages , pan-European styles of Romanesque and Gothic cathedrals and abbeys emerged while the Renaissance favored Classical forms implemented by architects known by name. Later, the roles of architects and engineers became separated.
Modern architecture began after World War I as an avant-garde movement that sought to develop a completely new style appropriate for a new post-war social and economic order focused on meeting the needs of the middle and working classes. Emphasis was put on modern techniques, materials, and simplified geometric forms, paving the way for high-rise superstructures. Many architects became disillusioned with modernism which they perceived as ahistorical and anti-aesthetic, and postmodern and contemporary architecture developed. Over the years, the field of architectural construction has branched out to include everything from ship design to interior decorating. ( Full article... )
Classical architecture usually denotes architecture which is more or less consciously derived from the principles of Greek and Roman architecture of classical antiquity , or sometimes more specifically, from De architectura (c. 10 AD) by the Roman architect Vitruvius . Different styles of classical architecture have arguably existed since the Carolingian Renaissance , and prominently since the Italian Renaissance , and in the later period known as neoclassical architecture or Classical revival. Although classical styles of architecture can vary greatly, they can in general all be said to draw on a common "vocabulary" of decorative and constructive elements. In much of the Western world , different classical architectural styles have dominated the history of architecture from the Renaissance until World War II . Classical architecture continues to inform many architects.
The term classical architecture also applies to any mode of architecture that has evolved to a highly refined state, such as classical Chinese architecture, or classical Mayan architecture. It can also refer to any architecture that employs classical aesthetic philosophy. The term might be used differently from "traditional" or " vernacular architecture " although it can share underlying axioms with it. ( Full article... )
Architects : Matthew Brettingham , William Bruce , William Burges , John Douglas , Charles Holden , El Lissitzky , Benjamin Mountfort , I. M. Pei , Albert Speer , Rudolf Wolters . Buildings : 7 World Trade Center , Angkor Wat , Baden-Powell House , Belton House , Borobudur , BP Pedestrian Bridge , Bramall Hall , Buckingham Palace , Buildings and architecture of Bristol , Buildings of Jesus College, Oxford , Buildings of Nuffield College, Oxford , Building of the World Trade Center , Castell Coch , Catherine de' Medici's building projects , Chartwell , Chicago Board of Trade Building , Cragside , Heian Palace , Holkham Hall , IG Farben Building , House with Chimaeras , Hoysala architecture , City of Manchester Stadium , Monnow Bridge , Mosque , Michigan State Capitol , New Orleans Mint , Oregon State Capitol , Oriel College, Oxford , Palazzo Pitti , Palladian architecture , Pennsylvania State Capitol , Round Church, Preslav , Sandringham House , Sanssouci , Santa Maria de Ovila , Scottish Parliament building , Sicilian Baroque , St Donat's Castle , St. Michael's Cathedral, Qingdao , St. Michael's Golden-Domed Monastery , St Nicholas, Blakeney , Vkhutemas , The Tower House , West Wycombe Park
Featured lists Chicago Landmarks , National Treasures of Japan (castles) , National Treasures of Japan (shrines) , Pritzker Prize , New churches by John Douglas , Church restorations, amendments and furniture by John Douglas , Houses and associated buildings by John Douglas , Non-ecclesiastical and non-residential works by John Douglas , Scheduled monuments in Maidstone , Works by Charles Holden , Grade I listed buildings in: Bath and North East Somerset , Maidstone , Mendip , North Somerset , Sedgemoor , South Somerset , Taunton Deane , West Somerset , List of tallest buildings in: Boston , Chicago , Cleveland , Dallas , Detroit , Dubai , Hong Kong , Las Vegas , London , Los Angeles , Manchester , Miami , Minneapolis , Philadelphia , Providence , San Francisco , Shanghai , Singapore , Tokyo , Toronto , Tulsa , Vancouver , Listed buildings in: Runcorn (urban area) , Runcorn (rural area) , Widnes
Architects : William Adam , Eustace Balfour , Antoni Gaudí , Thomas Harrison , Zvi Hecker , Bjarke Ingels , E. G. Paley , Timothy L. Pflueger , Antonin Raymond , Kenzo Tange . Buildings : 108 North State Street , 5th Avenue Theatre , Algonquin Hotel , Andriyivskyy Descent , AT&T Corporate Center , Ballard Carnegie Library , Baths of Zeuxippus , Beaumont House , Benjaminville Friends Meeting House and Burial Ground , Blackstone Library , Boughton Monchelsea Place , The Casbah Coffee Club , Central Troy Historic District , Chana School , Chester Rows , Chicago Spire , Chicago Theatre , Chrysler Building , Churche's Mansion , Clinton Presidential Center , Crown Fountain , Dolphinarium , Eaton Hall, Cheshire , Édifice Price , Edinburgh Place Ferry Pier , Ellwood House , The Exchange, Bristol , Forbidden City , Harold Washington Cultural Center , Heller House , Historic Michigan Boulevard District , Hull House , Imbrex and tegula , Imperial War Museum North , Jay Pritzker Pavilion , Joffrey Tower , Joseph F. Glidden House , Linton Park , Liverpool Town Hall , Louvre , Manila Hotel , Marquette Building (Chicago) , Millennium Stadium , National Gallery, London , National Police Memorial , New Bedford Historic District , Old Louisville , One Bayfront Plaza , One Times Square , Onion dome , Oregon Public Library , Pavillon de Flore , Presidio of Santa Barbara , Queen's Pier , Rancho Camulos , Robot Building , Rock N Roll McDonald's , Roman Baths (Bath) , Rookery Building , Senate House (University of London) , Shamrock Hotel , Sycamore Historic District , Taipei 101 , TCF Bank Stadium , United States Institute of Peace Headquarters , University Mall (Little Rock, Arkansas) , University of Illinois Observatory , University of Virginia , Upper Brook Street Chapel, Manchester , Valley of the Kings , Via della Conciliazione , Victoria Rooms (Bristol) , Waller Hall , Wales Millennium Centre , World Trade Center . Castles and fortifications : Beaumaris Castle , Berkhamsted Castle , Bowes Castle , Buckton Castle , Caernarfon Castle , Caludon Castle , Château Gaillard , Château de Chinon , Conwy Castle , Dolbadarn Castle , Dunstaffnage Castle , Fort Greble , Fort Pasir Panjang , Fortress of Klis , Golubac fortress , Goodrich Castle , Haapsalu Castle , Hadleigh Castle , Halton Castle , Himeji Castle , Hylton Castle , Kaunas Fortress , Kenilworth Castle , Loch Leven Castle , Longtown Castle , Okehampton Castle , Oxford Castle , Peckforton Castle , Castle Rising , Roslin Castle , Smederevo Fortress , St Briavels Castle , Vilnius Castle Complex , Walls of Constantinople , Walls of Dubrovnik , York Castle . Religious buildings : Akhtala monastery , Akshardham Temple , Al-Aqsa Mosque , Al-Masjid an-Nabawi , Bath Abbey , Cathedral of the Immaculate Conception (Hong Kong) , Chester Cathedral , College of All Saints, Maidstone , Elgin Cathedral , Etchmiadzin Cathedral , Ganting Grand Mosque , Hurva Synagogue , Jesuit Missions of Chiquitos , Liverpool Metropolitan Cathedral , Mexico City Metropolitan Cathedral , Mezhyhirskyi Monastery , Old St Paul's Cathedral , St Mary's Church, Acton , St Mary's Church, Nantwich , St Mary's Church, Nether Alderley , St Thomas the Martyr's Church, Oxford , Sunol Water Temple , Uppsala Cathedral , Wells Cathedral , Zagreb Synagogue , Zhenguo Temple . Cities, countries and regions : Architecture of Denmark , Architecture of Leeds , Architecture of Madagascar , Architecture of Norway , Architecture of Scotland , Architecture of the medieval cathedrals of England , Buildings and architecture of Bath , Castles in Great Britain and Ireland , Grade I listed buildings in Somerset , Architecture of the Song Dynasty , Fatimid architecture .
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Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition , subtraction , multiplication , and division . In a wider sense, it also includes exponentiation , extraction of roots , and taking logarithms . ( Full article... )
The Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC. Later Roman numerals, descended from tally marks used for counting. The continuous development of modern arithmetic starts with ancient Greece, although it originated much later than the Babylonian and Egyptian examples. Euclid is often credited as the first mathematician to separate study of arithmetic from philosophical and mystical beliefs. Greek numerals were used by Archimedes , Diophantus and others in a positional notation not very different from ours. The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra. The ancient Chinese used a positional notation similar to that of the Greeks. The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base and the use of a digit representing zero (0). This allowed the system to consistently represent both large and small integers. This approach eventually replaced all other systems. In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities. The flourishing of algebra in the medieval Islamic world and in Renaissance Europe was an outgrowth of the enormous simplification of computation through decimal notation.
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