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The Penrose–Lucas argument is a logical argument partially based on a theory developed by mathematician and logician Kurt Gödel . In 1931, he proved that every effectively generated theory capable of proving basic arithmetic either fails to be consistent or fails to be complete . Due to human ability to see the truth of formal systems' Gödel sentences , it is argued that the human mind cannot be computed on a Turing Machine that works on Peano arithmetic because the latter can't see the truth value of its Gödel sentence, while human minds can. Mathematician Roger Penrose modified the argument in his first book on consciousness , The Emperor's New Mind (1989), where he used it to provide the basis of his theory of consciousness: orchestrated objective reduction .
Gödel showed that any such theory also including a statement of its own consistency is inconsistent. A key element of the proof is the use of Gödel numbering to construct a "Gödel sentence" for the theory, which encodes a statement of its own incompleteness: "This theory can't prove this statement"; or "I am not provable in this system". Either this statement and its negation are both unprovable (the theory is incomplete) or both provable (the theory is inconsistent). In the first eventuality the statement is intuitively true [ 1 ] (since it is not provable); otherwise, the statement is intuitively false - though provable.
An analogous statement has been used to show that humans are subject to the same limits as machines: “Lucas cannot consistently assert this formula”. In defense of Lucas , J. E. Martin and K. H. Engleman argued in The Mind's I Has Two Eyes [ 2 ] that Lucas can recognise that the sentence is true, as there's a point of view from which he can understand how the sentence tricks him. [ 3 ] From this point of view Lucas can appreciate that he can't assert the sentence-and consequently he can recognise its truth. [ 4 ] Still, this criticism only works if we assume that we can replace Lucas' reasoning with a formal system whose theorems can be listed by an algorithm that has a Gödel sentence, but the Penrose-Lucas argument tries to prove otherwise: our ability to understand this level of arithmetic is not an effective procedure that can be simulated in a Turing machine .
Penrose argued that while a formal proof system cannot prove its own consistency, Gödel-unprovable results are provable by human mathematicians. [ 5 ] He takes this disparity to mean that human mathematicians are not describable as formal proof systems (which theorems can be proved using an abstract object such as a computer), and are therefore running a non-computable algorithm . Similar claims about the implications of Gödel's theorem were originally espoused by Turing in the late 1940s, by Gödel himself in his 1951 Gibbs lecture, by E. Nagel and J.R. Newman in 1958, [ 6 ] and were subsequently popularized by the philosopher John Lucas of Merton College, Oxford in 1961 . [ 7 ]
The inescapable conclusion seems to be: Mathematicians are not using a knowably sound calculation procedure in order to ascertain mathematical truth. We deduce that mathematical understanding – the means whereby mathematicians arrive at their conclusions with respect to mathematical truth – cannot be reduced to blind calculation!
If correct, the Penrose–Lucas argument creates a need to understand the physical basis of non-computable behaviour in the brain. [ 9 ] Most physical laws are computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process.
In quantum mechanics , particles are treated differently from the objects of classical mechanics . Particles are described by wave functions that evolve according to the Schrödinger equation . Non-stationary wave functions are linear combinations of the eigenstates of the system, a phenomenon described by the superposition principle . When a quantum system interacts with a classical system—i.e. when an observable is measured—the system appears to collapse to a random eigenstate of that observable from a classical vantage point.
If collapse is truly random, then no process or algorithm can deterministically predict its outcome. This provided Penrose with a candidate for the physical basis of the non-computable process that he hypothesized to exist in the brain. However, he disliked the random nature of environmentally induced collapse, as randomness was not a promising basis for mathematical understanding. Penrose proposed that isolated systems may still undergo a new form of wave function collapse , which he called objective reduction (OR). [ 10 ]
Penrose sought to reconcile general relativity and quantum theory using his own ideas about the possible structure of spacetime . [ 5 ] [ 11 ] He suggested that at the Planck scale curved spacetime is not continuous, but discrete. Penrose postulated that each separated quantum superposition has its own piece of spacetime curvature , a blister in spacetime. Penrose suggests that gravity exerts a force on these spacetime blisters, which become unstable above the Planck scale of 10 − 35 m {\displaystyle 10^{-35}{\text{m}}} and collapse to just one of the possible states. The rough threshold for OR is given by Penrose's indeterminacy principle:
where:
Thus, the greater the mass-energy of the object, the faster it will undergo OR and vice versa. Atomic-level superpositions would require 10 million years to reach OR threshold, while an isolated 1 kilogram object would reach OR threshold in 10 −37 s. Objects somewhere between these two scales could collapse on a timescale relevant to neural processing. [ 10 ] [ citation needed ] [ 12 ]
An essential feature of Penrose's theory is that the choice of states when objective reduction occurs is selected neither randomly (as are choices following wave function collapse ) nor algorithmically. Rather, states are selected by a "non-computable" influence embedded in the Planck scale of spacetime geometry. Penrose claimed that such information is Platonic , representing pure mathematical truth, aesthetic and ethical values at the Planck scale. This relates to Penrose's ideas concerning the three worlds: physical, mental, and the Platonic mathematical world. In his theory, the Platonic world corresponds to the geometry of fundamental spacetime that is claimed to support noncomputational thinking. [ 10 ] [ citation needed ] [ 13 ] [ 14 ]
The Penrose–Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence was criticized by mathematicians, [ 15 ] [ 16 ] [ 17 ] [ 18 ] computer scientists, [ 19 ] and philosophers, [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] and the consensus among experts [ which? ] [ 6 ] in these fields is that the argument fails, [ 25 ] [ 26 ] [ 27 ] with different authors attacking different aspects of the argument. [ 27 ] [ 28 ]
Feferman faulted detailed points in Penrose's second book, Shadows of the Mind . He argued that mathematicians do not progress by mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines do not share this approach with humans. He pointed out that everyday mathematics can be formalized. He also rejected Penrose's Platonism . [ 16 ] Still, this does not account for his core argument of the alleged ability of the human mind to prove Gödel-unprovable sentences . Also, Artificial Intelligence based on Reinforcement Learning can work by taking actions in an environment in order to maximize the notion of cumulative reward , acting like trial-and-error procedures. [ 29 ] [ 30 ] [ 31 ]
LaForte pointed out that in order to know the truth of an unprovable Gödel sentence, one must already know the formal system is consistent (although this was not the point Lucas tried to make); referencing Benacerraf , he tried to demonstrate that humans cannot prove that they are consistent, [ 15 ] and in all likelihood human brains are inconsistent algorithms that use some sort of paraconsistent logic , pointing to alleged contradictions within Penrose's own writings as examples. Similarly, Minsky argued that because humans can believe false ideas to be true, human mathematical understanding need not be consistent and consciousness may easily have a deterministic basis. [ 32 ] Penrose argued against Minsky stating that mistakes human mathematicians make are irrelevant because they are correctable, while logical truths are “unassailable truths” to persons , which are the outputs of a sound system and the only ones that matter. [ 33 ] Mistakes do not directly imply that the human mind is inconsistent per se: biological organisms are subject to cognitive turmoils, reduced long-term memory and attention shifts; these reduce our reasoning capabilities and make humans act unconsciously without taking into consideration all the possible variables of a system.
Thus, a disjunction holds: either the human mind is not a computation of a Turing Machine , and thus not a formal system ; or it is a product of an inconsistent Turing Machine that could be reasoning using some sort of paraconsistent logic . Gödel himself commented about this disjunction in 1953. [ 34 ] [ 35 ] | https://en.wikipedia.org/wiki/Penrose–Lucas_argument |
The Pensky–Martens closed-cup flash-point test is a test for the determination of the flash point of flammable liquids. It is standardized as ASTM D93, EN ISO 2719 and IP 34 [ 1 ] The United States Environmental Protection Agency (EPA) has also published Method 1010A: Test Methods for Flash Point by Pensky-Martens Closed Cup Tester, part of Test Methods for Evaluating Solid Waste, Physical/Chemical Methods , which references the ASTM standard series D93. The Pensky-Martens test is a closed-cup method as opposed to the Cleveland open-cup method .
A brass test cup is filled with a test specimen and closed with a lid, through which an ignition source can be introduced periodically. The sample is heated and stirred at specified rates depending on the material that is being tested. This allows the development of an equilibrium between the liquid and the air volume. The ignition source is directed into the cup at regular intervals with simultaneous interruption of stirring. The test concludes upon observation of a flash that spreads throughout the inside of the cup. The corresponding temperature is the liquid's flash point .
The different flash point methods depend on the controlled conditions in the laboratory and do not determine an intrinsic property of the material tested. They are however useful to compare different substances and is therefore widely used in road transportation and environmental safety regulations. [ 2 ]
Closed cup testers give lower values for the flashpoint than open-cup testers (typically 5–10 K) and are a better approximation to the temperature at which the vapour pressure reaches the " Lower flammable limit " (LFL). [ citation needed ]
This chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pensky–Martens_closed-cup_test |
Penta-graphene is a hypothetical carbon allotrope composed entirely of carbon pentagons and resembling the Cairo pentagonal tiling . [ 2 ] Penta-graphene was proposed in 2014 on the basis of analyses and simulations. [ 2 ] Further calculations predicted that it is unstable in its pure form, [ 3 ] but can be stabilized by hydrogenation. [ 1 ] Due to its atomic configuration, penta-graphene has an unusually negative Poisson’s ratio and very high ideal strength believed to exceed that of a similar material, graphene . [ 2 ]
Penta-graphene contains both sp 2 and sp 3 hybridized carbon atoms. Contrary to graphene, which is a good conductor of electricity, penta-graphene is predicted to be an insulator with an indirect band gap of 4.1–4.3 eV. Its hydrogenated form is called penta- graphane . It has a diamond-like structure with sp 3 and no sp 2 bonds, and therefore a wider band gap (ca. 5.8 eV) than penta-graphene. [ 1 ] Chiral penta-graphene nanotubes have also been studied as metastable allotropes of carbon. [ 4 ] [ 2 ] [ 5 ]
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Penta-graphene |
Pentabromodiphenyl ether (also known as pentabromodiphenyl oxide ) is a brominated flame retardant which belongs to the group of polybrominated diphenyl ethers (PBDEs). Because of their toxicity and persistence, their industrial production is to be eliminated under the Stockholm Convention , a treaty to control and phase out major persistent organic pollutants (POP).
Commercial pentaBDE is a technical mixture of different PBDE congeners , with BDE-47 (2,2',4,4'- tetrabromodiphenyl ether) and BDE-99 (2,2',4,4',5-pentabromodiphenyl ether) as the most abundant. [ 2 ] The term pentaBDE alone refers to isomers of pentabromodiphenyl ether (PBDE congener numbers 82-127). [ 3 ]
Only congeners with more than 1% listed.
Commercial pentaBDE is most commonly used as a flame retardant in flexible polyurethane foam; it was also used in printed circuit boards in Asia, and in other applications. [ 2 ] The annual demand worldwide was estimated as 7,500 tonnes in 2001, of which the Americas accounted for 7,100 tonnes, Europe 150 tonnes, and Asia 150 tonnes. [ 5 ] The global industrial demand increased from 4,000 tonnes annually in 1991 to 8,500 tonnes annually in 1999. [ 6 ] As of 2007, "there should be no current production of C-PentaBDE [commercial pentaBDE] in Europe, Japan, Canada, Australia and the US"; however, it is possible that production continues elsewhere in the world. [ 2 ]
PentaBDE is released by different processes into the environment, such as emissions from manufacture of pentaBDE-containing products and from the products themselves. [ 2 ] Elevated concentrations can be found in air, water, soil, food, sediment , sludge , and dust . [ 2 ] [ 7 ] [ 8 ]
PentaBDE may enter the body by ingestion or inhalation. [ 3 ] It is "stored mainly in body fat" and may stay in the body for years. [ 3 ] A 2007 study found that PBDE 47 (a tetraBDE) and PBDE 99 (a pentaBDE) had biomagnification factors in terrestrial carnivores and humans of 98, higher than any other industrial chemicals studied. [ 9 ] In an investigation carried out by the WWF , "the brominated flame retardant chemical (PBDE 153), which is a component of the penta- and octa- brominated diphenyl ether flame retardant products" was found in all blood samples of 14 ministers of health and environment of 13 European Union countries. [ 10 ]
The chemical has no proven health effects in humans; however, based on animal experiments, pentaBDE may have effects on "the liver, thyroid, and neurobehavioral development." [ 3 ]
In Germany , industrial users of pentaBDE "agreed to a voluntary phaseout in 1986." [ 11 ] In Sweden , the government "phase[d] out the production and use of the [pentaBDE] compounds by 1999 and a total ban on imports came into effect within just a few years." [ 11 ] The European Union (EU) has carried out a comprehensive risk assessment under the Existing Substances Regulation 793/93/EEC; [ 12 ] as a consequence, the EU has banned the use of pentaBDE since 2004. [ 13 ]
In the United States , as of 2005, "no new manufacture or import of" pentaBDE and octaBDE "can occur... without first being subject to EPA [i.e., United States Environmental Protection Agency ] evaluation." [ 14 ] As of mid-2007, a total of eleven states in the U.S. had banned pentaBDE. [ 15 ]
In May 2009, pentaBDE was added to the Stockholm Convention as it meets the criteria for the so-called persistent organic pollutants of persistence, bioaccumulation and toxicity .
The EPA organized a Furniture Flame Retardancy Partnership beginning in 2003 "to better understand fire safety options for the furniture industry" after pentaBDE "was voluntarily phased out of production by the sole U.S. manufacturer on December 31, 2004." [ 16 ] In 2005 the Partnership published evaluations of alternatives to pentaBDE, including triphenyl phosphate , tribromoneopentyl alcohol, tris(1,3-dicholoro-2-propyl)phosphate, and 12 proprietary chemicals. [ 17 ] | https://en.wikipedia.org/wiki/Pentabromodiphenyl_ether |
Pentachlorobenzene (PeCB) is an aryl chloride and a five-substituted chlorobenzene with the molecular formula C 6 HCl 5 which is a chlorinated aromatic hydrocarbon . It consists of a benzene ring substituted with five chlorine atoms. PeCB was once used industrially for a variety of uses, but because of environmental concerns there are currently no large scale uses of PeCB. [ 4 ] Pentachlorobenzene is a known persistent organic pollutant (POP) and banned globally by the Stockholm Convention on Persistent Organic Pollutants in 2009. [ 5 ]
PeCB can be produced as a byproduct of the manufacture of carbon tetrachloride and benzene. It is extracted by distillation and crystallization . The direct production of pure PeCB is not practical because of the simultaneous production of other chlorinated compounds. Since PeCB is generally produced in small quantities in the chlorination of benzene, it is also contained in other chlorobenzenes ( dichlorobenzenes , trichlorobenzenes etc.)
Today, a majority of the PeCB released into the environment is a result of backyard trash burning and municipal waste incineration. [ 4 ]
PeCB was used as an intermediate in the manufacture of pesticides, particularly the fungicide pentachloronitrobenzene . [ 3 ] Pentachloronitrobenzene is now made by
the chlorination of nitrobenzene in order to avoid the use of PeCB. [ 4 ]
PeCB was a component of a mixture of chlorobenzenes added to products containing polychlorinated biphenyls in order to reduce viscosity . [ 4 ] PeCB has also been used as a fire retardant. [ 3 ]
PeCB is a persistent organic pollutant , allowing an accumulation in the food chain. [ 1 ] [ 4 ] Consequently, pentachlorobenzene was added in 2009 to the list of chemical compounds covered by the Stockholm Convention , an international treaty which restricts the production and use of persistent organic pollutants. [ 6 ] [ 7 ] PeCB has been banned in the European Union since 2002.
PeCB is very toxic to aquatic organisms, and decomposes on heating or on burning with the formation of toxic, corrosive fumes including hydrogen chloride . [ 1 ] Combustion of PeCB may also result in the formation of polychlorinated dibenzodioxins ("dioxins") and polychlorinated dibenzofurans . | https://en.wikipedia.org/wiki/Pentachlorobenzene |
Pentachloronitrobenzene , typically abbreviated PCNB , is a registered fungicide formally derived from nitrobenzene . It is a off-white to yellow crystalline solid with a musty odor.
PCNB was originally synthesized in the laboratory in 1868. It was introduced to the agricultural world in the 1930s in Germany by Bayer AG as a substitute to mercurial pesticides . PCNB is prepared by chlorination of nitrobenzene at 60–70 °C in chlorosulfuric acid , with iodine as a catalyst . It can also be produced by the nitration of chlorinated benzenes. A side product of the synthesis of PCNB is hexachlorobenzene (HCB), which is considered as hazardous as PCNB. [ 1 ]
Reaction with ethanol and potassium hydroxide yields pentachlorophenetole , indicating its high reactivity: [ 2 ]
Although PCNB has a long shelflife, it is labile in soil, with a half life of 1.8 days. It degrades to other metabolites, mainly reducing to pentachloroaniline (PCA), but also to pentachlorophenol (PCP) through hydrolysis and pentachlorothioanisole (PCTA). Another metabolite is methyl pentachlorophenyl sulfide (MPCPS). Little information is available about the degradation mechanisms. [ 3 ] [ 4 ]
PCNB is used as a fungicide to suppress the growth of fungi in various crops, such as cotton, rice, and seed grains. It is also used to prevent the formation of slime in industrial waters. Residual amounts of the compound and its metabolites can be found in crops. The degradation products, PCA and PCTA have been found in farming soils and in river sediments. [ 5 ]
In April 1993, PCNB was declared a hazardous air pollutant in the U.S. [ 6 ] PCNB was reexamined for re-registration eligibility by the U.S. EPA in 2006 as part of the 1996 Food Protection Quality Act (FPQA) and as a result, use on a number of crops were ended or limited. In August 2010, in response to the discovery of a potentially toxic metabolite in technical grade PCNB to be used in fungicide formulations, the sale of PCNB was halted by the U.S. EPA until the issue could be resolved. [ 7 ] In November 2011, the EPA approved certain registrations for PCNB, allowing it back on the market for golf course turf, potato, cotton, ornamental bulb and cole crop uses in the United States. [ 8 ] PCNB is used widely as a fungicide in other countries, such as China and Japan, [ 5 ] however, "it is no longer approved for use within the European Union". [ 9 ] | https://en.wikipedia.org/wiki/Pentachloronitrobenzene |
Pentachlorophenol ( PCP ) is an organochlorine compound used as a pesticide and a disinfectant . First produced in the 1930s, it is marketed under many trade names. [ 5 ] It can be found as pure PCP, or as the sodium salt of PCP, the latter of which dissolves easily in water. It can be biodegraded by some bacteria, including Sphingobium chlorophenolicum .
PCP has been used as a herbicide , insecticide , fungicide , algaecide , and disinfectant and as an ingredient in antifouling paint . [ 5 ] Some applications were in agricultural seeds (for nonfood uses), leather, masonry, wood preservation , cooling-tower water, rope, and paper. It has previously been used in the manufacture of food packaging materials. [ 6 ] Its use has declined due to its high toxicity and slow biodegradation. [ 7 ]
Two general methods are used for preserving wood. The pressure process method involves placing wood in a pressure-treating vessel, where it is immersed in PCP and then subjected to applied pressure. In the nonpressure process method, PCP is applied by spraying, brushing, dipping, or soaking.
Pentachlorophenol esters can be used as active esters in peptide synthesis , much like more popular pentafluorophenyl esters .
People may be exposed to PCP in occupational settings through the inhalation of contaminated workplace air and dermal contact with wood products treated with PCP. Also, general population exposure may occur through contact with contaminated environment media, particularly in the vicinity of wood-treatment facilities and hazardous-waste sites. In addition, some other important routes of exposure seem to be the inhalation of contaminated air, ingestion of contaminated ground water used as a source of drinking water, ingestion of contaminated food, and dermal contact with soils or products treated with the chemical. [ 8 ]
Short-term exposure to large amounts of PCP can cause harmful effects on the liver, kidneys, blood, lungs, nervous system, [ 5 ] immune system, and gastrointestinal tract. Elevated temperature, profuse sweating, uncoordinated movement, muscle twitching, and coma are additional side effects.
Contact with PCP (particularly in the form of vapor) can irritate the skin, eyes, and mouth. Long-term exposure to low levels, such as those that occur in the workplace, can cause damage to the liver, kidneys, blood, and nervous system. [ 5 ] Finally, exposure to PCP is also associated with carcinogenic, renal, and neurological effects. The U.S. Environmental Protection Agency toxicity class classifies PCP in group B2 (probable human carcinogen ).
Pentachlorophenol may be measured in plasma or urine as an index of excessive exposure. This is usually performed by gas chromatography with electron-capture or mass-spectrometric detection. Since urine contains predominantly conjugated PCP in chronic exposure situations, prior hydrolysis of specimens is recommended. The current ACGIH biological exposure limits for occupational exposure to PCP are 5 mg/L in an end-of-shift plasma specimen and 2 mg/g creatinine in an end-of-shift urine specimen. [ 9 ] [ 10 ]
PCP is quickly absorbed through the gastrointestinal tract following ingestion. Accumulation is not common, but if it does occur, the major sites are the liver, kidneys, plasma protein , spleen , and fat . Unless kidney and liver functions are impaired, PCP is quickly eliminated from tissues and blood, and is excreted, mainly unchanged or in conjugated form, via the urine. Single doses of PCP have half-lives in blood of 30 to 50 hours in humans. Biomagnification of PCP in the food chain is not thought to be significant due to the fairly rapid metabolism of the compound by exposed organisms.
PCP has been detected in surface waters and sediments, rainwater, drinking water, aquatic organisms, soil, and food, as well as in human milk, adipose tissue , and urine. As PCP is generally used for its properties as a biocidal agent, considerable concern exists about adverse ecosystem effects in areas of PCP contamination.
Releases to the environment are decreasing as a result of declining consumption and changing use methods. However, PCP is still released to surface waters from the atmosphere by wet deposition , from soil by run off and leaching, and from manufacturing and processing facilities. PCP is released directly into the atmosphere via volatilization from treated wood products and during production. Finally, releases to the soil can be by leaching from treated wood products, atmospheric deposition in precipitation (such as rain and snow), spills at industrial facilities, and at hazardous waste sites.
After PCP is released into the atmosphere, it decomposes through photolysis . The main biodegradative pathway for PCP is reductive dehalogenation. In this process, the compound PCP is broken down to tetrachlorophenols, trichlorophenols , and dichlorophenols . Another pathway is methylation to pentachloroanisole (a more lipid-soluble compound). These two methods eventually lead to ring cleavage and complete degradation.
In shallow waters, PCP is also quickly removed by photolysis. In deep or turbid water processes, sorption and biodegradation take place.
In reductive soil and sediments, PCP can be degraded within 14 days to 5 years, depending on the anaerobic soil bacteria that are present. However, adsorption of PCP in soils is pH dependent because it increases under acidic conditions and decreases in neutral and basic conditions.
PCP can be produced by the chlorination of phenol in the presence of catalyst (anhydrous aluminium or ferric chloride ) and a temperature up to about 191 °C. This process does not result in complete chlorination and commercial PCP is only 84–90% pure. The main contaminants include other polychlorinated phenols, polychlorinated dibenzo-p-dioxins , and polychlorinated dibenzofurans . Some of these species are even more toxic than the PCP itself.
Pentachlorophenol is classified as a persistent organic pollutant (POP) . In May 2015, countries which have signed the Stockholm Convention voted 90–2 to ban pentachlorophenol use. The United States is not a signatory and has not banned the chemical. [ 11 ]
PCP was used in New Zealand as a timber preservative and antisapstain treatment, but since 1988 is no longer used. [ 12 ]
It was also sold as a moss killer to the general public (by Shell, at least) in the form of a 115g/L aqueous solution and labelled as a poison.
Since the early 1980s, the purchase and use of PCP in the U.S. has not been available to the general public. Nowadays, most of the PCP used in the U.S. is restricted to the treatment of utility poles and railroad ties . In the United States, any drinking-water supply with a PCP concentration exceeding the MCL , 1 ppb , must be notified by the water supplier to the public. [ 5 ] Disposal of PCP and PCP-contaminated substances are regulated under RCRA as F-listed (F021) or D-listed (D037) hazardous wastes. Bridges and similar structures such as piers can still be treated with pentachlorophenol.
PCP was widely used in Chile until the early 1990s as a fungicide to combat the so-called "blue stain" in pine timber under the name of Basilit. [ citation needed ] | https://en.wikipedia.org/wiki/Pentachlorophenol |
In organic chemistry , pentadiene is any hydrocarbon with an open chain of five carbons , connected by two single bonds and two double bonds . All those compounds have the same molecular formula C 5 H 8 . The inventory of pentadienes include:
Well known derivatives containing pentadiene groups include hexadienes , cyclopentadiene , and especially three fatty acids linoleic acid , α- linolenic acid , and arachidonic acid as well as their triglyceride esters (fats).
1,4-Pentadiene can be prepared from 1,5-pentadiol via the diacetate. [ 6 ]
1,3-Pentadiene, like 1,3-butadiene , undergoes a variety of cycloaddition reactions. For example, it forms a sulfolene upon treatment with sulfur dioxide . [ 7 ]
Pentadienyl refers to the organic radical , anion, or cation with the formula [CH 2 (CH) 3 CH 2 ] z , where z = 0, −1, +1, respectively.
Methylene-interrupted polyenes are 1,4-pentadiene groups found in polyunsaturated fatty acids linoleic acid , α- linolenic acid , and arachidonic acid . These pentadiene derivatives are susceptible to lipid peroxidation , far moreso than monounsaturated or saturated fatty acids. The basis for this reactivity is the weakness of doubly allylic C-H bonds, leading to pentadienyl radicals. A range of reactions with oxygen occur. Products include fatty acid hydroperoxides , epoxy-hydroxy polyunsaturated fatty acids, jasmonates , divinylether fatty acids , and leaf aldehydes . Some of these derivatives are signallng molecules, some are used in plant defense ( antifeedants ), some are precursors to other metabolites that are used by the plant. [ 8 ]
Cyclooxygenases ("COX") are enzymes that generate prostanoids , including thromboxane and prostaglandins such as prostacyclin . Aspirin and ibuprofen exert their effects through inhibition of COX.
Fats containing 1,4-pentadiene groups are drying oils , i.e. film-forming liquids suitable as paints. One practical consequence is that polyunsaturated fatty acids have poor shelf life owing to their tendency toward autoxidation , leading, in the case of edibles, to rancidification . Metals accelerate the degradation.
In organometallic chemistry , the pentadienyl anion is a ligand, the acyclic analogue of the more-common cyclopentadienyl anion . The pentadienyl anion is generated by deprotonation of pentadiene . A number of complexes are known, including bis(pentadienyl) iron, Fe(C 5 H 7 ) 2 , the "open" analog of ferrocene . Only few pentadienyl complexes feature simple C 5 H 7 ligands. More common is the dimethyl derivative 2,4- Me 2 C 5 H 5 . Additionally, many pentadienyl ligands are cyclic, being derived from the addition of hydride to η 6 -arene complexes or hydride abstraction from cyclohexadiene complexes. [ 10 ] [ 11 ]
The first pentadienyl complex to be reported was derived from protonolysis of a complex of pentadienol: [ 12 ]
Treatment of this cation with sodium borohydride gives the pentadiene complex: | https://en.wikipedia.org/wiki/Pentadiene |
Pentaerythritol tetranitrate ( PETN ), also known as PENT , pentyl , PENTA ( ПЕНТА , primarily in Russian), TEN (tetraeritrit nitrate), corpent , or penthrite (or, rarely and primarily in German, as nitropenta ), is an explosive material. It is the nitrate ester of pentaerythritol , and is structurally very similar to nitroglycerin . Penta refers to the five carbon atoms of the neopentane skeleton. PETN is a very powerful explosive material with a relative effectiveness factor of 1.66. [ 2 ] When mixed with a plasticizer , PETN forms a plastic explosive . [ 3 ] Along with RDX it is the main ingredient of Semtex .
PETN is also used as a vasodilator drug to treat certain heart conditions, such as for management of angina . [ 4 ] [ 5 ]
Pentaerythritol tetranitrate was first prepared and patented in 1894 by the explosives manufacturer Rheinisch-Westfälische Sprengstoff A.G. [ de ] of Cologne, Germany . [ 6 ] [ 7 ] [ 8 ] [ 9 ] The production of PETN started in 1912, when the improved method of production was patented by the German government. PETN was used by the German Military in World War I . [ 10 ] [ 11 ] It was also used in the MG FF/M autocannons and many other weapon systems of the Luftwaffe in World War II. [ citation needed ]
PETN is practically insoluble in water (0.01 g/100 mL at 50 °C), weakly soluble in common nonpolar solvents such as aliphatic hydrocarbons (like gasoline) or tetrachloromethane , but soluble in some other organic solvents, particularly in acetone (about 15 g/100 g of the solution at 20 °C, 55 g/100 g at 60 °C) and dimethylformamide (40 g/100 g of the solution at 40 °C, 70 g/100 g at 70 °C). It is a non-planar molecule that crystallizes in the space group P 4 2 1 c . [ 12 ] PETN forms eutectic mixtures with some liquid or molten aromatic nitro compounds , e.g. trinitrotoluene (TNT) or tetryl . Due to the steric hindrance of the adjacent neopentyl-like moiety, PETN is resistant to attack by many chemical reagents ; it does not hydrolyze in water at room temperature or in weaker alkaline aqueous solutions . Water at 100 °C or above causes hydrolysis to dinitrate; the presence of 0.1% nitric acid accelerates the reaction.
The chemical stability of PETN is of interest, because of the presence of PETN in aging weapons. [ 13 ] Neutron radiation degrades PETN, producing carbon dioxide and some pentaerythritol dinitrate and trinitrate . Gamma radiation increases the thermal decomposition sensitivity of PETN, lowers melting point by few degrees Celsius, and causes swelling of the samples. Like other nitrate esters, the primary degradation mechanism is the loss of nitrogen dioxide ; this reaction is autocatalytic . [ citation needed ] Studies were performed on thermal decomposition of PETN. [ 14 ]
In the environment, PETN undergoes biodegradation . Some bacteria denitrate PETN to trinitrate and then dinitrate, which is then further degraded. [ 15 ] PETN has low volatility and low solubility in water, and therefore has low bioavailability for most organisms. Its toxicity is relatively low, and its transdermal absorption also seems to be low. It poses a threat for aquatic organisms . It can be degraded to pentaerythritol by iron . [ 16 ]
Production is by the reaction of pentaerythritol with concentrated nitric acid to form a precipitate which can be recrystallized from acetone to give processable crystals. [ 17 ]
Variations of a method first published in US Patent 2,370,437 by Acken and Vyverberg (1945 to Du Pont) form the basis of all current commercial production. [ citation needed ]
PETN is manufactured by numerous manufacturers as a powder, or together with nitrocellulose and plasticizer as thin plasticized sheets (e.g. Primasheet 1000 or Detasheet ). PETN residues are easily detectable in hair of people handling it. [ 18 ] The highest residue retention is on black hair; some residues remain even after washing. [ 19 ] [ 20 ]
The most common use of PETN is as an explosive with high brisance . It is a secondary explosive , meaning it is more difficult to detonate than primary explosives , so dropping or igniting it will typically not cause an explosion (at standard atmospheric pressure it is difficult to ignite and burns vigorously), but is more sensitive to shock and friction than other secondary explosives such as TNT or tetryl . [ 17 ] [ 21 ] Under certain conditions a deflagration to detonation transition can occur, just like that of ammonium nitrate .
It is rarely used alone in military operations due to its lower stability, but is primarily used in the main charges of plastic explosives (such as C4 ) along with other explosives (especially RDX ), booster and bursting charges of small caliber ammunition , in upper charges of detonators in some land mines and shells, as the explosive core of detonation cord . [ 22 ] [ 23 ] PETN is the least stable of the common military explosives, but can be stored without significant deterioration for longer than nitroglycerin or nitrocellulose . [ 24 ]
During World War II , PETN was most importantly used in exploding-bridgewire detonators for the atomic bombs. These exploding-bridgewire detonators gave more precise detonation compared to primacord . PETN was used for these detonators because it was safer than primary explosives like lead azide : while it was sensitive, it would not detonate below a threshold amount of energy. [ 25 ] Exploding bridgewires containing PETN remain used in current nuclear weapons. In spark detonators, PETN is used to avoid the need for primary explosives; the energy needed for a successful direct initiation of PETN by an electric spark ranges between 10–60 mJ.
Its basic explosion characteristics are:
PETN is used in a number of compositions. It is a major ingredient of the Semtex plastic explosive . It is also used as a component of pentolite , a castable mixture with TNT (usually 50/50 but may contain more TNT), which is, along with pure PETN, a common explosive for boosters for the blasting work (as in mining ). [ 26 ] [ 27 ] The XTX8003 extrudable explosive, used in the W68 and W76 nuclear warheads, is a mixture of 80% PETN and 20% of Sylgard 182, a silicone rubber . [ 28 ] It is often phlegmatized by addition of 5–40% of wax , or by polymers (producing polymer-bonded explosives ); in this form it is used in some cannon shells up to 30 mm caliber , though it is unsuitable for higher calibers. It is also used as a component of some gun propellants and solid rocket propellants . Nonphlegmatized PETN is stored and handled with approximately 10% water content. PETN alone cannot be cast as it explosively decomposes slightly above its melting point, [ citation needed ] [ clarification needed ] but it can be mixed with other explosives to form castable mixtures.
PETN can be initiated by a laser . [ 29 ] A pulse with duration of 25 nanoseconds and 0.5–4.2 joules of energy from a Q-switched ruby laser can initiate detonation of a PETN surface coated with a 100 nm thick aluminium layer in less than half of a microsecond. [ citation needed ]
PETN has been replaced in many applications by RDX , which is thermally more stable and has a longer shelf life . [ 30 ] PETN can be used in some ram accelerator types. [ 31 ] Replacement of the central carbon atom with silicon produces Si-PETN, which is extremely sensitive. [ 32 ] [ 33 ]
Ten kilograms of PETN was used in the 1980 Paris synagogue bombing .
In 1983, 307 people were killed after a truck bomb filled with PETN was detonated at the Beirut barracks .
In 1983, the "Maison de France" house in Berlin was brought to a near-total collapse by the detonation of 24 kilograms (53 lb) of PETN by terrorist Johannes Weinrich . [ 34 ]
In 1999, Alfred Heinz Reumayr used PETN as the main charge for his fourteen improvised explosive devices that he constructed in a thwarted attempt to damage the Trans-Alaska Pipeline System .
In 2001, al-Qaeda member Richard Reid , the "Shoe Bomber", used PETN in the sole of his shoe in his unsuccessful attempt to blow up American Airlines Flight 63 from Paris to Miami. [ 20 ] [ 35 ] He had intended to use the solid triacetone triperoxide (TATP) as a detonator. [ 21 ]
In 2009, PETN was used in an attempt by al-Qaeda in the Arabian Peninsula to assassinate the Saudi Arabian Deputy Minister of Interior Prince Muhammad bin Nayef , by Saudi suicide bomber Abdullah Hassan al Asiri . The target survived and the bomber died in the blast. The PETN was hidden in the bomber's rectum , which security experts described as a novel technique. [ 36 ] [ 37 ] [ 38 ]
On 25 December 2009, PETN was found in the underwear of Umar Farouk Abdulmutallab , the "Underwear bomber", a Nigerian with links to al-Qaeda in the Arabian Peninsula. [ 39 ] According to US law enforcement officials, [ 40 ] he had attempted to blow up Northwest Airlines Flight 253 while approaching Detroit from Amsterdam. [ 41 ] Abdulmutallab had tried, unsuccessfully, to detonate approximately 80 grams (2.8 oz) of PETN sewn into his underwear by adding liquid from a syringe; [ 42 ] however, only a small fire resulted. [ 21 ]
In the al-Qaeda in the Arabian Peninsula October 2010 cargo plane bomb plot , two PETN-filled printer cartridges were found at East Midlands Airport and in Dubai on flights bound for the US on an intelligence tip. Both packages contained sophisticated bombs concealed in computer printer cartridges filled with PETN. [ 43 ] [ 44 ] The bomb found in England contained 400 grams (14 oz) of PETN, and the one found in Dubai contained 300 grams (11 oz) of PETN. [ 44 ] Hans Michels, professor of safety engineering at University College London , told a newspaper that 6 grams (0.21 oz) of PETN—"around 50 times less than was used—would be enough to blast a hole in a metal plate twice the thickness of an aircraft's skin". [ 45 ] In contrast, according to an experiment conducted by a BBC documentary team designed to simulate Abdulmutallab's Christmas Day bombing, using a Boeing 747 plane, even 80 grams of PETN was not sufficient to materially damage the fuselage. [ 46 ]
On 12 July 2017, 150 grams of PETN was found in the Assembly of Uttar Pradesh , [ 47 ] [ 48 ] India's most populous state. [ 49 ] [ 50 ]
PETN was used by Israel in the manufacturing of pagers provided to Hezbollah . On September 17, 2024, the pagers detonated , killing 12 people and injuring thousands. [ 51 ]
In the wake of terrorist PETN bomb plots, an article in Scientific American noted PETN is difficult to detect because it does not readily vaporize into the surrounding air. [ 43 ] The Los Angeles Times noted in November 2010 that PETN's low vapor pressure makes it difficult for bomb-sniffing dogs to detect. [ 20 ]
Many technologies can be used to detect PETN, including chemical sensors, X-rays, infrared, microwaves [ 52 ] and terahertz, [ 53 ] some of which have been implemented in public screening applications, primarily for air travel. PETN is one of the explosive chemicals typically of interest in that area, and it belongs to a family of common nitrate-based explosive chemicals which can often be detected by the same tests.
One detection system in use at airports involves analysis of swab samples obtained from passengers and their baggage. Whole-body imaging scanners that use radio-frequency electromagnetic waves , low-intensity X-rays , or T-rays of terahertz frequency that can detect objects hidden under clothing are not widely used because of cost, concerns about the resulting traveler delays, and privacy concerns. [ 54 ]
Both parcels in the 2010 cargo plane bomb plot were x-rayed without the bombs being spotted. [ 55 ] Qatar Airways said the PETN bomb "could not be detected by x-ray screening or trained sniffer dogs ". [ 56 ] The Bundeskriminalamt received copies of the Dubai x-rays, and an investigator said German staff would not have identified the bomb either. [ 55 ] [ 57 ] New airport security procedures followed in the U.S., largely to protect against PETN. [ 20 ]
Like nitroglycerin (glyceryl trinitrate) and other nitrates , PETN is also used medically as a vasodilator in the treatment of heart conditions . [ 4 ] [ 5 ] These drugs work by releasing the signaling gas nitric oxide in the body. The heart medicine Lentonitrat is nearly pure PETN. [ 58 ]
Monitoring of oral usage of the drug by patients has been performed by determination of plasma levels of several of its hydrolysis products, pentaerythritol dinitrate, pentaerythritol mononitrate and pentaerythritol, in plasma using gas chromatography-mass spectrometry . [ 59 ] | https://en.wikipedia.org/wiki/Pentaerythritol_tetranitrate |
Pentafluorophenyl ( PFP ) esters are chemical compounds with the generic formula RC(O)OC 6 F 5 . They are active esters derived from pentafluorophenol (HOC 6 F 5 ).
PFP esters are useful for attaching fluorophores such as fluorescein [ 1 ] or haptens [ 2 ] to primary amines in biomolecules. They also are valuable in laboratory peptide synthesis . Pentafluorophenyl esters produce amide bonds as effectively as succinimidyl esters and various similar agents do, but PFP esters are particularly useful because they are less susceptible to spontaneous hydrolysis during conjugation reactions. [ 3 ] | https://en.wikipedia.org/wiki/Pentafluorophenyl_esters |
Pentagastrin (trade name Peptavlon ) is a synthetic polypeptide that has effects like gastrin when given parenterally . [ 2 ] It stimulates the secretion of gastric acid , pepsin , and intrinsic factor , and has been used as a diagnostic aid as the pentagastrin-stimulated calcitonin test .
Pentagastrin binds to the cholecystokinin -B receptor, which is expressed widely in the brain. Activation of these receptors activates the phospholipase C second messenger system. When given intravenously it may cause panic attacks. [ 3 ]
Pentagastrin's IUPAC chemical name is "N-((1,1-dimethylethoxy)carbonyl)-beta-alanyl-L-tryptophyl-L-methionyl-L-alpha-aspartyl-L-phenylalaninamide".
Pentagastrin is also used as a stimulation test to elevate of several hormones, such as serotonin . It provokes flushing and is useful in evaluating patients who describe flushing, but have normal or only marginally elevated biochemical markers for carcinoid syndrome . [ citation needed ]
It has been used to stimulate ectopic gastric mucosa for the detection of Meckels diverticulum by nuclear medicine . [ citation needed ]
The pentagastrin-stimulated calcitonin test is a diagnostic test for medullary carcinoma of the thyroid (MTC). MTC is a malignancy of the calcitonin -secreting cells of the thyroid gland , and thus MTC is commonly associated with an elevated calcitonin level, but an elevated level may not always be obvious. The pentagastrin-stimulated calcitonin test is useful in cases of suspected MTC that are not associated with elevated calcitonin. In these patients, injecting pentagastrin will cause calcitonin levels to rise significantly above the normal or basal range. [ 4 ] After a total thyroidectomy for medullary thyroid carcinoma , the pentagastrin-stimulated calcitonin release can be used to detect residual parafollicular C-cells . | https://en.wikipedia.org/wiki/Pentagastrin-stimulated_calcitonin_test |
In chemistry , a pentagonal bipyramid is a molecular geometry with one atom at the centre with seven ligands at the corners of a pentagonal bipyramid . A perfect pentagonal bipyramid belongs to the molecular point group D 5h .
The pentagonal bipyramid is a case where bond angles surrounding an atom are not identical (see also trigonal bipyramidal molecular geometry ). [ 1 ] [ page needed ] This is one of the three common shapes for heptacoordinate transition metal complexes, along with the capped octahedron and the capped trigonal prism . [ 2 ] [ 3 ] [ page needed ]
Pentagonal bipyramids are claimed to be promising coordination geometries for lanthanide -based single-molecule magnets , since they present no extradiagonal crystal field terms, therefore minimising spin mixing, and all of their diagonal terms are in first approximation protected from low-energy vibrations, minimising vibronic coupling . [ 4 ] | https://en.wikipedia.org/wiki/Pentagonal_bipyramidal_molecular_geometry |
In chemistry , the pentagonal planar molecular geometry describes the shape of compounds where five atoms , groups of atoms, or ligands are arranged around a central atom, defining the vertices of a pentagon .
The only two pentagonal planar species known are the isoelectronic (nine valence electrons ) ions [XeF 5 ] − (pentafluoroxenate(IV)) and [IF 5 ] 2− (pentafluoroiodate(III)). [ 1 ] Both are derived from the pentagonal bipyramid with two lone pairs occupying the apical positions and the five fluorine atoms all equatorial.
This stereochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentagonal_planar_molecular_geometry |
In chemistry , pentagonal pyramidal molecular geometry describes the shape of compounds where in six atoms or groups of atoms or ligands are arranged around a central atom, at the vertices of a pentagonal pyramid . It is one of the few molecular geometries with uneven bond angles . [ 1 ]
Pentagonal pyramid , Wolfram MathWorld
This stereochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentagonal_pyramidal_molecular_geometry |
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon , formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon . Drawing a circle around the five points creates a similar symbol referred to as the pentacle , [ 1 ] which is used widely by Wiccans and in paganism , or as a sign of life and connections.
The word pentagram comes from the Greek word πεντάγραμμον ( pentagrammon ), [ 2 ] from πέντε ( pente ), "five" + γραμμή ( grammē ), "line". [ 3 ] The word pentagram refers to just the star and the word pentacle refers to the star within a circle, although there is some overlap in usage. [ 4 ] The word pentalpha is a 17th-century revival of a post-classical Greek name of the shape. [ 5 ]
Early pentagrams have been found on Sumerian pottery from Ur c. 3500 BCE , and the five-pointed star was at various times the symbol of Ishtar or Marduk . [ 6 ] [ 7 ]
Pentagram symbols from about 5,000 years ago were found in the Liangzhu culture of China . [ 9 ] [ 10 ] A pentagram appeared in a Chinese text on music theory from the Warring States period ( c. 475 – 221 BC) as a diagram of the mathematical relations between the five notes in a particular Chinese musical scale . [ 10 ]
The pentagram was known to the ancient Greeks , with a depiction on a vase possibly dating back to the 7th century BCE. [ 11 ] Pythagoreanism originated in the 6th century BCE and used the pentagram as a symbol of mutual recognition, of wellbeing, and to recognize good deeds and charity. [ 12 ]
From around 300–150 BCE the pentagram stood as the symbol of Jerusalem, marked by the 5 Hebrew letters ירשלם spelling its name. [ 13 ]
In Neoplatonism , the pentagram was said to have been used as a symbol or sign of recognition by the Pythagoreans , who called the pentagram ὑγιεία hugieia "health". [ 14 ] [ 15 ]
In Serer religion and Serer cosmogony , the pentagram, called Yoonir (or "Yooniir" in Serer ) is the symbol of the Universe amongst the Serer people . [ 16 ] [ 17 ] In Serer religion and Serer primordial time, the peak of the Star represents the Serer supreme deity and creator, Roog . The other four points represent the cardinal points of the Universe. The crossing of the lines ("bottom left" and "top right" and "top left and bottom right") pinpoints the axis of the Universe, that all energies pass. The top point is "the point of departure and conclusion, the origin and the end". [ 18 ] Yoonir also represents "good fortune and destiny" – in a Serer religious sense, and in an enthno nationlistic sense–following centuries of their religious and ethnic persecution , it also represents the Serer people, [ 18 ] [ 19 ] an ethnoreligious group and nation–today, found in Senegal , Gambia , and Mauritania . [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] The Serer have a detailed pictorial representation of the Universe , representing the three worlds in Serer primordial time: the invisible world, the terrestrial world, and the nocturnal world. [ 25 ]
The pentagram was used in ancient times as a Christian symbol for the five senses , [ 26 ] or of the five wounds of Christ . The pentagram plays an important symbolic role in the 14th-century English poem Sir Gawain and the Green Knight , in which the symbol decorates the shield of the hero, Gawain . The unnamed poet credits the symbol's origin to King Solomon , and explains that each of the five interconnected points represents a virtue tied to a group of five: Gawain is perfect in his five senses and five fingers, faithful to the Five Wounds of Christ, takes courage from the five joys that Mary had of Jesus, and exemplifies the five virtues of knighthood , [ 27 ] which are generosity, friendship, chastity, chivalry, and piety. [ 28 ]
The North rose of Amiens Cathedral (built in the 13th century) exhibits a pentagram-based motif. Some sources interpret the unusual downward-pointing star as symbolizing the Holy Spirit descending on people.
Heinrich Cornelius Agrippa and others perpetuated the popularity of the pentagram as a magic symbol, attributing the five neoplatonic elements to the five points, in typical Renaissance fashion. Agrippa depicts the human body inscribed in an 'upright' (point-up) pentagram and another with its hands in rotated pentagrams, among numerous other geometrical figures, in the section on 'the proportions and harmonious measures of the human body', and an 'inverted' (point-down) version of the Pythagorean 'hygeia' pentagram in the section on 'characters, received only by revelation, which no other kind of reasoning can discover', alongside variations of the Chi-Rho and the Hebrew word Makabi .
'Of this type are the signet shown to Constantine , which most people called a cross, inscribed in Latin letters, ' in this conquer ', and another revealed to Antiochus who was surnamed Soteris , in the shape of a pentagon, which issued health, for resolved into letters, it issued the word ὑγίεα, that is, 'health', in the confidence and virtue of which signs, each of the kings won a notable victory against their enemies. Thus Judas, who for this reason was afterwards known as Maccabeus, was about to fight with the Jews against Antiochus Eupatorus, and received that noble seal מׄכׄבׄיׄ from the angel'. [ 15 ]
By the mid-19th century, a further distinction had developed amongst occultists regarding the pentagram's orientation. With a single point upwards it depicted spirit presiding over the four elements of matter, and was essentially "good". However, the influential but controversial writer Éliphas Lévi , known for believing that magic was a real science, had called it evil whenever the symbol appeared the other way up:
The apotropaic (protective) use in German folklore of the pentagram symbol (called Drudenfuss in German) is referred to by Goethe in Faust (1808), where a pentagram prevents Mephistopheles from leaving a room (but did not prevent him from entering by the same way, as the outward pointing corner of the diagram happened to be imperfectly drawn):
Mephistopheles:
Faust:
Mephistopheles:
Also protective is the use in Icelandic folklore of a gestured or carved rather than painted pentagram (called smèrhnút in Icelandic), according to 19th century folklorist Jón Árnason : [ 33 ]
Based on Renaissance-era occultism, the pentagram found its way into the symbolism of modern occultists. Its major use is a continuation of the ancient Babylonian use of the pentagram as an apotropaic charm to protect against evil forces. [ 35 ] Éliphas Lévi claimed that "The Pentagram expresses the mind's domination over the elements and it is by this sign that we bind the demons of the air, the spirits of fire, the spectres of water, and the ghosts of earth." [ 36 ] In this spirit, the Hermetic Order of the Golden Dawn developed the use of the pentagram in the lesser banishing ritual of the pentagram , which is still used to this day by those who practice Golden Dawn-type magic.
Aleister Crowley made use of the pentagram in the system of magick used in Thelema : an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of Lon Milo DuQuette . [ 37 ] Crowley contradicted his old comrades in the Hermetic Order of the Golden Dawn , who, following Levi, considered this orientation of the symbol evil and associated it with the triumph of matter over spirit.
The five-pointed star is a symbol of the Baháʼí Faith . [ 38 ] [ 39 ] In the Baháʼí Faith, the star is known as the Haykal ( Arabic : "temple" ), and it was initiated and established by the Báb . The Báb and Bahá'u'lláh wrote various works in the form of a pentagram. [ 40 ] [ 41 ]
The Church of Jesus Christ of Latter-day Saints is theorized to have begun using both upright and inverted five-pointed stars in Temple architecture, dating from the Nauvoo Illinois Temple dedicated on 30 April 1846. [ 42 ] Other temples decorated with five-pointed stars in both orientations include the Salt Lake Temple and the Logan Utah Temple . These usages come from the symbolism found in Revelation chapter 12: "And there appeared a great wonder in heaven; a woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars." [ 43 ]
Because of a perceived association with Satanism and occultism, many United States schools in the late 1990s sought to prevent students from displaying the pentagram on clothing or jewelry. [ 44 ] In public schools, such actions by administrators were determined in 2000 to be in violation of students' First Amendment right to free exercise of religion . [ 45 ]
The encircled pentagram (referred to as a pentacle by the plaintiffs) was added to the list of 38 approved religious symbols to be placed on the tombstones of fallen service members at Arlington National Cemetery on 24 April 2007. The decision was made following ten applications from families of fallen soldiers who practiced Wicca . The government paid the families US$225,000 to settle their pending lawsuits. [ 46 ] [ 47 ]
The inverted pentagram is broadly used in Satanism , sometimes depicted with the goat 's head of Baphomet , as popularized by the Church of Satan since 1968. LaVeyan Satanists pair the goat head with Hebrew letters at the five points of the pentagram to form the Sigil of Baphomet . The Baphomet sigil was adapted for the Joy of Satan Ministries logo, using cuneiform characters at the five points of the pentagram, reflecting the shape's earliest use in Sumeria . The inverted pentagram also appears in The Satanic Temple logo, with an alternative depiction of Baphomet's head. Other depictions of the Satanic goat's head resemble the inverted pentagram without its explicit outline.
The five-pointed star is a symbol of the Serer religion and the Serer people of West Africa. Called Yoonir in their language , it symbolizes the universe in the Serer creation myth , and also represents the star Sirius . [ 48 ] [ 49 ]
The pentagram is the simplest regular star polygon . The pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the Schläfli symbol {5/2}. Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of order 10.
It can be seen as a net of a pentagonal pyramid although with isosceles triangles.
The pentagram can be constructed by connecting alternate vertices of a pentagon ; see details of the construction . It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.
The golden ratio , φ = (1 + √ 5 ) / 2 ≈ 1.618, satisfying:
plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in the golden ratio: the ratio of the length of the edge to the longer segment is φ , as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram's center) is φ . As the four-color illustration shows:
The pentagram includes ten isosceles triangles : five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ . The acute triangles are golden triangles . The obtuse isosceles triangle highlighted via the colored lines in the illustration is a golden gnomon .
As a result, in an isosceles triangle with one or two angles of 36°, the longer of the two side lengths is φ times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.
A pentagram can be drawn as a star polygon on a sphere, composed of five great circle arcs, whose all internal angles are right angles. This shape was described by John Napier in his 1614 book Mirifici logarithmorum canonis descriptio (Description of the wonderful rule of logarithms) along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides). It was studied later by Carl Friedrich Gauss .
Several polyhedra incorporate pentagrams:
Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:
All ten 4-dimensional Schläfli–Hess 4-polytopes have either pentagrammic faces or vertex figure elements.
The pentagram of Venus is the apparent path of the planet Venus as observed from Earth . Successive inferior conjunctions of Venus repeat with an orbital resonance of approximately 13:8—that is, Venus orbits the Sun approximately 13 times for every eight orbits of Earth—shifting 144° at each inferior conjunction. [ 52 ] The tips of the five loops at the center of the figure have the same geometric relationship to one another as the five vertices , or points, of a pentagram, and each group of five intersections equidistant from the figure's center have the same geometric relationship.
The pentagram has these Unicode code points that enable them to be included in documents: | https://en.wikipedia.org/wiki/Pentagram |
In mathematics , the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane . The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper [ 1 ] though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch [ 2 ] and a 1945 paper of Theodore Motzkin . [ 3 ] The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism . It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon. [ 4 ]
Suppose that the vertices of the polygon P are given by P 1 , P 3 , P 5 , … {\displaystyle P_{1},P_{3},P_{5},\ldots } The image of P under the pentagram map is the polygon Q with vertices Q 2 , Q 4 , Q 6 , … {\displaystyle Q_{2},Q_{4},Q_{6},\ldots } as shown in the figure. Here Q 4 {\displaystyle Q_{4}} is the intersection of the diagonals ( P 1 P 5 ) {\displaystyle (P_{1}P_{5})} and ( P 3 P 7 ) {\displaystyle (P_{3}P_{7})} , and so on.
On a basic level, one can think of the pentagram map as an operation defined on convex polygons in the plane . From a more sophisticated point of view, the pentagram map is defined for a polygon contained in the projective plane over a field provided that the vertices are in sufficiently general position . The pentagram map commutes with projective transformations and thereby induces a mapping on the moduli space of projective equivalence classes of polygons.
The map P → Q {\displaystyle P\to Q} is slightly problematic, in the sense that the indices of the P -vertices are naturally odd integers whereas the indices of Q -vertices are naturally even integers. A more conventional approach to the labeling would be to label the vertices of P and Q by integers of the same parity. One can arrange this either by adding or subtracting 1 from each of the indices of the Q -vertices. Either choice is equally canonical. An even more conventional choice would be to label the vertices of P and Q by consecutive integers, but again there are two natural choices for how to align these labellings: Either Q k {\displaystyle Q_{k}} is just clockwise from P k {\displaystyle P_{k}} or just counterclockwise. In most papers on the subject, some choice is made once and for all at the beginning of the paper and then the formulas are tuned to that choice.
There is a perfectly natural way to label the vertices of the second iterate of the pentagram map by consecutive integers. For this reason, the second iterate of the pentagram map is more naturally considered as an iteration defined on labeled polygons. See the figure.
The pentagram map is also defined on the larger space of twisted polygons. [ 5 ]
A twisted N -gon is a bi-infinite sequence of points in the projective plane that is N -periodic modulo a projective transformation That is, some projective transformation M carries P k {\displaystyle P_{k}} to P N + k {\displaystyle P_{N+k}} for all k . The map M is called the monodromy of the twisted N -gon. When M is the identity, a twisted N -gon can be interpreted as an ordinary N -gon whose vertices have been listed out repeatedly. Thus, a twisted N -gon is a generalization of an ordinary N -gon.
Two twisted N -gons are equivalent if a projective transformation carries one to the other. The moduli space of twisted N -gons is the set of equivalence classes of twisted N -gons. The space of twisted N -gons contains the space of ordinary N -gons as a sub-variety of co-dimension 8. [ 5 ] [ 6 ]
The pentagram map is the identity on the moduli space of pentagons . [ 1 ] [ 2 ] [ 3 ] This is to say that there is always a projective transformation carrying a pentagon to its image under the pentagram map.
The map T 2 {\displaystyle T^{2}} is the identity on the space of labeled hexagons . [ 1 ] Here T is the second iterate of the pentagram map, which acts naturally on labeled hexagons, as described above. This is to say that the hexagons H {\displaystyle H} and T 2 ( H ) {\displaystyle T^{2}(H)} are equivalent by a label-preserving projective transformation . More precisely, the hexagons H ′ {\displaystyle H'} and T ( H ) {\displaystyle T(H)} are projectively equivalent, where H ′ {\displaystyle H'} is the labeled hexagon obtained from H {\displaystyle H} by shifting the labels by 3. [ 1 ] See the figure. It seems entirely possible that this fact was also known in the 19th century.
The action of the pentagram map on pentagons and hexagons is similar in spirit to classical configuration theorems in projective geometry such as Pascal's theorem , Desargues's theorem and others. [ 7 ]
The iterates of the pentagram map shrink any convex polygon exponentially fast to a point. [ 1 ] This is to say that the diameter of the nth iterate of a convex polygon is less than K a n {\displaystyle Ka^{n}} for constants K > 0 {\displaystyle K>0} and 0 < a < 1 {\displaystyle 0<a<1} which depend on the initial polygon. Here we are taking about the geometric action on the polygons themselves, not on the moduli space of projective equivalence classes of polygons.
This section is meant to give a non-technical overview for much of the remainder of the article. The context for the pentagram map is projective geometry . Projective geometry is the geometry of our vision. When one looks at the top of a glass, which is a circle , one typically sees an ellipse . When one looks at a rectangular door, one sees a typically non-rectangular quadrilateral . Projective transformations convert between the various shapes one can see when looking at same object from different points of view. This is why it plays such an important role in old topics like perspective drawing and new ones like computer vision . Projective geometry is built around the fact that a straight line looks like a straight line from any perspective. The straight lines are the building blocks for the subject. The pentagram map is defined entirely in terms of points and straight lines. This makes it adapted to projective geometry. If you look at the pentagram map from another point of view ( i.e. , you tilt the paper on which it is drawn) then you are still looking at the pentagram map. This explains the statement that the pentagram map commutes with projective transformations.
The pentagram map is fruitfully considered as a mapping on the moduli space of polygons . A moduli space is an auxiliary space whose points index other objects. For example, in Euclidean geometry , the sum of the angles of a triangle is always 180 degrees. You can specify a triangle (up to scale) by giving 3 positive numbers, x , y , z {\displaystyle x,y,z} such that x + y + z = 180. {\displaystyle x+y+z=180.} So, each point ( x , y , z ) {\displaystyle (x,y,z)} , satisfying the constraints just mentioned, indexes a triangle (up to scale). One might say that ( x , y , z ) {\displaystyle (x,y,z)} are coordinates for the moduli space of scale equivalence classes of triangles. If you want to index all possible quadrilaterals, either up to scale or not, you would need some additional parameters . This would lead to a higher-dimensional moduli space. The moduli space relevant to the pentagram map is the moduli space of projective equivalence classes of polygons. Each point in this space corresponds to a polygon, except that two polygons which are different views of each other are considered the same. Since the pentagram map is adapted to projective geometry, as mentioned above, it induces a mapping on this particular moduli space. That is, given any point in the moduli space, you can apply the pentagram map to the corresponding polygon and see what new point you get.
The reason for considering what the pentagram map does to the moduli space is that it gives more salient features of the map. If you just watch, geometrically, what happens to an individual polygon, say a convex polygon , then repeated application shrinks the polygon to a point. [ 1 ] To see things more clearly, you might dilate the shrinking family of polygons so that they all have, say, the same area . If you do this, then typically you will see that the family of polygons gets long and thin. [ 1 ] Now you can change the aspect ratio so as to try to get yet a better view of these polygons. If you do this process as systematically as possible, you find that you are simply looking at what happens to points in the moduli space. The attempts to zoom in to the picture in the most perceptive possible way lead to the introduction of the moduli space.
To explain how the pentagram map acts on the moduli space, one must say a few words about the torus . One way to roughly define the torus is to say that it is the surface of an idealized donut . Another way is that it is the playing field for the Asteroids video game. Yet another way to describe the torus is to say that it is a computer screen with wrap, both left-to-right and up-to-down. The torus is a classical example of what is known in mathematics as a manifold . This is a space that looks somewhat like ordinary Euclidean space at each point, but somehow is hooked together differently. A sphere is another example of a manifold. This is why it took people so long to figure out that the Earth was not flat; on small scales one cannot easily distinguish a sphere from a plane . So, too, with manifolds like the torus. There are higher-dimensional tori as well. You could imagine playing Asteroids in your room, where you can freely go through the walls and ceiling/floor, popping out on the opposite side.
One can do experiments with the pentagram map, where one looks at how this mapping acts on the moduli space of polygons. One starts with a point and just traces what happens to it as the map is applied over and over again. One sees a surprising thing: These points seem to line up along multi-dimensional tori. [ 1 ] These invisible tori fill up the moduli space somewhat like the way the layers of an onion fill up the onion itself, or how the individual cards in a deck fill up the deck. The technical statement is that the tori make a foliation of the moduli space. The tori have half the dimension of the moduli space. For instance, the moduli space of 7 {\displaystyle 7} -gons is 6 {\displaystyle 6} dimensional and the tori in this case are 3 {\displaystyle 3} dimensional.
The tori are invisible subsets of the moduli space. They are only revealed when one does the pentagram map and watches a point move round and round, filling up one of the tori. Roughly speaking, when dynamical systems have these invariant tori, they are called integrable systems . Most of the results in this article have to do with establishing that the pentagram map is an integrable system, that these tori really exist. The monodromy invariants, discussed below, turn out to be the equations for the tori. The Poisson bracket, discussed below, is a more sophisticated math gadget that sort of encodes the local geometry of the tori. What is nice is that the various objects fit together exactly, and together add up to a proof that this torus motion really exists.
When the field underlying all the constructions is F , the affine line is just a copy of F . The affine line is a subset of the projective line . Any finite list of points in the projective line can be moved into the affine line by a suitable projective transformation .
Given the four points t 1 , t 2 , t 3 , t 4 {\displaystyle t_{1},t_{2},t_{3},t_{4}} in the affine line one defines the (inverse) cross ratio
Most authors consider 1/ X to be the cross-ratio , and that is why X is called the inverse cross ratio. The inverse cross ratio is invariant under projective transformations and thus makes sense for points in the projective line. However, the formula above only makes sense for points in the affine line.
In the slightly more general set-up below, the cross ratio makes sense for any four collinear points in projective space One just identifies the line containing the points with the projective line by a suitable projective transformation and then uses the formula above. The result is independent of any choices made in the identification. The inverse cross ratio is used in order to define a coordinate system on the moduli space of polygons, both ordinary and twisted.
The corner invariants are basic coordinates on the space of twisted polygons. [ 5 ] [ 6 ] [ 8 ] Suppose that P is a polygon . A flag of P is a pair ( p , L ), where p is a vertex of P and L is an adjacent line of P . Each vertex of P is involved in two flags, and likewise each edge of P is involved in two flags. The flags of P are ordered according to the orientation of P , as shown in the figure. In this figure, a flag is represented by a thick arrow. Thus, there are 2 N flags associated to an N-gon.
Let P be an N -gon, with flags F 1 , … , F 2 N {\displaystyle F_{1},\ldots ,F_{2N}} To each flag F, we associate the inverse cross ratio of the points t 1 , t 2 , t 3 , t 4 {\displaystyle t_{1},t_{2},t_{3},t_{4}} shown in the figure at left. In this way, one associates numbers x 1 , … , x 2 n {\displaystyle x_{1},\ldots ,x_{2n}} to an n-gon. If two n-gons are related by a projective transformation, they get the same coordinates. Sometimes the variables x 1 , y 1 , x 2 , y 2 , … {\displaystyle x_{1},y_{1},x_{2},y_{2},\ldots } are used in place of x 1 , x 2 , x 3 , x 4 , … . {\displaystyle x_{1},x_{2},x_{3},x_{4},\ldots \,.}
The corner invariants make sense on the moduli space of twisted polygons. When one defines the corner invariants of a twisted polygon, one obtains a 2 N -periodic bi-infinite sequence of numbers. Taking one period of this sequence identifies a twisted N -gon with a point in F 2 N {\displaystyle F^{2N}} where F is the underlying field. Conversely, given almost any (in the sense of measure theory ) point in F 2 N {\displaystyle F^{2N}} one can construct a twisted N -gon having this list of corner invariants. Such a list will not always give rise to an ordinary polygon; there are an additional 8 equations which the list must satisfy for it to give rise to an ordinary N -gon.
There is a second set of coordinates for the moduli space of twisted polygons, developed by Sergei Tabachnikov and Valentin Ovsienko. [ 6 ] One describes a polygon in the projective plane by a sequence of vectors … V 1 , V 2 , V 3 , … {\displaystyle \ldots V_{1},V_{2},V_{3},\ldots } in R 3 {\displaystyle R^{3}} so that each consecutive triple of vectors spans a parallelepiped having unit volume. This leads to the relation
The coordinates a 1 , b 1 , a 2 , b 2 , … {\displaystyle a_{1},b_{1},a_{2},b_{2},\ldots } serve as coordinates for the moduli space of twisted N -gons as long as N is not divisible by 3.
The (ab) coordinates bring out the close analogy between twisted polygons and solutions of 3rd order linear ordinary differential equations , normalized to have unit Wronskian .
Here is a formula for the pentagram map, expressed in corner coordinates. [ 5 ] The equations work more gracefully when one considers the second iterate of the pentagram map, thanks to the canonical labelling scheme discussed above. The second iterate of the pentagram map is the composition B ∘ A {\displaystyle B\circ A} . The maps A {\displaystyle A} and B {\displaystyle B} are birational mappings of order 2, and have the following action.
where
(Note: the index 2 k + 0 is just 2 k . The 0 is added to align the formulas.) In these coordinates, the pentagram map is a birational mapping of F 2 N {\displaystyle F^{2N}}
The formula for the pentagram map has a convenient interpretation as a certain compatibility rule for labelings on the edges of triangular grid, as shown in the figure. [ 5 ] In this interpretation, the corner invariants of a polygon P label the non-horizontal edges of a single row, and then the non-horizontal edges of subsequent rows are labeled by the corner invariants of A ( P ) {\displaystyle A(P)} , B ( A ( P ) ) {\displaystyle B(A(P))} , A ( B ( A ( P ) ) ) {\displaystyle A(B(A(P)))} , and so forth. the compatibility rules are
These rules are meant to hold for all configurations which are congruent to the ones shown in the figure. In other words, the figures involved in the relations can be in all possible positions and orientations. The labels on the horizontal edges are simply auxiliary variables introduced to make the formulas simpler. Once a single row of non-horizontal edges is provided, the remaining rows are uniquely determined by the compatibility rules.
It follows directly from the formula for the pentagram map, in terms of corner coordinates, that the two quantities
are invariant under the pentagram map. This observation is closely related to the 1991 paper of Joseph Zaks [ 4 ] concerning the diagonals of a polygon.
When N = 2 k is even, the functions
are likewise seen, directly from the formula, to be invariant functions. All these products turn out to be Casimir invariants with respect to the invariant Poisson bracket discussed below. At the same time, the functions O k {\displaystyle O_{k}} and E k {\displaystyle E_{k}} are the simplest examples of the monodromy invariants defined below.
The level sets of the function f = O N E N {\displaystyle f=O_{N}E_{N}} are compact , when f is restricted to the moduli space of real convex polygons . [ 1 ] Hence, each orbit of the pentagram map acting on this space has a compact closure .
The pentagram map, when acting on the moduli space X of convex polygons, has an invariant volume form . [ 9 ] At the same time, as was already mentioned, the function f = O N E N {\displaystyle f=O_{N}E_{N}} has compact level sets on X . These two properties combine with the Poincaré recurrence theorem to imply that the action of the pentagram map on X is recurrent: The orbit of almost any equivalence class of convex polygon P returns infinitely often to every neighborhood of P . [ 9 ] This is to say that, modulo projective transformations, one typically sees nearly the same shape, over and over again, as one iterates the pentagram map. (One is considering the projective equivalence classes of convex polygons. The fact that the pentagram map visibly shrinks a convex polygon is irrelevant.)
The recurrence result is subsumed by the complete integrability results discussed below. [ 6 ] [ 10 ]
The so-called monodromy invariants are a collection of functions on the moduli space that are invariant under the pentagram map. [ 5 ]
With a view towards defining the monodromy invariants, say that a block is either a single integer or a triple of consecutive integers, for instance 1 and 567. Say that a block is odd if it starts with an odd integer. Say that two blocks are well-separated if they have at least 3 integers between them. For instance 123 and 567 are not well separated but 123 and 789 are well separated. Say that an odd admissible sequence is a finite sequence of integers that decomposes into well separated odd blocks. When we take these sequences from the set 1, ..., 2 N , the notion of well separation is meant in the cyclic sense. Thus, 1 and 2 N − 1 are not well separated.
Each odd admissible sequence gives rise to a monomial in the corner invariants. This is best illustrated by example
The sign is determined by the parity of the number of single-digit blocks in the sequence. The monodromy invariant O k {\displaystyle O_{k}} is defined as the sum of all monomials coming from odd admissible sequences composed of k blocks. The monodromy invariant E k {\displaystyle E_{k}} is defined the same way, with even replacing odd in the definition.
When N is odd, the allowable values of k are 1, 2, ..., ( n − 1)/2. When N is even, the allowable values of k are 1, 2, ..., n /2. When k = n /2, one recovers the product invariants discussed above. In both cases, the invariants O N {\displaystyle O_{N}} and E N {\displaystyle E_{N}} are counted as monodromy invariants, even though they are not produced by the above construction.
The monodromy invariants are defined on the space of twisted polygons, and restrict to give invariants on the space of closed polygons. They have the following geometric interpretation. The monodromy M of a twisted polygon is a certain rational function in the corner coordinates. The monodromy invariants are essentially the homogeneous parts of the trace of M . There is also a description of the monodromy invariants in terms of the (ab) coordinates. In these coordinates, the invariants arise as certain determinants of 4-diagonal matrices . [ 6 ] [ 8 ]
Whenever P has all its vertices on a conic section (such as a circle) one has O k ( P ) = E k ( P ) {\displaystyle O_{k}(P)=E_{k}(P)} for all k . [ 8 ]
A Poisson bracket is an anti-symmetric linear operator { ⋅ , ⋅ } {\displaystyle \{\cdot ,\cdot \}} on the space of functions which satisfies the Leibniz Identity and the Jacobi identity . In a 2010 paper, [ 6 ] Valentin Ovsienko, Richard Schwartz and Sergei Tabachnikov produced a Poisson bracket on the space of twisted polygons which is invariant under the pentagram map. They also showed that monodromy invariants commute with respect to this bracket. This is to say that
for all indices.
Here is a description of the invariant Poisson bracket in terms of the variables.
There is also a description in terms of the (ab) coordinates, but it is more complicated. [ 6 ]
Here is an alternate description of the invariant bracket. Given any function f {\displaystyle f} on the moduli space, we have the so-called Hamiltonian vector field
where a summation over the repeated indices is understood. Then
The first expression is the directional derivative of g {\displaystyle g} in the direction of the vector field H ( f ) {\displaystyle H(f)} . In practical terms, the fact that the monodromy invariants Poisson-commute means that the corresponding Hamiltonian vector fields define commuting flows.
The monodromy invariants and the invariant bracket combine to establish Arnold–Liouville integrability of the pentagram map on the space of twisted N -gons. [ 6 ] The situation is easier to describe for N odd. In this case, the two products
are Casimir invariants for the bracket, meaning (in this context) that
for all functions f. A Casimir level set is the set of all points in the space having a specified value for both O n {\displaystyle O_{n}} and E n {\displaystyle E_{n}} .
Each Casimir level set has an iso-monodromy foliation , namely, a decomposition into the common level sets of the remaining monodromy functions. The Hamiltonian vector fields associated to the remaining monodromy invariants generically span the tangent distribution to the iso-monodromy foliation. The fact that the monodromy invariants Poisson-commute means that these vector fields define commuting flows. These flows in turn define local coordinate charts on each iso-monodromy level such that the transition maps are Euclidean translations. That is, the Hamiltonian vector fields impart a flat Euclidean structure on the iso-monodromy levels, forcing them to be flat tori when they are smooth and compact manifolds . This happens for almost every level set. Since everything in sight is pentagram-invariant, the pentagram map, restricted to an iso-monodromy leaf, must be a translation. This kind of motion is known as quasi-periodic motion . This explains the Arnold-Liouville integrability.
From the point of view of symplectic geometry , the Poisson bracket gives rise to a symplectic form on each Casimir level set.
In a 2011 preprint, [ 10 ] Fedor Soloviev showed that the pentagram map has a Lax representation with a spectral parameter, and proved its algebraic-geometric integrability. This means that the space of polygons (either twisted or ordinary) is parametrized in terms of a spectral curve with marked points and a divisor . The spectral curve is determined by the monodromy invariants, and the divisor corresponds to a point on a torus—the Jacobi variety of the spectral curve. The algebraic-geometric methods guarantee that the pentagram map exhibits quasi-periodic motion on a torus (both in the twisted and the ordinary case), and they allow one to construct explicit solutions formulas using Riemann theta functions (i.e., the variables that determine the polygon as explicit functions of time). Soloviev also obtains the invariant Poisson bracket from the Krichever–Phong universal formula.
In 2022, [ 11 ] PhD student Max Weinreich generalized the integrability results obtained by Soloviev on the field of complex numbers to any algebraically closed field of characteristic different from 2. The translation on a torus is replaced by a translation on an abelian variety .
The octahedral recurrence is a dynamical system defined on the vertices of the octahedral tiling of space. Each octahedron has 6 vertices, and these vertices are labelled in such a way that
Here a i {\displaystyle a_{i}} and b i {\displaystyle b_{i}} are the labels of antipodal vertices. A common convention is that a 2 , b 2 , a 3 , b 3 {\displaystyle a_{2},b_{2},a_{3},b_{3}} always lie in a central horizontal plane and a_1,b_1 are the top and bottom vertices. The octahedral recurrence is closely related to C. L. Dodgson's method of condensation for computing determinants . [ 5 ] Typically one labels two horizontal layers of the tiling and then uses the basic rule to let the labels propagate dynamically.
Max Glick used the cluster algebra formalism to find formulas for the iterates of the pentagram map in terms of alternating sign matrices . [ 12 ] These formulas are similar in spirit to the formulas found by David P. Robbins and Harold Rumsey for the iterates of the octahedral recurrence.
Alternatively, the following construction relates the octahedral recurrence directly to the pentagram map. [ 5 ] Let T {\displaystyle T} be the octahedral tiling. Let π : T → R 2 {\displaystyle \pi :T\to R^{2}} be the linear projection which maps each octahedron in T {\displaystyle T} to the configuration of 6 points shown in the first figure. Say that an adapted labeling of T {\displaystyle T} is a labeling so that all points in the (infinite) inverse image of any point in G = π ( T ) {\displaystyle G=\pi (T)} get the same numerical label. The octahedral recurrence applied to an adapted labeling is the same as a recurrence on G {\displaystyle G} in which the same rule as for the octahedral recurrence is applied to every configuration of points congruent to the configuration in the first figure. Call this the planar octahedral recurrence.
Given a labeling of G {\displaystyle G} which obeys the planar octahedral recurrence, one can create a labeling of the edges of G {\displaystyle G} by applying the rule
to every edge. This rule refers to the figure at right and is meant to apply to every configuration that is congruent to the two shown.
When this labeling is done, the edge-labeling of G satisfies the relations for the pentagram map.
The continuous limit of a convex polygon is a parametrized convex curve in the plane. When the time parameter is suitably chosen, the continuous limit of the pentagram map is the classical Boussinesq equation . [ 5 ] [ 6 ] This equation is a classical example of an integrable partial differential equation .
Here is a description of the geometric action of the Boussinesq equation. Given a locally convex curve C : R → R 2 {\displaystyle C:R\to R^{2}} , and real numbers x and t, we consider the chord connecting C ( x − t ) {\displaystyle C(x-t)} to C ( x + t ) {\displaystyle C(x+t)} . The envelope of all these chords is a new curve C t ( x ) {\displaystyle C_{t}(x)} . When t is extremely small, the curve C t ( x ) {\displaystyle C_{t}(x)} is a good model for the time t evolution of the original curve C 0 ( x ) {\displaystyle C_{0}(x)} under the Boussinesq equation. This geometric description makes it fairly obvious that the B-equation is the continuous limit of the pentagram map. At the same time, the pentagram invariant bracket is a discretization of a well known invariant Poisson bracket associated to the Boussinesq equation. [ 6 ]
Recently, there has been some work on higher-dimensional generalizations of the pentagram map and its connections to Boussinesq-type partial differential equations [ 13 ]
The pentagram map and the Boussinesq equation are examples of projectively natural geometric evolution equations. Such equations arise in diverse fields of mathematics, such as projective geometry and computer vision . [ 14 ] [ 15 ]
In a 2010 paper [ 12 ] Max Glick identified the pentagram map as a special case of a cluster algebra . | https://en.wikipedia.org/wiki/Pentagram_map |
In the geometry of hyperbolic 4-space , the pentagrammic-order 600-cell honeycomb is one of four regular star- honeycombs . With Schläfli symbol {3,3,5,5/2}, it has five 600-cells around each face in a pentagrammic arrangement. It is dual to the small stellated 120-cell honeycomb . It can be considered the higher-dimensional analogue of the 4-dimensional icosahedral 120-cell and the 3-dimensional great dodecahedron . It is related to the order-5 icosahedral 120-cell honeycomb and great 120-cell honeycomb : the icosahedral 120-cells and great 120-cells in each honeycomb are replaced by the 600-cells that are their convex hulls, thus forming the pentagrammic-order 600-cell honeycomb.
This honeycomb can also be constructed by taking the order-5 5-cell honeycomb and replacing clusters of 600 5-cells meeting at a vertex with 600-cells. Each 5-cell belongs to five such clusters, and thus the pentagrammic-order 600-cell honeycomb has density 5.
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentagrammic-order_600-cell_honeycomb |
Pentamethylantimony or pentamethylstiborane is an organometalllic compound containing five methyl groups bound to an antimony atom with formula Sb(CH 3 ) 5 . It is an example of a hypervalent compound. The molecular shape is trigonal bipyramid . [ 1 ] Some other antimony(V) organometallic compounds include pentapropynylantimony (Sb(CCCH 3 ) 5 ) and pentaphenyl antimony (Sb(C 6 H 5 ) 5 ). [ 2 ] Other known pentamethyl-pnictides include pentamethylbismuth and pentamethylarsenic .
Pentamethylantimony can be made by reacting Sb(CH 3 ) 3 Br 2 with two equivalents of methyl lithium . [ 3 ] Another production route is to convert trimethylstibine to the trimethyl antimony dichloride, and then replace the chlorine with methyl groups with methyl lithium. [ 2 ]
Pentamethylantimony is colourless. [ 3 ] At -143 °C it crystallizes in the orthorhombic system with space group Ccmm . Unit cell dimensions are a=6.630 Å b=11.004 Å c=11.090 Å. There are four formula per unit cell. Unit cell volume is 809.1 Å 3 . [ 3 ] The trigonal bipyramid shape has three equatorial positions for carbon, and two axial positions at the peaks of the pyramids. The length of the antimony-carbon bond is around 214 pm for equatorial methyl groups and 222 pm for the axial positions. The bond angles are 120° for ∠C-Sb-C across the equator, and 90° for ∠C-Sb-C between equator and axis. [ 3 ] The molecules rapidly change carbon atom position, so that in NMR spectrum as low as −100 °C, there is only one kind of hydrogen position. [ 2 ]
Pentamethylantimony is more stable than pentamethylbismuth , because in lower energy trimethylbismuth , the non-bonding pair of electrons is more shielded due to the f-electrons and the lanthanoid contraction . Trimethylantimony is higher in energy, and thus less is released in a decomposition of pentamethylantimony. [ 3 ] Pentamethylantimony can be stored as a liquid in clean glass at room temperature. [ 4 ]
Pentamethylantimony melts at -19 °C. Although it decomposes when boiling is attempted and can explode, it has a high vapour pressure at 8 mmHg at 25 °C. [ 4 ]
There are two absorption bands in the ultraviolet at 2380 and 2500 Å. [ 4 ]
Pentamethylantimony reacts with methyl lithium to yield a colourless lithium hexamethylantimonate in tetrahydrofuran . [ 3 ]
Pentamethylantimony reacts with silsesquioxanes to yield tetramethylstibonium silsesquioxanes. eg ( cyclo -C 6 H 11 ) 7 Si 7 O 9 (OH) 3 yields ( cyclo -C 6 H 11 ) 7 Si 7 O 9 (OSb(CH 3 ) 4 ) 3 . The reaction happens quickly when there are more than two OH groups. [ 5 ]
Phosphonic acids and phosphinic acids combine with pentamethylantimony to yield compounds like (CH 3 ) 4 SbOP(O)Ph 2 , (CH 3 ) 4 SbOP(O)(OH)Ph and (CH 3 ) 4 SbOP(O)(OH) 3 , eliminating methane. [ 6 ]
Stannocene Sn(C 5 H 5 ) 2 combines with pentamethylantimony to produce bis(tetramethylstibonium)tetracyclopentadienylstannate ([(CH 3 ) 4 Sb] 2 Sn(C 5 H 5 ) 4 ). [ 7 ]
Pentamethylantimony reacts with many very weak acids to form a tetramethylstibonium salt or tetramethylstibonium derivative with the acid. Such acids include water (H 2 O), alcohols , thiols , phenol , carboxylic acids , hydrogen fluoride , thiocyanic acid , hydrazoic acid , difluorophosphoric acid , thiophosphinic acids , and alkylsilols. [ 8 ]
With halogens, pentamethylantimony has one or two methyl groups replaced by the halogen atoms. [ 8 ] Lewis acids also react to form tetramethyl stibonium salts, including [(CH 3 ) 4 Sb]TlBr 4 , [(CH 3 ) 4 Sb][CH 3 SbCl 5 ], [ 8 ]
Pentamethylantimony reacts with the surface of silica to coat it with Si-O-Sb(CH 3 ) 4 groups. Over 250 °C this decomposes to Sb(CH 3 ) and leaves methyl groups attached to the silica surface. [ 9 ] | https://en.wikipedia.org/wiki/Pentamethylantimony |
Pentamethylarsenic (or pentamethylarsorane [ 1 ] ) is an organometalllic compound containing five methyl groups bound to an arsenic atom with formula As(CH 3 ) 5 . It is an example of a hypervalent compound. The molecular shape is trigonal bipyramid . [ 2 ]
The first claim to make pentamethylarsenic was in 1862 in a reaction of tetramethylarsonium iodide with dimethylzinc by A. Cahours. [ 3 ] [ 4 ] For many years all the reproductions of this proved fruitless, so the production proved not to be genuine. [ 1 ] [ 5 ] It was actually discovered by Karl-Heinz Mitschke and Hubert Schmidbaur in 1973. [ 6 ]
Trimethylarsine is chlorinated to trimethylarsine dichloride , which then reacts with methyl lithium to yield pentamethylarsenic. [ 6 ]
Side products include As(CH 3 ) 4 Cl and As(CH 3 ) 3 =CH 2 . [ 1 ]
Pentamethylarsenic is not produced by biological organisms. [ 7 ]
Pentamethylarsenic smells the same as pentamethylantimony , but is otherwise unique. [ 1 ]
The bond lengths in the molecule are for the three equatorial As−C bonds 1.975 Å and the two axial As−C bonds 2.073 Å. [ 8 ]
The infrared spectrum of pentamethylarsenic shows strong bands at 582 and 358 cm −1 due to axial C-As vibration, and weaker bands at 265 and 297 cm −1 due to equatorial C-As vibration. [ 9 ] Raman spectrum shows a strong feature at 519, 388, and 113 cm −1 , and weak lines at 570 and 300 cm −1 . [ 9 ]
Pentamethylarsenic reacts slowly with weak acids. With water it forms tetramethylarsonium hydroxide As(CH 3 ) 4 OH and trimethylarsenic oxide As(CH 3 ) 3 O. With methanol, tetramethylmethoxyarsorane As(CH 3 ) 4 OCH 3 is produced. Hydrogen halides react resulting in the formation of tetramethylarsonium halide salts. [ 1 ]
When pentamethylarsenic is heated to 100° it decomposes forming trimethylarsine , methane , and ethylene . [ 10 ]
When trimethylindium reacts with pentamethylarsenic in benzene solution, a salt precipitates: tetramethylarsenic(V)tetramethylindate(III). [ 11 ] | https://en.wikipedia.org/wiki/Pentamethylarsenic |
Pentamethylbismuth (or pentamethylbismuthorane [ 2 ] ) is an organometalllic compound containing five methyl groups bound to a bismuth atom with formula Bi(CH 3 ) 5 . It is an example of a hypervalent compound. The molecular shape is trigonal bipyramid . [ 3 ]
Pentamethylbismuth is produced in a two step process. First, trimethylbismuth is reacted with sulfuryl chloride to yield dichloro trimethylbismuth, which is then reacted with two equivalents of methyllithium dissolved in ether. [ 4 ] The blue solution is cooled to −110 °C to precipitate the solid product.
At -110 °C, Bi(CH 3 ) 5 is a blue-violet solid. The methyl groups are arranged in a trigonal bipyramid, and the bond-lengths of methyl with bismuth are all the same. However, the molecule is not rigid, as can be determined from the nuclear magnetic resonance spectrum that shows all methyl groups are equivalent. [ 4 ] It is stable as a solid, but in the gas phase, when heated or in solution decomposes to trimethylbismuth . [ 3 ] [ 4 ] The colour is unusual for bismuth or other hypervalent pnictide compounds, which are colourless. Calculations show that the colour is due to HOMO -LUMO transition. The HOMO is ligand based, whereas the LUMO is modified by relativistically stabilised bismuth 6s orbitals. [ 5 ]
If excess methyllithium is used in production, an orange hexamethylbismuth salt, LiBi(CH 3 ) 6 , is formed. [ 6 ] [ 4 ] | https://en.wikipedia.org/wiki/Pentamethylbismuth |
Pentamethyltantalum is a homoleptic organotantalum compound.
It has a propensity to explode when it is melted. [ 4 ] Its discovery was part of a sequence that led to Richard R. Schrock 's Nobel Prize winning discovery in olefin metathesis . [ 5 ]
Pentamethyltantalum can be made from the reaction of methyllithium with dichlorotrimethyltantalum . [ 6 ] Ta(CH 3 ) 3 Cl 2 is in turn made from tantalum pentachloride and dimethylzinc . [ 7 ]
The preparation was inspired by the existence of pentaphenylphosphorus , and the discovery of hexamethyltungsten . The discoverer Richard R. Schrock considered tantalum to be a metallic phosphorus, and thus tried the use of methyllithium. [ 8 ]
The pentamethyltantalum adopts a square pyramid shape. Ignoring the C-H bonds, the molecule has C 4v symmetry. The four carbon atoms at the base of the pyramid are called basal, and the carbon atom at the top is called apical or apex. The distance from tantalum to the apical carbon atom is 2.11 Å, and to the basal carbon atoms is 2.180 Å. The distance from hydrogen to carbon in the methyl groups is 1.106 Å. The angle subtended by two basal carbon bonds is 82.2°, and the angle between the bonds to the apex and a carbon on the base is about 111.7°. [ 9 ] [ 10 ]
At room temperature pentamethyltantalum can spontaneously explode, so samples are usually stored in a -20°c freezer. [ 10 ]
With many carbon-hydrogen bonds near Ta, analogues of pentamethyltantalum are susceptible to alpha elimination . [ 5 ]
Excess methyllithium reacts to yield higher coordinated methyl tantalum ions [Ta(CH 3 ) 6 ] − and [Ta(CH 3 ) 7 ] 2− . [ 6 ]
Pentamethyltantalum in solution forms stable insoluble complex material when mixed with dmpe (CH 3 ) 2 PCH 2 CH 2 P(CH 3 ) 2 . [ 6 ]
With nitric oxide it gives a white coloured dimer with formula {TaMe 3 [ON(Me)NO] 2 } 2 (Me=CH 3 ). [ 11 ] | https://en.wikipedia.org/wiki/Pentamethyltantalum |
This page provides supplementary chemical data on n -pentane .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as eChemPortal , and follow its directions.
Table data obtained from CRC Handbook of Chemistry and Physics 47th ed. | https://en.wikipedia.org/wiki/Pentane_(data_page) |
Pentane interference or syn -pentane interaction is the steric hindrance that the two terminal methyl groups experience in one of the chemical conformations of n-pentane . The possible conformations are combinations of anti conformations and gauche conformations and are anti-anti, anti-gauche + , gauche + - gauche + and gauche + - gauche − of which the last one is especially energetically unfavorable. In macromolecules such as polyethylene pentane interference occurs between every fifth carbon atom. The 1,3-diaxial interactions of cyclohexane derivatives is a special case of this type of interaction, although there are additional gauche interactions shared between substituents and the ring in that case. A clear example of the syn -pentane interaction is apparent in the diaxial versus diequatorial heats of formation of cis 1,3-dialkyl cyclohexanes. Relative to the diequatorial conformer, the diaxial conformer is 2-3 kcal/mol higher in energy than the value that would be expected based on gauche interactions alone. Pentane interference helps explain molecular geometries in many chemical compounds, product ratios, and purported transition states. One specific type of syn -pentane interaction is known as 1,3 allylic strain or ( A 1,3 strain).
For instance in certain aldol adducts with 2,6-disubstituted aryl groups the molecular geometry has the vicinal hydrogen atoms in an antiperiplanar configuration both in a crystal lattice ( X-ray diffraction ) and in solution proton ( NMR coupling constants ) normally reserved for the most bulky groups i.d. both arenes: [ 1 ]
The other contributing factor explaining this conformation is reduction in allylic strain by minimizing the dihedral angle between the arene double bond and the methine proton.
Syn-pentane interactions are responsible for the backbone-conformation dependence of protein side chain rotamer frequencies and their mean dihedral angles, [ 2 ] which is evident from statistical analysis of protein side-chain rotamers in the Backbone-dependent rotamer library . | https://en.wikipedia.org/wiki/Pentane_interference |
In organic chemistry , pentanonide is a functional group which is composed of a cyclic ketal of a diol with 3-pentanone . [ 1 ] It is seen in amcinafal (triamcinolone pentanonide). [ 1 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentanonide |
Pentanoyl chloride is an acyl chloride derived from pentanoic acid . It is a colorless liquid that is used to attach the valeroyl group. It is usually produced by chlorination of valeric acid . [ 1 ]
Like related acyl chlorides , valeryl chloride hydrolyzes readily:
Alcohols react to give esters:
Amines react to give amides:
Benzene reacts under conditions of the Friedel-Crafts reaction to give valerophenone :
This article about an organic halide is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentanoyl_chloride |
Pentaoxidane is an inorganic compound of hydrogen and oxygen with the chemical formula H 2 O 5 . [ 1 ] This is one of the most unstable hydrogen polyoxides . [ 2 ] [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Pentaoxidane |
Pentaoxygen difluoride is a binary inorganic compound of fluorine and oxygen with the chemical formula O 5 F 2 . [ 1 ] [ 2 ] The compound is one of many known oxygen fluorides .
The compound can be prepared by electric discharges through the F 2 — O 2 mixture of the certain molar ratio at 60 to 77 K. The ratio is predicted to be 5:2. [ 3 ]
Pentaoxygen difluoride is an oxidizing agent . At 90 K, the compound looks like a reddish-brown liquid and as an oil at 77 K. [ 3 ]
At 77 K, the compound is insoluble in liquid N 2 , soluble in liquid O 2 and CH 4 . At 65 K, it is soluble in liquid OF 2 . [ 3 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentaoxygen_difluoride |
Pentaphenylantimony is an organoantimony compound containing five phenyl groups attached to one antimony atom. It has formula Sb(C 6 H 5 ) 5 (or SbPh 5 ).
The structure of pentaphenylantimony has been the subject of several studies, and a definite ground state remains uncertain. The molecule adopts a roughly square pyramidal shape in the unsolvated crystal. In crystals of the solvate with cyclohexane or tetrahydrofuran , the compound adopts a trigonal bipyramid shape. [ 1 ] When dissolved, molecules are also trigonal bipyramidal. [ 1 ] According to solution NMR measurements, the phenyl groups all appear to be equivalent, indicating fluxionality . [ 2 ]
Solid pure pentaphenylantimony forms triclinic crystals in the P 1 space group . The unit cell has a=10.286 b=10.600 and c=13.594 Å, α=79.20° β=70.43° γ=119.52°. The basal Sb-C bond length is 2.216 Å whereas the apex Sb-C length is 2.115 Å. [ 3 ]
Pentaphenylantimony reacts with a variety of protic reagents (hydrogen halides, carboxylic acids, methanol, etc). Benzene is one product as well as a tetraphenylantimony(V) compound: [ 4 ]
Halogens also cleave one Sb-phenyl bond:
When heated, pentaphenylantimony forms triphenylstibine , biphenyl and p -quaterphenyl . [ 5 ]
A reaction with carbon tetrachloride yields tetraphenylstibonium chloride, chlorobenzene, and benzene. Some of these reactions may proceed by radical pathways. [ 5 ]
Pentaphenylantimony can be formed by reacting dichlorotriphenylantimony with phenyl lithium . [ 3 ] | https://en.wikipedia.org/wiki/Pentaphenylantimony |
In mathematics , pentation (or hyper-5 ) is the fifth hyperoperation . Pentation is defined to be repeated tetration , similarly to how tetration is repeated exponentiation , exponentiation is repeated multiplication , and multiplication is repeated addition . The concept of "pentation" was named by English mathematician Reuben Goodstein in 1947, when he came up with the naming scheme for hyperoperations.
The number a pentated to the number b is defined as a tetrated to itself b - 1 times. This may variously be denoted as a [ 5 ] b {\displaystyle a[5]b} , a ↑ ↑ ↑ b {\displaystyle a\uparrow \uparrow \uparrow b} , a ↑ 3 b {\displaystyle a\uparrow ^{3}b} , a → b → 3 {\displaystyle a\to b\to 3} , or b a {\displaystyle {_{b}a}} , depending on one's choice of notation.
For example, 2 pentated to the 2 is 2 tetrated to the 2, or 2 raised to the power of 2, which is 2 2 = 4 {\displaystyle 2^{2}=4} . As another example, 2 pentated to the 3 is 2 tetrated to the result of 2 tetrated to the 2. Since 2 tetrated to the 2 is 4, 2 pentated to the 3 is 2 tetrated to the 4, which is 2 2 2 2 = 65536 {\displaystyle 2^{2^{2^{2}}}=65536} .
Based on this definition, pentation is only defined when a and b are both positive integers , though progress has been made to allow for any value of a .
Pentation is the next hyperoperation (infinite sequence of arithmetic operations, based on the previous one each time) after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity). This is similar to tetration, as tetration is iterated right-associative exponentiation . [ 1 ] It is a binary operation defined with two numbers a and b , where a is tetrated to itself b − 1 times.
The type of hyperoperation is typically denoted by a number in brackets, []. For instance, using hyperoperation notation for pentation and tetration, 2 [ 5 ] 3 {\displaystyle 2[5]3} means tetrating 2 to itself 2 times, or 2 [ 4 ] ( 2 [ 4 ] 2 ) {\displaystyle 2[4](2[4]2)} . This can then be reduced to 2 [ 4 ] ( 2 2 ) = 2 [ 4 ] 4 = 2 2 2 2 = 2 2 4 = 2 16 = 65 , 536 {\displaystyle 2[4](2^{2})=2[4]4=2^{2^{2^{2}}}=2^{2^{4}}=2^{16}=65,536} .
The word "pentation" was coined by Reuben Goodstein in 1947 from the roots penta- (five) and iteration . It is part of his general naming scheme for hyperoperations . [ 2 ]
There is little consensus on the notation for pentation; as such, there are many different ways to write the operation. However, some are more used than others, and some have clear advantages or disadvantages compared to others.
The values of the pentation function may also be obtained from the values in the fourth row of the table of values of a variant of the Ackermann function : if A ( n , m ) {\displaystyle A(n,m)} is defined by the Ackermann recurrence A ( m − 1 , A ( m , n − 1 ) ) {\displaystyle A(m-1,A(m,n-1))} with the initial conditions A ( 1 , n ) = a n {\displaystyle A(1,n)=an} and A ( m , 1 ) = a {\displaystyle A(m,1)=a} , then a [ 5 ] b = A ( 4 , b ) {\displaystyle a[5]b=A(4,b)} . [ 7 ]
Although tetration, its base operation, was extended to non-integer heights (more generally any height, real or complex) in 2017, [ 8 ] building on Hellmuth Kneser 's work, [ 9 ] pentation a [ 5 ] b {\displaystyle a[5]b} is currently only defined for integer values of b where a > 0 and b ≥ −2, such as e [ 5 ] 2 = e [ 4 ] e ≈ 2075.96834... {\displaystyle e[5]2=e[4]e\approx 2075.96834...} . As with all hyperoperations of order 3 ( exponentiation ) and higher, pentation has the following trivial cases (identities) which holds for all values of a and b within its domain:
Additionally, we can also introduce the following defining relations:
Other than the trivial cases shown above, pentation generates extremely large numbers very quickly. As a result, there are only a few non-trivial cases that produce numbers that can be written in conventional notation, which are all listed below.
Some of these numbers are written in power tower notation due to their extreme size. Note that exp 10 ( n ) = 10 n {\displaystyle \exp _{10}(n)=10^{n}} . | https://en.wikipedia.org/wiki/Pentation |
In chemistry , the pentazenium cation (also known as pentanitrogen ) is a positively-charged polyatomic ion with the chemical formula N + 5 and structure N−N−N−N−N . Together with solid nitrogen polymers and the azide anion, it is one of only three poly- nitrogen species obtained in bulk quantities.
Within the High Energy Density Matter research program, run by the U.S. Air Force since 1986, systematic attempts to approach polynitrogen compounds began in 1998, when Air Force Research Laboratory at Edwards AFB became interested in researching alternatives to the highly toxic hydrazine -based rocket fuel and simultaneously funded several such proposals. Karl O. Christe , then, a senior investigator at AFRL, chose to attempt building linear N + 5 out of N 2 F + and N − 3 , based on the proposed bond structure: [ 1 ]
The reaction succeeded, and [N 5 ] + [AsF 6 ] − was created in sufficient quantities to be fully characterized by NMR, IR and Raman spectroscopy in 1999. [ 2 ] The salt was highly explosive, but when AsF 5 was replaced by SbF 5 , a stronger Lewis acid, much more stable [N 5 ] + [SbF 6 ] − was produced, shock-resistant and thermally stable up to 60–70 °C. This made bulk quantities, easy handling, and X-ray crystal structure analysis possible. [ 3 ]
Actually N5+ had been predicted by ab initio calculations as a member of the dicyanamide isoelectronic series by Pyykkö and Runeberg in 1991 and this was quoted as ref. [10] of Christe [2] in 1999.
Reaction of N 2 F + and HN 3 in dry HF at −78 °C is the only known method so far:
N + 5 is capable of oxidizing water, NO, NO 2 and Br 2 , but not Cl 2 or O 2 ; its electron affinity is 10.44 eV (1018.4 kJ/mol). For this reason, N + 5 must be prepared and handled in a dry environment:
Due to stability of the fluoroantimonate, it is used as the precursor for all other known salts, typically accomplished by metathesis reactions in non-aqueous solvents such as HF, SO 2 , CHF 3 , or CH 3 CN , where suitable hexafluoroantimonates are insoluble:
The most stable salts of N + 5 decompose when heated to 50–60 °C: [N 5 ] + [SbF 6 ] − , [N 5 ] + [SnF 5 ] − , and [N 5 ] + [B(CF 3 ) 4 ] − , while the most unstable salts that were obtained and studied, [N 5 ] + [P(N 3 ) 6 ] − and [N 5 ] + [B(N 3 ) 4 ] − were extremely shock and temperature sensitive, exploding in solutions as dilute as 0.5 mmol. A number of salts, such as fluoride, azide, nitrate, or perchlorate, cannot be formed. [ 1 ]
In valence bond theory , pentazenium can be described by six resonance structures :
where the last three structures have smaller contributions to the overall structure because they have less favorable formal charge states than the first three. [ 4 ] [ better source needed ]
According to both ab initio calculations and the experimental X-ray structure, the cation is planar, symmetric, and approximately V-shaped, with bond angles 111° at the central atom (angle N2–N3–N4) and 168° at the second and fourth atoms (angles N1–N2–N3 and N3–N4–N5). The bond lengths for N1–N2 and N4–N5 are 1.10 Å and the bond lengths N2–N3 and N3–N4 are 1.30 Å. [ 3 ] | https://en.wikipedia.org/wiki/Pentazenium |
Pentazine is a hypothetical chemical compound that consists of a six-membered aromatic ring containing five nitrogen atoms with the molecular formula C H N 5 . The name pentazine is used in the nomenclature of derivatives of this compound.
Pentazine is predicted to be unstable and to decompose into hydrogen cyanide (HCN) and nitrogen (N 2 ). [ 1 ] The activation energy required is predicted to be around 20 kJ/mol. [ 2 ]
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pentazine |
Pentazole is an aromatic molecule consisting of a five-membered ring with all nitrogen atoms, one of which is bonded to a hydrogen atom. It has the molecular formula HN 5 . Although strictly speaking a homocyclic , inorganic compound , pentazole has historically been classed as the last in a series of heterocyclic azole compounds containing one to five nitrogen atoms. This set contains pyrrole , imidazole , pyrazole , triazoles , tetrazole , and pentazole.
Substituted analogs of pentazole are collectively known as pentazoles. As a class, they are unstable and often highly explosive compounds. The first pentazole synthesized was phenylpentazole , where the pentazole ring is highly stabilized by conjugation with the phenyl ring. The derivative 4-dimethylaminophenylpentazole is among the most stable pentazole compounds known, although it still decomposes at temperatures over 50 °C. It is known that electron-donating groups stabilize aryl pentazole compounds. [ 2 ]
The cyclic pentazolium cation ( N + 5 ) is not known due to its probable antiaromatic character; whereas the open-chained pentazenium cation ( N + 5 ) is known. Butler et al. first demonstrated the presence of the cyclic N − 5 in solution through the decomposition of substituted aryl pentazoles at low temperature. The presence of N 5 H and N − 5 (held in solution through the interaction with zinc ions) was proven primarily using 15 N NMR techniques of the decomposition products. [ 3 ] These results were initially challenged by some authors, [ 4 ] but subsequent experiments involving the detailed analysis of the decomposition products, complemented by computational studies, bore out the initial conclusion. [ 5 ] [ 6 ] [ 7 ] The pentazolide anion is not expected to last longer than a few seconds in aqueous solution without the aid of complexing agents. The discovery of pentazoles spurred attempts to create all-nitrogen salts such as N + 5 N − 5 , which should be highly potent propellants for space travel .
In 2002, the pentazolate anion was first detected with electrospray ionization mass spectrometry [ 8 ] In 2016, the ion was also detected in solution. [ 9 ] In 2017, white cubic crystals of the pentazolate salt, (N 5 ) 6 (H 3 O) 3 (NH 4 ) 4 Cl were announced. In this salt, the N − 5 rings are planar. The bond lengths in the ring are 1.309 Å, 1.310 Å, 1.310 Å, 1.324 Å, and 1.324 Å. [ 10 ] When heated, the salt is stable up to 117 °C, and over this temperature it decomposes to ammonium azide . [ 10 ] Under extreme pressure conditions, the pentazolate ion was also synthesized. It was first obtained in 2016 in the form of the CsN 5 salt by compressing and laser-heating a mixture of CsN 3 embedded in molecular N 2 at 60 GPa. Following the pressure release, it was found metastable down to 18 GPa. [ 11 ] In 2018, another team reported the high pressure synthesis of LiN 5 above 45 GPa from a pure lithium surrounded by molecular nitrogen. This compound could be retained down to ambient conditions after the complete release of pressure. [ 12 ] | https://en.wikipedia.org/wiki/Pentazole |
Pentosans are polymers composed of pentoses . In contrast to cellulose , which is composed of hexose ( glucose ) monomers , pentosans are derived from five-carbon sugars such as xylose . Pentosan-rich biomass is the precursor to furfural . [ 1 ]
The pentosan content has been determined for many natural materials: [ 1 ]
Pentosans can act as heparinoids , glycosaminoglycans which are derivatives of heparin .
They can have an influence on bread quality. [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Pentosan |
Pentosidine is a biomarker for advanced glycation endproducts , or AGEs. It is a well characterized and easily detected member of this large class of compounds.
AGEs are biochemicals formed continuously under normal circumstances, but more rapidly under a variety of stresses, especially oxidative stress and hyperglycemia . They serve as markers of stress and act as toxins themselves. Pentosidine is typical of the class, except that it fluoresces , which allows it to be seen and measured easily. Because it is well characterized, it is often studied to provide new insight into the biochemistry of AGE compounds in general.
Derived from ribose , a pentose , pentosidine forms fluorescent cross-links between the arginine and lysine residues in collagen . It is formed in a reaction of the amino acids with the Maillard reaction products of ribose. [ 1 ]
Although it is present only in trace concentrations among tissue proteins, it is useful for assessing cumulative damage to
proteins— advanced glycation endproducts —by non-enzymatic browning reactions with carbohydrates . [ 2 ] [ 3 ] [ 4 ]
In vivo , AGEs form pentosidine through sugar fragmentation. In patients with diabetes mellitus type 2 , pentosidine correlates with the presence and severity of diabetic complications. [ 5 ] | https://en.wikipedia.org/wiki/Pentosidine |
A pepper-spray projectile , also called a pepper-spray ball , pepper-ball , pepper bomb , or pepper-spray pellet , is a frangible projectile containing a powdered chemical that irritates the eyes and nose in a manner similar to pepper spray . These projectiles are fired from specially designed forced compliance weapons or modified paintball guns .
A pepper-spray projectile may be a sphere, hence the name pepper- ball , but it may also come in other shapes. The irritant payload may differ from product to product but is usually a powder , less frequently a liquid , gas or aerosol . Some companies offer different substances as payload for their projectiles and launcher systems, so potential sellers can choose a substance that is certified for use in their country. Also, projectiles with an inert dummy payload are often offered, for training and testing purposes.
A powder called PAVA (capsaicin II) pepper is often used. PAVA is a capsaicinoid that can be synthesized for cheaper than grown peppers, although it is also found in nature.
Pepper-spray weapons systems are used by law enforcement, military and other organizations, and individuals. The weapon is used generally in the role of stand-off weapons, where physical proximity to a suspect is deemed dangerous but deadly force is not warranted. The systems are not limited to classic standoff situations and allow agents to apply as many rounds as required to bring individual suspects , multiple suspects, or crowds into compliance.
The projectile is usually sold to be used with a launcher or gun by the same company, to provide best reliability. [ 1 ] The different companies usually also sell other types of projectiles for non-lethal use or projectiles with combined effects. Such effects may include: [ 2 ] [ 3 ]
Although generally considered less-than-lethal when properly used (targets should exclude the face, eyes, throat or spine), [ 4 ] one death has occurred when they have been fired at inappropriate areas. In one well-publicized incident in 2004, the Boston Police Department 's use of an FN 303 during a crowd control situation resulted in the fatal shooting of Victoria Snelgrove , when the projectile struck her in the eye. [ 5 ] Also in 2004, University of California, Davis (UC Davis) police who wanted to break up a block party shot a pepperball at an unarmed student and damaged his eye—the student subsequently lost his athletic scholarship and dropped out of college. In 2012, a federal appeals court ruled that the police could be sued over the incident. [ 6 ] In 2013, the student was awarded $774,000. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Pepper-spray_projectile |
Pepper spray , oleoresin capsicum spray , OC spray , capsaicin spray , mace , or capsicum spray is a lachrymator (tear gas) product containing as its active ingredient the chemical compound capsaicin , which irritates the eyes with burning and pain sensations and so causes them to close, bringing temporary blindness. This blindness allows officers to more easily restrain subjects and permits people in danger to use pepper spray in self-defense for an opportunity to escape. It also causes temporary discomfort and burning of the lungs which causes shortness of breath. Pepper spray is used as a less lethal weapon in policing , riot control , crowd control , and self-defense , including defense against dogs and bears. [ 5 ] [ 6 ]
Pepper spray was engineered originally for defense against bears, cougars , wolves and other dangerous predators, and is often referred to colloquially as bear spray .
Kamran Loghman, who developed it for use in riot control, wrote the guide for police departments on how it should be used. It was successfully adopted, except for improper usages such as when police sprayed peaceful protestors at University of California, Davis, in 2011 . Loghman commented, "I have never seen such an inappropriate and improper use of chemical agents", prompting court rulings completely barring its use on docile persons. [ 7 ] [ 8 ] [ 9 ]
The active ingredient in pepper spray is capsaicin , which is derived from the fruit of plants in the genus Capsicum , including chilis in the form of oleoresin capsicum (OC). Extraction of OC from peppers requires capsicum to be finely ground, from which capsaicin is then extracted using an organic solvent such as ethanol . The solvent is then evaporated, and the remaining waxlike resin is the oleoresin capsaicin. [ 10 ]
An emulsifier such as propylene glycol is used to suspend OC in water, and the suspension is then pressurized to make an aerosol pepper spray. Other sprays may use an alcohol (such as isopropyl alcohol ) base for a more penetrating product, but a risk of fire is present if they are used in combination with a taser. [ 11 ]
Determining the strength of pepper sprays made by different manufacturers can be confusing and difficult. Statements a company makes about their product strength are not regulated.
There are several counterparts of pepper spray developed and legal to possess in some countries.
Pepper spray is an inflammatory agent. It inflames the mucous membranes in the eyes, nose, throat and lungs. [ 15 ]
It causes immediate closing of the eyes, difficulty breathing, runny nose, and coughing. [ 16 ] The duration of its effects depends on the strength of the spray; the average full effect lasts from 20 to 90 minutes, but eye irritation and redness can last for up to 24 hours. [ 17 ]
The Journal of Investigative Ophthalmology and Visual Science published a study that concluded that single exposure of the eye to OC is harmless, but repeated exposure can result in long-lasting changes in corneal sensitivity. They found no lasting decrease in visual acuity . [ 18 ]
The European Parliament Scientific and Technological Options Assessment (STOA) published in 1998 "An Appraisal of Technologies of Political Control" [ 19 ] The STOA appraisal states:
For those taking drugs, or those subjected to restraining techniques that restrict the breathing passages, there is a risk of death. In 1995, the Los Angeles Times reported at least 61 deaths associated with police use of pepper spray since 1990 in the USA. [ 20 ] The American Civil Liberties Union (ACLU) documented 27 people in police custody who died after exposure to pepper spray in California since 1993. [ 21 ] [ 22 ] However, the ACLU report counts all deaths occurring within hours of exposure to pepper spray regardless of prior interaction, taser use, or if drugs are involved. In all 27 cases listed by the ACLU, the coroners' report listed other factors as the primary cause of death; in a few cases the use of pepper spray may have been a contributing factor.
The US Army performed studies in 1993 at Aberdeen Proving Ground , and a UNC study in 2000 stated that the compound in peppers, capsaicin, is mildly mutagenic, and 10% of mice exposed to it developed cancer. Where the study also found many beneficial effects of capsaicin, the Occupational Safety and Health Administration released statements declaring exposure of employees to OC is an unnecessary health risk. As of 1999, it was in use by more than 2,000 public safety agencies. [ 23 ]
The head of the FBI's Less-Than-Lethal Weapons Program at the time of the 1991 study, Special Agent Thomas W. W. Ward, was fired by the FBI and was sentenced to two months in prison for receiving payments from a pepper-gas manufacturer while conducting and authoring the FBI study that eventually approved pepper spray for FBI use. [ 24 ] [ 25 ] Prosecutors said that from December 1989 through 1990, Ward received about $5,000 a month for a total of $57,500, from Luckey Police Products, a Fort Lauderdale, Florida-based company that was a major producer and supplier of pepper spray. The payments were paid through a Florida company owned by Ward's wife. [ 26 ]
Direct close-range spray can cause more serious eye irritation by attacking the cornea with a concentrated stream of liquid (the so-called "hydraulic needle" effect). Some brands have addressed this problem by means of an elliptically cone-shaped spray pattern.
Pepper spray has been associated with positional asphyxiation of individuals in police custody. There is much debate over the actual cause of death in these cases. There have been few controlled clinical studies of the human health effects of pepper spray marketed for police use, and those studies are contradictory. Some studies have found no harmful effects beyond the effects described above. [ 27 ] Due to these studies and deaths, many law enforcement agencies have moved to include policies and training to prevent positional deaths. [ 28 ] [ 29 ] However, there are some scientific studies that argue the positional asphyxiation claim is a myth due to pinpoint pressure on a person. The study by two universities stressed that no pressure should be applied to the neck area. They concluded that the person's own weight is not enough to stop their breathing with the rest of their body supported. [ 30 ]
For individuals not previously exposed to OC effects, the general feelings after being sprayed can be best likened to being "set alight". The initial reaction, should the spray be directed at the face, is the involuntary closing of the eyes, an instant sensation of the restriction of the airways and the general feeling of sudden and intense searing pain about the face, nose, and throat. This is due to irritation of mucous membranes. Many people experience fear and are disoriented due to sudden restriction of vision even though it is temporary. There is associated shortness of breath, although studies performed with asthmatics have not produced any asthma attacks in those individuals, and monitoring is still needed for the individuals after exposure. [ 31 ] Police are trained to repeatedly instruct targets to breathe normally if they complain of difficulty, as the shock of the exposure can generate considerable panic as opposed to actual physical symptoms.
Capsaicin is not soluble in water, and even large volumes of water will not wash it off, only dilute it. In general, victims are encouraged to blink vigorously in order to encourage tears, which will help flush the irritant from the eyes.
A study of five often-recommended treatments for skin pain ( Maalox , 2% lidocaine gel, baby shampoo , milk, or water) concluded that: "...there was no significant difference in pain relief provided by five different treatment regimens. Time after exposure appeared to be the best predictor for a decrease in pain...". [ 32 ]
Many ambulance services and emergency departments carry saline to remove the spray. Some of the OC and CS will remain in the respiratory system, but a recovery of vision and the coordination of the eyes can be expected within 7 to 15 minutes. [ 33 ]
Some "triple-action" pepper sprays also contain "tear gas" ( CS gas ), which can be neutralized with sodium metabisulfite ( Campden tablets ), though it is not for use on a person, only for area cleanup. [ 34 ]
Pepper spray typically comes in canisters, which are often small enough to be carried or concealed in a pocket or purse. Pepper spray can also be purchased concealed in items such as rings . There are also pepper spray projectiles available, which can be fired from a paintball gun or similar platform. It has been used for years against demonstrators and aggressive animals like bears. There are also many types such as foam, gel, foggers, and spray. [ 35 ]
Oleoresin capsicum, also known as capsicum oleoresin, is also used in food and medicine. [ 36 ] In food, it serves as a concentrated and predictable source of spiciness. The food industry has accordingly changed to prefer a combination of milder and more predictable strains of jalapeno and OC for flavoring. [ 37 ] In medicine, OC is used in a number of products for external use. [ 38 ]
OC used for food is generally rated between 80 000 and 500 000 SHU, roughly equivalent to 0.6-3.9% capsaicin. Paprika oleoresin is a different extract, containing very little heat and mostly used for coloring. [ 39 ]
Pepper spray is banned for use in war by Article I.5 of the Chemical Weapons Convention , which bans the use of all riot control agents in warfare whether lethal or less-than-lethal. [ 40 ] Depending on the location, it may be legal to use for self-defense .
Pepper spray designed to be used against people is considered a prohibited weapon in Canada. The definition under regulation states "any device designed to be used for the purpose of injuring, immobilizing or otherwise incapacitating any person by the discharge therefrom of (a) tear gas, Mace or other gas, or (b) any liquid, spray, powder or other substance that is capable of injuring, immobilizing or otherwise incapacitating any person" is a prohibited weapon. [ 74 ]
Only law enforcement officers may legally carry or possess pepper spray labeled for use on persons. Any similar canister with the labels reading "dog spray" or "bear spray" is regulated under the Pest Control Products Act —while legal to be carried by anyone, it is against the law if its use causes "a risk of imminent death or serious bodily harm to another person" or harming the environment and carries a penalty up to a fine of $500,000 and jail time of maximum 3 years. [ 75 ] Carrying bear spray in public, without justification, may also lead to charges under the Criminal Code . [ 76 ]
It is a federal offense to carry/ship pepper spray on a commercial airliner or possess it in the secure area of an airport. State law and local ordinances regarding possession and use vary across the country. Pepper spray up to 4 oz. is permitted in checked baggage. [ 77 ]
When pepper spray is used in the workplace, OSHA requires a pepper spray Safety Data Sheet (SDS) be available to all employees. [ 78 ]
Pepper spray can be legally purchased and carried in all 50 states and the District of Columbia. [ 79 ] Some states regulate the maximum allowed strength of the pepper spray, age restriction, content and use. [ 80 ]
In June 2002, West Australian resident Rob Hall was convicted for using a canister of pepper spray to break up an altercation between two guests at his home in Midland. He was sentenced to a good behavior bond and granted a spent conviction order, which he appealed to the Supreme Court. Justice Christine Wheeler ruled in his favor, thereby legalizing pepper spray in the state on a case-by-case basis for those who are able to show a reasonable excuse. [ 98 ] [ 103 ]
On 14 March 2012, a person dressed entirely in black entered the public gallery of the New South Wales Legislative Council and launched a paper plane into the air in the form of a petition to Police Minister Mike Gallacher calling on the government to allow civilians to carry capsicum spray. [ 104 ]
Media related to Pepper sprays at Wikimedia Commons | https://en.wikipedia.org/wiki/Pepper_spray |
Pepperl+Fuchs SE (sometimes referenced by the initialism P+F ) is a German multinational company headquartered in Mannheim , Germany . The company manufactures electronic products for fabrication and process automation. It specializes in sensor manufacturing, such as sensors used in automatic doors in elevators, encoders, AS interfaces , RFID systems, [ 1 ] barcode solutions, [ 2 ] and explosion protection, [ 3 ] as well as components for the automotive industry , and plant engineering. [ 4 ]
In 2022, the company's revenue exceeded €1 billion for the first time. [ 5 ] [ 6 ]
As of April 2024, the company had approximately 6,850 employees worldwide, [ 7 ] with more than 40 [ 8 ] foreign subsidiaries on six continents, and manufacturing facilities in Germany , USA , Singapore , Hungary , China , Indonesia , and Vietnam . A new US headquarters is scheduled to open in late 2025. [ 9 ]
Pepperl+Fuchs was founded in 1945 [ 3 ] by Walter Pepperl and Ludwig Fuchs in Mannheim. The company initially operated as a workshop for repairing radio equipment while simultaneously manufacturing transformers. By 1948, Pepperl+Fuchs had expanded to produce other electronics, leading to the development of the first inductive proximity switch , an electronic device capable of measuring the position of objects and commonly used in packaging and filling systems, in 1958. Alongside this, Pepperl+Fuchs also created the first transistor amplifier with an intrinsically safe control circuit. [ 10 ]
Increasing demand for the proximity switch prompted Pepperl+Fuchs to expand its focus into areas such as sensing technology, intrinsic safety , and explosion protection technology, [ 10 ] Starting in the 1970s, the company established subsidiaries for production and sales in countries including China, India, Indonesia, Italy, Singapore, Hungary, and the United States. During this period, Pepperl+Fuchs transitioned from a general partnership into a GmbH & Co. KG. [ 11 ]
In 1987, the two founders retired from the management team and the legal form of the company was changed to a limited liability entity. [ 12 ]
Initially based in Mannheim- Sandhofen , the headquarters of Pepperl+Fuchs moved to Schönau in 1971. [ 13 ] In Germany, the company also operates in Neuhausen ob Eck , where all of its rotary encoders are designed and manufactured. [ 14 ] In Asia, production occurs in various locations, including Vietnam. [ 15 ]
Since 2000, Pepperl+Fuchs has expanded through several acquisitions, increasing its turnover to over 500 million DM. [ 4 ] Acquisitions included Visolux from Berlic, Elcon from Milan, and the proximity switches and photoelectric sensors division from Honeywell International. [ 4 ] In 2010, Pepperl+Fuchs further expanded by acquiring Siemens' proximity switch business, enhancing its capabilities in ultrasonic sensor technology. [ 16 ]
In 2019, Pepperl+Fuchs Comtrol partnered with Callisto Integration , in the manufacturing industry. [ 17 ]
In 2019, Pepperl+Fuchs changed its legal structure from Gesellschaft mit beschränkter Haftung (GmbH) to Aktiengesellschaft (AG) and again in 2020 to Societas Europea (SE). [ 8 ] [ 18 ]
In 2023, the company attained IEC 62443-4-1 cybersecurity certification. [ 19 ]
As of April 2024, the company had approximately 6,850 employees worldwide, [ 7 ] with more than 40 [ 8 ] foreign subsidiaries on six continents, and manufacturing facilities in Germany , USA , Singapore , Hungary , China , Indonesia , and Vietnam .
Pepperl+Fuchs manufactures, among other things, contactless sensors , rotary encoders , counters, switching units, converters, fieldbus components and systems, data light barriers, identification systems, safety barriers, and image processing products. [ 20 ]
The company categorizes its portfolio into industrial sensors and process interfaces for factory and process automation. [ 21 ]
Additionally, Pepperl+Fuchs provides systems for process automation in potentially explosive atmospheres, developed in engineering centers located in Bühl and other locations. [ 22 ]
The acquisition of ecom instruments GmbH expanded its portfolio to include explosion-protected products in mobile computing, communication, measurement and calibration technology, and hand lamps. [ 23 ]
Pepperl+Fuchs operates a European warehouse in Mannheim and logistics centers in America and Asia, with a Global Distribution Center established in Singapore. [ 24 ]
The Factory Automation division is a manufacturer of industrial sensors . It makes a range of inductive, capacitive, photoelectric , and ultrasonic sensors as well as identification systems, barcode and camera systems, rotary encoders , position measurement systems, cordsets, and other accessories. [ 25 ]
The Process Automation division is a manufacturer of explosion protection products. It makes a range of intrinsic safety barriers, signal conditioners , remote I/O systems, HART interface solutions, surge protection , HMI systems , electrical explosion protection equipment, purge and pressurization systems, power supplies, and level measurement . [ 25 ]
In 2003, Pepperl+Fuchs acquired Bebco EPS, a manufacturer of purge and pressurization systems. [ 26 ]
In 2010, the company acquired the proximity sensor business of Siemens. [ 27 ]
In 2019, Pepperl+Fuchs acquired Comtrol Corporation, a US company specializing in Ethernet-based industrial communication and IO-Link master gateways. [ 28 ] The Pepperl+Fuchs Comtrol Hospitality division offers a library of interfaces for property management systems and guest service systems. [ 29 ]
In 2021, Pepperl+Fuchs acquired the Finnish company, Aava Mobile Oy, expanding its reach in the industrial tablet computer and smartphone industry. [ 30 ]
Pepperl+Fuchs is actively involved in the Smart Factory initiative, collaborating with the Technical University of Kaiserslautern and other partners to advance automation and manufacturing technologies. [ 31 ]
In May 2024 Pepperl+Fuchs signed a contract agreeing to partner with the Mannheim TECHNOSEUM to set up a student laboratory, centred on STEM programs and sensor technology. [ 32 ] [ 33 ] [ 34 ] | https://en.wikipedia.org/wiki/Pepperl+Fuchs |
Pepscan is a procedure for mapping and characterizing epitopes involving the synthesis of overlapping peptides and analysis of the peptides in enzyme-linked immunosorbent assays (ELISAs). The method is based on combinatorial chemistry and was pioneered by Mario Geysen and coworkers. [ 1 ]
Rob Meloen was one of Geysen's co-workers. He also played an important role in the development of numerous other new technologies, including vaccine and diagnostic product development for several viral diseases. From 1994 to 2010, Meloen was Professor of Special Appointment (Chair: Biomolecular Recognition) at Utrecht University . He was one of the co-founders of the company Pepscan ( Lelystad , the Netherlands) and became Scientific Director (CSO). Pepscan is now part of the Biosynth Group. [ 2 ]
Twenty-five years later, the Pepscan methodology, evolved and modernized with the latest insights, is still an important part of Pepscan’s epitope mapping platform, which is instrumental in therapeutic antibody development. | https://en.wikipedia.org/wiki/Pepscan |
In bio-informatics , a peptide-mass fingerprint or peptide-mass map is a mass spectrum of a mixture of peptides that comes from a digested protein being analyzed. The mass spectrum serves as a fingerprint in the sense that it is a pattern that can serve to identify the protein. [ 1 ] The method for forming a peptide-mass fingerprint, developed in 1993, consists of isolating a protein, breaking it down into individual peptides, and determining the masses of the peptides through some form of mass spectrometry. [ 2 ] Once formed, a peptide-mass fingerprint can be used to search in databases for related protein or even genomic sequences, making it a powerful tool for annotation of protein-coding genes. [ 3 ]
One major advantage to mass fingerprinting is that it is significantly faster to carry out than peptide sequencing , yet the results are equally useful. [ 4 ] Disadvantages include the need for a single protein for analysis and the requirement that the protein sequence is located, at least with significant homology, in a database. Because the mass of individual peptides is measured in forming a fingerprint, mixtures of different proteins can yield unreliable results. Therefore, sample preparation is an important step in the process. Even then, if reliable results are obtained, there must be a matching peptide sequence in the database you are searching in order for the results to be useful. [ 5 ]
Before analyzing with mass spectrometry, a protein must be accurately isolated and digested. If not isolated, the results will represent a mixture of two or more proteins and will therefore be unreliable in protein identification. Because of this sensitivity, sample preparation is likely the most important step in forming a peptide-mass fingerprint.
Isolation of a specific protein is most often done through a form of gel electrophoresis , in which proteins are separated by size and can be subsequently extracted for further preparation. However, they can also be isolated by liquid chromatography . This method also separates proteins by size. [ 6 ]
Once an individual protein is isolated, it needs to be digested and fractionated for further analysis by a spectrometer. This is done by the addition of proteolytic enzymes such as trypsin and chymotrypsin . [ 7 ]
Another method commonly used that combines both the isolation and digestion steps is SDS-PAGE , a form of electrophoresis that separates and fractionates proteins simultaneously.
The digested protein can be analyzed with different types of mass spectrometers such as ESI-TOF or MALDI-TOF . MALDI-TOF is often the preferred instrument because it allows a high sample throughput and several proteins can be analyzed in a single experiment, if complemented by MS/MS analysis. [ 8 ]
In matrix-assisted laser desorption ionization (MALDI), a fragmented peptide sample is loaded onto a matrix and ionized through the use of a high energy laser. The fragmented ions are then separated by mass-to-charge ratio based on the time of flight (TOF) through the spectrometer. They can then be further fragmented and re-analyzed in tandem mass spectrometry, often with a quadrupole ion trap , [ 9 ] but also possible with tandem time of flight. [ 10 ]
The output received from a mass spectrometer comes in the form of a peak list. This spectrum shows the masses and relative abundances of the peptide fragments present in the sample. In reading a spectrum like the one shown, all possible major fragmentations of a protein would need to be considered. Then the masses of those fragments would correlate to the numbers in the peaks of the spectrum. While it can be analyzed to some degree on its own, in forming a peptide-mass fingerprint, the peak list is run through a database search to find homologous peptide sequences.
The peak list obtained through spectrometric means is used as the query in a database search using the software MASCOT . [ 11 ] The MASCOT software uses an algorithm that looks for significant peptide sequence homology to present the most statistically likely protein in the sample, based on the results.
In performing the search, you much choose a database to go through. Such databases include, among others, Swissprot, often used when researching well characterized organisms like humans, mice, and yeasts; and NCBInr for more general, robust searches.
A detailed tutorial on using MASCOT software can be found in a link below.
The use of a peptide-mass fingerprint is fairly widespread in proteomic research. Some specific examples of how it has been used in the field are as follows:
The authors of this study sought to determine which yeasts were metabolically active at lower temperatures and could therefore be used for colder industrial processes. They grew various yeasts on medium at different temperatures, then determined enzyme activity by separating proteins on a gel and fingerprinting the individual bands. Through database search they found the enzyme of interest and discovered two individual yeasts that had higher activity at lower temperatures. [ 12 ]
The authors of this study sought to determine the effect on metabolism of the drug risperidone in schizophrenia patients. After discovering that risperidone did have negative metabolic side effects, they tested membrane proteins for glucose and lipid transport in control and experimental groups by MALDI-TOF and fingerprinting. Results showed altered fingerprints and therefore altered levels of folding in the proteins. So, they concluded that risperidone negatively effects glucose and lipid transport proteins in the cell membranes of patients. [ 13 ] | https://en.wikipedia.org/wiki/Peptide-mass_fingerprint |
Peptide PHI, also known as peptide histidine isoleucine , is a peptide which functions as a hormone . This peptide contains a composition of 27 amino acids with histidine on the N-terminus and isoleucine on the C-terminus . It was originally isolated from the mammalian small intestine amongst mammalian neurons called intramural neurons which function in the motor activity of the intestinal walls. [ 1 ] An example of this was revealed in a study that demonstrated that this peptide regulates water and electrolyte transportation in the human jejunum ; similar to its inhibitory effects on fluid absorption in the small intestine of pigs and rats. [ 2 ]
Peptide histidine isoleucine (PHI) is part of family that plays a vital role in the cell growth rate such as in the intestine as well as in brain. [ 3 ] It was derived from glucagon family called the pituitary adenylate cyclase-activating polypeptide (PACAP) and it has an amino acid sequence homology to vasoactive intestinal peptide , secretin , glucagon , and other growth hormone releasing factor. [ 4 ] Human studies have shown that the release of PHI into the stomach regulates the neuroendocrine cell processes that affect gastrointestinal physiology . This peptide is present within the central nervous system that help regulate food consumption behavior, while at peripheral nervous system this peptide accumulates in the stomach which controls the digestion of food. [ 5 ]
It also plays a role in the regulation of prolactin in humans. [ 6 ] It functions specifically function in the G protein signaling pathway through G protein , which is a transmembrane protein that causes the cascade phosphorylation. It is located throughout the entire length of intestine while PHI is mostly concentrated in the colon region. [ 7 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peptide_PHI |
In organic chemistry , a peptide bond is an amide type of covalent chemical bond linking two consecutive alpha-amino acids from C1 ( carbon number one) of one alpha-amino acid and N2 ( nitrogen number two) of another, along a peptide or protein chain. [ 1 ]
It can also be called a eupeptide bond [ 1 ] to distinguish it from an isopeptide bond , which is another type of amide bond between two amino acids.
When two amino acids form a dipeptide through a peptide bond , [ 1 ] it is a type of condensation reaction . [ 2 ] In this kind of condensation, two amino acids approach each other, with the non- side chain (C1) carboxylic acid moiety of one coming near the non-side chain (N2) amino moiety of the other. One loses a hydrogen and oxygen from its carboxyl group (COOH) and the other loses a hydrogen from its amino group (NH 2 ). This reaction produces a molecule of water (H 2 O) and two amino acids joined by a peptide bond (−CO−NH−). The two joined amino acids are called a dipeptide.
The amide bond is synthesized when the carboxyl group of one amino acid molecule reacts with the amino group of the other amino acid molecule, causing the release of a molecule of water (H 2 O), hence the process is a dehydration synthesis reaction.
The formation of the peptide bond consumes energy, which, in organisms, is derived from ATP . [ 3 ] Peptides and proteins are chains of amino acids held together by peptide bonds (and sometimes by a few isopeptide bonds ). Organisms use enzymes to produce nonribosomal peptides , [ 4 ] and ribosomes to produce proteins via reactions that differ in details from dehydration synthesis. [ 5 ]
Some peptides, like alpha-amanitin , are called ribosomal peptides as they are made by ribosomes, [ 6 ] but many are nonribosomal peptides as they are synthesized by specialized enzymes rather than ribosomes. For example, the tripeptide glutathione is synthesized in two steps from free amino acids , by two enzymes : glutamate–cysteine ligase (forms an isopeptide bond , which is not a peptide bond) and glutathione synthetase (forms a peptide bond). [ 7 ] [ 8 ]
A peptide bond can be broken by hydrolysis (the addition of water). The hydrolysis of peptide bonds in water releases 8–16 kJ / mol (2–4 kcal / mol ) of Gibbs energy . [ 9 ] This process is extremely slow, with the half life at 25 °C of between 350 and 600 years per bond. [ 10 ]
In living organisms, the process is normally catalyzed by enzymes known as peptidases or proteases , although there are reports of peptide bond hydrolysis caused by conformational strain as the peptide/protein folds into the native structure. [ 11 ] This non-enzymatic process is thus not accelerated by transition state stabilization, but rather by ground-state destabilization.
The wavelength of absorption for a peptide bond is 190–230 nm, [ 12 ] which makes it particularly susceptible to UV radiation.
Significant delocalisation of the lone pair of electrons on the nitrogen atom gives the group a partial double-bond character. The partial double bond renders the amide group planar , occurring in either the cis or trans isomers . In the unfolded state of proteins, the peptide groups are free to isomerize and adopt both isomers; however, in the folded state, only a single isomer is adopted at each position (with rare exceptions). The trans form is preferred overwhelmingly in most peptide bonds (roughly 1000:1 ratio in trans:cis populations). However, X-Pro peptide groups tend to have a roughly 30:1 ratio, presumably because the symmetry between the C α and C δ atoms of proline makes the cis and trans isomers nearly equal in energy, as shown in the figure below.
The dihedral angle associated with the peptide group (defined by the four atoms C α –C'–N–C α ) is denoted ω {\displaystyle \omega } ; ω = 0 ∘ {\displaystyle \omega =0^{\circ }} for the cis isomer ( synperiplanar conformation), and ω = 180 ∘ {\displaystyle \omega =180^{\circ }} for the trans isomer ( antiperiplanar conformation). Amide groups can isomerize about the C'–N bond between the cis and trans forms, albeit slowly ( τ ∼ 20 {\displaystyle \tau \sim 20} seconds at room temperature). The transition states ω = ± 90 ∘ {\displaystyle \omega =\pm 90^{\circ }} require that the partial double bond be broken, so that the activation energy is roughly 80 kJ/mol (20 kcal/mol). However, the activation energy can be lowered (and the isomerization catalyzed ) by changes that favor the single-bonded form, such as placing the peptide group in a hydrophobic environment or donating a hydrogen bond to the nitrogen atom of an X-Pro peptide group. Both of these mechanisms for lowering the activation energy have been observed in peptidyl prolyl isomerases (PPIases), which are naturally occurring enzymes that catalyze the cis-trans isomerization of X-Pro peptide bonds.
Conformational protein folding is usually much faster (typically 10–100 ms) than cis-trans isomerization (10–100 s). A nonnative isomer of some peptide groups can disrupt the conformational folding significantly, either slowing it or preventing it from even occurring until the native isomer is reached. However, not all peptide groups have the same effect on folding; nonnative isomers of other peptide groups may not affect folding at all.
Due to its resonance stabilization, the peptide bond is relatively unreactive under physiological conditions, even less than similar compounds such as esters . Nevertheless, peptide bonds can undergo chemical reactions, usually through an attack of an electronegative atom on the carbonyl carbon , breaking the carbonyl double bond and forming a tetrahedral intermediate. This is the pathway followed in proteolysis and, more generally, in N–O acyl exchange reactions such as those of inteins . When the functional group attacking the peptide bond is a thiol , hydroxyl or amine , the resulting molecule may be called a cyclol or, more specifically, a thiacyclol, an oxacyclol or an azacyclol, respectively. | https://en.wikipedia.org/wiki/Peptide_bond |
Peptide computing is a form of computing which uses peptides , instead of traditional electronic components . The basis of this computational model is the affinity of antibodies towards peptide sequences. Similar to DNA computing , the parallel interactions of peptide sequences and antibodies have been used by this model to solve a few NP-complete problems. Specifically, the hamiltonian path problem (HPP) and some versions of the set cover problem are a few NP-complete problems which have been solved using this computational model so far. This model of computation has also been shown to be computationally universal (or Turing complete).
This model of computation has some critical advantages over DNA computing . For instance, while DNA is made of four building blocks, peptides are made of twenty building blocks. The peptide-antibody interactions are also more flexible with respect to recognition and affinity than an interaction between a DNA strand and its reverse complement. However, unlike DNA computing, this model is yet to be practically realized. The main limitation is the availability of specific monoclonal antibodies required by the model.
This computer science article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peptide_computing |
A peptide library is a tool for studying proteins . Peptide libraries typically contain a large number of peptides that have a systematic combination of amino acids . Usually, solid phase synthesis, e.g. resin as a flat surface or beads, is used for peptide library generation. Peptide libraries are a popular tool for experiments in drug design , protein–protein interactions , and other biochemical and pharmaceutical applications.
Synthetic peptide libraries are synthesized without utilizing biological systems such as phage or in vitro translation. [ 1 ] [ 2 ] There are at least five subtypes of synthetic peptide libraries that differ from each other by the design of the library and/or the method used for the synthesis of the library. The subtypes include:
Solid phase peptide synthesis is limited to a peptide chain length of approximately 70 amino acids and is generally unsuitable for the study of larger proteins. Many libraries utilize peptide chains much shorter than 70 amino acids. For 20 encoded amino acids at maximally 70 positions, this results in an upper limit of 20 70 , or more than 10 quindecillion (1x10 91 ), possible combinations, not accounting for the potential use of amino acids with post-translational modifications or amino acids not encoded in the genetic code, such as selenocysteine and pyrrolysine . Peptide libraries generally encompass only a fraction of this diversity, selected for depending on the needs of the experiment, for instance keeping some amino acids constant at certain positions.
Large random peptide libraries are often used for the synthesis of certain peptide molecules, such as ultra-large chemical libraries for the discovery of high-affinity peptide binders. [ 4 ] Any increase in the library size severely affects parameters, such as the synthesis scale, the number of library members, the sequence deconvolution and peptide structure elucidation. To mitigate these technical challenges, an algorithm-supported approach to peptide library design may use molecular mass and amino acid diversity to simplify the laborious permutation identification in complex mixtures when using mass spectrometry. This approach is used to avoid mass redundancy. [ 5 ]
Biological reagent companies, such as Pepscan, [ 6 ] ProteoGenix, [ 7 ] Mimotopes, [ 8 ] GenScript and many others, manufacture customized peptide libraries. [ 9 ]
A peptide chain of 10 residues in length is used in native chemical ligation with a larger recombinantly expressed protein.
With 7 possibilities at Residue 2 and 20 possibilities at Residue 3, the total would be 20 × 7 {\displaystyle 20\times 7} or 140 different polypeptides in the library.
This peptide library would be useful for analyzing the effect of the post-translational modification acetylation on lysine which neutralizes the positive charge. Having the library of different peptides at residue 2 and 3 would let the investigator see if some change in chemical properties in the N-terminal tail of the ligated protein makes the protein more useful or useful in a different way. | https://en.wikipedia.org/wiki/Peptide_library |
Peptide mass fingerprinting ( PMF ), also known as protein fingerprinting , is an analytical technique for protein identification in which the unknown protein of interest is first cleaved into smaller peptides , whose absolute masses can be accurately measured with a mass spectrometer such as MALDI-TOF or ESI-TOF . [ 1 ] The method was developed in 1993 by several groups independently. [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] The peptide masses are compared to either a database containing known protein sequences or even the genome. This is achieved by using computer programs that translate the known genome of the organism into proteins, then theoretically cut the proteins into peptides, and calculate the absolute masses of the peptides from each protein. They then compare the masses of the peptides of the unknown protein to the theoretical peptide masses of each protein encoded in the genome. The results are statistically analyzed to find the best match.
The advantage of this method is that only the masses of the peptides have to be known. A disadvantage is that the protein sequence has to be present in the database of interest. Additionally most PMF algorithms assume that the peptides come from a single protein. [ 7 ] The presence of a mixture can significantly complicate the analysis and potentially compromise the results. Typical for the PMF-based protein identification is the requirement for an isolated protein. Mixtures exceeding a number of 2–3 proteins typically require the additional use of MS/MS -based protein identification to achieve sufficient specificity of identification. Therefore, typical PMF samples are isolated proteins from two-dimensional gel electrophoresis (2D gels) or isolated SDS-PAGE bands. Additional analyses by MS/MS can either be direct, e.g., MALDI-TOF/TOF analysis or downstream nanoLC-ESI-MS/MS analysis of gel spot eluates. [ 7 ] [ 8 ]
Due to the long, tedious process of analyzing proteins, peptide mass fingerprinting was developed. Edman degradation was used in protein analysis, and it required almost an hour to analyze one amino acid residue. [ 9 ] SDS-PAGE was also used to separate proteins in very complex mixtures, which also employed methods of electroblotting and staining. [ 10 ] Then, bands would be extracted from the gel and sequenced, automatically. A recurring problem in the process was that interfering proteins would also purify with the protein of interest. The sequences of these interfering proteins were compiled into what came to known as the Dayhoff database. [ 11 ] Ultimately, having the sequences of these known protein contaminants in databases decreased instrument time and expenses involved in protein analysis.
Protein samples can be derived from SDS-PAGE [ 7 ] or reversed phase HPLC , and are then subject to some chemical modifications. Disulfide bridges in proteins are reduced and cysteine amino acids are carbamidomethylated chemically or acrylamidated during the gel electrophoresis.
Then the proteins are cut into several fragments using proteolytic enzymes such as trypsin , chymotrypsin or Glu-C . A typical sample:protease ratio is 50:1. The proteolysis is typically carried out overnight and the resulting peptides are extracted with acetonitrile and dried under vacuum. The peptides are then dissolved in a small amount of distilled water or further concentrated and purified and are ready for mass spectrometric analysis.
The digested protein can be analyzed with different types of mass spectrometers such as ESI-TOF or MALDI-TOF . MALDI-TOF is often the preferred instrument because it allows a high sample throughput and several proteins can be analyzed in a single experiment, if complemented by MS/MS analysis. LC/ESI-MS and CE/ESI-MS are also great techniques for peptide mass fingerprinting. [ 12 ] [ 13 ]
A small fraction of the peptide (usually 1 microliter or less) is pipetted onto a MALDI target and a chemical called a matrix is added to the peptide mix. Common matrices are sinapinic acid , Alpha-Cyano-4-hydroxycinnamic acid , and 2,3-Dihydroxybenzoic acid . The matrix molecules are required for the desorption of the peptide molecules. Matrix and peptide molecules co-crystallize on the MALDI target and are ready to be analyzed. There is one predominantly MALDI-MS sample preparation technique, namely dried droplet technique. [ 14 ] The target is inserted into the vacuum chamber of the mass spectrometer and the desorption and ionisation of the polypeptide fragments is initiated by a pulsed laser beam which transfers high amounts of energy into the matrix molecules. The energy transfer is sufficient to promote the ionisation and transition of matrix molecules and peptides from the solid phase into the gas phase. The ions are accelerated in the electric field of the mass spectrometer and fly towards an ion detector where their arrival is detected as an electric signal. Their mass-to-charge ratio is proportional to their time of flight (TOF) in the drift tube and can be calculated accordingly.
Coupling ESI with capillary LC can separate peptides from protein digests, while obtaining their molecular masses at the same time. [ 15 ] Capillary electrophoresis coupled with ESI-MS is another technique; however, it works best when analyzing small amounts of proteins. [ 13 ]
The mass spectrometric analysis produces a list of molecular weights which is often called a peak list. The peptide masses are compared to protein databases such as Swissprot , which contain protein sequence information. Software performs in silico digests on proteins in the database with the same enzyme (e.g. trypsin) used in the chemical cleavage reaction. The mass of these peptides is then calculated and compared to the peak list of measured masses. The results are statistically analyzed and possible matches are returned in a results table. | https://en.wikipedia.org/wiki/Peptide_mass_fingerprinting |
A peptide microarray (also commonly known as peptide chip or peptide epitope microarray) is a collection of peptides displayed on a solid surface, usually a glass or plastic chip. Peptide chips are used by scientists in biology, medicine and pharmacology to study binding properties and functionality and kinetics of protein-protein interactions in general. In basic research, peptide microarrays are often used to profile an enzyme (like kinase , phosphatase , protease , acetyltransferase , histone deacetylase etc.), to map an antibody epitope or to find key residues for protein binding. Practical applications are seromarker discovery , profiling of changing humoral immune responses of individual patients during disease progression, monitoring of therapeutic interventions, patient stratification and development of diagnostic tools and vaccines .
The assay principle of peptide microarrays is similar to an ELISA protocol.
The peptides (up to tens of thousands in several copies) are linked to the surface of a glass chip typically the size and shape of a microscope slide. This peptide chip can directly be incubated with a variety of different biological samples like purified enzymes or antibodies , patient or animal sera , cell lysates and then be detected through a label-dependent fashion, for example, by a primary antibody that targets the bound protein or modified substrates. After several washing steps a secondary antibody with the needed specificity (e.g. anti IgG human/mouse or anti phosphotyrosine or anti myc) is applied. Usually, the secondary antibody is tagged by a fluorescence label that can be detected by a fluorescence scanner. [ 2 ] Other label-dependent detection methods includes chemiluminescence, colorimetric or autoradiography.
Label-dependent assays are rapid and convenient to perform, but risk giving rise to false positive and negative results. [ 3 ] More recently, label-free detection including surface plasmon resonance (SPR) spectroscopy, mass spectrometry (MS) and many other optical biosensors [ 4 ] [ 5 ] [ 6 ] [ 7 ] have been employed to measuring a broad range of enzyme activities. [ 8 ]
Peptide microarrays show several advantages over protein microarrays :
A peptide microarray is a planar slide with peptides spotted onto it or assembled directly on the surface by in-situ synthesis. Whereas peptides spotted can undergo quality controls that include mass spectrometer analysis and concentration normalization before spotting and result from a single synthetic batch, peptides synthesized directly on the surface may suffer from batch-to-batch variation and limited quality control options. However, peptide synthesis on chip allows the parallel synthesis of tens of thousands of peptides providing larger peptide libraries paired with lower synthesis costs. [ 9 ] Peptides are ideally covalently linked through a chemoselective bond leading to peptides with the same orientation for interaction profiling. Some alternative procedures describe unspecific covalent binding and adhesive immobilization.
However, lithographic methods can be used to overcome the problem of excessive number of coupling cycles. Combinatorial synthesis of peptide arrays onto a microchip by laser printing has been described, [ 9 ] [ 10 ] where a modified colour laser printer is used in combination with conventional solid-phase peptide synthesis chemistry. [ 11 ] Amino acids are immobilized within toner particles, and the peptides are printed onto the chip surface in consecutive, combinatorial layers. Melting of the toner upon the start of the coupling reaction ensures that delivery of the amino acids and the coupling reaction can be performed independently. Another advantage of this method is that each amino acid can be produced and purified separately, followed by embedding it into the toner particles, which allows long-term storage.
Peptide microarrays can be used to study different kinds of protein-protein interactions, specially those involving modular protein substructures called peptide recognition modules or, most commonly, protein interaction domains. The reason for this is that such protein substructures recognize short linear motifs often exposed in natively unstructured regions of the binding partner, such that the interaction can be modelled in vitro by peptides as probes and the peptide recognition module as analyte. Most publications can be found in the context of immune monitoring and enzyme profiling.
Data analysis and evaluation of results is the most important part of every microarray experiment. [ 27 ] After scanning the microarray slides, the scanner records a 20-bit, 16-bit or 8-bit numeric image in tagged image file format (*.tif). The .tif-image enables interpretation and quantification of each fluorescent spot on the scanned microarray slide. This quantitative data is the basis for performing statistical analysis on measured binding events or peptide modifications on the microarray slide. For evaluation and interpretation of detected signals an allocation of the peptide spot (visible in the image) and the corresponding peptide sequence has to be performed. The data for allocation is usually saved in the GenePix Array List (.gal) file and supplied together with the peptide microarray. The .gal-file (a tab-separated text file) can be opened using microarray quantification software-modules or processed with a text editor (e.g. notepad) or Microsoft Excel. This "gal" file is most often provided by the microarray manufacturer and is generated by input txt files and tracking software built into the robots that do the microarray manufacturing. | https://en.wikipedia.org/wiki/Peptide_microarray |
Peptide plane flipping is a type of conformational change that can occur in proteins by which the dihedral angles of adjacent amino acids undergo large-scale rotations with little displacement of the side chains . The plane flip is defined as a rotation of the dihedral angles φ,ψ at amino acids i and i+1 such that the resulting angles remain in structurally stable regions of Ramachandran space . The key requirement is that the sum of the ψ i angle of residue i and the φ i+1 angle of residue i+1 remain roughly constant; in effect, the flip is a crankshaft move about the axis defined by the C α -C¹ and N-C α bond vectors of the peptide group, which are roughly parallel. As an example, the type I and type II beta turns differ by a simple flip of the central peptide group of the turn.
The significance of peptide plane flips in the dynamics of the native state has been inferred in some proteins by comparing crystal structures of the same protein in multiple conformations . [ 1 ] For example, peptide flips have been described as significant in the catalytic cycle of flavodoxin [ 2 ] and in the formation of amyloid structures, where their ability to provide a low-energy pathway between beta sheet and the so-called alpha sheet conformation is suggested to facilitate the early stages of amyloidogenesis. [ 3 ] [ 4 ] [ 5 ] Peptide plane flipping may also be significant in the early stages of protein folding . [ 1 ]
In protein structures determined by X-ray crystallography , poor peptide-plane geometry has been described as a common problem; many structures need correction by peptide-plane flips or peptide bond flips. [ 6 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peptide_plane_flipping |
Protein primary structure is the linear sequence of amino acids in a peptide or protein . [ 1 ] By convention, the primary structure of a protein is reported starting from the amino -terminal (N) end to the carboxyl -terminal (C) end. Protein biosynthesis is most commonly performed by ribosomes in cells. Peptides can also be synthesized in the laboratory. Protein primary structures can be directly sequenced , or inferred from DNA sequences .
Amino acids are polymerised via peptide bonds to form a long backbone , with the different amino acid side chains protruding along it. In biological systems, proteins are produced during translation by a cell's ribosomes . Some organisms can also make short peptides by non-ribosomal peptide synthesis , which often use amino acids other than the encoded 22, and may be cyclised, modified and cross-linked.
Peptides can be synthesised chemically via a range of laboratory methods. Chemical methods typically synthesise peptides in the opposite order (starting at the C-terminus) to biological protein synthesis (starting at the N-terminus).
Protein sequence is typically notated as a string of letters, listing the amino acids starting at the amino -terminal end through to the carboxyl -terminal end. Either a three letter code or single letter code can be used to represent the 22 naturally encoded amino acids, as well as mixtures or ambiguous amino acids (similar to nucleic acid notation ). [ 1 ] [ 2 ] [ 3 ]
Peptides can be directly sequenced , or inferred from DNA sequences . Large sequence databases now exist that collate known protein sequences.
In general, polypeptides are unbranched polymers, so their primary structure can often be specified by the sequence of amino acids along their backbone. However, proteins can become cross-linked, most commonly by disulfide bonds , and the primary structure also requires specifying the cross-linking atoms, e.g., specifying the cysteines involved in the protein's disulfide bonds. Other crosslinks include desmosine .
The chiral centers of a polypeptide chain can undergo racemization . Although it does not change the sequence, it does affect the chemical properties of the sequence. In particular, the L -amino acids normally found in proteins can spontaneously isomerize at the C α {\displaystyle \mathrm {C^{\alpha }} } atom to form D -amino acids, which cannot be cleaved by most proteases . Additionally, proline can form stable trans-isomers at the peptide bond.
Additionally, the protein can undergo a variety of post-translational modifications , which are briefly summarized here.
The N-terminal amino group of a polypeptide can be modified covalently, e.g.,
The C-terminal carboxylate group of a polypeptide can also be modified, e.g.,
Finally, the peptide side chains can also be modified covalently, e.g.,
Most of the polypeptide modifications listed above occur post-translationally , i.e., after the protein has been synthesized on the ribosome , typically occurring in the endoplasmic reticulum , a subcellular organelle of the eukaryotic cell.
Many other chemical reactions (e.g., cyanylation) have been applied to proteins by chemists, although they are not found in biological systems.
In addition to those listed above, the most important modification of primary structure is peptide cleavage (by chemical hydrolysis or by proteases ). Proteins are often synthesized in an inactive precursor form; typically, an N-terminal or C-terminal segment blocks the active site of the protein, inhibiting its function. The protein is activated by cleaving off the inhibitory peptide.
Some proteins even have the power to cleave themselves. Typically, the hydroxyl group of a serine (rarely, threonine) or the thiol group of a cysteine residue will attack the carbonyl carbon of the preceding peptide bond, forming a tetrahedrally bonded intermediate [classified as a hydroxyoxazolidine (Ser/Thr) or hydroxythiazolidine (Cys) intermediate]. This intermediate tends to revert to the amide form, expelling the attacking group, since the amide form is usually favored by free energy, (presumably due to the strong resonance stabilization of the peptide group). However, additional molecular interactions may render the amide form less stable; the amino group is expelled instead, resulting in an ester (Ser/Thr) or thioester (Cys) bond in place of the peptide bond. This chemical reaction is called an N-O acyl shift .
The ester/thioester bond can be resolved in several ways:
The compression of amino acid sequences is a comparatively challenging task. The existing specialized amino acid sequence compressors are low compared with that of DNA sequence compressors, mainly because of the characteristics of the data. For example, modeling inversions is harder because of the reverse information loss (from amino acids to DNA sequence). The current lossless data compressor that provides higher compression is AC2. [ 5 ] AC2 mixes various context models using Neural Networks and encodes the data using arithmetic encoding.
The proposal that proteins were linear chains of α-amino acids was made nearly simultaneously by two scientists at the same conference in 1902, the 74th meeting of the Society of German Scientists and Physicians, held in Karlsbad. Franz Hofmeister made the proposal in the morning, based on his observations of the biuret reaction in proteins. Hofmeister was followed a few hours later by Emil Fischer , who had amassed a wealth of chemical details supporting the peptide-bond model. For completeness, the proposal that proteins contained amide linkages was made as early as 1882 by the French chemist E. Grimaux. [ 6 ]
Despite these data and later evidence that proteolytically digested proteins yielded only oligopeptides, the idea that proteins were linear, unbranched polymers of amino acids was not accepted immediately. Some scientists such as William Astbury doubted that covalent bonds were strong enough to hold such long molecules together; they feared that thermal agitations would shake such long molecules asunder. Hermann Staudinger faced similar prejudices in the 1920s when he argued that rubber was composed of macromolecules . [ 6 ]
Thus, several alternative hypotheses arose. The colloidal protein hypothesis stated that proteins were colloidal assemblies of smaller molecules. This hypothesis was disproved in the 1920s by ultracentrifugation measurements by Theodor Svedberg that showed that proteins had a well-defined, reproducible molecular weight and by electrophoretic measurements by Arne Tiselius that indicated that proteins were single molecules. A second hypothesis, the cyclol hypothesis advanced by Dorothy Wrinch , proposed that the linear polypeptide underwent a chemical cyclol rearrangement C=O + HN → {\displaystyle \rightarrow } C(OH)-N that crosslinked its backbone amide groups, forming a two-dimensional fabric . Other primary structures of proteins were proposed by various researchers, such as the diketopiperazine model of Emil Abderhalden and the pyrrol/piperidine model of Troensegaard in 1942. Although never given much credence, these alternative models were finally disproved when Frederick Sanger successfully sequenced insulin [ when? ] and by the crystallographic determination of myoglobin and hemoglobin by Max Perutz and John Kendrew [ when? ] .
Any linear-chain heteropolymer can be said to have a "primary structure" by analogy to the usage of the term for proteins, but this usage is rare compared to the extremely common usage in reference to proteins. In RNA , which also has extensive secondary structure , the linear chain of bases is generally just referred to as the "sequence" as it is in DNA (which usually forms a linear double helix with little secondary structure). Other biological polymers such as polysaccharides can also be considered to have a primary structure, although the usage is not standard.
The primary structure of a biological polymer to a large extent determines the three-dimensional shape ( tertiary structure ). Protein sequence can be used to predict local features , such as segments of secondary structure, or trans-membrane regions. However, the complexity of protein folding currently prohibits predicting the tertiary structure of a protein from its sequence alone. Knowing the structure of a similar homologous sequence (for example a member of the same protein family ) allows highly accurate prediction of the tertiary structure by homology modeling . If the full-length protein sequence is available, it is possible to estimate its general biophysical properties , such as its isoelectric point .
Sequence families are often determined by sequence clustering , and structural genomics projects aim to produce a set of representative structures to cover the sequence space of possible non-redundant sequences. | https://en.wikipedia.org/wiki/Peptide_sequence |
A peptide spectral library is a curated, annotated and non-redundant collection/database of LC-MS /MS peptide spectra. One essential utility of a peptide spectral library is to serve as consensus templates supporting the identification of peptides and proteins based on the correlation between the templates with experimental spectra. [ citation needed ]
One potential application of peptide spectral libraries is the identification of new, currently unknown mass spectra . Here, the spectra from the library are compared to the new spectra and if a match is found, the unknown spectra can be assigned the identity of the known peptide in the library.
Spectral libraries have been used in the small molecules mass spectra identification since the 1980s. [ 1 ] In the early years of shotgun proteomics , pioneer investigations suggested that a similar approach might be applicable in shotgun proteomics for peptide/protein identification. [ 2 ]
Modern tandem mass spectrometry (MS) instruments combine features of fast duty cycle, exquisite sensitivity, and unprecedented mass accuracy. Tandem mass spectrometry, which is an ideal match for the large-scale protein identification and quantification in complex biological systems. In a shotgun proteomics approach, proteins in a complex mixture are digested by proteolytic enzymes such as trypsin . Subsequently, one or more chromatographic separations are applied to resolve resulting peptides, which are then ionized and analyzed in a mass spectrometer . To acquire tandem mass spectra, a particular peptide precursor is isolated, and fragmented in a mass spectrometer; the mass spectra corresponding to the fragments of peptide precursor is recorded. Tandem mass spectra contains specific information regarding the sequence of the peptide precursor, which can aid the identification of the peptide/protein.
Sequence database searching is widely used currently for mass spectra based protein identification. In this approach, a protein sequence database is used to calculate all putative peptide candidates in the given setting (proteolytic enzymes, miscleavages, post-translational modifications ). The sequence search engines use various heuristics to predict the fragmentation pattern of each peptide candidate. Such derivative patterns are used as templates to find a sufficiently close match within experimental mass spectra, which serves as the basis for peptide/protein identification. Many tools have been developed for this practice, which have enabled many past discoveries, e.g. SEQUEST , [ 3 ] Mascot . [ 4 ]
Due to the complex nature of peptide fragmentation in a mass spectrometer, derivative fragmentation patterns fall short of reproducing experimental mass spectra, especially relative intensities among distinct fragments. [ citation needed ] Thus, sequence database searching faces a bottleneck of limited specificity. Sequence database searching also demands vast search space, which still could not cover all possibilities of peptide dynamics, exhibiting limited efficiency post-translational modifications). The search process is sometimes slow and requires costly high-performance computers. In addition, the nature of sequence database searching disconnects the research discoveries among different groups or at different times.
First, a greatly reduced search space will decrease the searching time. Second, by taking full advantage of all spectral features including relative fragment intensities, neutral losses from fragments and various additional specific fragments, the process of spectra searching will be more specific, and it will generally provide better discrimination between true and false matches. [ citation needed ]
Spectral library searching is not applicable in a situation where the discovery of novel peptides or proteins is the goal. However, more and more high-quality mass spectra are being acquired by the collective contribution of the scientific community, which will continuously expand the coverage of peptide spectral libraries.
For a peptide spectral library, to reach a maximal coverage is a long-term goal, even with the support of scientific community and ever-growing proteomic technologies. [ citation needed ] However, the optimization for a particular module of the peptide spectra library is a more manageable goal, e.g. the proteins in a particular organelle or relevant to a particular biological phenotype. For example, a researcher studying the mitochondrial proteome will likely focus on analyses within protein modules within the mitochondria . The research community focused peptide spectral library supports targeted research in a comprehensive fashion for a particular research community. [ citation needed ] | https://en.wikipedia.org/wiki/Peptide_spectral_library |
In organic chemistry , peptide synthesis is the production of peptides , compounds where multiple amino acids are linked via amide bonds, also known as peptide bonds . Peptides are chemically synthesized by the condensation reaction of the carboxyl group of one amino acid to the amino group of another. Protecting group strategies are usually necessary to prevent undesirable side reactions with the various amino acid side chains. [ 1 ] Chemical peptide synthesis most commonly starts at the carboxyl end of the peptide (C-terminus), and proceeds toward the amino-terminus ( N-terminus ). [ 2 ] Protein biosynthesis (long peptides) in living organisms occurs in the opposite direction.
The chemical synthesis of peptides can be carried out using classical solution-phase techniques, although these have been replaced in most research and development settings by solid-phase methods (see below). [ 3 ] Solution-phase synthesis retains its usefulness in large-scale production of peptides for industrial purposes moreover.
Although recombinant protein is more cost effective for large-scale production, [ 4 ] chemical synthesis facilitates the production of peptides that are difficult to express in bacteria, the incorporation of unnatural amino acids, peptide/protein backbone modification, and the synthesis of D-proteins, which consist of D-amino acids .
The established method for the production of synthetic peptides in the lab is known as solid phase peptide synthesis (SPPS). [ 2 ] Pioneered by Robert Bruce Merrifield , [ 5 ] [ 6 ] SPPS allows the rapid assembly of a peptide chain through successive reactions of amino acid derivatives on a macroscopically insoluble solvent-swollen beaded resin support. [ 7 ]
The solid support consists of small, polymeric resin beads functionalized with reactive groups (such as amine or hydroxyl groups) that link to the nascent peptide chain. [ 2 ] Since the peptide remains covalently attached to the support throughout the synthesis, excess reagents and side products can be removed by washing and filtration. This approach circumvents the comparatively time-consuming isolation of the product peptide from solution after each reaction step, which would be required when using conventional solution-phase synthesis. [ 7 ]
Each amino acid to be coupled to the peptide chain N-terminus must be protected on its N-terminus and side chain using appropriate protecting groups such as Boc (acid-labile) or Fmoc (base-labile), depending on the side chain and the protection strategy used (see below). [ 1 ]
The general SPPS procedure is one of repeated cycles of alternate N-terminal deprotection and coupling reactions. The resin can be washed between each steps. [ 2 ] Reactions in SPPS are conducted as follows: [ 8 ]
SPPS is limited by reaction yields due to the exponential accumulation of by-products, and typically peptides and proteins in the range of 70 amino acids are pushing the limits of synthetic accessibility. [ 2 ] Synthetic difficulty also is sequence dependent; typically aggregation-prone sequences such as amyloids [ 12 ] are difficult to make. Longer lengths can be accessed by using ligation approaches such as native chemical ligation , where two shorter fully deprotected synthetic peptides can be joined in solution.
An important feature that has enabled the broad application of SPPS is the generation of extremely high yields in the coupling step. [ 2 ] Highly efficient amide bond-formation conditions are required. To illustrate the impact of suboptimal coupling yields for a given synthesis, consider the case where each coupling step were to have at least 99% yield: this would result in a 77% overall crude yield for a 26-amino acid peptide (assuming 100% yield in each deprotection); if each coupling were 95% efficient, the overall yield would be 25%. [ 13 ] [ 14 ] and adding an excess of each amino acid (between 2- and 10-fold). The minimization of amino acid racemization during coupling is also of vital importance to avoid epimerization in the final peptide product. [ citation needed ]
Amide bond formation between an amine and carboxylic acid is slow , and as such usually requires 'coupling reagents' or 'activators'. A wide range of coupling reagents exist, due in part to their varying effectiveness for particular couplings, [ 15 ] [ 16 ] many of these reagents are commercially available.
Carbodiimides such as dicyclohexylcarbodiimide (DCC) and diisopropylcarbodiimide (DIC) are frequently used for amide bond formation. [ 14 ] The reaction proceeds via the formation of a highly reactive O -acyliso urea . This reactive intermediate is attacked by the peptide N-terminal amine, forming a peptide bond. Formation of the O -acyliso urea proceeds fastest in non-polar solvents such as dichloromethane. [ 17 ]
DIC is particularly useful for SPPS since as a liquid it is easily dispensed, and the urea byproduct is easily washed away. Conversely, the related carbodiimide 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) is often used for solution-phase peptide couplings as its urea byproduct can be removed by washing during aqueous work-up . [ 14 ]
Carbodiimide activation opens the possibility for racemization of the activated amino acid. [ 14 ] Racemization can be circumvented with 'racemization suppressing' additives such as the triazoles 1-hydroxy-benzotriazole (HOBt), and 1-hydroxy-7-aza-benzotriazole (HOAt). These reagents attack the O -acylisourea intermediate to form an active ester , which subsequently reacts with the peptide to form the desired peptide bond. [ 18 ] Ethyl cyanohydroxyiminoacetate (Oxyma), an additive for carbodiimide coupling, acts as an alternative to HOAt. [ 19 ]
To avoid epimerization through the O-acylisourea intermediate formed when using a carbodiimide reagent, an amidinium - or phosphonium -reagent can be employed These reagents have two parts: an electrophilic moiety which deoxygenates the carboxylic acid ( blue ) and masked nucleophilic moiety ( red ). Nucleophilic attack of the carboxylic acid on the electrophilic amidinium or phosphonium moiety leads to a short lived intermediate which is rapidly trapped by the unmasked nucleophile to form the activated ester intermediate and either a urea or phosphoramide by-product. These cationic reagents have non-coordinating counteranions such as a hexafluorophosphate or a tetrafluoroborate . [ 13 ] The identity of this anion is typically indicated by the first letter in the reagent’s acronym, although the nomenclature can be inconsistent. For example H BTU is a hexafluorophosphate salt while T BTU is a tetrafluoroborate salt. In addition to HBTU and HATU other common reagents include HCTU (6-ClHOBt), TCFH (chloride) and COMU (ethyl cyano(hydroxyimino)acetate). Amidinium reagents incorporating hydroxybenzotriazole moieties can exist in an N-form (guanadinium) or an O-form (uronium), but the N-form is generally more stable. [ 20 ] Phosphonium reagents include BOP (HOBt), PyBOP (HOBt) and PyAOP (HOAt). [ 21 ] Although these reagents can lead to the same activated ester intermediates as a carbodiimide reagent, the rate of activation is higher due to the high electrophilicty of these cationic reagents. [ 22 ] Amidinium reagents are capable of reacting with the peptide N-terminus to form an inactive guanidino by-product, whereas phosphonium reagents are not. [ 23 ]
Since late 2000s, propanephosphonic acid anhydride , sold commercially under various names such as "T3P", has become a useful reagent for amide bond formation in commercial applications. It converts the oxygen of the carboxylic acid into a leaving group, whose peptide-coupling byproducts are water-soluble and can be easily washed away. In a performance comparison between propanephosphonic acid anhydride and other peptide coupling reagents for the preparation of a nonapeptide drug, it was found that this reagent was superior to other reagents with regards to yield and low epimerization. [ 24 ]
Solid supports for peptide synthesis are selected for physical stability, to permit the rapid filtration of liquids. Suitable supports are inert to reagents and solvents used during SPPS and allow for the attachment of the first amino acid. [ 25 ] Swelling is of great importance because peptide synthesis takes place inside the swollen pores of the solid support. [ 26 ]
Three primary types of solid supports are: gel-type supports, surface-type supports, and composites. [ 25 ] Improvements to solid supports used for peptide synthesis enhance their ability to withstand the repeated use of TFA during the deprotection step of SPPS. [ 27 ] Two primary resins are used, based on whether a C-terminal carboxylic acid or amide is desired. The Wang resin was, as of 1996 [update] , the most commonly used resin for peptides with C-terminal carboxylic acids. [ 28 ] [ needs update ]
As described above, the use of N-terminal and side chain protecting groups is essential during peptide synthesis to avoid undesirable side reactions, such as self-coupling of the activated amino acid leading to ( polymerization ). [ 1 ] This would compete with the intended peptide coupling reaction, resulting in low yield or even complete failure to synthesize the desired peptide. [ citation needed ]
Two principle protecting group schemes are typically used in solid phase peptide synthesis: so-called Boc/benzyl and Fmoc/ tert- butyl approaches. [ 2 ] The Boc/Bzl strategy utilizes TFA -labile N-terminal Boc protection alongside side chain protection that is removed using anhydrous hydrogen fluoride during the final cleavage step (with simultaneous cleavage of the peptide from the solid support). Fmoc/tBu SPPS uses base-labile Fmoc N-terminal protection, [ 29 ] with side chain protection and a resin linkage that are acid-labile (final acidic cleavage is carried out via TFA treatment). Both approaches, including the advantages and disadvantages of each, are outlined in more detail below.
Before the advent of SPPS, solution methods for chemical peptide synthesis relied on tert -butyloxycarbonyl (abbreviated 'Boc') as a temporary N-terminal α-amino protecting group. The Boc group is removed with acid, such as trifluoroacetic acid (TFA). This forms a positively charged amino group in the presence of excess TFA (note that the amino group is not protonated in the image on the right), which is neutralized and coupled to the incoming activated amino acid. [ 30 ] Neutralization can either occur prior to coupling or in situ during the basic coupling reaction.
The Boc/Bzl approach retains its usefulness in reducing peptide aggregation during synthesis. [ 31 ] In addition, Boc/benzyl SPPS may be preferred over the Fmoc/ tert- butyl approach when synthesizing peptides containing base-sensitive moieties (such as depsipeptides or thioester moeities), as treatment with base is required during the Fmoc deprotection step (see below).
Permanent side-chain protecting groups used during Boc/benzyl SPPS are typically benzyl or benzyl-based groups. [ 1 ] Final removal of the peptide from the solid support occurs simultaneously with side chain deprotection using anhydrous hydrogen fluoride via hydrolytic cleavage. The final product is a fluoride salt which is relatively easy to solubilize. Scavengers such as cresol must be added to the HF in order to prevent reactive cations from generating undesired byproducts.
The use of N-terminal Fmoc protection allows for a milder deprotection scheme than used for Boc/Bzl SPPS, and this protection scheme is truly orthogonal under SPPS conditions. [ 33 ] Fmoc deprotection utilizes a base, typically 20–50% piperidine in DMF . [ 25 ] The exposed amine is therefore neutral, and consequently no neutralization of the peptide-resin is required, as in the case of the Boc/Bzl approach. The lack of electrostatic repulsion between the peptide chains can lead to increased risk of aggregation with Fmoc/ t Bu SPPS however. Because the liberated fluorenyl group is a chromophore, Fmoc deprotection can be monitored by UV absorbance of the reaction mixture, a strategy which is employed in automated peptide synthesizers.
The ability of the Fmoc group to be cleaved under relatively mild basic conditions while being stable to acid allows the use of side chain protecting groups such as Boc and t Bu that can be removed in milder acidic final cleavage conditions (TFA) than those used for final cleavage in Boc/Bzl SPPS (HF). Scavengers such as water and triisopropylsilane (TIPS) are most commonly added during the final cleavage in order to prevent side reactions with reactive cationic species released as a result of side chain deprotection. Nevertheless, many other scavenger compounds could be used as well. [ 34 ] [ 35 ] [ 36 ] The resulting crude peptide is obtained as a TFA salt, which is potentially more difficult to solubilize than the fluoride salts generated in Boc SPPS.
Fmoc/ t Bu SPPS is less atom-economical , as the fluorenyl group is much larger than the Boc group. Accordingly, prices for Fmoc amino acids were high until the large-scale piloting of one of the first synthesized peptide drugs, enfuvirtide , began in the 1990s, when market demand adjusted the relative prices of Fmoc- vs Boc- amino acids.
The (Z) group is another carbamate-type amine protecting group, discovered by Leonidas Zervas in the early 1930s and usually added via reaction with benzyl chloroformate . [ 37 ]
It is removed under harsh conditions using HBr in acetic acid , or milder conditions of catalytic hydrogenation .
This methodology was first used in the synthesis of oligopeptides by Zervas and Max Bergmann in 1932. [ 38 ] Hence, this became known as the Bergmann-Zervas synthesis, which was characterised "epoch-making" and helped establish synthetic peptide chemistry as a distinct field. [ 37 ] It constituted the first useful lab method for controlled peptide synthesis, enabling the synthesis of previously unattainable peptides with reactive side-chains, while Z-protected amino acids are also prevented form undergoing racemization . [ 37 ] [ 38 ]
The use of the Bergmann-Zervas method remained the standard practice in peptide chemistry for two full decades after its publication, superseded by newer methods (such as the Boc protecting group) in the early 1950s. [ 37 ] Nowadays, while it has been used periodically for α-amine protection, it is much more commonly used for side chain protection.
The allyloxycarbonyl (alloc) protecting group is sometimes used to protect an amino group (or carboxylic acid or alcohol group) when an orthogonal deprotection scheme is required. It is also sometimes used when conducting on-resin cyclic peptide formation, where the peptide is linked to the resin by a side-chain functional group. The Alloc group can be removed using tetrakis(triphenylphosphine)palladium(0) . [ 39 ]
For special applications like synthetic steps involving protein microarrays , protecting groups sometimes termed "lithographic" are used, which are amenable to photochemistry at a particular wavelength of light, and so which can be removed during lithographic types of operations. [ 40 ] [ 41 ] [ 42 ] [ 43 ]
The formation of multiple native disulfides remains challenging of native peptide synthesis by solid-phase methods. Random chain combination typically results in several products with nonnative disulfide bonds. [ 44 ] Stepwise formation of disulfide bonds is typically the preferred method, and performed with thiol protecting groups. [ 45 ] Different thiol protecting groups provide multiple dimensions of orthogonal protection. These orthogonally protected cysteines are incorporated during the solid-phase synthesis of the peptide. Successive removal of these groups, to allow for selective exposure of free thiol groups, leads to disulfide formation in a stepwise manner. The order of removal of the groups must be considered so that only one group is removed at a time.
Thiol protecting groups used in peptide synthesis requiring later regioselective disulfide bond formation must possess multiple characteristics. [ 46 ] [ 47 ] First, they must be reversible with conditions that do not affect the unprotected side chains. Second, the protecting group must be able to withstand the conditions of solid-phase synthesis. Third, the removal of the thiol protecting group must be such that it leaves intact other thiol protecting groups, if orthogonal protection is desired. That is, the removal of PG A should not affect PG B. Some of the thiol protecting groups commonly used include the acetamidomethyl (Acm), tert -butyl (But), 3-nitro-2-pyridine sulfenyl (NPYS), 2-pyridine-sulfenyl (Pyr), and trityl (Trt) groups. [ 46 ] Importantly, the NPYS group can replace the Acm PG to yield an activated thiol. [ 48 ]
Using this method, Kiso and coworkers reported the first total synthesis of insulin in 1993. [ 49 ] In this work, the A-chain of insulin was prepared with following protecting groups in place on its cysteines: CysA6(But), CysA7(Acm), and CysA11(But), leaving CysA20 unprotected. [ 49 ]
Microwave-assisted peptide synthesis has been used to complete long peptide sequences with high degrees of yield and low degrees of racemization. [ 50 ] [ 51 ]
The first article relating to continuous flow peptide synthesis was published in 1986, [ 52 ] but due to technical limitations, it was not until the early 2010's when more academic groups started using continuous flow for the rapid synthesis of peptides. [ 53 ] [ 54 ] The advantages of continuous flow over traditional batch methods is the ability to heat reagents with good temperature control, allowing the speed of reaction kinetics while minimising side reactions. [ 55 ] cycles times vary from 30 seconds, up to 6 minutes, depending on reaction conditions and excess of reagent.
Thanks to inline analytics, such as UV/Vis spectroscopy and the use of Variable Bed Flow reactor (VBFR) that monitor the resin volume, on-resin aggregation can be identified and coupling efficiency can be evaluated. [ 56 ]
Stepwise elongation, in which the amino acids are connected step-by-step in turn, is ideal for small peptides containing between 2 and 100 amino acid residues. Another method is fragment condensation , in which peptide fragments are coupled. [ 57 ] [ 58 ] [ 59 ] Although the former can elongate the peptide chain without racemization , the yield drops if only it is used in the creation of long or highly polar peptides. Fragment condensation is better than stepwise elongation for synthesizing sophisticated long peptides, but its use must be restricted in order to protect against racemization. Fragment condensation is also undesirable since the coupled fragment must be in gross excess, which may be a limitation depending on the length of the fragment. [ 60 ]
A new development for producing longer peptide chains is chemical ligation : unprotected peptide chains react chemoselectively in aqueous solution. A first kinetically controlled product rearranges to form the amide bond. The most common form of native chemical ligation uses a peptide thioester that reacts with a terminal cysteine residue. [ 61 ]
Other methods applicable for covalently linking polypeptides in aqueous solution include the use of split inteins , [ 62 ] spontaneous isopeptide bond formation [ 63 ] and sortase ligation. [ 64 ]
In order to optimize synthesis of long peptides , a method was developed in Medicon Valley for converting peptide sequences . [ citation needed ] The simple pre-sequence (e.g. Lysine (Lysn); Glutamic Acid (Glun); (LysGlu)n) that is incorporated at the C-terminus of the peptide to induce an alpha-helix -like structure. This can potentially increase biological half-life , improve peptide stability and inhibit enzymatic degradation without altering pharmacological activity or profile of action. [ 65 ] [ 66 ]
Peptides can be cyclized on a solid support. A variety of cyclization reagents can be used such as HBTU/HOBt/DIEA, PyBop/DIEA, PyClock/DIEA. [ 67 ] Head-to-tail peptides can be made on the solid support. The deprotection of the C-terminus at some suitable point allows on-resin cyclization by amide bond formation with the deprotected N-terminus. Once cyclization has taken place, the peptide is cleaved from resin by acidolysis and purified. [ 68 ] [ 69 ]
The strategy for the solid-phase synthesis of cyclic peptides is not limited to attachment through Asp, Glu or Lys side chains. Cysteine has a very reactive sulfhydryl group on its side chain. A disulfide bridge is created when a sulfur atom from one Cysteine forms a single covalent bond with another sulfur atom from a second cysteine in a different part of the protein. These bridges help to stabilize proteins, especially those secreted from cells. Some researchers use modified cysteines using S-acetomidomethyl (Acm) to block the formation of the disulfide bond but preserve the cysteine and the protein's original primary structure. [ 70 ]
Off-resin cyclization is a solid-phase synthesis of key intermediates, followed by the key cyclization in solution phase, the final deprotection of any masked side chains is also carried out in solution phase. This has the disadvantages that the efficiencies of solid-phase synthesis are lost in the solution phase steps, that purification from by-products, reagents and unconverted material is required, and that undesired oligomers can be formed if macrocycle formation is involved. [ 71 ]
The use of pentafluorophenyl esters (FDPP, [ 72 ] PFPOH [ 73 ] ) and BOP-Cl [ 74 ] are useful for cyclising peptides.
The first protected peptide was synthesised by Theodor Curtius in 1882 and the first free peptide was synthesised by Emil Fischer in 1901. [ 3 ] | https://en.wikipedia.org/wiki/Peptide_synthesis |
Peptidoglycan or murein is a unique large macromolecule, a polysaccharide , consisting of sugars and amino acids that forms a mesh-like layer (sacculus) that surrounds the bacterial cytoplasmic membrane. [ 1 ] The sugar component consists of alternating residues of β-(1,4) linked N -acetylglucosamine (NAG) and N -acetylmuramic acid (NAM). Attached to the N -acetylmuramic acid is an oligopeptide chain made of three to five amino acids. The peptide chain can be cross-linked to the peptide chain of another strand forming the 3D mesh-like layer. [ 1 ] [ 2 ] Peptidoglycan serves a structural role in the bacterial cell wall, giving structural strength, as well as counteracting the osmotic pressure of the cytoplasm . This repetitive linking results in a dense peptidoglycan layer which is critical for maintaining cell form and withstanding high osmotic pressures, and it is regularly replaced by peptidoglycan production. Peptidoglycan hydrolysis and synthesis are two processes that must occur in order for cells to grow and multiply, a technique carried out in three stages: clipping of current material, insertion of new material, and re-crosslinking of existing material to new material. [ 3 ]
The peptidoglycan layer is substantially thicker in gram-positive bacteria (20 to 80 nanometers) than in gram-negative bacteria (7 to 8 nanometers). [ 4 ] Depending on pH growth conditions, the peptidoglycan forms around 40 to 90% of the cell wall 's dry weight of gram-positive bacteria but only around 10% of gram-negative strains. Thus, presence of high levels of peptidoglycan is the primary determinant of the characterisation of bacteria as gram-positive. [ 5 ] In gram-positive strains, it is important in attachment roles and serotyping purposes. [ 6 ] For both gram-positive and gram-negative bacteria, particles of approximately 2 nm can pass through the peptidoglycan. [ 7 ]
It is difficult to tell whether an organism is gram-positive or gram-negative using a microscope; Gram staining , created by Hans Christian Gram in 1884, is required. The bacteria are stained with the dyes crystal violet and safranin . Gram positive cells are purple after staining, while Gram negative cells stain pink. [ 8 ]
The peptidoglycan layer within the bacterial cell wall is a crystal lattice structure formed from linear chains of two alternating amino sugars , namely N -acetylglucosamine (GlcNAc or NAG) and N -acetylmuramic acid (MurNAc or NAM). The alternating sugars are connected by a β-(1,4)- glycosidic bond . Each MurNAc is attached to a short (4- to 5-residue) amino acid chain, containing L - alanine , D - glutamic acid , meso -diaminopimelic acid , and D -alanine in the case of Escherichia coli (a gram-negative bacterium); or L -alanine, D - glutamine , L - lysine , and D -alanine with a 5- glycine interbridge between tetrapeptides in the case of Staphylococcus aureus (a gram-positive bacterium). Peptidoglycan is one of the most important sources of D -amino acids in nature. [ citation needed ]
By enclosing the inner membrane, the peptidoglycan layer protects the cell from lysis caused by the turgor pressure of the cell. When the cell wall grows, it retains its shape throughout its life, so a rod shape will remain a rod shape, and a spherical shape will remain a spherical shape for life. This happens because the freshly added septal material of synthesis transforms into a hemispherical wall for the offspring cells. [ 9 ]
Cross-linking between amino acids in different linear amino sugar chains occurs with the help of the enzyme DD -transpeptidase and results in a 3-dimensional structure that is strong and rigid. The specific amino acid sequence and molecular structure vary with the bacterial species . [ 10 ]
The different peptidoglycan types of bacterial cell walls and their taxonomic implications have been described. [ 11 ] Archaea ( domain Archaea ) [ 12 ] do not contain peptidoglycan (murein). [ 13 ] Some Archaea contain pseudopeptidoglycan (pseudomurein, see below). [ 14 ]
Peptidoglycan is involved in binary fission during bacterial cell reproduction. L-form bacteria and mycoplasmas , both lacking peptidoglycan cell walls, do not proliferate by binary fission, but by a budding mechanism. [ 15 ] [ 16 ]
In the course of early evolution, the successive development of boundaries (membranes, walls) protecting first structures of life against their environment must have been essential for the formation of the first cells ( cellularisation ).
The invention of rigid peptidoglycan (murein) cell walls in bacteria (domain Bacteria [ 12 ] ) was probably the prerequisite for their survival, extensive radiation and colonisation of virtually all habitats of the geosphere and hydrosphere. [ 17 ] [ 18 ]
The peptidoglycan monomers are synthesized in the cytosol and are then attached to a membrane carrier bactoprenol . Bactoprenol transports peptidoglycan monomers across the cell membrane where they are inserted into the existing peptidoglycan. [ 19 ]
Each of these reactions requires the energy source ATP. [ 20 ] This is all referred to as Stage one.
Stage two occurs in the cytoplasmic membrane. It is in the membrane where a lipid carrier called bactoprenol carries peptidoglycan precursors through the cell membrane.
In some archaea , i.e. members of the Methanobacteriales and in the genus Methanopyrus , pseudopeptidoglycan (pseudomurein) has been found. [ 14 ] In pseudopeptidoglycan the sugar residues are β-(1,3) linked N -acetylglucosamine and N -acetyltalosaminuronic acid . This makes the cell walls of such archaea insensitive to lysozyme . [ 23 ] The biosynthesis of pseudopeptidoglycan has been described. [ 24 ]
Peptidoglycan recognition is an evolutionarily conserved process. [ 25 ] The overall structure is similar between bacterial species, but various modifications can increase the diversity. These include modifications of the length of sugar polymers, modifications in the sugar structures, variations in cross-linking or substitutions of amino acids (primarily at the third position). [ 25 ] [ 26 ] The aim of these modifications is to alter the properties of the cell wall, which plays a vital role in pathogenesis . [ 25 ]
Peptidoglycans can be degraded by several enzymes ( lysozyme , glucosaminidase, endopeptidase ... [ 25 ] ), producing immunostimulatory fragments (sometimes called muropeptides [ 27 ] ) that are critical for mediating host-pathogen interactions . [ 26 ] These include MDP ( muramyl dipeptide ), NAG ( N-acetylglucosamine ) or iE-DAP (γ-d-glutamyl-meso-diaminopimelic acid). [ 25 ] [ 27 ]
Peptidoglycan from intestinal bacteria (both pathogens and commensals) crosses the intestinal barrier even under physiological conditions. [ 27 ] Mechanisms through which peptidoglycan or its fragments enter the host cells can be direct (carrier-independent) or indirect (carrier-dependent), and they are either bacteria-mediated (secretion systems, membrane vesicles ) or host cell-mediated (receptor-mediated, peptide transporters). [ 27 ] Bacterial secretion systems are protein complexes used for the delivery of virulence factors across the bacterial cell envelope to the exterior environment. [ 28 ] Intracellular bacterial pathogens invade eukaryotic cells (which may lead to the formation of phagolysosomes and/or autophagy activation), or bacteria may be engulfed by phagocytes ( macrophages , monocytes , neutrophils ...). The bacteria-containing phagosome may then fuse with endosomes and lysosomes , leading to degradation of bacteria and generation of polymeric peptidoglycan fragments and muropeptides. [ 27 ]
Innate immune system senses intact peptidoglycan and peptidoglycan fragments using numerous PRRs ( pattern recognition receptors ) that are secreted, expressed intracellularly or expressed on the cell surface. [ 25 ]
PGLYRPs are conserved from insects to mammals . [ 27 ] Mammals produce four secreted soluble peptidoglycan recognition proteins ( PGLYRP-1 , PGLYRP-2 , PGLYRP-3 and PGLYRP-4 ) that recognize muramyl pentapeptide or tetrapeptide. [ 25 ] They can also bind to LPS and other molecules by using binding sites outside of the peptidoglycan-binding groove. [ 28 ] After recognition of peptidoglycan, PGLYRPs activate polyphenol oxidase (PPO) molecules, Toll, or immune deficiency (IMD) signalling pathways. That leads to production of antimicrobial peptides (AMPs). [ 28 ]
Each of the mammalian PGLYRPs display unique tissue expression patterns. PGLYRP-1 is mainly expressed in the granules of neutrophils and eosinophils . [ 25 ] PGLYRP-3 and 4 are expressed by several tissues such as skin, sweat glands, eyes or the intestinal tract. [ 27 ] PGLYRP-1, 3 and 4 form disulphide-linked homodimers and heterodimers essential for their bactericidal activity. [ 27 ] Their binding to bacterial cell wall peptidoglycans can induce bacterial cell death by interaction with various bacterial transcriptional regulatory proteins. [ 25 ] PGLYRPs are likely to assist in bacterial killing by cooperating with other PRRs to enhance recognition of bacteria by phagocytes. [ 25 ]
PGLYRP-2 is primarily expressed by the liver and secreted into the circulation. [ 25 ] Also, its expression can be induced in skin keratinocytes , oral and intestinal epithelial cells. [ 27 ] In contrast with the other PGLYRPs, PGLYRP-2 has no direct bactericidal activity. It possesses peptidoglycan amidase activity, it hydrolyses the lactyl-amide bond between the MurNAc and the first amino acid of the stem peptide of peptidoglycan. [ 25 ] [ 27 ] It is proposed, that the function of PGLYRP-2 is to prevent over-activation of the immune system and inflammation -induced tissue damage in response to NOD2 ligands (see below), as these muropeptides can no longer be recognized by NOD2 upon separation of the peptide component from MurNAc. [ 27 ] Growing evidence suggests that peptidoglycan recognition protein family members play a dominant role in the tolerance of intestinal epithelial cells toward the commensal microbiota. [ 28 ] [ 29 ] It has been demonstrated that expression of PGLYRP-2 and 4 can influence the composition of the intestinal microbiota . [ 28 ]
Recently, it has been discovered, that PGLYRPs (and also NOD-like receptors and peptidoglycan transporters) are highly expressed in the developing mouse brain . [ 30 ] PGLYRP-2 and is highly expressed in neurons of several brain regions including the prefrontal cortex , hippocampus , and cerebellum , thus indicating potential direct effects of peptidoglycan on neurons. PGLYRP-2 is highly expressed also in the cerebral cortex of young children, but not in most adult cortical tissues. PGLYRP-1 is also expressed in the brain and continues to be expressed into adulthood. [ 30 ]
Probably the most well-known receptors of peptidoglycan are the NOD-like receptors (NLRs), mainly NOD1 and NOD2 . The NOD1 receptor is activated after iE-DAP (γ-d-glutamyl-meso-diaminopimelic acid) binding, while NOD2 recognizes MDP (muramyl dipeptide), by their LRR domains . [ 28 ] Activation leads to self-oligomerization, resulting in activation of two signalling cascades. One triggers activation of NF-κB (through RIP2, TAK1 and IKK [ 31 ] ), second leads to MAPK signalling cascade. Activation of these pathways induces production of inflammatory cytokines and chemokines . [ 25 ]
NOD1 is expressed by diverse cell types, including myeloid phagocytes, epithelial cells [ 25 ] and neurons. [ 30 ] NOD2 is expressed in monocytes and macrophages, epithelial intestinal cells, Paneth cells , dendritic cells , osteoblasts , keratinocytes and other epithelial cell types. [ 27 ] As cytosolic sensors, NOD1 and NOD2 must either detect bacteria that enter the cytosol, or peptidoglycan must be degraded to generate fragments that must be transported into the cytosol for these sensors to function. [ 25 ]
Recently, it was demonstrated that NLRP3 is activated by peptidoglycan, through a mechanism that is independent of NOD1 and NOD2. [ 27 ] In macrophages, N-acetylglucosamine generated by peptidoglycan degradation was found to inhibit hexokinase activity and induce its release from the mitochondrial membrane . It promotes NLRP3 inflammasome activation through a mechanism triggered by increased mitochondrial membrane permeability. [ 27 ]
NLRP1 is also considered as a cytoplasmic sensor of peptidoglycan. It can sense MDP and promote IL-1 secretion through binding NOD2. [ 28 ] [ 26 ]
C-type lectins are a diverse superfamily of mainly Ca 2+ -dependent proteins that bind a variety of carbohydrates (including the glycan skeleton of peptidoglycan), and function as innate immune receptors. [ 27 ] CLR proteins that bind to peptidoglycan include MBL ( mannose binding lectin ), ficolins , Reg3A (regeneration gene family protein 3A) and PTCLec1. [ 28 ] In mammals, they initiate the lectin-pathway of the complement cascade. [ 27 ]
The role of TLRs in direct recognition of peptidoglycan is controversial. [ 25 ] In some studies, has been reported that peptidoglycan is sensed by TLR2 . [ 32 ] But this TLR2-inducing activity could be due to cell wall lipoproteins and lipoteichoic acids that commonly co-purify with peptidoglycan. Also variation in peptidoglycan structure in bacteria from species to species may contribute to the differing results on this topic. [ 25 ] [ 27 ]
Peptidoglycan is immunologically active, which can stimulate immune cells to increase the expression of cytokines and enhance antibody-dependent specific response when combined with vaccine or as adjuvant alone. [ 28 ] MDP, which is the basic unit of peptidoglycan, was initially used as the active component of Freund's adjuvant . [ 28 ] Peptidoglycan from Staphylococcus aureus was used as a vaccine to protect mice, showing that after vaccine injection for 40 weeks, the mice survived from S. aureus challenge at an increased lethal dose . [ 33 ]
Some antibacterial drugs such as penicillin interfere with the production of peptidoglycan by binding to bacterial enzymes known as penicillin-binding proteins or DD -transpeptidases . [ 6 ] Penicillin-binding proteins form the bonds between oligopeptide crosslinks in peptidoglycan. For a bacterial cell to reproduce through binary fission , more than a million peptidoglycan subunits (NAM-NAG+oligopeptide) must be attached to existing subunits. [ 34 ] Mutations in genes coding for transpeptidases that lead to reduced interactions with an antibiotic are a significant source of emerging antibiotic resistance . [ 35 ] Since peptidoglycan is also lacking in L-form bacteria and in mycoplasmas, both are resistant against penicillin.
Other steps of peptidoglycan synthesis can also be targeted. The topical antibiotic bacitracin targets the utilization of C55-isoprenyl pyrophosphate . Lantibiotics , which includes the food preservative nisin , attack lipid II. [ 36 ]
Lysozyme , which is found in tears and constitutes part of the body's innate immune system exerts its antibacterial effect by breaking the β-(1,4)-glycosidic bonds in peptidoglycan (see above). Lysozyme is more effective in acting against gram-positive bacteria , in which the peptidoglycan cell wall is exposed, than against gram-negative bacteria , which have an outer layer of LPS covering the peptidoglycan layer. [ 31 ] Several bacterial peptidoglycan modifications can result in resistance to degradation by lysozyme. Susceptibility of bacteria to degradation is also considerably affected by exposure to antibiotics . Exposed bacteria synthesize peptidoglycan that contains shorter sugar chains that are poorly crosslinked and this peptidoglycan is then more easily degraded by lysozyme. [ 28 ] | https://en.wikipedia.org/wiki/Peptidoglycan |
A peptidomimetic is a small protein-like chain designed to mimic a peptide . [ 1 ] [ 2 ] They typically arise either from modification of an existing peptide, or by designing similar systems that mimic peptides, such as peptoids and β-peptides . Irrespective of the approach, the altered chemical structure is designed to advantageously adjust the molecular properties such as stability or biological activity . This can have a role in the development of drug-like compounds from existing peptides. Peptidomimetics can be prepared by cyclization of linear peptides or coupling of stable unnatural amino acids. [ 3 ] These modifications involve changes to the peptide that will not occur naturally (such as altered backbones and the incorporation of nonnatural amino acids ). Unnatural amino acids can be generated from their native analogs via modifications such as amine alkylation, side chain substitution, structural bond extension cyclization, and isosteric replacements within the amino acid backbone. [ 3 ] Based on their similarity with the precursor peptide, peptidomimetics can be grouped into four classes (A – D) where A features the most and D the least similarities. Classes A and B involve peptide-like scaffolds, while classes C and D include small molecules (Figure 1). [ 1 ]
This group includes modified peptides that are mainly composed of proteogenic amino acids thereby closely resembling a natural peptide binding epitope. [ 1 ] Introduced modifications usually aim to increase the stability of the peptide, its affinity for a desired binding partner, oral availability or cell permeability. The design of class A peptidomimetics often involves macrocyclization strategies as for example in stapled peptides .
This class of peptidomimetics encompasses peptides with a large number of non-natural amino acids, major backbone modifications or larger non-natural building fragments that resemble the conformation of a particular peptide binding motif. [ 1 ] Examples involve D-peptide and peptidic foldamers such as beta-peptides .
These structural mimetics include molecules that are highly modified when compared to their parent peptide sequence. [ 4 ] Usually, a small-molecular scaffold is appyled to project groups in analogy to the bioactive conformation of a peptide.
These mechanistic mimetics do not directly recapitulate the side chains or conformation of a peptide but mimic its mode-of-action . [ 1 ] Class D peptidomimetics can be directly designed from a small peptide sequence or identified the screening of compound libraries. For example, Nirmatrelvir is an orally-active small molecule drug derived from lufotrelvir , a modified L-peptide. [ 5 ]
The use of peptides as drugs has some disadvantages because of their bioavailability and biostability. Rapid degradation, poor oral availability, difficult transportation through cell membranes, nonselective receptor binding, and challenging multistep preparation are the major limitations of peptides as active pharmaceutical ingredients. [ 3 ] Therefore, small protein-like chains called peptidomimetics could be designed and used to mimic native analogs and conceivably exhibit better pharmacological properties. [ 3 ] Many peptidomimetics are utilized as FDA-approved drugs, such as Romidepsin (Istodax), Atazanavir (Reyataz), Saquinavir (Invirase), Oktreotid (Sandostatin), Lanreotide (Somatuline), Plecanatide (Trulance), Ximelagatran (Exanta), Etelcalcetide (Parsabiv), and Bortezomib (Velcade).
Peptidomimetic approaches have been utilized to design small molecules that selectively target cancer cells, an approach known as targeted chemotherapy , by inducing programmed cell death by a process called apoptosis . The following two examples mimic proteins involved in key Protein–protein interactions that reactivate the apoptotic pathway in cancer but do so by distinct mechanisms. [ 6 ]
In 2004, Walensky and co-workers reported a stabilized alpha helical peptide that mimics pro-apoptotic BH3-only proteins, such as BID and BAD . [ 7 ] This molecule was designed to stabilize the native helical structure by forming a macrocycle between side chains that are not involved in binding. This process, referred to as peptide stapling , uses non-natural amino acids to facilitate macrocyclization by ring-closing olefin metathesis . [ 8 ] In this case, a stapled BH3 helix was identified which specifically activates the mitochondrial apoptotic pathway by antagonizing the sequestration of BH3-only proteins by anti-apoptotic proteins (e.g. Bcl-2 , see also intrinsic and extrinsic inducers of the apoptosis). This molecule suppressed growth of human leukemia in a mouse xenograft model. [ 7 ]
Also in 2004, Harran and co-workers reported a dimeric small molecule that mimics the proapoptotic protein Smac (see mitochondrial regulation in apoptosis). [ 9 ] This molecule mimics the N-terminal linear motif Ala-Val-Pro-Ile. Uniquely, the dimeric structure of this peptidomimetic led to a marked increase in activity over an analogous monomer. This binding cooperativity results from the molecule's ability to also mimic the homodimeric structure of Smac, which is functionally important for reactivating caspases. [ 10 ] Smac mimetics of this type can sensitize an array of non-small-cell lung cancer cells to conventional chemotherapeutics (e.g. Gemcitabine , Vinorelbine ) both in vitro and in mouse xenograft models. [ 11 ]
Heterocycles are often used to mimic the amide bond of peptides. Thiazoles, for example, are found in naturally occurring peptides and used by researchers to mimic the amide bond of peptides. [ 12 ] | https://en.wikipedia.org/wiki/Peptidomimetic |
The peptization of a liquid mixture is the process of converting the mixture into a colloid by shaking it with a suitable electrolyte called a peptizing agent . [ 1 ] That is, the insoluble solid particles which have settled out of the mixture (i.e. the precipitate ) are reformed into microscopic particles suspended in the mixture. Peptization is the reverse of flocculation , the aggregation of colloidal particles into precipitate; as such, it is also known as deflocculation .
This is particularly important in colloid chemistry or for precipitation reactions in an aqueous solution . When colloidal particles bear a same sign electric charge , they mutually repel each other and cannot aggregate together . Freshly precipitated aluminium or iron hydroxide is extremely difficult to filter because the very fine colloidal particles directly pass through a paper filter . To facilitate the filtration, the colloidal suspension must be first flocculated by adding a concentrated solution of salt to the system. Multivalent cations are more efficient flocculants than monovalent cations: AlCl 3 > CaCl 2 > NaCl . The electrical charges present at the surface of the particles are so " neutralised " and disappear. More correctly speaking, the electrical double layer existing at the surface of the particles is compressed by the added electrolyte and collapses at high ionic strength . The electrical repulsion no longer hinders the aggregation of particles and they can then coalesce to form a flocculent precipitate that is easy to filter. If the precipitate is washed with an excessive volume of deionised water , the electrical double layer present at the surface of the particles expands again and the electrical repulsion reappears: the precipitate peptizes and the particles pass again through the filter.
Peptization is also used in nanoparticle synthesis to make a large grouping of particles split into many primary particles. This is done by changing the surface properties, applying a charge, or by adding a surfactant .
In the synthesis of titania ( titanium dioxide ) nanoparticles, peptization involves adsorption of quaternary ammonium cation on the titania surface. This causes the surface to become positively charged. Electrostatic repulsion of the primary particles in the agglomerated titania breaks up the agglomerate into primary particles. [ 2 ] The efficacy of adsorbates or suspension modification in imparting interparticle electrostatic repulsion is most commonly studied in terms of zeta potential .
This chemistry -related article is a stub . You can help Wikipedia by expanding it .
This nanotechnology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peptization |
In nanobiotechnology , a peptoid nanosheet is a synthetic protein structure made from peptoids . Peptoid nanosheets have a thickness of about three nanometers and a length of up to 100 micrometers, meaning that they have a two-dimensional, flat shape that resembles paper on the nanoscale. [ 1 ] [ 2 ]
For assembly, a purified amphiphilic polypeptoid of specific sequence is dissolved in aqueous solution. [ 3 ] These form a monolayer ( Langmuir–Blodgett film ) on the air-water interface with their hydrophobic side chains oriented in air and hydrophilic side chains in the water. When this mono-layer is shrunk, it buckles into a bilayer with the hydrophobic groups forming the interior core of the peptoid nanosheet. [ 4 ] This method has been standardized by repetitively tilting vials of peptoid solution at 85° before returning the vials to the upright position. This repetitive vial “rocking” motion lessens the interfacial area of the air-water interface inside the vial, compressing the peptoid mono-layer by a factor of four and causing the mono-layer to buckle into peptoid nanosheets. Using this method, nanosheets are produced in high yield, and 95% of the peptoid polymer starting material is efficiently converted into peptoid nanosheets after rocking the vials several hundred times.
Peptoid nanosheets have a very high surface area, which can be readily functionalized to serve as a platform for sensing and templating. [ 5 ] Also, their hydrophobic interiors can accommodate hydrophobic small molecule cargos, which have been demonstrated by the sequestration of Nile red when this dye was injected into an aqueous solution of the peptoid nanosheets. [ 6 ] For these reasons, the hydrophobic interior of the 2D nanosheets could be an attractive platform for loading or embedding hydrophobic cargo, such as drug molecules, fluorophores , aromatic compounds, and metal nanoparticles . | https://en.wikipedia.org/wiki/Peptoid_nanosheet |
Per-Olov Löwdin (October 28, 1916 – October 6, 2000) was a Swedish physicist , professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993.
A former graduate student under Ivar Waller , Löwdin formulated in 1950 the symmetric orthogonalization scheme for atomic and molecular orbital calculations, greatly simplifying the tight-binding method. [ 1 ] [ 2 ] This scheme is the basis of the zero-differential overlap (ZDO) approximation used in semiempirical theories. In 1956 he introduced the canonical orthogonalization scheme, which is optimal for eliminating approximate linear dependencies of a basis set. [ 3 ] These orthogonalization procedures are widely used today in all modern quantum chemistry calculations. [ 4 ] [ 5 ]
The famous 'Löwdin's pairing theorem' used in restricted open-shell Hartree–Fock (ROHF), unrestricted Hartree–Fock (UHF) and generalized valence bond (RES-GVB) theories is not his. According to himself, George G. Hall and King made the formal proposition after an informal suggestion by Löwdin. [ citation needed ]
His Löwdin partitioning technique for quantum chemistry problems is best appreciated through the series of 14 papers on perturbation theory published between 1963 and 1971.
He was also a very active teacher, starting the Summer Schools of Quantum Chemistry at Uppsala around 1958. In 1959 and 1960, Löwdin started the Quantum Theory Project at the University of Florida as a sister project to the Uppsala Quantum Chemistry Group. In 1964 he was joined by John C. Slater from MIT. The International Winter Institutes (held initially at Sanibel Island, and later at Gainesville) provided the initiation into quantum chemistry for hundreds of young Latin American scientists during the 1980s and 1990s. In 1960 he founded the Sanibel Symposium in conjunction with the Winter Institute, held every year since then.
Löwdin was elected a member of the Royal Swedish Academy of Sciences in 1969, the American Philosophical Society in 1983, [ 6 ] and was a member of the committee for the Nobel Prize in Physics from 1972 to 1984. He was the founder of the International Journal of Quantum Chemistry and of the series Advances in Quantum Chemistry . He was a foundation member of the International Academy of Quantum Molecular Science . | https://en.wikipedia.org/wiki/Per-Olov_Löwdin |
Per- and polyfluoroalkyl substances (also PFAS , [ 1 ] PFASs , [ 2 ] and sometimes referred to as " forever chemicals " [ 3 ] [ 4 ] ) are a group of synthetic organofluorine chemical compounds that have multiple fluorine atoms attached to an alkyl chain; there are 7 million such chemicals according to PubChem . [ 5 ] PFAS came into use with the invention of Teflon in 1938 to make fluoropolymer coatings and products that resist heat, oil, stains, grease, and water. They are now used in products including waterproof fabric such as Nylon , yoga pants , carpets, shampoo, feminine hygiene products, mobile phone screens, wall paint, furniture, adhesives, food packaging , firefighting foam , and the insulation of electrical wire. [ 6 ] [ 7 ] [ 8 ] PFAS are also used by the cosmetic industry in most cosmetics and personal care products , including lipstick , eye liner , mascara , foundation , concealer , lip balm , blush , and nail polish . [ 9 ] [ 10 ]
Many PFAS such as PFOS and PFOA pose health and environmental concerns because they are persistent organic pollutants ; they were branded as "forever chemicals" in an article in The Washington Post in 2018. [ 11 ] Some have half-lives of over eight years in the body, due to a carbon-fluorine bond , one of the strongest in organic chemistry . [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] They move through soils and bioaccumulate in fish and wildlife, which are then eaten by humans. Residues are now commonly found in rain , drinking water , and wastewater . [ 12 ] [ 17 ] [ 18 ] [ 7 ] Since PFAS compounds are highly mobile, they are readily absorbed through human skin and through tear ducts , and such products on lips are often unwittingly ingested. [ 19 ] Due to the large number of PFAS, it is challenging to study and assess the potential human health and environmental risks; more research is necessary and is ongoing. [ 20 ] [ 12 ] [ 21 ] [ 6 ]
Exposure to PFAS, some of which have been classified as carcinogenic and/or as endocrine disruptors , has been linked to cancers such as kidney , prostate and testicular cancer , ulcerative colitis , thyroid disease , suboptimal antibody response / decreased immunity, decreased fertility, hypertensive disorders in pregnancy, reduced infant and fetal growth and developmental issues in children, obesity, dyslipidemia (abnormally high cholesterol ), and higher rates of hormone interference. [ 6 ] [ 22 ] [ 23 ]
The use of PFAS has been regulated internationally by the Stockholm Convention on Persistent Organic Pollutants since 2009, with some jurisdictions, such as China and the European Union , planning further reductions and phase-outs. However, major producers and users such as the United States, Israel, and Malaysia have not ratified the agreement and the chemical industry has lobbied governments to reduce regulations [ 24 ] or have moved production to countries such as Thailand, where there is less regulation. [ 25 ] [ 26 ]
The market for PFAS was estimated to be US$28 billion in 2023 and the majority are produced by 12 companies: 3M , AGC Inc. , Archroma, Arkema , BASF , Bayer , Chemours , Daikin , Honeywell , Merck Group , Shandong Dongyue Chemical, and Solvay . [ 27 ] Sales of PFAS, which cost approximately $20 per kilogram, generate a total industry profit of $4 billion per year on 16% profit margins . [ 28 ] Due to health concerns, several companies have ended or plan to end the sale of PFAS or products that contain them; these include W. L. Gore & Associates (the maker of Gore-Tex ), H&M , Patagonia , REI , and 3M . [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] PFAS producers have paid billions of dollars to settle litigation claims, the largest being a $10.3 billion settlement paid by 3M for water contamination in 2023. [ 35 ] Studies have shown that companies have known of the health dangers since the 1970s – DuPont and 3M were aware that PFAS was "highly toxic when inhaled and moderately toxic when ingested". [ 36 ] External costs , including those associated with remediation of PFAS from soil and water contamination, treatment of related diseases, and monitoring of PFAS pollution, may be as high as US$17.5 trillion annually, according to ChemSec . [ 28 ] The Nordic Council of Ministers estimated health costs to be at least €52–84 billion in the European Economic Area . [ 37 ] In the United States, PFAS-attributable disease costs are estimated to be $6–62 billion. [ 38 ] [ 39 ]
In January 2025, reports stated that the cost of cleaning up toxic PFAS pollution in the UK and Europe could exceed £1.6 trillion over the next 20 years, averaging £84 billion annually. [ 40 ]
Per- and polyfluoroalkyl substances are a group of synthetic organofluorine chemical compounds that have multiple fluorine atoms attached to an alkyl chain. Different organizations use different definitions for PFAS, leading to estimates of between 8,000 and 7 million chemicals within the group. The EPA toxicity database, DSSTox, lists 14,735 unique PFAS chemical compounds. [ 41 ] [ 42 ]
An early definition required that they contain at least one perfluoroalkyl moiety , −C n F 2 n +1 . [ 13 ] Beginning in 2021, the OECD expanded its terminology, stating that "PFAS are defined as fluorinated substances that contain at least one fully fluorinated methyl or methylene carbon atom (without any H/Cl/Br/I atom attached to it), i.e., with a few noted exceptions, any chemical with at least a perfluorinated methyl group ( −CF 3 ) or a perfluorinated methylene group ( −CF 2 − ) is a PFAS." [ 2 ] [ 43 ] This definition notably includes Carbon tetrafluoride .
The United States Environmental Protection Agency (EPA) defines PFAS in the Drinking Water Contaminant Candidate List 5 as substances that contain "at least one of the following three structures: R−CF 2 −CF(R')R" , where both the −CF 2 − and −CF− moieties are saturated carbons, and none of the R groups can be hydrogen; R−CF 2 −O−CF 2 −(R') , where both the −CF 2 − moieties are saturated carbons, and none of the R groups can be hydrogen; or CF 3 −C−(CF 3 )RR' , where all the carbons are saturated, and none of the R groups can be hydrogen. [ 44 ] A summary table of some PFAS definitions is provided in Hammel et al (2022). [ 45 ]
Fluorinated surfactants or fluorosurfactants are a subgroup of PFAS characterized by a hydrophobic fluorinated "tail" and a hydrophilic "head" that behave as surfactants . These are more effective at reducing the surface tension of water than comparable hydrocarbon surfactants. [ 46 ] They include the perfluorosulfonic acids , such as perfluorooctanesulfonic acid (PFOS), and the perfluorocarboxylic acids like perfluorooctanoic acid (PFOA).
As with other surfactants, fluorosurfactants tend to concentrate at the phase interfaces . [ 47 ] Fluorocarbons are both lipophobic and hydrophobic, repelling both oil and water. Their lipophobicity results from the relative lack of London dispersion forces compared to hydrocarbons, a consequence of fluorine's large electronegativity and small bond length, which reduce the polarizability of the surfactants' fluorinated molecular surface. Fluorosurfactants are more stable than hydrocarbon surfactants due to the stability of the carbon–fluorine bond . Perfluorinated surfactants persist in the environment for the same reason. [ 17 ]
Fluorosurfactants such as PFOS, PFOA, and perfluorononanoic acid (PFNA) have caught the attention of regulatory agencies because of their persistence, toxicity, and widespread occurrence in the blood of general populations. [ 48 ] [ 49 ]
PFASs are used in emulsion polymerization to produce fluoropolymers , used in stain repellents, polishes, paints, and coatings . [ 50 ]
PFASs were originally considered to be chemically inert . [ 51 ] [ 52 ] Early occupational studies revealed elevated levels of fluorochemicals, including perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA, C8), in the blood of exposed industrial workers, but cited no ill health effects. [ 53 ] [ 54 ] These results were consistent with the measured serum concentrations of PFOS and PFOA in 3M plant workers ranging from 0.04 to 10.06 ppm and 0.01 to 12.70 ppm, respectively, well below toxic and carcinogenic levels cited in animal studies. [ 54 ] Given, however, the serum elimination half-life of four to five years and widespread environmental contamination, molecules have been shown to accumulate in humans sufficiently to cause adverse health outcomes. [ 51 ]
In 2022, levels of at least four perfluoroalkyl acids (PFAAs) in rain water worldwide greatly exceeded the EPA's lifetime drinking water health advisories as well as comparable Danish, Dutch, and European Union safety standards, leading to the conclusion that "the global spread of these four PFAAs in the atmosphere has led to the planetary boundary for chemical pollution being exceeded". [ 57 ]
It had been thought that PFAAs would eventually end up in the oceans, where they would be diluted over decades, but a field study published in 2021 by researchers at Stockholm University found that they are often transferred from water to air when waves reach land, are a significant source of air pollution , and eventually get into rain. The researchers concluded that pollution may impact large areas. [ 58 ] [ 59 ] [ 60 ]
In 2024, a worldwide study of 45,000 groundwater samples found that 31% of samples contained levels of PFAS that were harmful to human health; these samples were taken from areas not near any obvious source of contamination. [ 61 ]
Soil is also contaminated and the chemicals have been found in remote areas such as Antarctica . [ 62 ] Soil contamination can result in higher levels of PFAs found in foods such as white rice, coffee, and animals reared on contaminated ground. [ 63 ] [ 64 ] [ 65 ]
From 2005 to 2013, three epidemiologists known as the C8 Science Panel conducted health studies in the Mid-Ohio Valley as part of a contingency to a class action lawsuit brought by communities in the Ohio River Valley against DuPont in response to landfill and wastewater dumping of PFAS-laden material from DuPont's West Virginia Washington Works plant. [ 66 ] The panel measured PFOA (also known as C8) serum concentrations in 69,000 individuals from around DuPont's Washington Works Plant and found a mean concentration of 83 ng/mL, compared to 4 ng/mL in a standard population of Americans. [ 67 ] This panel reported probable links between elevated PFOA blood concentration and hypercholesterolemia , ulcerative colitis , thyroid disease , testicular cancer , kidney cancer as well as pregnancy-induced hypertension and preeclampsia . [ 68 ] [ 69 ] [ 70 ] [ 71 ] [ 72 ]
The severity of PFAS-associated health effects can vary based on the length of exposure, level of exposure, and health status. [ 73 ]
Exposure to PFAS is a risk factor for various hypertensive disorders in pregnancy, including preeclampsia and high blood pressure . It is not clear whether PFAS exposure is associated with wider cardiovascular disorders during pregnancy. [ 74 ] Human breast milk can harbor PFASs, which can be transferred from mother to infant via breastfeeding. [ 75 ] [ 64 ]
Use of various personal care products, such as nail care products, fragrances, makeup, hair dyes and hair sprays, by pregnant women and lactating mothers has been shown to be associated with significantly higher levels of PFAS in the blood and breastmilk of the mothers. For example, PFOS levels of women who dyed their hair at least twice during pregnancy were more than a third higher than those who did not. PFOS is one of the most common and most dangerous of the PFAS compounds. [ 76 ]
Endocrine disruptors , including PFASs, are linked with the male infertility crisis . [ 77 ]
A report in 2023 by the Icahn School of Medicine at Mount Sinai linked high exposure to PFAS with a 40% decrease in the ability for a woman to have a successful pregnancy as well as hormone disruption and delayed puberty onset. [ 78 ] [ 79 ]
Fetuses and children are especially vulnerable to the harms of PFAS chemicals because they have been shown to be linked to major adverse health conditions, including abnormally small birth weight syndrome in newborns, preterm birth , shorter lactation periods, breastmilk of diminished nutritional content, one or more neurodevelopmental disorders , and decreased response to childhood vaccines . [ 76 ]
A meta-analysis for associations between PFASs and human clinical biomarkers for liver injury, analyzing PFAS effects on liver biomarkers and histological data from rodent experimental studies, concluded that evidence exists that PFOA, perfluorohexanesulfonic acid (PFHxS), and perfluorononanoic acid (PFNA) caused hepatotoxicity in humans. [ 80 ]
PFOA is classified as carcinogenic to humans (Group 1) by the International Agency for Research on Cancer (IARC) based on "sufficient" evidence for cancer in animals and "strong" mechanistic evidence in exposed humans. IARC also classified PFOS as possibly carcinogenic to humans (Group 2b) based on "strong" mechanistic evidence. [ 23 ] There is a lack of high-quality epidemiological data on the associations between many specific PFAS chemicals and specific cancer types, and research is ongoing. [ 81 ]
A response is observed in humans where elevated PFOS levels were significantly associated with elevated total cholesterol and LDL cholesterol, highlighting significantly reduced PPAR expression and alluding to PPAR independent pathways predominating over lipid metabolism in humans compared to rodents. [ 82 ]
PFOA and PFOS have been shown to significantly alter immune and inflammatory responses in human and animal species. In particular, IgA , IgE (in females only) and C-reactive protein have been shown to decrease whereas antinuclear antibodies increase as PFOA serum concentrations increase. [ 83 ] These cytokine variations allude to immune response aberrations resulting in autoimmunity . One proposed mechanism is a shift towards anti-inflammatory M2 macrophages and/or T-helper (TH2) response in intestinal epithelial tissue which allows sulfate-reducing bacteria to flourish. Elevated levels of hydrogen sulfide result, which reduce beta-oxidation and nutrient production, leading to a breakdown of the colonic epithelial barrier. [ 84 ]
Hypothyroidism is the most common thyroid abnormality associated with PFAS exposure. [ 85 ] PFASs have been shown to decrease thyroid peroxidase , resulting in decreased production and activation of thyroid hormones in vivo. [ 86 ] Other proposed mechanisms include alterations in thyroid hormone signaling, metabolism and excretion as well as function of nuclear hormone receptor . [ 85 ]
Bioaccumulation controls internal concentrations of pollutants, including PFAS, in individual organisms. When bioaccumulation is looked at in the perspective of the entire food web, it is called biomagnification, which is important to track because lower concentrations of pollutants in environmental matrices such as seawater or sediments, can very quickly grow to harmful concentrations in organisms at higher trophic levels, including humans. Notably, concentrations in biota can even be greater than 5000 times those present in water for PFOS and C 10 –C 14 PFCAs . [ 87 ] PFAS can enter an organism by ingestion of sediment, through the water, or directly via their diet. It accumulates namely in areas with high protein content, in the blood and liver, but it is also found to a lesser extent in tissues. [ 88 ]
Biomagnification can be described using the estimation of the trophic magnification factor (TMF), which describes the relationship between the contamination levels in a species and their trophic level in the food web. TMFs are determined by graphing the log-transformed concentrations of PFAS against the assigned trophic level and taking the antilog of the regression slope (10 slope ). [ 17 ]
In a study done on a macrotidal estuary in Gironde, SW France, TMFs exceeded one for nearly all 19 PFAS compounds considered in the study and were particularly high for PFOA and PFNA (6.0 and 3.1 respectively). [ 17 ] A TMF greater than one signifies that the concentration of a chemical in organisms increases at successive trophic levels, thereby demonstrating biomagnification.
PFOS, a long-chain sulfonic acid, was found at the highest concentrations relative to other PFASs measured in fish and birds in northern seas such as the Barents Sea and the Canadian Arctic. [ 89 ]
A study published in 2023 analyzing 500 composite samples of fish fillets collected across the United States from 2013 to 2015 under the EPA's monitoring programs showed freshwater fish ubiquitously contain high levels of harmful PFAS, with a single serving typically significantly increasing the blood PFOS level. [ 90 ] [ 91 ]
Bioaccumulation and biomagnification of PFASs in marine species throughout the food web, particularly frequently consumed fish and shellfish, can have important impacts on human populations. [ 92 ] PFASs have been frequently documented in both fish and shellfish that are commonly consumed by human populations, [ 93 ] which poses health risks to humans and studies on the bioaccumulation in certain species are important to determine daily tolerable limits for human consumption, and where those limits may be exceeded causing potential health risks. [ 94 ] This has particular implications for populations that consume larger numbers of wild fish and shellfish species. [ 93 ] PFAS contamination has also resulted in disruptions to the food supply, such as closures and limits on fishing. [ 95 ]
Fluorosurfactants with shorter carbon chains may be less prone to accumulating in mammals; [ 50 ] there is still some concern that they may be harmful to both humans [ 96 ] [ 97 ] [ 98 ] and the environment. [ 99 ] [ 20 ]
Since the 1970s, DuPont and 3M were aware that PFAS was "highly toxic when inhaled and moderately toxic when ingested". [ 36 ] Producers used several strategies to influence science and regulation – most notably, suppressing unfavorable research and distorting public discourse. [ 36 ]
In 2018, under the Presidency of Donald Trump , White House staff and the EPA pressured the U.S. Agency for Toxic Substances and Disease Registry to suppress a study that showed PFASs to be even more dangerous than previously thought. [ 100 ] [ 101 ]
In 2024, research at McGill University in Quebec, [ 102 ] indicated that PFASs were being brought to the Arctic from polluted southern waters by migrating birds. [ 103 ] Although it is much less than compared to the introduction by wind and the oceans, the birds become vectors, transmitting the toxic chemicals. Rainer Lohmann, an oceanographer at the University of Rhode Island , noted that this has a significant localized affect that is devastating for Arctic predators who accumulate toxins in their bodies because the contaminants from the birds often enter the food chain directly since the birds are the prey of many species.
In 2017, the ABC 's current affairs program Four Corners reported that the storage and use of firefighting foams containing perfluorinated surfactants at Australian Defence Force facilities around Australia had contaminated nearby water resources. [ 104 ] In 2019, remediation efforts at RAAF Base Tindal and the adjacent town of Katherine were ongoing. [ 105 ] In the 2022 Australian federal budget $428 million was allocated for works at HMAS Albatross , RAAF Base Amberley , RAAF Base Pearce and RAAF Base Richmond including funding to remediate PFAS contamination. [ 106 ]
Although PFASs are not manufactured in Canada, they may be present in imported goods and products. In 2008, products containing PFOS as well as PFOA were banned in Canada, with exceptions for products used in firefighting, the military, and some forms of ink and photo media. [ 107 ]
Health Canada has published drinking water guidelines for maximum concentrations of PFOS and PFOA to protect the health of Canadians, including children, over a lifetime's exposure to these substances. The maximum allowable concentration for PFOS under the guidelines is 0.0002 milligrams per liter. The maximum allowable concentration for PFOA is 0.0006 milligrams per liter. [ 108 ] In August 2024, Health Canada established an objective of 30 ng/L for the sum of the concentration of 25 PFASs [ 109 ] detected in drinking water. [ 110 ]
The Environmental Protection Authority (New Zealand) has banned the use of PFAS in cosmetic products starting from 31 December 2026. This will make the country one of the first in the world to take this step on PFAS to protect people and the environment. [ 111 ]
The environmental consequences of PFAS, especially from firefighting activities, have been recognized since the mid-1990s and came to prominence after the Buncefield explosion on 11 December 2005. The Environment Agency has undertaken a series of projects to understand the scale and nature of PFAS in the environment. The Drinking Water Inspectorate requires water companies to report concentrations of 47 PFAS. [ 112 ]
Many PFASs are either not covered by European legislation or are excluded from registration obligations under the EU Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) chemical regulation. [ 113 ] Several PFASs have been detected in drinking water, [ 114 ] municipal wastewater, [ 115 ] and landfill leachates [ 116 ] worldwide.
In 2019, the European Council requested the European Commission to develop an action plan to eliminate all non-essential uses of PFAS due to the growing evidence of adverse effects caused by exposure to these substances; the evidence for the widespread occurrence of PFAS in water, soil, articles, and waste; and the threat it can pose to drinking water. [ 117 ] Germany, the Netherlands, Denmark, Norway, and Sweden submitted a so-called restriction proposal based on the REACH regulation to achieve a European ban on the production, use, sale and import of PFAS. [ 118 ] The proposal states that a ban is necessary for all use of PFAS, with different periods for different applications when the ban takes effect (immediately after the restriction comes into force, five years afterward, or 12 years afterward), depending on the function and the availability of alternatives. The proposal has not assessed the use of PFAS in medicines, plant protection products, and biocides because specific regulations apply to those substances (Biocidal Products Regulation, Plant Protection Products Regulation , Medicinal Products Regulation) that have an explicit authorization procedure that focuses on risk for health and the environment.
The proposal was submitted on 13 January 2023 and published by the European Chemicals Agency (ECHA) on 7 February. From 22 March to 21 September, citizens, companies, and other organizations commented on the proposal during a public consultation. [ 119 ] Based on the information in the restriction proposal and the consultation, two committees from ECHA formulate an opinion on the risk and socio-economic aspects of the proposed restriction. Within a year of publication, the opinions are sent to the European Commission, which makes a final proposal that is submitted to the EU Member States for discussion and decision. [ 120 ] Eighteen months after the publication of the restriction decision (which may differ from the original proposal), it will enter into force. [ 119 ]
127,000 residents in the Veneto region are estimated to have been exposed to contamination through tap water, and it is thought to be Europe's biggest PFAS-related environmental disaster. [ 21 ] [ 121 ] While Italy's National Health Institute (ISS, Istituto Superiore di Sanità ) set the threshold limit of PFOA in the bloodstream at 8 nanograms per milliliter (ng/mL), some residents had reached 262 and some industrial employees reach 91,900 ng/mL. In 2021 some data was disclosed by Greenpeace and local citizens after a long legal battle against the Veneto Region and ISS, which for years has denied access to data, despite values known since or even before 2017. The Veneto region has not carried out further monitoring or taken resolutive actions to eliminate pollution and reduce, at least gradually, the contamination of non-potable water. Although in 2020 the European Food Safety Agency (EFSA) has reduced by more than four times the maximum tolerable limit of PFAS that can be taken through the diet, the region has not carried out new assessments or implemented concrete actions to protect the population and the agri-food and livestock sectors. Some limits were added to monitoring the geographical area, which does not include the orange zone and other areas affected by contamination, as well as the insufficiency of analysis on important productions widespread in the areas concerned: eggs (up to 37,100 ng/kg), fish (18,600 ng/kg) spinach and radicchio (only one sampling carried out), kiwis, melons, watermelons, cereals (only one sample was analyzed), soy, wines and apples. [ 122 ]
A study of public water bodies ending in March 2022 showed that the sum of PFOS and PFOA concentrations exceeded 50 ng/L in 81 out of 1,133 test sites and in some cases are present at elevated levels in blood. This has led to pressure to increase regulations. [ 123 ]
Highly contaminated drinking water has been detected at several locations in Sweden. Such locations include Arvidsjaur, Lulnäset, Uppsala and Visby. [ 124 ] [ 125 ] In 2013, PFAS were detected at high concentrations in one of the two municipality drinking water treatment plants in the town of Ronneby, in southern Sweden. Concentrations of PFHxS and PFOS were found at 1700 ng/L and 8000 ng/L, respectively. [ 126 ] The source of contamination was later found to be a military fire-fighting exercise site in which PFAS containing fire-fighting foam had been used since the mid-1980s. [ 127 ]
Additionally, low-level contaminated drinking water has also been shown to be a significant exposure source of PFOA , PFNA , PFHxS and PFOS for Swedish adolescents (ages 10–21). Even though the median concentrations in the municipality drinking water were below one ng/L for each individual PFAS, positive associations were found between adolescent serum PFAS concentrations and PFAS concentrations in drinking water. [ 128 ]
An estimated 26,000 U.S. sites are contaminated with PFASs. [ 129 ] [ 130 ] More than 200 million Americans are estimated to live in places where the PFAS level in tap water, including PFOA and PFOS levels, exceeds the 1 ppt (part per trillion) limit set in 2022 by the EPA. [ 131 ]
Based on tap water studies from 716 locations from 2016 and 2021, the U.S. Geological Survey (USGS) found that the PFAS levels exceeded the EPA advisories in approximately 75% of the samples from urban areas and in approximately 25% of the rural area samples. [ 132 ]
Certain PFASs are no longer manufactured in the United States as a result of phase-outs including the PFOA Stewardship Program (2010–2015), in which eight major chemical manufacturers agreed to eliminate the use of PFOA and PFOA-related chemicals in their products and emissions from their facilities. However, they are still produced internationally and are imported into the U.S. in consumer goods. [ 133 ] [ 134 ] Some types of PFAS are voluntarily not included in food packaging . [ 135 ]
In 2021, Senators Susan Collins of Maine and Richard Blumenthal of Connecticut proposed the No PFAS in Cosmetics Act in the United States Senate . [ 136 ] It was also introduced in the United States House of Representatives by Michigan Representative Debbie Dingell , [ 137 ] but the Republican Party , supported by the U.S. chemical industry filibustered the bill. [ 24 ]
In February 2025, Minnesota became the first state to ban the sale of cookware containing PFAS. [ 138 ]
The water in and around at least 126 U.S. military bases has been contaminated by high levels of PFASs because of their use of firefighting foams since the 1970s, according to a study by the U.S. Department of Defense . Of these, 90 bases reported PFAS contamination that had spread to drinking water or groundwater off the base. [ 139 ]
In 2022, a report by the Pentagon acknowledged that approximately 175,000 U.S. military personnel at two dozen American military facilities drank water contaminated by PFAS that exceeded the U.S. EPA limit. However, according to the Environmental Working Group , the Pentagon report downplayed the number of people exposed to PFAS, which was probably over 640,000 at 116 military facilities. The EWG found that the Pentagon also omitted from its report some types of diseases that are likely to be caused by PFAS exposure, such as testicular cancer , kidney disease, and fetal abnormalities. [ 140 ]
The EPA has published non-enforceable drinking water health advisories for PFOA and PFOS. [ 141 ] [ 142 ] In March 2021 EPA announced that it would develop national drinking water standards for PFOA and PFOS. [ 143 ] Drinking water utilities are required to monitor PFAS levels and may receive subsidies to do so. [ 144 ] [ 145 ] There are also regulations regarding wastewater ( effluent guidelines ) for industries that use PFASs in the manufacturing process as well as biosolids (processed wastewater sludge used as fertilizer). [ 146 ] [ 147 ] [ 148 ] [ 149 ] [ 150 ]
The EPA issued health advisories for four specific PFASs in June 2022, significantly lowering their safe threshold levels for drinking water. PFOA was reduced from 70 ppt to 0.004 ppt, while PFOS was reduced from 70 ppt to 0.02 ppt. A safe level for the compound GenX was set at 10 ppt, while that for PFBS was set at 2000 ppt. While not enforceable, these health advisories are intended to be acted on by states in setting their own drinking water standards. [ 151 ]
In August 2022, the EPA proposed to add PFOA and PFOS to its list of hazardous substances under the Superfund law. [ 152 ] EPA issued a final rule in April 2024, which requires that polluters pay for investigations and cleanup of these substances. [ 153 ] [ 154 ]
In April 2024, the EPA issued a final drinking water rule for PFOA, PFOS, GenX , PFBS, PFNA, and PFHxS. Within three years, public water systems must remove these six PFAS to near-zero levels. States may be awarded grants up to $1 billion in aid to help with the initial testing and treatment of water for this purpose. [ 155 ] [ 156 ] [ 157 ] [ 158 ] [ 159 ]
In February 2017, DuPont and Chemours (a DuPont spin-off ) agreed to pay $671 million to settle lawsuits arising from 3,550 personal injury claims related to the releasing of PFASs from their Parkersburg, West Virginia , plant into the drinking water of several thousand residents. [ 160 ] This was after a court-created independent scientific panel—the C8 Science Panel—found a "probable link" between C8 exposure and six illnesses: kidney and testicular cancer, ulcerative colitis, thyroid disease, pregnancy-induced hypertension and high cholesterol. [ 66 ]
In October 2018, a class action suit was filed by an Ohio firefighter against several producers of fluorosurfactants, including 3M and DuPont, on behalf of all U.S. residents who may have adverse health effects from exposure to PFASs. [ 161 ] The story is told in the film Dark Waters . [ 162 ]
In June 2023, 3M reached a US$10.3 billion settlement with several US public water providers to resolve water pollution claims tied to PFAS, while Chemours , DuPont and Corteva settled similar claims for $1.19 billion. [ 35 ]
In December 2023, as part of a four-year legal battle, the EPA banned Inhance, a Houston, Texas-based manufacturer that produces an estimated 200 million containers annually with a process that creates PFOA, from using the manufacturing process. [ 163 ] [ 164 ] In March 2024, the United States Court of Appeals for the Fifth Circuit overturned the ban. While the court did not deny the containers’ health risks, it said that the EPA could not regulate the manufactured containers under Toxic Substances Control Act of 1976 , which only addresses "new" chemicals. [ 165 ]
In 2021, Maine became the first U.S. state to ban these compounds in all products by 2030, except for instances deemed "currently unavoidable". [ 166 ] [ 167 ]
As of October 2020 [update] , the states of California, Connecticut, Massachusetts, Michigan, Minnesota, New Hampshire, New Jersey, New York, Vermont, and Wisconsin had enforceable drinking water standards for between two and six types of PFAS. The six chemicals (termed by the Massachusetts Department of Environmental Protection as PFAS6) are measured either individually or summed as a group depending on the standard; they are: [ 168 ]
In 2021 California banned PFASs for use in food packaging and from infant and children's products and also required PFAS cookware in the state to carry a warning label. [ 169 ]
A program licensed and promoted by the Maine Department of Environmental Protection that provided free municipal wastewater sludge ( biosolids ) to farmers as fertilizer has resulted in PFAS contamination of local drinking water and farm-grown produce. [ 170 ] [ 171 ]
The Michigan PFAS Action Response Team (MPART) was launched in 2017 and is the first multi-agency action team of its kind in the nation. Agencies representing health, environment, and other branches of state government have joined together to investigate sources and locations of PFAS contamination in the state, take action to protect people's drinking water, and keep the public informed. Groundwater is tested at locations throughout the state by various parties to ensure safety, compliance with regulations, and proactively detect and remedy potential problems. In 2010, the Michigan Department of Environmental Quality (MDEQ) discovered levels of PFASs in groundwater monitoring wells at the former Wurtsmith Air Force Base . [ 172 ] In 2024, citizen-led testing near the base in Oscoda discovered high levels of PFAS in foam along the shore of Lake Huron . [ 173 ] As additional information became available from other national testing, Michigan expanded its investigations into other locations where PFAS compounds were potentially used. In 2018, the MDEQ's Remediation and Redevelopment Division (RRD) established cleanup criteria for groundwater used as drinking water of 70 ppt of PFOA and PFOS, individually or combined. The RRD staff are responsible for implementing these criteria as part of their ongoing efforts to clean up sites of environmental contamination. The RRD staff are the lead investigators at most of the PFAS sites on the MPART website and also conduct interim response activities, such as coordinating bottled water or filter installations with local health departments at sites under investigation or with known PFAS concerns. Most of the groundwater sampling at PFAS sites under RRD's lead is conducted by contractors familiar with PFAS sampling techniques. The RRD also has a Geologic Services Unit, with staff who install monitoring wells and are also well versed with PFAS sampling techniques. The MDEQ has been conducting environmental clean-up of regulated contaminants for decades. Due to the evolving nature of PFAS regulations as new science becomes available, the RRD is evaluating the need for regular PFAS sampling at Superfund sites and is including an evaluation of PFAS sampling needs as part of a Baseline Environmental Assessment review. Earlier in 2018, the RRD purchased lab equipment that will allow the MDEQ Environmental Lab to conduct analyses of certain PFAS samples. (Currently, most samples are shipped to one of the few labs in the country that conduct PFAS analysis, in California, although private labs in other parts of the country, including Michigan, are starting to offer these services.) As of August 2018, RRD has hired additional staff to work on developing the methodology and conducting PFAS analyses. [ 174 ]
In 2020 Michigan Attorney General Dana Nessel filed a lawsuit against 17 companies, including 3M, Chemours, and DuPont, for hiding known health and environmental risks from the state and its residents. Nessel's complaint identifies 37 sites with known contamination. [ 175 ] The Michigan Department of Environment, Great Lakes, and Energy introduced some of the strictest drinking water standards in the country for PFAS, setting maximum contaminant levels (MCLs) for PFOA and PFOS to 8 and 16 ppt respectively (down from previous existing groundwater cleanup standards of 70 ppt for both), and introducing MCLs for five other previously unregulated PFAS compounds, limiting PFNA to six ppt, PFHxA to 400,000 ppt, PFHxS to 51 ppt, PFBS to 420 ppt and HFPO-DA to 370 ppt. [ 176 ] The change adds 38 additional sites to the state's list of known PFAS contaminated areas, bringing the total number of known sites to 137. About half of these sites are landfills and 13 are former plating facilities . [ 177 ]
In 2022 PFOS was found in beef produced at a Michigan farm: the cattle had been fed crops fertilized with contaminated biosolids. State agencies issued a consumption advisory, but did not order a recall, because there currently is no PFOS contamination in beef government standards. [ 178 ]
A 2024 study found that "atmospheric deposition could be a significant environmental pathway, particularly for the Great Lakes." [ 179 ] [ 180 ]
In February 2018, 3M settled a lawsuit for $850 million related to contaminated drinking water in Minnesota. [ 181 ]
In January 2024, Minnesota banned PFAS in food packaging. [ 182 ] [ 183 ]
In January 2025, Minnesota became the first state to ban 11 categories of products that PFAS, including carpets or rugs, cleaning products, cookware, cosmetics, dental floss, fabric treatments, juvenile products, menstruation products, textile furnishings, ski wax, and upholstered furniture. [ 182 ] [ 184 ] [ 183 ]
In 2018 the New Jersey Department of Environmental Protection (NJDEP) published a drinking water standard for PFNA. Public water systems in New Jersey are required to meet an MCL standard of 13 ppt. [ 185 ] [ 186 ] In 2020 the state set a PFOA standard at 14 ppt and a PFOS standard at 13 ppt. [ 187 ]
In 2019 NJDEP filed lawsuits against the owners of two plants that had manufactured PFASs, and two plants that were cited for water pollution from other chemicals. The companies cited are DuPont, Chemours , and 3M. [ 188 ] NJDEP also declared five companies to be financially responsible for statewide remediation of the chemicals. Among the companies accused were Arkema and Solvay regarding a West Deptford Facility in Gloucester County , where Arkema manufactured PFASs, but Solvay claims to have never manufactured but only handled PFASs. [ 189 ] The companies denied liability and contested the directive. [ 190 ] In June 2020, the EPA and NJDEO published a paper reporting that a unique family of PFAS used by Solvay, chloroperfluoropolyether carboxylates (ClPFPECAs), were contaminating the soils of New Jersey as far from the Solvay facility as 150 km. [ 191 ] and the ClPFPECAs were found in water as well. [ 192 ]
Later in 2020, the New Jersey state attorney general filed suit in the New Jersey Superior Court against Solvay regarding PFAS contamination of the state's environment. [ 193 ] In May 2021, Solvay issued a press release that the company is "discontinuing the use of fluorosurfactants in the U.S.". [ 194 ]
In 2016, New York, along with Vermont and New Hampshire, acknowledged PFOA contamination by requesting the EPA to release water quality guidance measures. Contamination has been observed by the New York State Department of Environmental Conservation in Hoosick Falls, Newburgh, Petersburgh, Poestenkill, Mahopac, and Armonk. [ 195 ]
After a class action lawsuit, in 2021, the village of Hoosick Falls received a $65.25 million settlement from Saint-Gobain Performance Plastics, Honeywell, 3M, and DuPont due to the disposal of PFAS chemicals into the groundwater of the local water treatment plant. [ 196 ]
Five military installations in Washington State have been identified by EPA and the United States Senate Committee on Environment and Public Works as having PFAS contamination. [ 197 ] Toward environmental and consumer protections, the Washington State Department of Ecology published a Chemical Action Plan in November 2021, and in June 2022 the governor tasked the Washington State Department of Ecology with phasing out manufacture and import of products containing PFASs . Initial steps taken by the Washington State Department of Health to protect the public from exposure through drinking water have included setting State Action Levels for five PFASs (PFOA, PFOS, PFNA, PFHxS, and PFBS), which were implemented in November 2021. [ 198 ] [ 199 ] [ 200 ]
In 2009, PFOS, its salts, and perfluorooctanesulfonyl fluoride , as well as PFOA and PFHxS, including their salts and precursors, were listed as persistent organic pollutants under the Stockholm Convention on Persistent Organic Pollutants due to their ubiquitous, persistent, bioaccumulative, and toxic nature. [ 201 ] [ 202 ] The convention has been ratified by 186 jurisdictions, but has most notably not been ratified by the United States, Israel, and Malaysia. [ 203 ] The long-chain (C 9 –C 21 ) PFCAs are currently under review for listing. [ 204 ]
Occupational exposure to PFASs occurs in numerous industries due to the widespread use of the chemicals in products and as an element of industrial process streams. [ 73 ] PFASs are used in more than 200 different ways in industries as diverse as electronics and equipment manufacturing, plastic and rubber production, food and textile production, and building and construction. [ 205 ] Occupational exposure to PFASs can occur at fluorochemical facilities that produce them and other manufacturing facilities that use them for industrial processing like the chrome plating industry. [ 73 ] Workers who handle PFAS-containing products can also be exposed during their work, such as people who install PFAS-containing carpets and leather furniture with PFAS coatings, professional ski-waxers using PFAS-based waxes, and fire-fighters using PFAS-containing foam and wearing flame-resistant protective gear made with PFASs. [ 73 ] [ 206 ] [ 207 ]
People who are exposed to PFASs through their jobs typically have higher levels of PFASs in their blood than the general population. [ 73 ] [ 208 ] [ 209 ] While the general population is exposed to PFASs through ingested food and water, occupational exposure includes accidental ingestion, inhalation exposure, and skin contact in settings where PFAS become volatile. [ 210 ] [ 13 ]
Compared to the general public exposed to contaminated drinking water, professional ski wax technicians are more strongly exposed to PFASs (PFOA, PFNA, PFDA, PFHpA, PFDoDA) from the glide wax used to coat the bottom of skis to reduce the friction between the skis and snow. [ 211 ] During the coating process, the wax is heated, which releases fumes and airborne particles. [ 211 ] Compared to all other reported occupational and residential exposures, ski waxing had the highest total PFAS air concentrations. [ 212 ]
People who work at fluorochemical production plants and in manufacturing industries that use PFASs in the industrial process can be exposed to PFASs in the workplace. Much of what we know about PFAS exposure and health effects began with medical surveillance studies of workers exposed to PFASs at fluorochemical production facilities. These studies began in the 1940s and were conducted primarily at U.S. and European manufacturing sites. Between the 1940s and 2000s, thousands of workers exposed to PFASs participated in research studies that advanced scientific understanding of exposure pathways, toxicokinetic properties, and adverse health effects associated with exposure. [ 53 ] [ 213 ] [ 214 ]
The first research study to report elevated organic fluorine levels in the blood of fluorochemical workers was published in 1980. [ 53 ] It established inhalation as a potential route of occupational PFAS exposure by reporting measurable levels of organic fluorine in air samples at the facility. [ 53 ] Workers at fluorochemical production facilities have higher levels of PFOA and PFOS in their blood than the general population. Serum PFOA levels in fluorochemical workers are generally below 20,000 ng/mL but have been reported as high as 100,000 ng/mL, whereas the mean PFOA concentration among non-occupationally exposed cohorts in the same time frame was 4.9 ng/mL. [ 215 ] [ 54 ] Among fluorochemical workers, those with direct contact with PFASs have higher PFAS concentrations in their blood than those with intermittent contact or no direct PFAS contact. [ 213 ] [ 215 ] Blood PFAS levels have been shown to decline when direct contact ceases. [ 215 ] [ 216 ] PFOA and PFOS levels have declined in U.S. and European fluorochemical workers due to improved facilities, increased usage of personal protective equipment , and the discontinuation of these chemicals from production. [ 213 ] [ 217 ] Occupational exposure to PFASs in manufacturing continues to be an active area of study in China with numerous investigations linking worker exposure to various PFASs. [ 218 ] [ 219 ] [ 220 ]
PFASs are commonly used in Class B firefighting foams due to their hydrophobic and lipophobic properties, as well as the stability of the chemicals when exposed to high heat. [ 221 ]
Research into occupational exposure for firefighters is emergent, though frequently limited by underpowered study designs. A 2011 cross-sectional analysis of the C8 Health Studies found higher levels of PFHxS in firefighters compared to the sample group of the region, with other PFASs at elevated levels, without reaching statistical significance. [ 222 ] A 2014 study in Finland studying eight firefighters over three training sessions observed select PFASs (PFHxS and PFNA) increase in blood samples following each training event. [ 221 ] Due to this small sample size, a test of significance was not conducted. A 2015 cross-sectional study conducted in Australia found that PFOS and PFHxS accumulation was positively associated with years of occupational AFFF exposure through firefighting. [ 208 ]
Due to their use in training and testing, studies indicate occupational risk for military members and firefighters, as higher levels of PFASs exposure were indicated in military members and firefighters when compared to the general population. [ 223 ] PFAS exposure is prevalent among firefighters not only due to its use in emergencies but also because it is used in personal protective equipment . In support of these findings, states like Washington and Colorado have moved to restrict and penalize the use of Class B firefighting foam for firefighter training and testing. [ 224 ] [ 225 ]
The September 11 attacks and resulting fires caused the release of toxic chemicals used in materials such as stain-resistant coatings. [ 226 ] First responders to this incident were exposed to PFOA, PFNA, and PFHxS through inhalation of dust and smoke released during and after the collapse of the World Trade Center. [ 226 ]
Fire responders who were working at or near ground zero were assessed for respiratory and other health effects from exposure to emissions at the World Trade Center. Early clinical testing showed a high prevalence of respiratory health effects. Early symptoms of exposure often presented with persistent coughing and wheezing. PFOA and PFHxS levels were present in both smoke and dust exposure, but first responders exposed to smoke had higher concentrations of PFOA and PFHxS than those exposed to dust. [ 226 ]
Several strategies have been proposed as a way to protect those who are at greatest risk of occupational exposure to PFAS, including exposure monitoring, regular blood testing, and the use of PFAS-free alternatives such as fluorine-free firefighting foam and plant-based ski wax. [ 227 ]
PFASs were found in many plant-based straws, such as paper straws. [ 228 ] [ 229 ]
Several technologies are currently available for remediating PFASs in liquids. These technologies can be applied to drinking water supplies, groundwater, industrial wastewater, surface water, and other applications such as landfill leachate . Influent concentrations of PFASs can vary by orders of magnitude for specific media or applications. These influent values, along with other general water quality parameters (for example, pH) can influence the performance and operating costs of the treatment technologies. The technologies are:
Private and public sector applications of one or more of these methodologies above are being applied to remediation sites throughout the United States and other international locations. [ 235 ] Most solutions involve on-site treatment systems, while others are leveraging off-site infrastructure and facilities, such as a centralized waste treatment facility, to treat and dispose of the PFAS pool of compounds.
The US-based Interstate Technology and Regulatory Council (ITRC) has undertaken an extensive evaluation of ex-situ and in-situ treatment technologies for PFAS-impacted liquid matrices. These technologies are divided into field-implemented technologies, limited application technologies, and developing technologies and typically fit into one of three technology types: [ 233 ]
The type of PFAS remediation technology selected is often a reflection of the PFAS contamination levels and the PFAS signature (i.e. the combination of short- and long-chain PFAS substances present) in conjunction with the site-specific water chemistry and cross contaminants present in the liquid stream. More complex waters such as landfill leachates and WWTP waters require more robust treatment solutions which are less vulnerable to blockage.
Foam Fractionation utilizes the air/water interface of a rising air bubble to collect and harvest PFAS molecules. The hydrophobic tail of many long-chain criteria PFAS compounds adhere to this interface and rise to the water surface with the air bubble where they present as a foam for harvesting and further concentration. The foam fractionation technique is a derivation of traditional absorptive bubble separation techniques used by industries for decades to extract amphiphilic contaminants. The absence of a solid absorptive surface reduces consumables and waste byproducts and produces a liquid hyper-concentrate which can be fed into one of the various PFAS destruction technologies. Across various full-scale trials and field applications, this technique provides a simplistic and low operational cost alternative for complex PFAS-impacted waters. [ 236 ]
In 2007, it was found that high-temperature incineration of sewage sludge reduced the levels of perfluorinated compounds significantly. [ 237 ]
A 2022 study published in the Journal of Environmental Engineering found that a heat- and pressure-based technique known as supercritical water oxidation destroyed 99% of the PFAS present in a water sample. During this process, oxidizing substances are added to PFAS-contaminated water and then the liquid is heated above its critical temperature of 374 degrees Celsius at a pressure of more than 220 bars . The water becomes supercritical , and, in this state, water-repellent substances such as PFASs dissolve much more readily. [ 234 ]
A possible solution for PFAS-contaminated wastewater treatment has been developed by the Michigan State University - Fraunhofer team. Boron-doped diamond electrodes are used for the electrochemical oxidation system where it is capable of breaking PFAS molecular bonds which essentially eliminates the contaminates, leaving fresh water. [ 238 ]
Acidimicrobium sp. strain A6 has been shown to be a PFAS and PFOS remediator. [ 239 ] PFAS with unsaturated bonds are easier to break down: the commercial dechlorination culture KB1 (contains Dehalococcoides ) is capable of breaking down such substances, but not saturated PFAS. When alternative, easier-to-digest substrates are present, microbes may prefer them over PFAS. [ 240 ]
Researchers at the University of Missouri demonstrated in small scale the degradation of PFAS chemicals can be done using readily available Activated Carbon at significantly lower temperatures that previously needed, 300C as opposed to 700C. [ 241 ]
A study published in Science in August 2022 indicated that perfluoroalkyl carboxylic acids (PFCAs) can be mineralized via heating in a polar aprotic solvent such as dimethyl sulfoxide . Heating PFCAs in an 8 to 1 mixture of dimethyl sulfoxide and water at 80–120 °C (176–248 °F) in the presence of sodium hydroxide caused the removal of the carboxylic acid group at the end of the carbon chain, creating a perfluoroanion that mineralizes into sodium fluoride and other salts such as sodium trifluoroacetate , formate , carbonate , oxalate , and glycolate . The process does not work on perfluorosulfonic acids such as PFOS. [ 242 ] A 2022 study published in Chemical Science shows breakdown of C-F bonds and their mineralization as YF 3 or YF 6 clusters. [ 243 ] Another study in the Journal of the American Chemical Society described the PFASs breakdown using metal-organic frameworks (MOFs). [ 244 ]
Analytical methods for PFAS analysis fall into one of two general categories; targeted analysis or non-targeted analysis. Targeted analyses use reference standards to determine concentrations of specific PFAS, but this requires a high-purity standard for each compound of interest. Due to the large number of possible targets, unusual PFAS may go unreported by these methods. Non-targeted analyses measure other factors, such as total organic fluorine, which can be used to estimate the total concentration of PFAS in a sample, but cannot provide concentrations of individual compounds. The two types of analyses are often combined; by subtracting the mass of target analytes from the non-targeted analysis results, one can get an estimate for what fraction of PFAS has been "missed" by the targeted analysis.
Targeted analysis generally use liquid chromatography–mass spectrometry (LC-MS) instruments. Currently, EPA Method 537.1 is approved for use in drinking water and includes 18 PFAS. [ 245 ] EPA Method 1633 is undergoing review for use in wastewater, surface water, groundwater, soil, biosolids, sediment, landfill leachate, and fish tissue for 40 PFAS, but is currently being used by many laboratories in the United States. [ 246 ] Regulatory limits for PFOA and PFOS set by the US EPA (4 parts-per-trillion) are limited by the capability of methods to detect low level concentrations. [ 247 ]
Non-targeted analyses include total organic fluorine (TOF, including variations, e.g., adsorbable organic fluorine, AOF; extractable organic fluorine, EOF), total oxidizable precursor assay , and other methods in development. [ 248 ] [ 249 ]
Some common per- and polyfluoroalkyl substances include: [ 250 ] [ 251 ]
PFAS have been a subject of multiple lawsuits worldwide. [ 252 ] [ 253 ] [ 254 ] In the United States, settlements stemming from PFAS pollution claims have reached $18 billion by 2024. [ 255 ] In 2023, Sweden's Supreme Court set a legal precedent by awarding damages to citizens who were supplied PFAS contaminated drinking water. [ 256 ] | https://en.wikipedia.org/wiki/Per-_and_polyfluoroalkyl_substances |
In the power systems analysis field of electrical engineering , a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per-unit do not change when they are referred from one side of a transformer to the other. This can be a pronounced advantage in power system analysis where large numbers of transformers may be encountered. Moreover, similar types of apparatus will have the impedances lying within a narrow numerical range when expressed as a per-unit fraction of the equipment rating, even if the unit size varies widely. Conversion of per-unit quantities to volts, ohms, or amperes requires a knowledge of the base that the per-unit quantities were referenced to. The per-unit system is used in power flow , short circuit evaluation, motor starting studies etc.
The main idea of a per unit system is to absorb large differences in absolute values into base relationships. Thus, representations of elements in the system with per unit values become more uniform.
A per-unit system provides units for power , voltage , current , impedance , and admittance . With the exception of impedance and admittance, any two units are independent and can be selected as base values; power and voltage are typically chosen. All quantities are specified as multiples of selected base values. For example, the base power might be the rated power of a transformer , or perhaps an arbitrarily selected power which makes power quantities in the system more convenient. The base voltage might be the nominal voltage of a bus . Different types of quantities are labeled with the same symbol ( pu ); it should be clear whether the quantity is a voltage, current, or other unit of measurement.
There are several reasons for using a per-unit system:
The per-unit system was developed to make manual analysis of power systems easier. Although power-system analysis is now done by computer, results are often expressed as per-unit values on a convenient system-wide base.
Generally base values of power and voltage are chosen. The base power may be the rating of a single piece of apparatus such as a motor or generator. If a system is being studied, the base power is usually chosen as a convenient round number such as 10 MVA or 100 MVA. The base voltage is chosen as the nominal rated voltage of the system. All other base quantities are derived from these two base quantities. Once the base power and the base voltage are chosen, the base current and the base impedance are determined by the natural laws of electrical circuits. The base value should only be a magnitude, while the per-unit value is a phasor. The phase angles of complex power, voltage, current, impedance, etc., are not affected by the conversion to per unit values.
The purpose of using a per-unit system is to simplify conversion between different transformers. Hence, it is appropriate to illustrate the steps for finding per-unit values for voltage and impedance. First, let the base power ( S base ) of each end of a transformer become the same. Once every S is set on the same base, the base voltage and base impedance for every transformer can easily be obtained. Then, the real numbers of impedances and voltages can be substituted into the per-unit calculation definition to get the answers for the per-unit system. If the per-unit values are known, the real values can be obtained by multiplying by the base values.
By convention, the following two rules are adopted for base quantities:
With these two rules, a per-unit impedance remains unchanged when referred from one side of a transformer to the other. This allows the ideal transformer to be eliminated from a transformer model.
The relationship between units in a per-unit system depends on whether the system is single-phase or three-phase .
Assuming that the independent base values are power and voltage, we have:
Alternatively, the base value for power may be given in terms of reactive or apparent power , in which case we have, respectively,
or
The rest of the units can be derived from power and voltage using the equations S = I V {\displaystyle S=IV} , P = S cos ( ϕ ) {\displaystyle P=S\cos(\phi )} , Q = S sin ( ϕ ) {\displaystyle Q=S\sin(\phi )} and V _ = I _ Z _ {\displaystyle {\underline {V}}={\underline {I}}{\underline {Z}}} ( Ohm's law ), Z {\displaystyle Z} being represented by Z _ = R + j X = Z cos ( ϕ ) + j Z sin ( ϕ ) {\displaystyle {\underline {Z}}=R+jX=Z\cos(\phi )+jZ\sin(\phi )} . We have:
Power and voltage are specified in the same way as single-phase systems. However, due to differences in what these terms usually represent in three-phase systems, the relationships for the derived units are different. Specifically, power is given as total (not per-phase) power, and voltage is line-to-line voltage.
In three-phase systems the equations P = S cos ( ϕ ) {\displaystyle P=S\cos(\phi )} and Q = S sin ( ϕ ) {\displaystyle Q=S\sin(\phi )} also hold. The apparent power S {\displaystyle S} now equals S base = 3 V base I base {\displaystyle S_{\text{base}}={\sqrt {3}}V_{\text{base}}I_{\text{base}}}
As an example of how per-unit is used, consider a three-phase power transmission system that deals with powers of the order of 500 MW and uses a nominal voltage of 138 kV for transmission. We arbitrarily select S b a s e = 500 M V A {\displaystyle S_{\mathrm {base} }=500\,\mathrm {MVA} } , and use the nominal voltage 138 kV as the base voltage V b a s e {\displaystyle V_{\mathrm {base} }} . We then have:
If, for example, the actual voltage at one of the buses is measured to be 136 kV, we have:
The following tabulation of per-unit system formulas is adapted from Beeman's Industrial Power Systems Handbook .
It can be shown that voltages, currents, and impedances in a per-unit system will have the same values whether they are referred to primary or secondary of a transformer . [ 1 ] : 85
For instance, for voltage, we can prove that the per unit voltages of two sides of the transformer, side 1 and side 2, are the same. Here, the per-unit voltages of the two sides are E 1pu and E 2pu respectively.
(source: Alexandra von Meier Power System Lectures, UC Berkeley)
E 1 and E 2 are the voltages of sides 1 and 2 in volts. N 1 is the number of turns the coil on side 1 has. N 2 is the number of turns the coil on side 2 has. V base1 and V base2 are the base voltages on sides 1 and 2.
For current, we can prove that the per-unit currents of the two sides are the same below.
(source: Alexandra von Meier Power System Lectures, UC Berkeley)
where I 1,pu and I 2,pu are the per-unit currents of sides 1 and 2 respectively. In this, the base currents I base1 and I base2 are related in the opposite way that V base1 and V base2 are related, in that
The reason for this relation is for power conservation
The full load copper loss of a transformer in per-unit form is equal to the per-unit value of its resistance:
P cu,FL = full-load copper loss = I R 1 2 R e q 1 {\displaystyle {\begin{aligned}P_{\text{cu,FL}}&={\text{full-load copper loss}}\\&=I_{R1}^{2}R_{eq1}\\\end{aligned}}}
P cu,FL,pu = P cu,FL P base = I R 1 2 R e q 1 V R 1 I R 1 = R eq1 V R 1 / I R 1 = R eq1 Z B 1 = R eq1,pu {\displaystyle {\begin{aligned}P_{\text{cu,FL,pu}}&={\frac {P_{\text{cu,FL}}}{P_{\text{base}}}}\\&={\frac {I_{R1}^{2}R_{eq1}}{V_{R1}I_{R1}}}\\&={\frac {R_{\text{eq1}}}{V_{R1}/I_{R1}}}\\&={\frac {R_{\text{eq1}}}{Z_{B1}}}\\&=R_{\text{eq1,pu}}\\\end{aligned}}}
Therefore, it may be more useful to express the resistance in per-unit form as it also represents the full-load copper loss. [ 1 ] : 86
As stated above, there are two degrees of freedom within the per unit system that allow the engineer to specify any per unit system. The degrees of freedom are the choice of the base voltage ( V base ) and the base power ( S base ). By convention, a single base power ( S base ) is chosen for both sides of the transformer and its value is equal to the rated power of the transformer. By convention, there are actually two different base voltages that are chosen, V base1 and V base2 which are equal to the rated voltages for either side of the transformer. By choosing the base quantities in this manner, the transformer can be effectively removed from the circuit as described above. For example:
Take a transformer that is rated at 10 kVA and 240/100 V. The secondary side has an impedance equal to 1∠0° Ω. The base impedance on the secondary side is equal to:
Z base,2 = V base,2 2 S base = ( 100 V ) 2 10000 VA = 1 Ω {\displaystyle {\begin{aligned}Z_{\text{base,2}}&={\frac {V_{\text{base,2}}^{2}}{S_{\text{base}}}}\\&={\frac {(100{\text{ V}})^{2}}{10000{\text{ VA}}}}\\&={\text{1 }}\Omega \\\end{aligned}}}
This means that the per unit impedance on the secondary side is 1∠0° Ω / 1 Ω = 1∠0° pu When this impedance is referred to the other side, the impedance becomes:
Z 2 = ( 240 100 ) 2 × 1∠0° Ω = 5.76∠0° Ω {\displaystyle {\begin{aligned}Z_{2}&=\left({\frac {240}{100}}\right)^{2}\times {\text{1∠0° }}\Omega \\&={\text{5.76∠0° }}\Omega \\\end{aligned}}}
The base impedance for the primary side is calculated the same way as the secondary:
Z base,1 = V base,1 2 S base = ( 240 V ) 2 10000 VA = 5.76 Ω {\displaystyle {\begin{aligned}Z_{\text{base,1}}&={\frac {V_{\text{base,1}}^{2}}{S_{\text{base}}}}\\&={\frac {(240{\text{ V}})^{2}}{10000{\text{ VA}}}}\\&={\text{5.76 }}\Omega \\\end{aligned}}}
This means that the per unit impedance is 5.76∠0° Ω / 5.76 Ω = 1∠0° pu, which is the same as when calculated from the other side of the transformer, as would be expected.
Another useful tool for analyzing transformers is to have the base change formula that allows the engineer to go from a base impedance with one set of a base voltage and base power to another base impedance for a different set of a base voltage and base power. This becomes especially useful in real life applications where a transformer with a secondary side voltage of 1.2 kV might be connected to the primary side of another transformer whose rated voltage is 1 kV. The formula is as shown below.
Z pu,new = Z pu,old × Z base,old Z base,new = Z pu,old × ( V base,old V base,new ) 2 × ( S base,new S base,old ) {\displaystyle {\begin{aligned}Z_{\text{pu,new}}&=Z_{\text{pu,old}}\times {\frac {Z_{\text{base,old}}}{Z_{\text{base,new}}}}=Z_{\text{pu,old}}\times \left({\frac {V_{\text{base,old}}}{V_{\text{base,new}}}}\right)^{2}\times \left({\frac {S_{\text{base,new}}}{S_{\text{base,old}}}}\right)\\\end{aligned}}} | https://en.wikipedia.org/wiki/Per-unit_system |
Per-user unitary rate control ( PU 2 RC ) is a multi-user MIMO (multiple-input and multiple-output) scheme. PU 2 RC uses both transmission pre-coding and multi-user scheduling. By doing that, the network capacity is further enhanced than the capacity of the single-user MIMO scheme.
Recently, PU 2 RC has been adopted in the IEEE 802.16m system description documentation (SDD) and the concept of this scheme was included in 3GPP LTE standard.
Per-user unitary rate control (PU 2 RC) is a practical multi-user MIMO solution. PU 2 RC allows a base station to transmit different data streams to multiple users simultaneously. The base station selects target users from candidate users based on the information fed by users. Transmission data are multiplied by a pre-coding matrix selected from the set of predefined matrices before transmission. The selection of a pre-coding matrix is determined based on the information provided by users. The selection of both target users and a pre-coding matrix according to the information provided by mobiles enables the utilization of multi-user diversity and data multiplexing at the same time. Moreover, using predefined precoding matrices reduces feedback overhead from users to the base station. Pre-coding matrices used in this scheme is unitary. The use of unitary pre-coding matrices facilitates the estimation of interference from other users' data to the unintended user.
The operation of PU 2 RC is mathematically described for the transmitter and receiver sides, respectively.
It is assumed that the base station employs N t {\displaystyle N_{t}} transmission antennas. The N t × 1 {\displaystyle N_{t}\times 1} transmission signal vector is given by
where w i {\displaystyle \mathbf {w} _{i}} is the N t × 1 {\displaystyle N_{t}\times 1} linear precoding vector. PU 2 RC generates w i {\displaystyle \mathbf {w} _{i}} based on the received finite channel status information, which is delivered to the base station from the user equipment (UE) through uplink feedback signaling. The feedback signal consists of index in a look-up table of a precoding codebook.
Every receiver has a receive antenna array with N r {\displaystyle N_{r}} elements. The receive signal vector at user k ( = 1 , 2 , … , K ) {\displaystyle k(=1,2,\ldots ,K)} is modeled as follows:
where y k {\displaystyle \mathbf {y} _{k}} and n k {\displaystyle \mathbf {n} _{k}} are the N r × 1 {\displaystyle N_{r}\times 1} received symbol and noise, respectively, and H k {\displaystyle \mathbf {H} _{k}} is the N r × N t {\displaystyle N_{r}\times N_{t}} matrix with the channel coefficients.
The figure illustrates the throughput advantage of PU 2 RC over the conventional single-user and no scheduling scheme, assuming that the codebook size is one, i.e., ( G = 1 ) {\displaystyle (G=1)} . For larger codebook sizes the performance can be better than the performance of the unit-size codebook. Because of codebook-based multi-user scheduling, PU 2 RC outperforms the conventional single-user and no scheduling scheme when the number of users is larger than one. Note that the performance plotted in the figure for the two systems were obtained assuming linear receiver. | https://en.wikipedia.org/wiki/Per-user_unitary_rate_control |
The phrase per meg indicates a fraction equal to 0.001 permil , or 0.0001 percent , or 1 part per million ( ppm ). It is typically used as a unit in isotope analysis , where multiplying an isotope ratio in delta annotation, for example δ 18 O , by 1000000 yields a value in per meg. [ 1 ] [ 2 ] This notation is most frequently used in studies of atmospheric trace gases, where a high precision is needed for interpretation of the results. [ 3 ]
This standards - or measurement -related article is a stub . You can help Wikipedia by expanding it .
This geochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Per_meg |
Perceived performance , in computer engineering , refers to how quickly a software feature appears to perform its task. The concept applies mainly to user acceptance aspects.
The amount of time an application takes to start up, or a file to download, is not made faster by showing a startup screen (see Splash screen ) or a file progress dialog box . However, it satisfies some human needs: it appears faster to the user as well as providing a visual cue to let them know the system is handling their request.
In most cases, increasing real performance increases perceived performance, but when real performance cannot be increased due to physical limitations, techniques can be used to increase perceived performance at the cost of marginally decreasing real performance. For example, drawing and refreshing a progress bar while loading a file satisfies the user who is watching, but steals time from the process that is actually loading the file, but usually this is only a very small amount of time. All such techniques must exploit the inability of the user to accurately judge real performance, or they would be considered detrimental to performance.
Techniques for improving perceived performance may include more than just decreasing the delay between the user's request and visual feedback. Sometimes an increase in delay can be perceived as a performance improvement, such as when a variable controlled by the user is set to a running average of the users input. This can give the impression of smoother motion, but the controlled variable always reaches the desired value a bit late. Since it smooths out hi-frequency jitter, when the user is attempting to hold the value constant, they may feel like they are succeeding more readily. This kind of compromise would be appropriate for control of a sniper rifle in a video game. Another example may be doing trivial computation ahead of time rather than after a user triggers an action, such as pre-sorting a large list of data before a user wants to see it.
A technique to measure and interpret perceived performance remote systems is shown in a 2003 [ 1 ] and updated in 2005 for virtual machines. [ 2 ]
For Web Performance optimization, perceived performance plays an important role. It tricks the user into thinking a site loads faster than it actually is. To achieve that, render-blocking resources will be loaded last in order to let the browser render the other elements first: like text content, images. In this way, even though the browser loads the same elements, by loading the non-blocking resources first, the user starts to see some content immediately. This trick improves the perceived performance, improving the overall user experience.
Here are the main perceived performance steps for better user experiences:
Minimize initial page load
Load only the resources you need in order to display the first content seen by the user. After these resources are loaded, the rest of the resources can be loaded.
Interactive elements should be available
Elements that are interactive, that the user can click on or interact with, should be able to perform those actions as soon as possible. Even with the rest of the page being still loaded, if the user can interact faster with the page, the user will perceive the site as being fast.
Avoid rendering elements that can cause flicker on screen
Elements like fonts or content that takes longer to load should be avoided as much as possible. When loading fonts, try to adjust their size and appearance closer to the default browser styles. In this way, when the font will be loaded, the switch won't look weird and be obvious. For images, charts, or embedded content, make sure you have a placeholder that has the same with and height. In this way when the content comes, the screen won't flicker and the height of the page won't change.
In order to improve the perceived performance of a web page, there are numerous tools that can be helpful:
Google Chrome : DevTools provides ways to measure the performance of a site giving you insights on how to improve.
Webpagetest - SpeedIndex represents the average time it takes for the visible part of a site to be displayed. | https://en.wikipedia.org/wiki/Perceived_performance |
In human visual perception , the visual angle , denoted θ , subtended by a viewed object sometimes looks larger or smaller than its actual value. One approach to this phenomenon posits a subjective correlate to the visual angle: the perceived visual angle or perceived angular size . An optical illusion where the physical and subjective angles differ is then called a visual angle illusion or angular size illusion .
Angular size illusions are most obvious as relative angular size illusions, in which two objects that subtend the same visual angle appear to have different angular sizes; it is as if their equal-sized images on the retina were of different sizes. Angular size illusions are contrasted with linear size illusions, in which two objects that are the same physical size do not appear so. An angular size illusion may be accompanied by (or cause) a linear size illusion at the same time.
The perceived visual angle paradigm begins with a rejection of the classical size–distance invariance hypothesis (SDIH), which states that the ratio of perceived linear size to perceived distance is a simple function of the visual angle. The SDIH does not explain some illusions, such as the Moon illusion , in which the Moon appears larger when it is near the horizon. It is replaced by a perceptual SDIH, in which the visual angle is replaced by the perceived visual angle. This new formulation avoids some of the paradoxes of the SDIH, but it remains difficult to explain why a given illusion occurs.
This paradigm is not universally accepted; many textbook explanations of size and distance perception do not refer to the perceived visual angle, and some researchers deny that it exists. Some recent evidence supporting the idea, reported by Murray, Boyaci and Kersten (2006), suggests a direct relationship between the perceived angular size of an object and the size of the neural activity pattern it excites in the primary visual cortex .
Visual angle illusions have been explicitly described by many vision researchers, including Joynson (1949) , (McCready 1963 , 1965 , 1985 , 1999 ), Rock & McDermott (1964) , Baird (1970), Ono (1970), Roscoe (1985, 1989), Hershenson (1982, 1989), Reed (1984, 1989), Enright (1989), Plug & Ross (1989, 1994), Higashiyama & Shimono (1994), Gogel, & Eby (1997), Ross & Plug (2002), and Murray, Boyaci & Kersten (2006). Specifically, these researchers cited have advocated a relatively new idea: that many of the best-known size illusions demonstrate that for most observers the (subjective) perceived visual angle, θ′ , can change for a viewed target that subtends a constant (physical) visual angle θ .
Indeed, various experiments have revealed most of the factors responsible for these visual angle illusions, and a few different explanations for them have been published (Baird, Wagner, & Fuld, 1990, Enright, 1987, 1989, Hershenson, 1982, 1989, Komoda & Ono, 1974, McCready, 1965, 1985, 1986, 1994, Ono, 1970, Oyama, 1977, Reed, 1984, 1989, Restle, 1970, Roscoe, 1985, 1989).
On the other hand, nearly all discussions (and explanations) of those classic size illusions found in textbooks, the popular media, and on the internet use, instead, an older hypothesis that the visual angle is not perceivable (Gregory, 2008, Kaufman & Kaufman, 2002). They can describe and explain only a linear size illusion, which is why they do not properly describe or explain the illusions that most people experience.
In order to clarify the new paradigm which replaces the old one, it helps to keep in mind that an angle is the difference between two directions from a common point (the vertex). Accordingly, as described below, the visual angle θ is the difference between two real (optical) directions in the field of view , while the perceived visual angle θ′ , is the difference by which the directions of two viewed points from oneself appear to differ in the visual field .
Figure 1 illustrates an observer's eye looking at a frontal extent AB that has a linear size S (also called its "metric size" or "tape-measure size"). The extent's lower endpoint at B lies at a distance D from point O , which for present purposes can represent the center of the eye's entrance pupil .
The line from B through O indicates the chief ray of the bundle of light rays that form the optical image of B on the retina at point b , let's say, on the fovea . Likewise, endpoint A is imaged at point a .
The optical (physical) angle between those chief rays is the visual angle θ which can be calculated:
The retinal images at b and a are separated by the distance R , given by the equation
in which n is the eye's nodal distance that averages about 17 mm. That is, a viewed object's retinal image size is approximately given by R = 17 S / D mm .
The line from point O outward through object point B specifies the optical direction, d B , of the object's base from the eye, let's say toward the horizon . The line from point O through point A specifies that endpoint's optical direction, d A , toward some specific elevation value (say, 18 degrees). The difference between those real directions ( d A − d B ) is, again, the visual angle θ .
Figure 2 diagrams the perceived (subjective) values for a viewed object.
Point O ′ represents the place from which the observer feels that he or she is viewing the world. For present purposes, O ′ can represent the cyclopean eye (Ono, 1970, Ono, Mapp & Howard, 2002). [ 1 ]
In Figure 2, D′ is the perceived distance of the subjective point B ′ from O ′. The observer might simply say how far away point B ′ looks, in inches or meters or miles.
Similarly, S′ is the perceived linear extent by which the subjective point A ′ appears directly above point B ′. The observer could simply say how many inches or meters that vertical distance looks. For a viewed object, S′ thus is its perceived linear size in meters, (or apparent linear size).
The perceived endpoint at B ′ has the perceived direction, d′ B , and the observer might simply say "it looks straight ahead and toward the horizon."
This concept of the (subjective) visual direction is very old. [ 2 ] However, as Wade, Ono & Mapp (2006) noted, it unfortunately has been ignored in many current theories of size perception, and size illusions.
The object's other perceived endpoint, A ′, has a perceived direction d′ A ;, about which the observer might say "it appears toward a higher elevation than point B ′." The difference between the two perceived directions ( d′ A − d′ B ) is the perceived visual angle θ′ , also called the perceived angular size or apparent angular size.
It is not easy to quantify θ′ . For instance, a well-trained observer might say that point A ′ "looks about 25 degrees higher" than B ′, but most cannot reliably say how large a direction difference looks. That skill is not practiced because it is easier to use pointing gestures (Ono, 1970): For example, one often tells another person about the change in the directions seen for two viewed points by pointing something, say a finger or the eyes from one point to the other.
Therefore, in some experiments the observers aimed a pointer from one viewed point to the other, so the angle through which the pointer rotated was the measure of θ′ , (Komodo, 1970, Komodo & Ono, 1974, Ono, Muter, & Mitson, 1974, Gogel & Eby, 1997).
Also, because θ′ , specifies the amount by which one should rotate one's eye to quickly look from one seen point to another eye tracking , saccade , observers in other experiments shifted their gaze from one object endpoint to the other, and the angle the eye rotated through was measured as θ′ for that object (Yarbus (1967).
It is important to understand how θ′ differs from S′ . Consider an example illustrated by the sketch at the right.
Suppose one is looking through a window at a 30-foot-wide (9.1 m) house 240 feet away, so it subtends a visual angle of about 7 degrees. The 30-inch-wide (760 mm) window opening is 10 feet away, so it subtends a visual angle of 14 degrees.
It can be said that the house "looks larger and farther away" than the window, meaning that the perceived linear size S′ for the house's width is much larger than S′ for the window; for instance a person might say the house "looks about 40 feet wide" and the window "looks about 3 feet wide."
One can also say that the house "looks smaller and farther away" than the window, and that does not contradict the other statement because now we mean that the amount ( θ′ ) by which directions of the house's edges appear to differ is, say, about half the apparent direction difference for the window edges.
Notice that humans experience both the linear size and the angular size comparisons at the same time, along with the distance comparison (Joynson, 1949). Thus any report merely that one object "looks larger" than another object is ambiguous. It needs to specify whether "looks larger" refers to the perceived angular size ( θ′ ) or to the perceived linear size ( S′ ) or to both of those qualitatively different "size" experiences (Joynson, 1949, McCready, 1965, 1985, Ono, 1970). Notice that in everyday conversations "looks larger" often refers to an angular size comparison rather than a linear size comparison.
Additional confusion has resulted from widespread use of the ambiguous terms "apparent size" and "perceived size", because they sometimes have referred to θ′ and sometimes to S′ without clarification, so the reader must try to ascertain what they mean. Also, in astronomy, " apparent size " refers to the physical angle θ rather than to the subjective apparent visual angle θ′ .
How the three perceived values θ′ , S′ , and D′ would be expected to relate to each other for a given object is illustrated by Figure 2 and stated by the following equation (McCready, 1965, 1985, Ono, 1970, Komoda and Ono, 1974, Reed, 1989, Kaneko & Uchikawa, 1997).
Ross & Plug (2002, Page 31) dubbed this new rule the "perceptual size–distance invariance hypothesis".
As already noted, the magnitude of an object's visual angle θ determines the size R of its retinal image. And, the size of the retinal image normally determines the extent of the neural activity pattern the retina's neural activity eventually generates in the primary visual cortex , area V1 or Brodmann area 17 . This cortical area harbors a distorted but spatially isomorphic "map" of the retina (see Retinotopy ). This neurological relationship recently was confirmed by Murray, Boyaci, & Kersten (2006) using functional magnetic resonance imaging .
The retinal image is not perceived or sensed. That is, experimental psychologists long ago rejected any idea that people "sense" a proximal stimulus such as the retinal image. As Gogel (1969, 1997) has repeatedly emphasized, there is no "sensation" which could be called the "perceived retinal image size", R′ .
Also rejected is a popular idea that an object's "perceived size" results from a "scaling of retinal size"; an illogical process that somehow "magnifies" the very small "retinal size" to yield the viewed object's much larger perceived linear size S′ .
Instead, the physical retinal extent R normally determines the magnitude of the perceived visual angle θ′ . But, as already noted, "other factors" can intervene to slightly change θ′ for a target forming a constant sized retinal image (and thereby create a visual angle illusion). Indeed, the major discovery by Murray et al. (2006) concerns this flexible relationship between R and θ′ , as described below.
The Murray, et al. (2006) observers viewed a flat picture with two disks that subtended the same visual angle θ and formed retinal images of the same size ( R ), but the perceived angular size, θ′ , for one disk was larger than θ′ for the other (say, 17% larger) due to differences in their background patterns. And, in cortical Area V1, the sizes of the activity patterns related to the disks were unequal, despite the fact that the retinal images were the same size. The difference between these "cortical sizes" in Area V1 for the illusion disks was essentially the same as the difference produced by two non-illusory disks whose retinal image sizes differed by, say, 17%.
The researchers pointed out that their findings dramatically disagree with the hypothetical models of neural events being proposed in nearly all current theories of visual spatial perception.
Murray, et al. (2006) also noted that the flat illusion pattern they used can represent other classic "size" illusions, such as the Ponzo illusion and, as well, the moon illusion which is a visual angle illusion for most observers, (McCready, 1965, 1986, Restle 1970, Plug & Ross, 1989, p. 21, Ross & Plug, 2002).
A detailed meta-analysis of the Murray et al. (2006) results is available in McCready (2007, Appendix B).
Conventional "textbook" theories of "size" and distance perception do not refer to the perceived visual angle (e.g., Gregory, 1963, 1970, 1998, 2008) and some researchers even deny that it exists (Kaufman & Kaufman, 2002). This idea that one does not see the different directions in which objects lie from oneself is a basis of the so-called "size–distance invariance hypothesis" (SDIH).
That old SDIH logic (geometry) is typically illustrated using a diagram that resembles Figure 2, but has the physical visual angle θ substituted for the perceived visual angle θ′ . The equation for the SDIH thus is
Here, S′ is typically called the "perceived size" or "apparent size"; more precisely it is the perceived linear size, measured in meters.
When rearranged as S′ = D′ tan θ , the equation expresses Emmert's law .
However, at least since 1962, researchers have pointed out that many classic "size" and distance illusions can be neither described nor explained using the SDIH, so a new hypothesis is needed (Boring 1962, Gruber, 1956, McCready, 1965, Baird, 1970, Ono 1970). For instance, consider the simple Ebbinghaus illusion.
The two central circles are the same linear size S and the same viewing distance D , so they subtend the same visual angle θ and form equal-sized retinal images. But the lower one "looks larger" than the upper one.
According to the SDIH, "looks larger" can mean only that S′ is greater, and with the physical angle θ the same for both, the SDIH requires that D′ be greater for the lower one than for the upper one. However, for most observers, both circles appear unequal while also appearing at the same distance (on the same page).
This commonly found disagreement between published data and the SDIH is known as the "size–distance paradox" (Gruber, 1956, Ono, et al. 1974).
The "paradox" completely vanishes, however, when the illusion is described, instead, as basically a visual angle illusion: That is, the perceived visual angle θ′ is larger for the lower circle than for the upper circle: It is as if its retinal image were larger. So. according to the "new" perceptual invariance hypothesis, ( S′ / D′ = tan θ′ ), with θ′ larger for the lower circle, and with D′ correctly the same for both circles, then S′ becomes larger for the lower one by the same ratio that θ′ is larger. That is, the reason the lower one looks a larger linear size on the page is because it looks a larger angular size than the upper one.
The new hypothesis that includes θ′ along with S′ describes the Ebbinghaus illusion and many other classic "size" illusions more completely and more logically than does the popular SDIH. What still needs to be explained, however, is why the basic visual angle illusion occurs in each example.
Describing the few existing explanations for visual angle illusions is beyond the scope of this present entry. The most recent theories have been presented mostly in articles concerning the moon illusion (Baird et al., 1990, Enright, 1989a, 1989b, Hershenson, 1982, 1989b, Higashiyama, 1992, McCready 1986, 1999–2007, Plug & Ross, 1989, Reed, 1989, Roscoe, 1989, and especially in two "moon illusion" books (Hershenson, 1989; Ross & Plug, 2002) which make it quite clear that vision scientists have not yet agreed upon any particular theory of visual angle illusions.
There also is the lesser-known, but evidently the largest visual angle illusion of oculomotor micropsia ( convergence micropsia ) for which a few different explanations are being considered (McCready, 1965, 2007, Ono, 1970, Komoda & Ono, 1974, Ono, et al. 1974, Enright, 1987b, 1989a, 1989b).
This is a partial list of "size and distance" illusions that begin as visual angle illusions (angular size illusions) for most observers. | https://en.wikipedia.org/wiki/Perceived_visual_angle |
The percent sign % (sometimes per cent sign in British English ) is the symbol used to indicate a percentage , a number or ratio as a fraction of 100. Related signs include the permille (per thousand) sign ‰ and the permyriad (per ten thousand) sign ‱ (also known as a basis point ), which indicate that a number is divided by one thousand or ten thousand, respectively. Higher proportions use parts-per notation .
English style guides prescribe writing the percent sign following the number without any space between (e.g. 50%). [ sources 1 ] However, the International System of Units and ISO 31-0 standard prescribe a space between the number and percent sign, [ 8 ] [ 9 ] [ 10 ] in line with the general practice of using a non-breaking space between a numerical value and its corresponding unit of measurement .
Other languages have other rules for spacing in front of the percent sign:
It is often recommended that the percent sign only be used in tables and other places with space restrictions. In running text, it should be spelled out as percent or per cent (often in newspapers). For example, not "Sales increased by 24% over 2006" but "Sales increased by 24 percent over 2006". [ 22 ] [ 23 ] [ 24 ]
Prior to 1425, there is no known evidence of a special symbol being used for percentages. The Italian term per cento , "for a hundred", was used as well as several different abbreviations (e.g. "per 100", "p 100", "p cento"). Examples of this can be seen in the 1339 arithmetic text (author unknown) depicted below. [ 25 ] The letter p with its descender crossed by a horizontal or diagonal stroke (to indicate abbreviation) conventionally stood for per, por, par, or pur in Medieval and Renaissance palaeography . [ 26 ]
At some point, a scribe used the abbreviation pc with a tiny loop or circle (depicting the ending -o used in Italian ordinals , as in primo , secondo ; it is analogous to the English -th as in 25th ). This appears in some additional pages of a 1425 text which were probably added around 1435. [ 27 ]
The pc with a loop eventually evolved into a horizontal fraction sign by 1650 (see below for an example in a 1684 text) [ 29 ] and thereafter lost the per . [ 28 ]
In 1925, D. E. Smith wrote, "The solidus form ( ) is modern." [ 30 ]
The Unicode code points are:
The ASCII code for the percent character is 37, or 0x25 in hexadecimal .
Names for the percent sign include percent sign (in ITU-T ), mod , grapes (in hacker jargon ), [ citation needed ] and the humorous double-oh-seven (in INTERCAL ).
In computing , the percent character is also used for the modulo operation in programming languages that derive their syntax from the C programming language , which in turn acquired this usage from the earlier B . [ 32 ]
In the textual representation of URIs , a % immediately followed by a 2-digit hexadecimal number denotes an octet specifying (part of) a character that might otherwise not be allowed in URIs (see percent-encoding ).
In SQL , the percent sign is a wildcard character in "LIKE" expressions, for example SELECT * FROM table WHERE fullname LIKE 'Lisa %' will fetch all records whose names start with " Lisa ".
In TeX (and therefore also in LaTeX ) and PostScript , and in GNU Octave and MATLAB , [ 33 ] a % denotes a line comment .
In BASIC , Visual Basic , ASP , and VBA a trailing % after a variable name marks it as an integer .
In ASP , the percent sign can be used to indicate the start and end of the ASP code <%...... %>
In Perl % is the sigil for hashes .
In many programming languages' string formatting operations (performed by functions such as printf and scanf ), the percent sign denotes parts of the template string that will be replaced with arguments. (See printf format string .) In Python and Ruby the percent sign is also used as the string formatting operator. [ 34 ] [ 35 ] [ 36 ]
In the command processors COMMAND.COM (DOS) and CMD.EXE (OS/2 and Windows), %1, %2 ,... stand for the first, second,... parameters of a batch file . %0 stands for the specification of the batch file itself as typed on the command line. The % sign is also used similarly in the FOR command.
%VAR1% represents the value of an environment variable named VAR1. Thus: set PATH = c:\; %PATH% sets a new value for PATH, that being the old value preceded by " c:\; ".
Because these uses give the percent sign special meaning, the sequence %% (two percent signs) is used to represent a literal percent sign, so that: set PATH = c:\; %% PATH %% would set PATH to the literal value " c:\;%PATH% ".
In the C Shell and Zsh , % is part of the default command prompt .
In linguistics, the percent sign is prepended to an example sentence or other string to show that it is judged well-formed (grammatical) by some speakers and ill-formed by others. This may be due to differences in dialect or even individual idiolects . [ 37 ] [ 38 ] This use is similar to those of the asterisk to mark ill-formed strings, the question mark to mark strings where well-formedness is unclear, and the number sign to mark strings that are syntactically well-formed but semantically or pragmatically nonsensical. | https://en.wikipedia.org/wiki/Percent_sign |
A percentage point or percent point is the unit for the arithmetic difference between two percentages . For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). [ 1 ] In written text, the unit (the percentage point) is usually either written out, [ 2 ] or abbreviated as pp , p.p. , or %pt. to avoid confusion with percentage increase or decrease in the actual quantity. After the first occurrence, some writers abbreviate by using just "point" or "points".
Consider the following hypothetical example: In 1980, 50 percent of the population smoked, and in 1990 only 40 percent of the population smoked. One can thus say that from 1980 to 1990, the prevalence of smoking decreased by 10 percentage points (or by 10 percent of the population) or by 20 percent when talking about smokers only – percentages indicate proportionate part of a total.
Percentage-point differences are one way to express a risk or probability . Consider a drug that cures a given disease in 70 percent of all cases, while without the drug, the disease heals spontaneously in only 50 percent of cases. The drug reduces absolute risk by 20 percentage points. Alternatives may be more meaningful to consumers of statistics, such as the reciprocal , also known as the number needed to treat (NNT). In this case, the reciprocal transform of the percentage-point difference would be 1/(20pp) = 1/0.20 = 5. Thus if 5 patients are treated with the drug, one could expect to cure one more patient than would have gotten well without receiving the treatment.
For measurements involving percentages as a unit, such as, growth, yield , or ejection fraction , statistical deviations and related descriptive statistics , including the standard deviation and root-mean-square error , the result should be expressed in units of percentage points instead of percentage. [ citation needed ] Mistakenly using percentage as the unit for the standard deviation is confusing, since percentage is also used as a unit for the relative standard deviation , i.e. standard deviation divided by average value ( coefficient of variation ). | https://en.wikipedia.org/wiki/Percentage_point |
Perceptual Audio Coder ( PAC ) is a lossy audio compression algorithm. It is used by Sirius Satellite Radio for their digital audio radio service .
The original version of PAC developed by James Johnston and Anibal Ferreira at AT&T's Bell Labs has a flexible format and bitrate . It provides efficient compression of high-quality audio over a variety of formats from 16 kbit/s for a monophonic channel to 1024 kbit/s for a 5.1 format with four or six auxiliary audio channels, and provisions for an ancillary (fixed rate) and auxiliary (variable rate) side data channel. For stereo audio signals, it is claimed that it provides near-CD quality at about 56-64 kbit/s, with transparent coding at bit rates approaching 128 kbit/s. [ 1 ]
Over the years PAC has evolved considerably. A known software implementation of this codec is CelestialTech's AudioLib. Later, it was considerably improved and renamed to ePAC (enhanced Perceptual Audio Coder) by Lucent, available in the AudioVeda music library manager. [ citation needed ]
iBiquity initially tested PAC for the HD-Radio IBOC digital radio upgrade for FM and AM , but chose an MPEG4-derived codec, HE-AAC , instead. MPEG-2 AAC is substantially similar to the original AT&T PAC algorithm written by Johnston and Ferreira, including the specifics of stereo pair coding, bitstream sectioning, handling of 1 or 2 channels at a time, multiple codebooks responding to the same largest absolute value, and block switching triggers. The version of PAC tested for the MPEG-NBC (later to become AAC) trials used 1024/128 sample block lengths, rather than 512/128 sample block lengths.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perceptual_Audio_Coder |
A perceptual trap is an ecological scenario in which environmental change , typically anthropogenic , leads an organism to avoid an otherwise high-quality habitat . The concept is related to that of an ecological trap , in which environmental change causes preference towards a low-quality habitat.
In a 2004 article discussing source–sink dynamics , James Battin did not distinguish between high-quality habitats that are preferred or avoided, labelling both "sources". [ 2 ] The latter scenario, in which a high-quality habitat is avoided, was first recognised as an important phenomenon in 2007 by Gilroy and Sutherland, [ 3 ] who described them as "undervalued resources". The term "perceptual trap" was first proposed by Michael Patten and Jeffrey Kelly in a 2010 article. [ 1 ] Hans Van Dyck [ 4 ] argues that the term is misleading because perception is also a major component in other cases of trapping.
Animals use discrete environmental cues to select habitat. [ 5 ] A perceptual trap occurs if change in an environmental cue leads an organism to avoid a high-quality habitat. [ 1 ] It differs, therefore, from simple habitat avoidance, which may be a correct decision given the habitat's quality. [ 1 ] The concept of a perceptual trap is related to that of an ecological trap , in which environmental change causes preference towards a low-quality habitat. [ 1 ] There is expected to be strong natural selection against ecological traps, but not necessarily against perceptual traps, as Allee effects may restrict a population’s ability to establish itself. [ 1 ]
To support the concept of a perceptual trap, Patten and Kelly [ 1 ] cited a study of the lesser prairie-chicken ( Tympanuchus pallidicinctus ). The species' natural environment, shinnery oak grassland , is often treated with the herbicide tebuthiuron to increase grass cover for cattle grazing . [ 1 ] Herbicide treatment resulted in less shrub cover, a habitat cue that caused female lesser prairie-chickens to avoid the habitat in favour of untreated areas. However, females who nested in herbicide-treated areas achieved comparable nesting successes and clutch sizes to those in untreated areas. [ 1 ] Patten and Kelly suggest that the adverse effects of tebuthiuron treatment on nesting success are countered by various effects, such as greater nest concealment through increased grass cover. [ 1 ] Therefore, female birds are erroneously avoiding a high-quality habitat. Patten and Kelly [ 1 ] also cited as a possible perceptual trap the cases of the spotted towhee ( Pipilo maculatus ) and rufous-crowned sparrow ( Aimophila ruficeps ), which tend to avoid habitat fragments, even though birds nesting in habitat fragments achieve increased nesting success due to a reduction in snake predation. [ 6 ] | https://en.wikipedia.org/wiki/Perceptual_trap |
A perchlorate is a chemical compound containing the perchlorate ion , ClO − 4 , the conjugate base of perchloric acid ( ionic perchlorate ). As counterions, there can be metal cations , quaternary ammonium cations or other ions, for example, nitronium cation ( NO + 2 ).
The term perchlorate can also describe perchlorate esters or covalent perchlorates . [ 2 ] These are organic compounds that are alkyl or aryl esters of perchloric acid . They are characterized by a covalent bond between an oxygen atom of the ClO 4 moiety and an organyl group .
In most ionic perchlorates, the cation is non-coordinating . The majority of ionic perchlorates are commercially produced salts commonly used as oxidizers for pyrotechnic devices and for their ability to control static electricity in food packaging . [ 3 ] Additionally, they have been used in rocket propellants , fertilizers , and as bleaching agents in the paper and textile industries .
Perchlorate contamination of food and water endangers human health, primarily affecting the thyroid gland .
Ionic perchlorates are typically colorless solids that exhibit good solubility in water . The perchlorate ion forms when they dissolve in water, dissociating into ions. Many perchlorate salts also exhibit good solubility in non-aqueous solvents . [ 4 ] Four perchlorates are of primary commercial interest: ammonium perchlorate (NH 4 )ClO 4 , perchloric acid HClO 4 , potassium perchlorate KClO 4 and sodium perchlorate NaClO 4 .
Very few chemical oxidants are strong enough to convert chlorate to perchlorate. Persulfate , ozone , or lead dioxide are all known to do so, but the reactions are too delicate and low-yielding for commercial viability. [ 5 ]
Perchlorate salts are typically manufactured through the process of electrolysis , which involves oxidizing aqueous solutions of corresponding chlorates . This technique is commonly employed in the production of sodium perchlorate , which finds widespread use as a key ingredient in rocket fuel . [ 5 ] Perchlorate salts are also commonly produced by reacting perchloric acid with bases, such as ammonium hydroxide or sodium hydroxide . Ammonium perchlorate , which is highly valued, [ why? ] can also be produced via an electrochemical process. [ 6 ]
Perchlorate esters are formed in the presence of a nucleophilic catalyst via a perchlorate salt's nucleophilic substitution onto an alkylating agent . [ 7 ]
The perchlorate ion is the least redox reactive of the generalized chlorates . Perchlorate contains chlorine in its highest oxidation number (+7). A table of reduction potentials of the four chlorates shows that, contrary to expectation, perchlorate in aqueous solution is the weakest oxidant among the four. [ 12 ]
These data show that the perchlorate and chlorate are stronger oxidizers in acidic conditions than in basic conditions.
Gas phase measurements of heats of reaction (which allow computation of Δ f H °) of various chlorine oxides do follow the expected trend wherein Cl 2 O 7 exhibits the largest endothermic value of Δ f H ° (238.1 kJ/mol) while Cl 2 O exhibits the lowest endothermic value of Δ f H ° (80.3 kJ/mol). [ 13 ]
As perchloric acid is one of the strongest mineral acids, perchlorate is a very weak base in the sense of Brønsted–Lowry acid–base theory .
As it is also generally a weakly coordinating anion , perchlorate is commonly used as a background , or supporting, electrolyte .
Perchlorate compounds oxidize organic compounds, especially when the mixture is heated. The explosive decomposition of ammonium perchlorate is catalyzed by metals and heat. [ 14 ]
As perchlorate is a weak Lewis base ( i.e. , a weak electron pair donor) and a weak nucleophilic anion, it is also a very weakly coordinating anion . [ 14 ] This is why it is often used as a supporting electrolyte to study the complexation and the chemical speciation of many cations in aqueous solution or in electroanalytical methods ( voltammetry , electrophoresis …). [ 14 ] Although the perchlorate reduction is thermodynamically favorable (∆ G < 0; E ° > 0) , and that ClO − 4 is expected to be a strong oxidant , most often in aqueous solution, it is practically an inert species behaving as an extremely slow oxidant because of severe kinetics limitations . [ 15 ] [ 16 ] The metastable character of perchlorate in the presence of reducing cations such as Fe 2+ in solution is due to the difficulty to form an activated complex facilitating the electron transfer and the exchange of oxo groups in the opposite direction. These strongly hydrated cations cannot form a sufficiently stable coordination bridge with one of the four oxo groups of the perchlorate anion. Although thermodynamically a mild reductant, Fe 2+ ion exhibits a stronger trend to remain coordinated by water molecules to form the corresponding hexa-aquo complex in solution. The high activation energy of the cation binding with perchlorate to form a transient inner sphere complex more favourable to electron transfer considerably hinders the redox reaction. [ 17 ] The redox reaction rate is limited by the formation of a favorable activated complex involving an oxo-bridge between the perchlorate anion and the metallic cation. [ 18 ] It depends on the molecular orbital rearrangement ( HOMO and LUMO orbitals ) necessary for a fast oxygen atom transfer (OAT) [ 19 ] and the associated electron transfer as studied experimentally by Henry Taube (1983 Nobel Prize in Chemistry) [ 20 ] [ 21 ] and theoretically by Rudolph A. Marcus (1992 Nobel Prize in Chemistry), [ 22 ] both awarded for their respective works on the mechanisms of electron-transfer reactions with metal complexes and in chemical systems.
In contrast to the Fe 2+ cations which remain unoxidized in deaerated perchlorate aqueous solutions free of dissolved oxygen, other cations such as Ru(II) and Ti(III) can form a more stable bridge between the metal centre and one of the oxo groups of ClO − 4 . In the inner sphere electron transfer mechanism to observe the perchlorate reduction, the ClO − 4 anion must quickly transfer an oxygen atom to the reducing cation. [ 23 ] [ 24 ] When it is the case, metallic cations can readily reduce perchlorate in solution. [ 20 ] Ru(II) can reduce ClO − 4 to ClO − 3 , while V(II), V(III), Mo(III), Cr(II) and Ti(III) can reduce ClO − 4 to Cl − . [ 25 ]
Some metal complexes, especially those of rhenium , and some metalloenzymes can catalyze the reduction of perchlorate under mild conditions. [ 26 ] Perchlorate reductase (see below), a molybdoenzyme , also catalyzes the reduction of perchlorate. [ 27 ] Both the Re- and Mo-based catalysts operate via metal-oxo intermediates.
Over 40 phylogenetically and metabolically diverse microorganisms capable of growth using perchlorate as an electron acceptor [ 28 ] have been isolated since 1996. Most originate from the Pseudomonadota , but others include the Bacillota , Moorella perchloratireducens and Sporomusa sp., and the archaeon Archaeoglobus fulgidus . [ 29 ] [ 30 ] With the exception of A. fulgidus , microbes that grow via perchlorate reduction utilize the enzymes perchlorate reductase and chlorite dismutase , which collectively take perchlorate to chloride. [ 29 ] In the process, free oxygen ( O 2 ) is generated. [ 29 ]
Perchlorate is created by lightning discharges in the presence of chloride. Perchlorate has been detected in rain and snow samples from Florida and Lubbock, Texas . [ 31 ] It is also present in Martian soil .
Naturally occurring perchlorate at its most abundant can be found commingled with deposits of sodium nitrate in the Atacama Desert of northern Chile. These deposits have been heavily mined as sources for nitrate-based fertilizers. Chilean nitrate is in fact estimated to be the source of around 81,000 tonnes (89,000 tons) of perchlorate imported to the U.S. (1909–1997). Results from surveys of ground water, ice, and relatively unperturbed deserts have been used to estimate a 100,000 to 3,000,000 tonnes (110,000 to 3,310,000 tons) "global inventory" of natural perchlorate presently on Earth. [ 32 ]
Perchlorate was detected in Martian soil at the level of ~0.6% by weight. [ 33 ] [ 34 ] It was shown that at the Phoenix landing site it was present as a mixture of 60% Ca(ClO 4 ) 2 and 40% Mg(ClO 4 ) 2 . [ 35 ] These salts, formed from perchlorates, act as antifreeze and substantially lower the freezing point of water. Based on the temperature and pressure conditions on present-day Mars at the Phoenix lander site, conditions would allow a perchlorate salt solution to be stable in liquid form for a few hours each day during the summer. [ 36 ]
The possibility that the perchlorate was a contaminant brought from Earth was eliminated by several lines of evidence. The Phoenix retro-rockets used ultra pure hydrazine and launch propellants consisting of ammonium perchlorate or ammonium nitrate . Sensors on board Phoenix found no traces of ammonium nitrate , and thus the nitrate in the quantities present in all three soil samples is indigenous to the Martian soil. Perchlorate is widespread in Martian soils at concentrations between 0.5 and 1%. At such concentrations, perchlorate could be an important source of oxygen, but it could also become a critical chemical hazard to astronauts. [ 37 ]
In 2006, a mechanism was proposed for the formation of perchlorates that is particularly relevant to the discovery of perchlorate at the Phoenix lander site. It was shown that soils with high concentrations of chloride converted to perchlorate in the presence of titanium dioxide and sunlight/ultraviolet light. The conversion was reproduced in the lab using chloride-rich soils from Death Valley . [ 38 ] Other experiments have demonstrated that the formation of perchlorate is associated with wide band gap semiconducting oxides. [ 39 ] In 2014, it was shown that perchlorate and chlorate can be produced from chloride minerals under Martian conditions via UV using only NaCl and silicate. [ 40 ]
Further findings of perchlorate and chlorate in the Martian meteorite EETA79001 [ 41 ] and by the Mars Curiosity rover in 2012-2013 support the notion that perchlorates are globally distributed throughout the Martian surface. [ 42 ] [ 43 ] [ 44 ] With concentrations approaching 0.5% and exceeding toxic levels on Martian soil, Martian perchlorates would present a serious challenge to human settlement , [ 45 ] as well as microorganisms. [ 46 ] On the other hand, the perchlorate would provide a convenient source of oxygen for the settlements.
On September 28, 2015, NASA announced that analyses of spectral data from the Compact Reconnaissance Imaging Spectrometer for Mars instrument (CRISM) on board the Mars Reconnaissance Orbiter from four different locations where recurring slope lineae (RSL) are present found evidence for hydrated salts. The hydrated salts most consistent with the spectral absorption features are magnesium perchlorate, magnesium chlorate and sodium perchlorate. The findings strongly support the hypothesis that RSL form as a result of contemporary water activity on Mars. [ 47 ] [ 48 ] [ 49 ] [ 50 ] [ 51 ]
Perchlorates are of concern because of uncertainties about toxicity and health effects at low levels in drinking water, impact on ecosystems, and indirect exposure pathways for humans due to accumulation in vegetables. [ 11 ] They are water-soluble, exceedingly mobile in aqueous systems, and can persist for many decades under typical groundwater and surface water conditions. [ 52 ]
Perchlorates are used mostly in rocket propellants but also in disinfectants, bleaching agents, and herbicides. Perchlorate contamination is caused during both the manufacture and ignition of rockets and fireworks. [ 4 ] Fireworks are also a source of perchlorate in lakes. [ 53 ] Removal and recovery methods of these compounds from explosives and rocket propellants include high-pressure water washout, which generates aqueous ammonium perchlorate.
In 2000, perchlorate contamination beneath the former flare manufacturing plant Olin Corporation Flare Facility, Morgan Hill, California was first discovered several years after the plant had closed. The plant had used potassium perchlorate as one of the ingredients during its 40 years of operation. By late 2003, the State of California and the Santa Clara Valley Water District had confirmed a groundwater plume currently extending over nine miles through residential and agricultural communities. [ citation needed ] The California Regional Water Quality Control Board and the Santa Clara Valley Water District have engaged [ when? ] in a major outreach effort, a water well testing program has been underway for about 1,200 residential, municipal, and agricultural wells. Large ion exchange treatment units are operating in three public water supply systems which include seven municipal wells with perchlorate detection. The potentially responsible parties , Olin Corporation and Standard Fuse Incorporated, have been supplying bottled water to nearly 800 households with private wells, [ when? ] and the Regional Water Quality Control Board has been overseeing cleanup efforts. [ 54 ]
The source of perchlorate in California was mainly attributed to two manufacturers in the southeast portion of the Las Vegas Valley in Nevada, where perchlorate has been produced for industrial use. [ 55 ] This led to perchlorate release into Lake Mead in Nevada and the Colorado River which affected regions of Nevada, California and Arizona , where water from this reservoir is used for consumption, irrigation and recreation for approximately half the population of these states. [ 4 ] Lake Mead has been attributed [ when? ] as the source of 90% of the perchlorate in Southern Nevada's drinking water. Based on sampling, perchlorate has been affecting 20 million people, with highest detection in Texas , southern California, New Jersey , and Massachusetts, but intensive sampling of the Great Plains and other middle state regions may lead to revised estimates with additional affected regions. [ 4 ] An action level of 18 μg/L has been adopted [ when? ] by several affected states. [ 52 ]
In 2001, the chemical was detected at levels as high as 5 μg/L at Joint Base Cape Cod (formerly Massachusetts Military Reservation ), over the Massachusetts then state regulation of 2 μg/L. [ 56 ] [ 57 ]
As of 2009, low levels of perchlorate had been detected in both drinking water and groundwater in 26 states in the U.S., according to the Environmental Protection Agency (EPA). [ 58 ]
In 2004, the chemical was found in cow's milk in California at an average level of 1.3 parts per billion (ppb, or μg/L), which may have entered the cows through feeding on crops exposed to water containing perchlorates. [ 59 ] A 2005 study suggested human breast milk had an average of 10.5 μg/L of perchlorate. [ 60 ]
In some places, there is no clear source of perchlorate, and it may be naturally occurring. Natural perchlorate on Earth was first identified in terrestrial nitrate deposits /fertilizers of the Atacama Desert in Chile as early as the 1880s [ 61 ] and for a long time considered a unique perchlorate source. The perchlorate released from historic use of Chilean nitrate based fertilizer which the U.S.imported by the hundreds of tons in the early 19th century can still be found in some groundwater sources of the United States, for example Long Island, New York. [ 62 ] Recent improvements in analytical sensitivity using ion chromatography based techniques have revealed a more widespread presence of natural perchlorate, particularly in subsoils of Southwest USA, [ 63 ] salt evaporites in California and Nevada, [ 64 ] Pleistocene groundwater in New Mexico, [ 65 ] and even present in extremely remote places such as Antarctica . [ 66 ] The data from these studies and others indicate that natural perchlorate is globally deposited on Earth with the subsequent accumulation and transport governed by the local hydrologic conditions.
Despite its importance to environmental contamination, the specific source and processes involved in natural perchlorate production remain poorly understood. Laboratory experiments in conjunction with isotopic studies [ 67 ] have implied that perchlorate may be produced on earth by oxidation of chlorine species through pathways involving ozone or its photochemical products. [ 68 ] [ 69 ] Other studies have suggested that perchlorate can also be formed by lightning activated oxidation of chloride aerosols (e.g., chloride in sea salt sprays), [ 70 ] and ultraviolet or thermal oxidation of chlorine (e.g., bleach solutions used in swimming pools) in water. [ 71 ] [ 72 ] [ 73 ]
Although perchlorate as an environmental contaminant is usually associated with the manufacture, storage, and testing of solid rocket motors , [ 74 ] contamination of perchlorate has been focused as a side effect of the use of natural nitrate fertilizer and its release into ground water. The use of naturally contaminated nitrate fertilizer contributes to the infiltration of perchlorate anions into the ground water and threaten the water supplies of many regions in the US. [ 74 ]
One of the main sources of perchlorate contamination from natural nitrate fertilizer use was found to come from the fertilizer derived from Chilean caliche ( calcium carbonate ), because Chile has rich source of naturally occurring perchlorate anion. [ 75 ] Perchlorate concentration was the highest in Chilean nitrate, ranging from 3.3 to 3.98%. [ 52 ] Perchlorate in the solid fertilizer ranged from 0.7 to 2.0 mg g −1 , variation of less than a factor of 3 and it is estimated that sodium nitrate fertilizers derived from Chilean caliche contain approximately 0.5–2 mg g −1 of perchlorate anion. [ 75 ] The direct ecological effect of perchlorate is not well known; its impact can be influenced by factors including rainfall and irrigation, dilution, natural attenuation, soil adsorption, and bioavailability. [ 75 ] Quantification of perchlorate concentrations in nitrate fertilizer components via ion chromatography revealed that in horticultural fertilizer components contained perchlorate ranging between 0.1 and 0.46%. [ 52 ]
There have been many attempts to eliminate perchlorate contamination. Current remediation technologies for perchlorate have downsides of high costs and difficulty in operation. [ 76 ] Thus, there have been interests in developing systems that would offer economic and green alternatives. [ 76 ]
Several technologies can remove perchlorate, via treatments ex situ (away from the location) and in situ (at the location).
Ex situ treatments include ion exchange using perchlorate-selective or nitrite-specific resins, bioremediation using packed-bed or fluidized-bed bioreactors , and membrane technologies via electrodialysis and reverse osmosis . [ 77 ] In ex situ treatment via ion exchange, contaminants are attracted and adhere to the ion exchange resin because such resins and ions of contaminants have opposite charge. [ 78 ] As the ion of the contaminant adheres to the resin, another charged ion is expelled into the water being treated, in which then ion is exchanged for the contaminant. [ 78 ] Ion exchange technology has advantages of being well-suitable for perchlorate treatment and high volume throughput but has a downside that it does not treat chlorinated solvents . In addition, ex situ technology of liquid phase carbon adsorption is employed, where granular activated carbon (GAC) is used to eliminate low levels of perchlorate and pretreatment may be required in arranging GAC for perchlorate elimination. [ 77 ]
In situ treatments, such as bioremediation via perchlorate-selective microbes and permeable reactive barrier, are also being used to treat perchlorate. [ 77 ] In situ bioremediation has advantages of minimal above-ground infrastructure and its ability to treat chlorinated solvents, perchlorate, nitrate , and RDX simultaneously. However, it has a downside that it may negatively affect secondary water quality. In situ technology of phytoremediation could also be utilized, even though perchlorate phytoremediation mechanism is not fully founded yet. [ 77 ]
Bioremediation using perchlorate-reducing bacteria, which reduce perchlorate ions to harmless chloride, has also been proposed. [ 79 ]
Perchlorate is a potent competitive inhibitor of the thyroid sodium-iodide symporter . [ 80 ] Thus, it has been used to treat hyperthyroidism since the 1950s. [ 81 ] At very high doses (70,000–300,000 ppb ) the administration of potassium perchlorate was considered the standard of care in the United States, and remains the approved pharmacologic intervention for many countries.
In large amounts perchlorate interferes with iodine uptake into the thyroid gland. In adults, the thyroid gland helps regulate the metabolism by releasing hormones, while in children, the thyroid helps in proper development. The NAS , in its 2005 report, Health Implications of Perchlorate Ingestion , emphasized that this effect, also known as Iodide Uptake Inhibition (IUI) is not an adverse health effect. However, in January 2008, California's Department of Toxic Substances Control stated that perchlorate is becoming a serious threat to human health and water resources. [ 82 ] In 2010, the EPA's Office of the Inspector General determined that the agency's own perchlorate reference dose (RfD) of 24.5 parts per billion protects against all human biological effects from exposure, as the federal government is responsible for all US military base groundwater contamination. This finding was due to a significant shift in policy at the EPA in basing its risk assessment on non-adverse effects such as IUI instead of adverse effects. The Office of the Inspector General also found that because the EPA's perchlorate reference dose is conservative and protective of human health further reducing perchlorate exposure below the reference dose does not effectively lower risk. [ 83 ]
Because of ammonium perchlorate's adverse effects upon children, Massachusetts set its maximum allowed limit of ammonium perchlorate in drinking water at 2 parts per billion (2 ppb = 2 micrograms per liter). [ 84 ]
Perchlorate affects only thyroid hormone. Because it is neither stored nor metabolized , effects of perchlorate on the thyroid gland are reversible, though effects on brain development from lack of thyroid hormone in fetuses , newborns , and children are not. [ 85 ]
Toxic effects of perchlorate have been studied in a survey of industrial plant workers who had been exposed to perchlorate, compared to a control group of other industrial plant workers who had no known exposure to perchlorate. After undergoing multiple tests, workers exposed to perchlorate were found to have a significant systolic blood pressure rise compared to the workers who were not exposed to perchlorate, as well as a significant decreased thyroid function compared to the control workers. [ 86 ]
A study involving healthy adult volunteers determined that at levels above 0.007 milligrams per kilogram per day (mg/(kg·d)), perchlorate can temporarily inhibit the thyroid gland's ability to absorb iodine from the bloodstream ("iodide uptake inhibition", thus perchlorate is a known goitrogen ). [ 87 ] The EPA converted this dose into a reference dose of 0.0007 mg/(kg·d) by dividing this level by the standard intraspecies uncertainty factor of 10. The agency then calculated a "drinking water equivalent level" of 24.5 ppb by assuming a person weighs 70 kg (150 lb) and consumes 2 L (0.44 imp gal; 0.53 US gal) of drinking water per day over a lifetime. [ 88 ] [ needs update ]
In 2006, a study reported a statistical association between environmental levels of perchlorate and changes in thyroid hormones of women with low iodine. The study authors were careful to point out that hormone levels in all the study subjects remained within normal ranges. The authors also indicated that they did not originally normalize their findings for creatinine, which would have essentially accounted for fluctuations in the concentrations of one-time urine samples like those used in this study. [ 89 ] When the Blount research was re-analyzed with the creatinine adjustment made, the study population limited to women of reproductive age, and results not shown in the original analysis, any remaining association between the results and perchlorate intake disappeared. [ 90 ] Soon after the revised Blount Study was released, Robert Utiger, a doctor with the Harvard Institute of Medicine, testified before the US Congress and stated: "I continue to believe that that reference dose, 0.007 milligrams per kilo (24.5 ppb), which includes a factor of 10 to protect those who might be more vulnerable, is quite adequate." [ 91 ]
In 2014, a study was published, showing that environmental exposure to perchlorate in pregnant women with hypothyroidism is associated with a significant risk of low IQ in their children. [ 92 ]
Some studies suggest that perchlorate has pulmonary toxic effects as well. Studies have been performed on rabbits where perchlorate has been injected into the trachea. The lung tissue was removed and analyzed, and it was found that perchlorate injected lung tissue showed several adverse effects when compared to the control group that had been intratracheally injected with saline. Adverse effects included inflammatory infiltrates, alveolar collapse, subpleural thickening, and lymphocyte proliferation. [ 93 ]
In the early 1960s, potassium perchlorate used to treat Graves' disease was implicated in the development of aplastic anemia —a condition where the bone marrow fails to produce new blood cells in sufficient quantity—in thirteen patients, seven of whom died. [ 94 ] Subsequent investigations have indicated the connection between administration of potassium perchlorate and development of aplastic anemia to be "equivocable at best", which means that the benefit of treatment, if it is the only known treatment, outweighs the risk, and it appeared a contaminant poisoned the 13. [ 95 ]
In 1998, perchlorate was included in the U.S. EPA Contaminant Candidate List , primarily due to its detection in California drinking water. [ 96 ] [ 4 ]
In 2002, the EPA completed its draft toxicological review of perchlorate and proposed an reference dose of 0.00003 milligrams per kilogram per day (mg/kg/day) based primarily on studies that identified neurodevelopmental deficits in rat pups. These deficits were linked to maternal exposure to perchlorate. [ 97 ]
In 2003, a federal district court in California found that the Comprehensive Environmental Response, Compensation and Liability Act applied, because perchlorate is ignitable, and therefore was a "characteristic" hazardous waste. [ 98 ]
Subsequently, the U.S. National Research Council of the National Academy of Sciences (NAS) reviewed the health implications of perchlorate, and in 2005 proposed a much higher reference dose of 0.0007 mg/kg/day based primarily on a 2002 study by Greer et al. [ 97 ] During that study, 37 adult human subjects were split into four exposure groups exposed to 0.007 (7 subjects), 0.02 (10 subjects), 0.1 (10 subjects), and 0.5 (10 subjects) mg/kg/day. Significant decreases in iodide uptake were found in the three highest exposure groups. Iodide uptake was not significantly reduced in the lowest exposed group, but four of the seven subjects in this group experienced inhibited iodide uptake. In 2005, the RfD proposed by NAS was accepted by EPA and added to its integrated risk information system (IRIS).
Although there has generally been consensus with the Greer et al. study, there has been no consensus with regard to developing a perchlorate RfD. One of the key differences results from how the point of departure is viewed (i.e., NOEL or "lowest-observed-adverse-effect level", LOAEL ), or whether a benchmark dose should be used to derive the RfD. Defining the point of departure as a NOEL or LOAEL has implications when it comes to applying appropriate safety factors to the point of departure to derive the RfD. [ 99 ]
In early 2006, EPA issued a "Cleanup Guidance" and recommended a Drinking Water Equivalent Level (DWEL) for perchlorate of 24.5 μg/L. [ citation needed ] Both DWEL and Cleanup Guidance were based on a 2005 review of the existing research by the National Academy of Sciences (NAS). [ 100 ]
Lacking a federal drinking water standard, several states subsequently published their own standards for perchlorate including Massachusetts in 2006 [ citation needed ] and California in 2007. Other states, including Arizona, Maryland, Nevada, New Mexico, New York, and Texas have established non-enforceable, advisory levels for perchlorate. [ citation needed ]
In 2008, EPA issued an interim drinking water health advisory for perchlorate and with it a guidance and analysis concerning the impacts on the environment and drinking water. [ 101 ] California also issued guidance [ when? ] regarding perchlorate use. [ 102 ] Both the Department of Defense and some environmental groups voiced questions about the NAS report, [ citation needed ] but no credible science has emerged to challenge the NAS findings. [ citation needed ]
In February 2008, the U.S. Food and Drug Administration (FDA) reported that U.S. toddlers on average were being exposed to more than half of EPA's safe dose from food alone. [ 103 ] In March 2009, a Centers for Disease Control study found 15 brands of infant formula contaminated with perchlorate and that combined with existing perchlorate drinking water contamination, infants could be at risk for perchlorate exposure above the levels considered safe by EPA.
In 2010, the Massachusetts Department of Environmental Protection set a 10 fold lower RfD (0.07 μg/kg/day) than the NAS RfD using a much higher uncertainty factor of 100. They also calculated an Infant drinking water value, which neither US EPA nor CalEPA had done. [ 104 ]
On February 11, 2011, EPA determined that perchlorate meets the Safe Drinking Water Act criteria for regulation as a contaminant. [ 101 ] [ 105 ] The agency found that perchlorate may have an adverse effect on the health of persons and is known to occur in public water systems with a frequency and at levels that it presents a public health concern. Since then EPA has continued to determine what level of contamination is appropriate. EPA prepared extensive responses to submitted public comments. [ 106 ] [ better source needed ]
In 2016, the Natural Resources Defense Council (NRDC) filed a lawsuit to accelerate EPA's regulation of perchlorate. [ 107 ]
In 2019, EPA proposed a Maximum Contaminant Level of 0.056 mg/L for public water systems. [ 108 ]
On June 18, 2020, EPA announced that it was withdrawing its 2011 regulatory determination and its 2019 proposal, stating that it had taken "proactive steps" with state and local governments to address perchlorate contamination. [ 109 ] In September 2020 NRDC filed suit against EPA for its failure to regulate perchlorate, and stated that 26 million people may be affected by perchlorate in their drinking water. [ 110 ] On March 31, 2022, the EPA announced that a review confirmed its 2020 decision. [ 111 ] Following the NRDC lawsuit, in 2023 the US Court of Appeals for the DC Circuit ordered EPA to develop a perchlorate standard for public water systems. [ 112 ] EPA stated that it will publish a proposed standard for perchlorate in 2025, and issue a final rule in 2027. [ 113 ]
Although typically found as a non-coordinating anion, a few metal complexes are known. Hexaperchloratoaluminate and tetraperchloratoaluminate are strong oxidising agents .
Several perchlorate esters are known. [ 2 ] For example, methyl perchlorate is a high energy material that is a strong alkylating agent . Chlorine perchlorate is a covalent inorganic analog.
As discussed above, iodide is competitor in the thyroid glads. In the presence of reductants, perchlorate forms potentially explosive mixtures. The PEPCON disaster destroyed a production plant for ammonium perchlorate when a fire caused the ammonium perchlorate stored on site to react with the aluminum that the storage tanks were constructed with and explode. | https://en.wikipedia.org/wiki/Perchlorate |
Percobaltates are chemical compounds where the oxidation state of cobalt is +5. This is the highest established oxidation state of cobalt. [ 1 ] The simplest of these are bi-metallic Group 1 oxides such as sodium percobaltate (Na 3 CoO 4 ); which may be produced by the reaction of cobalt(II,III) oxide and sodium oxide , using oxygen as the oxidant:
The potassium salt can be synthesized similarly; its magnetic moment has indicated the existence of cobalt(V). [ 2 ] [ 3 ] No crystallographic analysis has been reported for either material. Percobaltates can be stabilized by use of oxides or fluorides . [ citation needed ]
A number of organometallic Co(V) complexes have also been reported. [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Percobaltate |
A percolation trench , also called an infiltration trench , is a type of best management practice (BMP) that is used to manage stormwater runoff , prevent flooding and downstream erosion , and improve water quality in an adjacent river , stream , lake or bay . It is a shallow excavated trench filled with gravel or crushed stone that is designed to infiltrate stormwater though permeable soils into the groundwater aquifer . [ 1 ] [ 2 ]
A percolation trench is similar to a dry well , which is typically an excavated hole filled with gravel. [ 3 ] Another similar drainage structure is a French drain , which directs water away from a building foundation , but is usually not designed to protect water quality.
Percolation trenches are often used to treat runoff from impervious surfaces , such as sidewalks and parking lots , on sites where there is limited space available for managing stormwater. They are effective at treating stormwater only if the soil has sufficient porosity . To function properly, a trench must be designed with a pretreatment structure such as a grass channel or swale , in order to capture sediment and avoid clogging the trench. [ 4 ] It may not be appropriate for sites where there is a possibility of groundwater contamination, or where there is soil with a high clay content that could clog the trench. [ 5 ] | https://en.wikipedia.org/wiki/Percolation_trench |
Percoll is a reagent consisting of colloidal silica particles used in cell biology and other laboratory settings. It was first formulated by Pertoft and colleagues, [ 2 ] and commercialized by Pharmacia Fine Chemicals . [ 3 ] Percoll is used for the isolation of cells , organelles , or viruses by density centrifugation .
Percoll was developed from previously reported uses of colloidal silica nanoparticles coated with polysaccharides or polymers for rate zonal, isopycnic, or equilibrium centrifugal separations. [ 4 ] Percoll itself specifically consists of polydisperse silica nanoparticles 15–30 nm diameter (23% w/w in water) which have been coated with polyvinylpyrrolidone (PVP).
Percoll is well suited for density gradient experiments because it possesses a low viscosity compared to alternatives, a low osmolarity , and no toxicity towards cells and their constituents.
Percoll is a registered trademark of Cytiva . [ 5 ]
Percoll does not notably diffuse over time, resulting in the formation of very stable gradients. Therefore, both discontinuous and continuous Percoll density gradients can be prepared weeks in advance, allowing great reproducibility & ease of use. [ 6 ]
Percoll was previously used in assisted reproductive technology (ART) to select sperm from semen by density gradient centrifugation, for use in techniques such as in vitro fertilization or intrauterine insemination . However, in 1996, Pharmacia sent out a letter to laboratories stating that Percoll should be used for research purposes only, not clinical. Pharmacia had not marketed it as a sperm preparation product; it had been repackaged and sold as such by third-party manufacturers. The FDA Warning Letter was due to concerns that PVP might cause damage to sperm (an unknown issue), and also that some batches of Percoll contained high levels of endotoxin (a known issue). The latter concern also applies to the use of Percoll with any other cells that might be injected back into a patient, since endotoxin can cause severe inflammation and fever. Since then it has been replaced with other colloids in the ART industry. [ 7 ] | https://en.wikipedia.org/wiki/Percoll |
In statistical mechanics the Percus–Yevick approximation [ 1 ] is a closure relation to solve the Ornstein–Zernike equation . It is also referred to as the Percus–Yevick equation . It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function . The approximation is named after Jerome K. Percus and George J. Yevick .
The direct correlation function represents the direct correlation between two particles in a system containing N − 2 other particles. It can be represented by
where g t o t a l ( r ) {\displaystyle g_{\rm {total}}(r)} is the radial distribution function , i.e. g ( r ) = exp [ − β w ( r ) ] {\displaystyle g(r)=\exp[-\beta w(r)]} (with w ( r ) the potential of mean force ) and g i n d i r e c t ( r ) {\displaystyle g_{\rm {indirect}}(r)} is the radial distribution function without the direct interaction between pairs u ( r ) {\displaystyle u(r)} included; i.e. we write g i n d i r e c t ( r ) = exp [ − β ( w ( r ) − u ( r ) ) ] {\displaystyle g_{\rm {indirect}}(r)=\exp[-\beta (w(r)-u(r))]} . Thus we approximate c ( r ) by
If we introduce the function y ( r ) = e β u ( r ) g ( r ) {\displaystyle y(r)=e^{\beta u(r)}g(r)} into the approximation for c ( r ) one obtains
This is the essence of the Percus–Yevick approximation for if we substitute this result in the Ornstein–Zernike equation , one obtains the Percus–Yevick equation :
The approximation was defined by Percus and Yevick in 1958.
For hard spheres , the potential u(r) is either zero or infinite, and therefore the Boltzmann factor e − u / k B T {\displaystyle {\text{e}}^{-u/k_{\text{B}}T}} is either one or zero, regardless of temperature T . Therefore structure of a hard-spheres fluid is temperature independent. This leaves just two parameters: the hard-core radius R (which can be eliminated by rescaling distances or wavenumbers), and the packing fraction η (which has a maximum value of 0.64 for random close packing ).
Under these conditions, the Percus–Yevick equation has an analytical solution, obtained by Wertheim in 1963. [ 2 ] [ 3 ] [ 4 ]
The static structure factor of the hard-spheres fluid in Percus–Yevick approximation can be computed using the following C function:
For hard spheres in shear flow , the function u(r) arises from the solution to the steady-state two-body Smoluchowski convection–diffusion equation or two-body Smoluchowski equation with shear flow. An approximate analytical solution to the Smoluchowski convection-diffusion equation was found using the method of matched asymptotic expansions by Banetta and Zaccone in Ref. [ 5 ]
This analytical solution can then be used together with the Percus–Yevick approximation in the Ornstein-Zernike equation . Approximate solutions for the pair distribution function in the extensional and compressional sectors of shear flow and hence the angular-averaged radial distribution function can be obtained, as shown in Ref., [ 6 ] which are in good parameter-free agreement with numerical data up to packing fractions η ≈ 0.5 {\displaystyle \eta \approx 0.5} . | https://en.wikipedia.org/wiki/Percus–Yevick_approximation |
The Percy L. Julian Award was first given in 1975 by the National Organization for the Professional Advancement of Black Chemists and Chemical Engineers (NOBCChE). The award is given every one to two years. It honors black scientists who have made significant contributions to the areas of pure or applied research in science or engineering. [ 1 ]
The award is named to honor chemist Percy Lavon Julian . In becoming director of research of a division in the Glidden Company of Chicago, Julian was the first African-American to lead a research group in a major corporation. He later founded Julian Laboratories, Julian Associates, Inc. and the Julian Research Institute. [ 1 ] | https://en.wikipedia.org/wiki/Percy_L._Julian_Award |
The Peregrine soliton (or Peregrine breather ) is an analytic solution of the nonlinear Schrödinger equation . [ 1 ] This soliton or breather solution was proposed in 1983 by Howell Peregrine , researcher at the mathematics department of the University of Bristol .
Contrary to the usual fundamental soliton that can maintain its profile unchanged during propagation, the Peregrine soliton presents a double spatio-temporal localization. Therefore, starting from a weak oscillation on a continuous background, the Peregrine soliton develops undergoing a progressive increase of its amplitude and a narrowing of its temporal duration. At the point of maximum compression, the amplitude is three times the level of the continuous background (and if one considers the intensity as it is relevant in optics, there is a factor 9 between the peak intensity and the surrounding background). After this point of maximal compression, the wave's amplitude decreases and its width increases.
These features of the Peregrine soliton are fully consistent with the quantitative criteria usually used in order to qualify a wave as a rogue wave . Therefore, the Peregrine soliton is an attractive hypothesis to explain the formation of those waves which have a high amplitude and may appear from nowhere and disappear without a trace. [ 2 ]
The Peregrine soliton is a solution of the one-dimensional nonlinear Schrödinger equation that can be written in normalized units as follows :
with ξ {\displaystyle \xi } the spatial coordinate and τ {\displaystyle \tau } the temporal coordinate. ψ ( ξ , τ ) {\displaystyle \psi (\xi ,\tau )} being the envelope of a surface wave in deep water. The dispersion is anomalous and the nonlinearity is self-focusing (note that similar results could be obtained for a normally dispersive medium combined with a defocusing nonlinearity).
The Peregrine analytical expression is: [ 1 ]
so that the temporal and spatial maxima are obtained for ξ = 0 {\displaystyle \xi =0} and τ = 0 {\displaystyle \tau =0} .
It is also possible to mathematically express the Peregrine soliton according to the spatial frequency η {\displaystyle \eta } : [ 3 ]
ψ ~ ( η , τ ) = 1 2 π ∫ ψ ( ξ , τ ) e i η ξ d ξ = 2 π e i τ [ 1 + 2 i τ 1 + 4 τ 2 exp ( − | η | 2 1 + 4 τ 2 ) − δ ( η ) ] {\displaystyle {\tilde {\psi }}(\eta ,\tau )={\frac {1}{\sqrt {2\pi }}}\int {\psi (\xi ,\tau )e^{i\eta \xi }d\xi }={\sqrt {2\pi }}e^{i\tau }\left[{\frac {1+2i\tau }{\sqrt {1+4\tau ^{2}}}}\exp \left(-{\frac {|\eta |}{2}}{\sqrt {1+4\tau ^{2}}}\right)-\delta (\eta )\right]}
with δ {\displaystyle \delta } being the Dirac delta function .
This corresponds to a modulus (with the constant continuous background here omitted) : | ψ ~ ( η , τ ) | = 2 π exp ( − | η | 2 1 + 4 τ 2 ) . {\displaystyle |{\tilde {\psi }}(\eta ,\tau )|={\sqrt {2\pi }}\exp \left(-{\frac {|\eta |}{2}}{\sqrt {1+4\tau ^{2}}}\right).}
One can notice that for any given time τ {\displaystyle \tau } , the modulus of the spectrum exhibits a typical triangular shape when plotted on a logarithmic scale. The broadest spectrum is obtained for τ = 0 {\displaystyle \tau =0} , which corresponds to the maximum of compression of the spatio-temporal nonlinear structure.
The Peregrine soliton is a first-order rational soliton.
The Peregrine soliton can also be seen as the limiting case of the space-periodic Akhmediev breather when the period tends to infinity. [ 4 ]
The Peregrine soliton can also be seen as the limiting case of the time-periodic Kuznetsov-Ma breather when the period tends to infinity.
Mathematical predictions by H. Peregrine had initially been established in the domain of hydrodynamics . This is however very different from where the Peregrine soliton has been for the first time experimentally generated and characterized.
In 2010, more than 25 years after the initial work of Peregrine, researchers took advantage of the analogy that can be drawn between hydrodynamics and optics in order to generate Peregrine solitons in optical fibers . [ 4 ] [ 6 ] In fact, the evolution of light in fiber optics and the evolution of surface waves in deep water are both modelled by the nonlinear Schrödinger equation (note however that spatial and temporal variables have to be switched). Such an analogy has been exploited in the past in order to generate optical solitons in optical fibers.
More precisely, the nonlinear Schrödinger equation can be written in the context of optical fibers under the following dimensional form :
i ∂ ψ ∂ z − β 2 2 ∂ 2 ψ ∂ t 2 + γ | ψ | 2 ψ = 0 {\displaystyle i{\frac {\partial \psi }{\partial z}}-{\frac {\beta _{2}}{2}}{\frac {\partial ^{2}\psi }{\partial t^{2}}}+\gamma |\psi |^{2}\psi =0}
with β 2 {\displaystyle \beta _{2}} being the second order dispersion (supposed to be anomalous, i.e. β 2 < 0 {\displaystyle \beta _{2}<0} ) and γ {\displaystyle \gamma } being the nonlinear Kerr coefficient. z {\displaystyle z} and t {\displaystyle t} are the propagation distance and the temporal coordinate respectively.
In this context, the Peregrine soliton has the following dimensional expression: [ 5 ]
L N L {\displaystyle L_{NL}} is a nonlinear length defined as L N L = 1 γ P 0 {\displaystyle L_{NL}={\dfrac {1}{\gamma P_{0}}}} with P 0 {\displaystyle P_{0}} being the power of the continuous background. T 0 {\displaystyle T_{0}} is a duration defined as T 0 = β 2 L N L {\displaystyle T_{0}={\sqrt {\beta _{2}L_{NL}}}} .
By using exclusively standard optical communication components, it has been shown that even with an approximate initial condition (in the case of this work, an initial sinusoidal beating), a profile very close to the ideal Peregrine soliton can be generated. [ 5 ] [ 7 ] However, the non-ideal input condition lead to substructures that appear after the point of maximum compression. Those substructures have also a profile close to a Peregrine soliton, [ 5 ] which can be analytically explained using a Darboux transformation. [ 8 ]
The typical triangular spectral shape has also been experimentally confirmed. [ 4 ] [ 5 ] [ 9 ]
These results in optics have been confirmed in 2011 in hydrodynamics [ 10 ] [ 11 ] with experiments carried out in a 15-m long water wave tank . In 2013, complementary experiments using a scale model of a chemical tanker ship have discussed the potential devastating effects on the ship. [ 12 ]
Other experiments carried out in the physics of plasmas have also highlighted the emergence of Peregrine solitons in other fields ruled by the nonlinear Schrödinger equation. [ 13 ] | https://en.wikipedia.org/wiki/Peregrine_soliton |
In botany , perennation is the ability of organisms , particularly plants , to survive from one germinating season to another, especially under unfavourable conditions such as drought or winter cold. It typically involves development of a perennating organ , which stores enough nutrients to sustain the organism during the unfavourable season, and develops into one or more new plants the following year. Common forms of perennating organs are storage organs (e.g. tubers , rhizomes and corm ), and buds . Perennation is closely related with vegetative reproduction , as the organisms commonly use the same organs for both survival and reproduction. [ 1 ]
This botany article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perennation |
In mathematical physics , the Peres metric is defined by the proper time
for any arbitrary function f . If f is a harmonic function with respect to x and y , then the corresponding Peres metric satisfies the Einstein field equations in vacuum . Such a metric is often studied in the context of gravitational waves . The metric is named for Israeli physicist Asher Peres , who first defined it in 1959.
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The Peres–Horodecki criterion is a necessary condition, for the joint density matrix ρ {\displaystyle \rho } of two quantum mechanical systems A {\displaystyle A} and B {\displaystyle B} , to be separable . It is also called the PPT criterion, for positive partial transpose . In the 2×2 and 2×3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states , where the Schmidt decomposition does not apply. The theorem was discovered in 1996 by Asher Peres [ 1 ] and the Horodecki family ( Michał , Paweł , and Ryszard ) [ 2 ]
In higher dimensions, the test is inconclusive, and one should supplement it with more advanced tests, such as those based on entanglement witnesses .
If we have a general state ρ {\displaystyle \rho } which acts on Hilbert space of H A ⊗ H B {\displaystyle {\mathcal {H}}_{A}\otimes {\mathcal {H}}_{B}}
Its partial transpose (with respect to the B party) is defined as
Note that the partial in the name implies that only part of the state is transposed. More precisely, ( I ⊗ T ) ( ρ ) {\displaystyle (I\otimes T)(\rho )} is the identity map applied to the A party and the transposition map applied to the B party.
This definition can be seen more clearly if we write the state as a block matrix:
Where n = dim H A {\displaystyle n=\dim {\mathcal {H}}_{A}} , and each block is a square matrix of dimension m = dim H B {\displaystyle m=\dim {\mathcal {H}}_{B}} . Then the partial transpose is
The criterion states that if ρ {\displaystyle \rho \;\!} is separable then all the eigenvalues of ρ T B {\displaystyle \rho ^{T_{B}}} are non-negative. In other words, if ρ T B {\displaystyle \rho ^{T_{B}}} has a negative eigenvalue, ρ {\displaystyle \rho \;\!} is guaranteed to be entangled . The converse of these statements is true if and only if the dimension of the product space is 2 × 2 {\displaystyle 2\times 2} or 2 × 3 {\displaystyle 2\times 3} .
The result is independent of the party that was transposed, because ρ T A = ( ρ T B ) T {\displaystyle \rho ^{T_{A}}=(\rho ^{T_{B}})^{T}} .
Consider this 2-qubit family of Werner states :
It can be regarded as the convex combination of | Ψ − ⟩ {\displaystyle |\Psi ^{-}\rangle } , a maximally entangled state ,
and the identity element, a maximally mixed state .
Its density matrix is
and the partial transpose
Its least eigenvalue is ( 1 − 3 p ) / 4 {\displaystyle (1-3p)/4} . Therefore, the state is entangled for 1 ≥ p > 1 / 3 {\displaystyle 1\geq p>1/3} .
If ρ is separable, it can be written as
In this case, the effect of the partial transposition is trivial:
As the transposition map preserves eigenvalues, the spectrum of ( ρ i B ) T {\displaystyle (\rho _{i}^{B})^{T}} is the same as the spectrum of ρ i B {\displaystyle \rho _{i}^{B}\;\!} , and in particular ( ρ i B ) T {\displaystyle (\rho _{i}^{B})^{T}} must still be positive semidefinite. Thus ρ T B {\displaystyle \rho ^{T_{B}}} must also be positive semidefinite. This proves the necessity of the PPT criterion.
Showing that being PPT is also sufficient for the 2 X 2 and 3 X 2 (equivalently 2 X 3) cases is more involved. It was shown by the Horodeckis that for every entangled state there exists an entanglement witness . This is a result of geometric nature and invokes the Hahn–Banach theorem (see reference below).
From the existence of entanglement witnesses, one can show that I ⊗ Λ ( ρ ) {\displaystyle I\otimes \Lambda (\rho )} being positive for all positive maps Λ is a necessary and sufficient condition for the separability of ρ, where Λ maps B ( H B ) {\displaystyle B({\mathcal {H}}_{B})} to B ( H A ) {\displaystyle B({\mathcal {H}}_{A})}
Furthermore, every positive map from B ( H B ) {\displaystyle B({\mathcal {H}}_{B})} to B ( H A ) {\displaystyle B({\mathcal {H}}_{A})} can be decomposed into a sum of completely positive and completely copositive maps, when dim ( H B ) = 2 {\displaystyle {\textrm {dim}}({\mathcal {H}}_{B})=2} and dim ( H A ) = 2 or 3 {\displaystyle {\textrm {dim}}({\mathcal {H}}_{A})=2\;{\textrm {or}}\;3} . In other words, every such map Λ can be written as
where Λ 1 {\displaystyle \Lambda _{1}} and Λ 2 {\displaystyle \Lambda _{2}} are completely positive and T is the transposition map. This follows from the Størmer-Woronowicz theorem.
Loosely speaking, the transposition map is therefore the only one that can generate negative eigenvalues in these dimensions. So if ρ T B {\displaystyle \rho ^{T_{B}}} is positive, I ⊗ Λ ( ρ ) {\displaystyle I\otimes \Lambda (\rho )} is positive for any Λ. Thus we conclude that the Peres–Horodecki criterion is also sufficient for separability when dim ( H A ⊗ H B ) ≤ 6 {\displaystyle {\textrm {dim}}({\mathcal {H}}_{A}\otimes {\mathcal {H}}_{B})\leq 6} .
In higher dimensions, however, there exist maps that can't be decomposed in this fashion, and the criterion is no longer sufficient. Consequently, there are entangled states which have a positive partial transpose. Such states have the interesting property that they are bound entangled , i.e. they can not be distilled for quantum communication purposes.
The Peres–Horodecki criterion has been extended to continuous variable systems. Rajiah Simon [ 3 ] formulated a particular version of the PPT criterion in terms of the second-order moments of canonical operators and showed that it is necessary and sufficient for 1 ⊕ 1 {\displaystyle 1\oplus 1} -mode Gaussian states (see Ref. [ 4 ] for a seemingly different but essentially equivalent approach). It was later found [ 5 ] that Simon's condition is also necessary and sufficient for 1 ⊕ n {\displaystyle 1\oplus n} -mode Gaussian states, but no longer sufficient for 2 ⊕ 2 {\displaystyle 2\oplus 2} -mode Gaussian states. Simon's condition can be generalized by taking into account the higher order moments of canonical operators [ 6 ] [ 7 ] or by using entropic measures. [ 8 ] [ 9 ]
For symmetric states of bipartite systems, the positivity of the partial transpose of the density matrix is related to the sign of certain two-body correlations. Here, symmetry means that
holds, where F A B {\displaystyle F_{AB}} is the flip or swap operator exchanging the two parties A {\displaystyle A} and B {\displaystyle B} .
A full basis of the symmetric subspace is of the form ( | n ⟩ A | m ⟩ B + | m ⟩ A | n ⟩ B ) / 2 {\displaystyle (\vert n\rangle _{A}\vert m\rangle _{B}+\vert m\rangle _{A}\vert n\rangle _{B})/{\sqrt {2}}} with m ≠ n {\displaystyle m\neq n} and | n ⟩ A | n ⟩ B . {\displaystyle \vert n\rangle _{A}\vert n\rangle _{B}.} Here for n {\displaystyle n} and m , {\displaystyle m,} 0 ≤ n , m ≤ d − 1 {\displaystyle 0\leq n,m\leq d-1} must hold, where d {\displaystyle d} is the dimension of the two parties.
It can be shown that for such states, ρ {\displaystyle \rho } has a positive partial transpose if and only if [ 10 ]
holds for all operators M . {\displaystyle M.} Hence, if ⟨ M ⊗ M ⟩ ρ < 0 {\displaystyle \langle M\otimes M\rangle _{\rho }<0} holds for some M {\displaystyle M} then the
state possesses non-PPT entanglement .
Moreover, a bipartite symmetric PPT state can be written as
where p k {\displaystyle p_{k}} are probabilities and M k {\displaystyle M_{k}} fulfill T r ( M k ) = 1 {\displaystyle {\rm {Tr}}(M_{k})=1} and T r ( M k 2 ) = 1. {\displaystyle {\rm {Tr}}(M_{k}^{2})=1.} However, for a subsystem larger than a qubit, M k {\displaystyle M_{k}} are not necessarily physical pure density matrices since they can have negative eigenvalues. In this case, even entangled states can be written as a mixture of tensor products of single-party aphysical states, very similar to the form of separable states .
In the qubit case, M k {\displaystyle M_{k}} are physical density matrices, which is consistent with the fact that for two qubits all PPT states are separable.
The concept of such pseudomixtures has been extended to non-symmetric states and to the multipartite case, by the definition of pseudoseparable states [ 11 ]
where N {\displaystyle N} is the number of subsystems and M k ( n ) {\displaystyle M_{k}^{(n)}} fulfill T r ( M k ( n ) ) = 1 {\displaystyle {\rm {Tr}}(M_{k}^{(n)})=1} and T r [ ( M k ( n ) ) 2 ] = 1. {\displaystyle {\rm {Tr}}[(M_{k}^{(n)})^{2}]=1.} The single subsystem aphysical states M k ( n ) {\displaystyle M_{k}^{(n)}} are just states that live on the higher dimensional equivalent of the Bloch sphere even for systems that are larger than a qubit. Separable states are the subset of the set of speudoseparable states, while for qubits the two sets coincide with each other. For systems larger than qubits, such quantum states can be entangled, and in this case they can have PPT or non-PPT bipartitions. | https://en.wikipedia.org/wiki/Peres–Horodecki_criterion |
Perfect Timing Holding (PTH) is a multinational group of companies headquartered in Turkey . It operates in Europe , Asia , America , and Africa . [ 1 ] [ 2 ]
PTH was established in 2000, through the merger of two family businesses: the Huseby company, founded in 1880 in America, and Yavuz, founded in 1925 in Turkey. PTH operates in several sectors, including real estate, higher education, information and communication technology, financial technology, healthcare, tourism, sports management and many more. [ 3 ]
In 1880, Henry Huseby, a Northern Europe immigrant to the United States founded the Huseby Family company, based in Chicago and trading in antiques. After his death, his children diversified the business into media and tourism, expanding it within America and into Europe. [ 4 ]
In 1925, Hüseyin Yavuz founded the Yavuz family business, a Turkish construction company operating in the Erzurum region of Turkey. His son, Mehmet Yavuz, expanded the company to Germany. In 1996, the eldest son, Şakir Yavuz took over the family business, diversifying into textiles, arts collection, consulting, sports management and media. [ 2 ]
In 2000, the two companies merged, forming Perfect Timing Holding (PTH). With its headquarters in Türkiye, PTH operates in 22 countries across Africa, Asia, Europe, and America. [ 5 ] Its subsidiaries include Atafom University International and the ConiaSoft software company. [ 2 ] | https://en.wikipedia.org/wiki/Perfect_Timing_Holding |
In algebra, a perfect complex of modules over a commutative ring A is an object in the derived category of A -modules that is quasi-isomorphic to a bounded complex of finite projective A -modules. A perfect module is a module that is perfect when it is viewed as a complex concentrated at degree zero. For example, if A is Noetherian , a module over A is perfect if and only if it is finitely generated and of finite projective dimension .
Perfect complexes are precisely the compact objects in the unbounded derived category D ( A ) {\displaystyle D(A)} of A -modules. [ 1 ] They are also precisely the dualizable objects in this category. [ 2 ]
A compact object in the ∞-category of (say right) module spectra over a ring spectrum is often called perfect; [ 3 ] see also module spectrum .
When the structure sheaf O X {\displaystyle {\mathcal {O}}_{X}} is not coherent, working with coherent sheaves has awkwardness (namely the kernel of a finite presentation can fail to be coherent). Because of this, SGA 6 Expo I introduces the notion of a pseudo-coherent sheaf .
By definition, given a ringed space ( X , O X ) {\displaystyle (X,{\mathcal {O}}_{X})} , an O X {\displaystyle {\mathcal {O}}_{X}} -module is called pseudo-coherent if for every integer n ≥ 0 {\displaystyle n\geq 0} , locally, there is a free presentation of finite type of length n ; i.e.,
A complex F of O X {\displaystyle {\mathcal {O}}_{X}} -modules is called pseudo-coherent if, for every integer n , there is locally a quasi-isomorphism L → F {\displaystyle L\to F} where L has degree bounded above and consists of finite free modules in degree ≥ n {\displaystyle \geq n} . If the complex consists only of the zero-th degree term, then it is pseudo-coherent if and only if it is so as a module.
Roughly speaking, a pseudo-coherent complex may be thought of as a limit of perfect complexes.
This abstract algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perfect_complex |
In electrostatics , a perfect conductor is an idealized model for real conducting materials. The defining property of a perfect conductor is that static electric field and the charge density both vanish in its interior. If the conductor has excess charge, it accumulates as an infinitesimally thin layer of surface charge . An external electric field is screened from the interior of the material by rearrangement of the surface charge. [ 1 ]
Alternatively, a perfect conductor is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity ( cf. perfect dielectric ). While perfect electrical conductors do not exist in nature, the concept is a useful model when electrical resistance is negligible compared to other effects. One example is ideal magnetohydrodynamics , the study of perfectly conductive fluids. Another example is electrical circuit diagrams , which carry the implicit assumption that the wires connecting the components have no resistance. Yet another example is in computational electromagnetics , where perfect conductor can be simulated faster, since the parts of equations that take finite conductivity into account can be neglected. [ citation needed ]
Perfect conductors:
Superconductors , in addition to having no electrical resistance, exhibit quantum effects such as the Meissner effect and quantization of magnetic flux .
In perfect conductors, the interior magnetic field must remain fixed but can have a zero or nonzero value. [ 2 ] In real superconductors, all magnetic flux is expelled during the phase transition to superconductivity (the Meissner effect ), and the magnetic field is always zero within the bulk of the superconductor.
This computational physics -related article is a stub . You can help Wikipedia by expanding it .
This electromagnetism -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perfect_conductor |
In number theory , a perfect digital invariant (PDI) is a number in a given number base ( b {\displaystyle b} ) that is the sum of its own digits each raised to a given power ( p {\displaystyle p} ). [ 1 ] [ 2 ]
Let n {\displaystyle n} be a natural number . The perfect digital invariant function (also known as a happy function , from happy numbers ) for base b > 1 {\displaystyle b>1} and power p > 0 {\displaystyle p>0} F p , b : N → N {\displaystyle F_{p,b}:\mathbb {N} \rightarrow \mathbb {N} } is defined as:
where k = ⌊ log b n ⌋ + 1 {\displaystyle k=\lfloor \log _{b}{n}\rfloor +1} is the number of digits in the number in base b {\displaystyle b} , and
is the value of each digit of the number. A natural number n {\displaystyle n} is a perfect digital invariant if it is a fixed point for F p , b {\displaystyle F_{p,b}} , which occurs if F p , b ( n ) = n {\displaystyle F_{p,b}(n)=n} . 0 {\displaystyle 0} and 1 {\displaystyle 1} are trivial perfect digital invariants for all b {\displaystyle b} and p {\displaystyle p} , all other perfect digital invariants are nontrivial perfect digital invariants .
For example, the number 4150 in base b = 10 {\displaystyle b=10} is a perfect digital invariant with p = 5 {\displaystyle p=5} , because 4150 = 4 5 + 1 5 + 5 5 + 0 5 {\displaystyle 4150=4^{5}+1^{5}+5^{5}+0^{5}} .
A natural number n {\displaystyle n} is a sociable digital invariant if it is a periodic point for F p , b {\displaystyle F_{p,b}} , where F p , b k ( n ) = n {\displaystyle F_{p,b}^{k}(n)=n} for a positive integer k {\displaystyle k} (here F p , b k {\displaystyle F_{p,b}^{k}} is the k {\displaystyle k} th iterate of F p , b {\displaystyle F_{p,b}} ), and forms a cycle of period k {\displaystyle k} . A perfect digital invariant is a sociable digital invariant with k = 1 {\displaystyle k=1} , and a amicable digital invariant is a sociable digital invariant with k = 2 {\displaystyle k=2} .
All natural numbers n {\displaystyle n} are preperiodic points for F p , b {\displaystyle F_{p,b}} , regardless of the base. This is because if k ≥ p + 2 {\displaystyle k\geq p+2} , n ≥ b k − 1 > b p k {\displaystyle n\geq b^{k-1}>b^{p}k} , so any n {\displaystyle n} will satisfy n > F b , p ( n ) {\displaystyle n>F_{b,p}(n)} until n < b p + 1 {\displaystyle n<b^{p+1}} . There are a finite number of natural numbers less than b p + 1 {\displaystyle b^{p+1}} , so the number is guaranteed to reach a periodic point or a fixed point less than b p + 1 {\displaystyle b^{p+1}} , making it a preperiodic point.
Numbers in base b > p {\displaystyle b>p} lead to fixed or periodic points of numbers n ≤ ( p − 2 ) p + p ( b − 1 ) p {\displaystyle n\leq (p-2)^{p}+p(b-1)^{p}} .
If b > p {\displaystyle b>p} , then the n < b p + 1 {\displaystyle n<b^{p+1}} bound can be reduced.
Let r {\displaystyle r} be the number for which the sum of squares of digits is largest among the numbers less than b p {\displaystyle b^{p}} .
Let s {\displaystyle s} be the number for which the sum of squares of digits is largest among the numbers less than ( p + 1 ) ( b − 1 ) p {\displaystyle (p+1)(b-1)^{p}} .
Let t {\displaystyle t} be the number for which the sum of squares of digits is largest among the numbers less than p b p {\displaystyle pb^{p}} .
Let u {\displaystyle u} be the number for which the sum of squares of digits is largest among the numbers less than F p , b ( t ) + 1 {\displaystyle F_{p,b}(t)+1} .
u ≤ F p , b ( u ) < F p , b ( t ) {\displaystyle u\leq F_{p,b}(u)<F_{p,b}(t)} . Thus, numbers in base b > p {\displaystyle b>p} lead to cycles or fixed points of numbers n ≤ F p , b ( u ) = ( p − 1 ) p + p ( b − 1 ) p {\displaystyle n\leq F_{p,b}(u)=(p-1)^{p}+p(b-1)^{p}} .
The number of iterations i {\displaystyle i} needed for F p , b i ( n ) {\displaystyle F_{p,b}^{i}(n)} to reach a fixed point is the perfect digital invariant function's persistence of n {\displaystyle n} , and undefined if it never reaches a fixed point.
F 1 , b {\displaystyle F_{1,b}} is the digit sum . The only perfect digital invariants are the single-digit numbers in base b {\displaystyle b} , and there are no periodic points with prime period greater than 1.
F p , 2 {\displaystyle F_{p,2}} reduces to F 1 , 2 {\displaystyle F_{1,2}} , as for any power p {\displaystyle p} , 0 p = 0 {\displaystyle 0^{p}=0} and 1 p = 1 {\displaystyle 1^{p}=1} .
For every natural number k > 1 {\displaystyle k>1} , if p < b {\displaystyle p<b} , ( b − 1 ) ≡ 0 mod k {\displaystyle (b-1)\equiv 0{\bmod {k}}} and ( p − 1 ) ≡ 0 mod ϕ ( k ) {\displaystyle (p-1)\equiv 0{\bmod {\phi }}(k)} , then for every natural number n {\displaystyle n} , if n ≡ m mod k {\displaystyle n\equiv m{\bmod {k}}} , then F p , b ( n ) ≡ m mod k {\displaystyle F_{p,b}(n)\equiv m{\bmod {k}}} , where ϕ ( k ) {\displaystyle \phi (k)} is Euler's totient function .
Let
be a natural number with j {\displaystyle j} digits, where 0 ≤ d i < b {\displaystyle 0\leq d_{i}<b} , and ( b − 1 ) ≡ 0 mod k {\displaystyle (b-1)\equiv 0{\bmod {k}}} , where k {\displaystyle k} is a natural number greater than 1.
According to the divisibility rules of base b {\displaystyle b} , if b − 1 ≡ 0 mod k {\displaystyle b-1\equiv 0{\bmod {k}}} , then if n ≡ m mod k {\displaystyle n\equiv m{\bmod {k}}} , then the digit sum
If a digit d i ≡ m mod k {\displaystyle d_{i}\equiv m{\bmod {k}}} , then d i p ≡ m p mod k {\displaystyle d_{i}^{p}\equiv m^{p}{\bmod {k}}} . According to Euler's theorem , if ( p − 1 ) ≡ 0 mod ϕ ( k ) {\displaystyle (p-1)\equiv 0{\bmod {\phi }}(k)} , m p mod k = m mod k {\displaystyle m^{p}{\bmod {k}}=m{\bmod {k}}} . Thus, if the digit sum F 1 , b ( n ) ≡ m mod k {\displaystyle F_{1,b}(n)\equiv m{\bmod {k}}} , then F p , b ( n ) ≡ m mod k {\displaystyle F_{p,b}(n)\equiv m{\bmod {k}}} .
Therefore, for any natural number k {\displaystyle k} , if p < b {\displaystyle p<b} , ( b − 1 ) ≡ 0 mod k {\displaystyle (b-1)\equiv 0{\bmod {k}}} and ( p − 1 ) ≡ 0 mod ϕ ( k ) {\displaystyle (p-1)\equiv 0{\bmod {\phi }}(k)} , then for every natural number n {\displaystyle n} , if n ≡ m mod k {\displaystyle n\equiv m{\bmod {k}}} , then F p , b ( n ) ≡ m mod k {\displaystyle F_{p,b}(n)\equiv m{\bmod {k}}} .
No upper bound can be determined for the size of perfect digital invariants in a given base and arbitrary power, and it is not currently known whether or not the number of perfect digital invariants for an arbitrary base is finite or infinite. [ 1 ]
By definition, any three-digit perfect digital invariant n = d 2 d 1 d 0 {\displaystyle n=d_{2}d_{1}d_{0}} for F 2 , b {\displaystyle F_{2,b}} with natural number digits 0 ≤ d 0 < b {\displaystyle 0\leq d_{0}<b} , 0 ≤ d 1 < b {\displaystyle 0\leq d_{1}<b} , 0 ≤ d 2 < b {\displaystyle 0\leq d_{2}<b} has to satisfy the cubic Diophantine equation d 0 2 + d 1 2 + d 2 2 = d 2 b 2 + d 1 b + d 0 {\displaystyle d_{0}^{2}+d_{1}^{2}+d_{2}^{2}=d_{2}b^{2}+d_{1}b+d_{0}} . d 2 {\displaystyle d_{2}} has to be equal to 0 or 1 for any b > 2 {\displaystyle b>2} , because the maximum value n {\displaystyle n} can take is n = ( 2 − 1 ) 2 + 2 ( b − 1 ) 2 = 1 + 2 ( b − 1 ) 2 < 2 b 2 {\displaystyle n=(2-1)^{2}+2(b-1)^{2}=1+2(b-1)^{2}<2b^{2}} . As a result, there are actually two related quadratic Diophantine equations to solve:
The two-digit natural number n = d 1 d 0 {\displaystyle n=d_{1}d_{0}} is a perfect digital invariant in base
This can be proven by taking the first case, where d 2 = 0 {\displaystyle d_{2}=0} , and solving for b {\displaystyle b} . This means that for some values of d 0 {\displaystyle d_{0}} and d 1 {\displaystyle d_{1}} , n {\displaystyle n} is not a perfect digital invariant in any base, as d 1 {\displaystyle d_{1}} is not a divisor of d 0 ( d 0 − 1 ) {\displaystyle d_{0}(d_{0}-1)} . Moreover, d 0 > 1 {\displaystyle d_{0}>1} , because if d 0 = 0 {\displaystyle d_{0}=0} or d 0 = 1 {\displaystyle d_{0}=1} , then b = d 1 {\displaystyle b=d_{1}} , which contradicts the earlier statement that 0 ≤ d 1 < b {\displaystyle 0\leq d_{1}<b} .
There are no three-digit perfect digital invariants for F 2 , b {\displaystyle F_{2,b}} , which can be proven by taking the second case, where d 2 = 1 {\displaystyle d_{2}=1} , and letting d 0 = b − a 0 {\displaystyle d_{0}=b-a_{0}} and d 1 = b − a 1 {\displaystyle d_{1}=b-a_{1}} . Then the Diophantine equation for the three-digit perfect digital invariant becomes
2 ( a 0 + a 1 ) > a 1 {\displaystyle 2(a_{0}+a_{1})>a_{1}} for all values of 0 < a 1 ≤ b {\displaystyle 0<a_{1}\leq b} . Thus, there are no solutions to the Diophantine equation, and there are no three-digit perfect digital invariants for F 2 , b {\displaystyle F_{2,b}} .
There are just four numbers, after unity, which are the sums of the cubes of their digits:
By definition, any four-digit perfect digital invariant n {\displaystyle n} for F 3 , b {\displaystyle F_{3,b}} with natural number digits 0 ≤ d 0 < b {\displaystyle 0\leq d_{0}<b} , 0 ≤ d 1 < b {\displaystyle 0\leq d_{1}<b} , 0 ≤ d 2 < b {\displaystyle 0\leq d_{2}<b} , 0 ≤ d 3 < b {\displaystyle 0\leq d_{3}<b} has to satisfy the quartic Diophantine equation d 0 3 + d 1 3 + d 2 3 + d 3 3 = d 3 b 3 + d 2 b 2 + d 1 b + d 0 {\displaystyle d_{0}^{3}+d_{1}^{3}+d_{2}^{3}+d_{3}^{3}=d_{3}b^{3}+d_{2}b^{2}+d_{1}b+d_{0}} . d 3 {\displaystyle d_{3}} has to be equal to 0, 1, 2 for any b > 3 {\displaystyle b>3} , because the maximum value n {\displaystyle n} can take is n = ( 3 − 2 ) 3 + 3 ( b − 1 ) 3 = 1 + 3 ( b − 1 ) 3 < 3 b 3 {\displaystyle n=(3-2)^{3}+3(b-1)^{3}=1+3(b-1)^{3}<3b^{3}} . As a result, there are actually three related cubic Diophantine equations to solve
We take the first case, where d 3 = 0 {\displaystyle d_{3}=0} .
Let k {\displaystyle k} be a positive integer and the number base b = 3 k + 1 {\displaystyle b=3k+1} . Then:
Let the digits of n 1 = d 2 b 2 + d 1 b + d 0 {\displaystyle n_{1}=d_{2}b^{2}+d_{1}b+d_{0}} be d 2 = k {\displaystyle d_{2}=k} , d 1 = 2 k + 1 {\displaystyle d_{1}=2k+1} , and d 0 = 0 {\displaystyle d_{0}=0} . Then
Thus n 1 {\displaystyle n_{1}} is a perfect digital invariant for F 3 , b {\displaystyle F_{3,b}} for all k {\displaystyle k} .
Let the digits of n 2 = d 2 b 2 + d 1 b + d 0 {\displaystyle n_{2}=d_{2}b^{2}+d_{1}b+d_{0}} be d 2 = k {\displaystyle d_{2}=k} , d 1 = 2 k + 1 {\displaystyle d_{1}=2k+1} , and d 0 = 1 {\displaystyle d_{0}=1} . Then
Thus n 2 {\displaystyle n_{2}} is a perfect digital invariant for F 3 , b {\displaystyle F_{3,b}} for all k {\displaystyle k} .
Let the digits of n 3 = d 2 b 2 + d 1 b + d 0 {\displaystyle n_{3}=d_{2}b^{2}+d_{1}b+d_{0}} be d 2 = k + 1 {\displaystyle d_{2}=k+1} , d 1 = 0 {\displaystyle d_{1}=0} , and d 0 = 2 k + 1 {\displaystyle d_{0}=2k+1} . Then
Thus n 3 {\displaystyle n_{3}} is a perfect digital invariant for F 3 , b {\displaystyle F_{3,b}} for all k {\displaystyle k} .
Let k {\displaystyle k} be a positive integer and the number base b = 3 k + 2 {\displaystyle b=3k+2} . Then:
Let the digits of n 1 = d 2 b 2 + d 1 b + d 0 {\displaystyle n_{1}=d_{2}b^{2}+d_{1}b+d_{0}} be d 2 = k {\displaystyle d_{2}=k} , d 1 = 2 k + 1 {\displaystyle d_{1}=2k+1} , and d 0 = 0 {\displaystyle d_{0}=0} . Then
Thus n 1 {\displaystyle n_{1}} is a perfect digital invariant for F 3 , b {\displaystyle F_{3,b}} for all k {\displaystyle k} .
Let k {\displaystyle k} be a positive integer and the number base b = 6 k + 4 {\displaystyle b=6k+4} . Then:
Let the digits of n 4 = d 2 b 2 + d 1 b + d 0 {\displaystyle n_{4}=d_{2}b^{2}+d_{1}b+d_{0}} be d 2 = k + 1 {\displaystyle d_{2}=k+1} , d 1 = 3 k + 2 {\displaystyle d_{1}=3k+2} , and d 0 = 2 k + 1 {\displaystyle d_{0}=2k+1} . Then
Thus n 4 {\displaystyle n_{4}} is a perfect digital invariant for F 3 , b {\displaystyle F_{3,b}} for all k {\displaystyle k} .
All numbers are represented in base b {\displaystyle b} .
16 → 52 → 41 → 23 → 16
4 → 20 → 4
5 → 31 → 12 → 5
15 → 32 → 15
58 → 108 → 72 → 58
75 → 82 → 75
5 → 23 → 12 → 5
68 → 91 → 75 → 68
5 → 21 → 5
8 → 54 → 35 → 2A → 88 → A8 → 118 → 56 → 51 → 22 → 8
18 → 55 → 42 → 18
68 → 84 → 68
79 → A0 → 79
98 → B2 → 98
29 → 61 → 29
8 → 44 → 22 → 8
15 → 1B → 82 → 48 → 55 → 35 → 24 → 15
2B → 85 → 5E → EB → 162 → 2B
4E → E2 → D5 → CE → 17A → A0 → 6A → 91 → 57 → 4E
9A → C1 → 9A
D6 → DA → 12E → D6
2 → 11 → 2
13 → 40 → 121 → 13
23 → 50 → 236 → 506 → 665 → 1424 → 254 → 401 → 122 → 23
51 → 240 → 132 → 51
160 → 430 → 160
161 → 431 → 161
466 → 1306 → 466
516 → 666 → 1614 → 552 → 516
38 → 658 → 1147 → 504 → 230 → 38
152 → 158 → 778 → 1571 → 572 → 578 → 1308 → 660 → 530 → 178 → 1151 → 152
638 → 1028 → 638
818 → 1358 → 818
55 → 250 → 133 → 55
136 → 244 → 136
160 → 217 → 352 → 160
919 → 1459 → 919
3 → 25 → 111 → 3
9 → 603 → 201 → 9
A → 82A → 1162 → 196 → 790 → 895 → 1032 → 33 → 4A → 888 → 1177 → 576 → 5723 → A3 → 8793 → 1210 → A
25A → 940 → 661 → 364 → 25A
366 → 388 → 876 → 894 → A87 → 1437 → 366
49A → 1390 → 629 → 797 → 1077 → 575 → 49A
121 → 200 → 121
122 → 1020 → 122
1234 → 2404 → 4103 → 2323 → 1234
2324 → 2434 → 4414 → 11034 → 2324
3444 → 11344 → 4340 → 4333 → 3444
3 → 3303 → 23121 → 10311 → 3312 → 20013 → 10110 → 3
3311 → 13220 → 10310 → 3311
Perfect digital invariants can be extended to the negative integers by use of a signed-digit representation to represent each integer.
In balanced ternary , the digits are 1, −1 and 0. This results in the following:
A happy number n {\displaystyle n} for a given base b {\displaystyle b} and a given power p {\displaystyle p} is a preperiodic point for the perfect digital invariant function F p , b {\displaystyle F_{p,b}} such that the m {\displaystyle m} -th iteration of F p , b {\displaystyle F_{p,b}} is equal to the trivial perfect digital invariant 1 {\displaystyle 1} , and an unhappy number is one such that there exists no such m {\displaystyle m} .
The example below implements the perfect digital invariant function described in the definition above to search for perfect digital invariants and cycles in Python . This can be used to find happy numbers . | https://en.wikipedia.org/wiki/Perfect_digital_invariant |
In graph theory , the perfect graph theorem of László Lovász ( 1972a , 1972b ) states that an undirected graph is perfect if and only if its complement graph is also perfect. This result had been conjectured by Berge ( 1961 , 1963 ), and it is sometimes called the weak perfect graph theorem to distinguish it from the strong perfect graph theorem [ 1 ] characterizing perfect graphs by their forbidden induced subgraphs .
A perfect graph is an undirected graph with the property that, in every one of its induced subgraphs , the size of the largest clique equals the minimum number of colors in a coloring of the subgraph. Perfect graphs include many important graphs classes including bipartite graphs , chordal graphs , and comparability graphs .
The complement of a graph has an edge between two vertices if and only if the original graph does not have an edge between the same two vertices. Thus, a clique in the original graph becomes an independent set in the complement and a coloring of the original graph becomes a clique cover of the complement.
The perfect graph theorem states:
Equivalently, in a perfect graph, the size of the maximum independent set equals the minimum number of cliques in a clique cover.
Let G be a cycle graph of odd length greater than three (a so-called "odd hole"). Then G requires at least three colors in any coloring, but has no triangle, so it is not perfect. By the perfect graph theorem, the complement of G (an "odd antihole") must therefore also not be perfect. If G is a cycle of five vertices, it is isomorphic to its complement , but this property is not true for longer odd cycles, and it is not as trivial to compute the clique number and chromatic number in an odd antihole as it is in an odd hole. As the strong perfect graph theorem states, the odd holes and odd antiholes turn out to be the minimal forbidden induced subgraphs for the perfect graphs.
In a nontrivial bipartite graph, the optimal number of colors is (by definition) two, and (since bipartite graphs are triangle-free ) the maximum clique size is also two. Also, any induced subgraph of a bipartite graph remains bipartite. Therefore, bipartite graphs are perfect. In n -vertex bipartite graphs, a minimum clique cover takes the form of a maximum matching together with an additional clique for every unmatched vertex, with size n − M , where M is the cardinality of the matching. Thus, in this case, the perfect graph theorem implies Kőnig's theorem that the size of a maximum independent set in a bipartite graph is also n − M , [ 2 ] a result that was a major inspiration for Berge's formulation of the theory of perfect graphs.
Mirsky's theorem characterizing the height of a partially ordered set in terms of partitions into antichains can be formulated as the perfection of the comparability graph of the partially ordered set, and Dilworth's theorem characterizing the width of a partially ordered set in terms of partitions into chains can be formulated as the perfection of the complements of these graphs. Thus, the perfect graph theorem can be used to prove Dilworth's theorem from the (much easier) proof of Mirsky's theorem, or vice versa. [ 3 ]
To prove the perfect graph theorem, Lovász used an operation of replacing vertices in a graph by cliques; it was already known to Berge that, if a graph is perfect, the graph formed by this replacement process is also perfect. [ 4 ] Any such replacement process may be broken down into repeated steps of doubling a vertex. If the doubled vertex belongs to a maximum clique of the graph, it increases both the clique number and the chromatic number by one. If, on the other hand, the doubled vertex does not belong to a maximum clique, form a graph H by removing the vertices with the same color as the doubled vertex (but not the doubled vertex itself) from an optimal coloring of the given graph. The removed vertices meet every maximum clique, so H has clique number and chromatic number one less than that of the given graph. The removed vertices and the new copy of the doubled vertex can then be added back as a single color class, showing that in this case the doubling step leaves the chromatic number unchanged. The same argument shows that doubling preserves the equality of the clique number and the chromatic number in every induced subgraph of the given graph, so each doubling step preserves the perfection of the graph. [ 5 ]
Given a perfect graph G , Lovász forms a graph G * by replacing each vertex v by a clique of t v vertices, where t v is the number of distinct maximum independent sets in G that contain v . It is possible to correspond each of the distinct maximum independent sets in G with one of the maximum independent sets in G *, in such a way that the chosen maximum independent sets in G * are all disjoint and each vertex of G * appears in a single chosen set; that is, G * has a coloring in which each color class is a maximum independent set. Necessarily, this coloring is an optimal coloring of G *. Because G is perfect, so is G *, and therefore it has a maximum clique K * whose size equals the number of colors in this coloring, which is the number of distinct maximum independent sets in G ; necessarily, K * contains a distinct representative for each of these maximum independent sets. The corresponding set K of vertices in G (the vertices whose expanded cliques in G * intersect K *) is a clique in G with the property that it intersects every maximum independent set in G . Therefore, the graph formed from G by removing K has clique cover number at most one less than the clique number of G , and independence number at least one less than the independence number of G , and the result follows by induction on this number. [ 6 ]
The strong perfect graph theorem of Chudnovsky et al. (2006) states that a graph is perfect if and only if none of its induced subgraphs are cycles of odd length greater than or equal to five, or their complements. Because this characterization is unaffected by graph complementation, it immediately implies the weak perfect graph theorem.
Cameron, Edmonds & Lovász (1986) proved that, if the edges of a complete graph are partitioned into three subgraphs in such a way that every three vertices induce a connected graph in one of the three subgraphs, and if two of the subgraphs are perfect, then the third subgraph is also perfect. The perfect graph theorem is the special case of this result when one of the three subgraphs is the empty graph . | https://en.wikipedia.org/wiki/Perfect_graph_theorem |
In mathematics , more specifically in group theory , a group is said to be perfect if it equals its own commutator subgroup , or equivalently, if the group has no non-trivial abelian quotients .
The smallest (non-trivial) perfect group is the alternating group A 5 . More generally, any non-abelian simple group is perfect since the commutator subgroup is a normal subgroup with abelian quotient. However, a perfect group need not be simple; for example, the special linear group over the field with 5 elements, SL(2,5) (or the binary icosahedral group , which is isomorphic to it) is perfect but not simple (it has a non-trivial center containing − ( 1 0 0 1 ) = ( 4 0 0 4 ) {\displaystyle -\!\left({\begin{smallmatrix}1&0\\0&1\end{smallmatrix}}\right)=\left({\begin{smallmatrix}4&0\\0&4\end{smallmatrix}}\right)} ).
The direct product of any two simple non-abelian groups is perfect but not simple; the commutator of two elements is [( a , b ),( c , d )] = ([ a , c ],[ b , d ]). Since commutators in each simple group form a generating set, pairs of commutators form a generating set of the direct product.
The fundamental group of S O ( 3 ) / I 60 {\displaystyle SO(3)/I_{60}} is a perfect group of order 120. [ 1 ]
More generally, a quasisimple group (a perfect central extension of a simple group) that is a non-trivial extension (and therefore not a simple group itself) is perfect but not simple; this includes all the insoluble non-simple finite special linear groups SL( n , q ) as extensions of the projective special linear group PSL( n , q ) (SL(2,5) is an extension of PSL(2,5), which is isomorphic to A 5 ). Similarly, the special linear group over the real and complex numbers is perfect, but the general linear group GL is never perfect (except when trivial or over F 2 {\displaystyle \mathbb {F} _{2}} , where it equals the special linear group), as the determinant gives a non-trivial abelianization and indeed the commutator subgroup is SL.
A non-trivial perfect group, however, is necessarily not solvable ; and 4 divides its order (if finite), moreover, if 8 does not divide the order, then 3 does. [ 2 ]
Every acyclic group is perfect, but the converse is not true: A 5 is perfect but not acyclic (in fact, not even superperfect ), see ( Berrick & Hillman 2003 ). In fact, for n ≥ 5 {\displaystyle n\geq 5} the alternating group A n {\displaystyle A_{n}} is perfect but not superperfect, with H 2 ( A n , Z ) = Z / 2 {\displaystyle H_{2}(A_{n},\mathbb {Z} )=\mathbb {Z} /2} for n ≥ 8 {\displaystyle n\geq 8} .
Any quotient of a perfect group is perfect. A non-trivial finite perfect group that is not simple must then be an extension of at least one smaller simple non-abelian group. But it can be the extension of more than one simple group. In fact, the direct product of perfect groups is also perfect.
Every perfect group G determines another perfect group E (its universal central extension ) together with a surjection f : E → G whose kernel is in the center of E, such that f is universal with this property. The kernel of f is called the Schur multiplier of G because it was first studied by Issai Schur in 1904; it is isomorphic to the homology group H 2 ( G ) {\displaystyle H_{2}(G)} .
In the plus construction of algebraic K-theory , if we consider the group GL ( A ) = colim GL n ( A ) {\displaystyle \operatorname {GL} (A)={\text{colim}}\operatorname {GL} _{n}(A)} for a commutative ring A {\displaystyle A} , then the subgroup of elementary matrices E ( R ) {\displaystyle E(R)} forms a perfect subgroup.
As the commutator subgroup is generated by commutators, a perfect group may contain elements that are products of commutators but not themselves commutators. Øystein Ore showed in 1951 that the alternating groups on five or more elements contained only commutators, and conjectured that this was so for all the finite non-abelian simple groups. Ore's conjecture was finally proven in 2008. The proof relies on the classification theorem . [ 3 ]
A basic fact about perfect groups is Grün's lemma ( Grün 1935 , Satz 4, [ note 1 ] p. 3), due to Otto Grün : the quotient of a perfect group by its center is centerless (has trivial center).
Proof: If G is a perfect group, let Z 1 and Z 2 denote the first two terms of the upper central series of G (i.e., Z 1 is the center of G , and Z 2 / Z 1 is the center of G / Z 1 ). If H and K are subgroups of G , denote the commutator of H and K by [ H , K ] and note that [ Z 1 , G ] = 1 and [ Z 2 , G ] ⊆ Z 1 , and consequently (the convention that [ X , Y , Z ] = [[ X , Y ], Z ] is followed):
By the three subgroups lemma (or equivalently, by the Hall-Witt identity ), it follows that [ G , Z 2 ] = [[ G , G ], Z 2 ] = [ G , G , Z 2 ] = {1}. Therefore, Z 2 ⊆ Z 1 = Z ( G ), and the center of the quotient group G / Z ( G ) is the trivial group .
As a consequence, all higher centers (that is, higher terms in the upper central series ) of a perfect group equal the center.
In terms of group homology , a perfect group is precisely one whose first homology group vanishes: H 1 ( G , Z ) = 0, as the first homology group of a group is exactly the abelianization of the group, and perfect means trivial abelianization. An advantage of this definition is that it admits strengthening:
Especially in the field of algebraic K-theory , a group is said to be quasi-perfect if its commutator subgroup is perfect; in symbols, a quasi-perfect group is one such that G (1) = G (2) (the commutator of the commutator subgroup is the commutator subgroup), while a perfect group is one such that G (1) = G (the commutator subgroup is the whole group). See ( Karoubi 1973 , pp. 301–411) and ( Inassaridze 1995 , p. 76). | https://en.wikipedia.org/wiki/Perfect_group |
In economics , perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition . With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market prices, their own utility, and own cost functions.
In game theory , a sequential game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the game (e.g. the starting hands of each player in a card game). [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Perfect information is importantly different from complete information , which implies common knowledge of each player's utility functions, payoffs, strategies and "types". A game with perfect information may or may not have complete information.
Games where some aspect of play is hidden from opponents – such as the cards in poker and bridge – are examples of games with imperfect information . [ 5 ] [ 6 ]
Chess is an example of a game with perfect information, as each player can see all the pieces on the board at all times. [ 2 ] Other games with perfect information include tic-tac-toe , Reversi , checkers , and Go . [ 3 ]
Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, but no secret information , and games with simultaneous moves are games of perfect information. [ 4 ] [ 7 ] [ 8 ] [ 9 ]
Games which are sequential (players alternate in moving) and which have chance events (with known probabilities to all players) but no secret information , are sometimes considered games of perfect information. This includes games such as backgammon and Monopoly . However, some academic papers do not regard such games as games of perfect information because the results of chance themselves are unknown prior to them occurring. [ 4 ] [ 7 ] [ 8 ] [ 9 ]
Games with simultaneous moves are generally not considered games of perfect information. This is because each player holds information, which is secret, and must play a move without knowing the opponent's secret information. Nevertheless, some such games are symmetrical , and fair. An example of a game in this category includes rock paper scissors . [ 4 ] [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Perfect_information |
Perfect mixing is a term heavily used in relation to the definition of models that predict the behavior of chemical reactors . Perfect mixing assumes that there are no spatial gradients in a given physical envelope , such as:
This physical chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perfect_mixing |
In game theory , perfect recall is a property of players within extensive-form games , introduced by Harold W. Kuhn in 1953. [ 1 ] it describes a player's ability to remember their past actions and the information they possessed at previous decision points. [ 2 ] [ 3 ] For example, in a simplified card game where a player makes multiple betting rounds, perfect recall means they remember their own previous bets and the cards they've seen. Essentially, it indicates that a player does not "forget" relevant information acquired during the game.
It is important to distinguish perfect recall from perfect information . While perfect information means all players know all previous actions of all players, perfect recall means a player remembers their own past actions and knowledge.
Perfect recall is crucial for the consistency of rational decision-making in sequential games . If a player forgets past information, their current decisions may contradict their earlier intentions. The concept plays a key role in the relationship between mixed and behavioral strategies . In games where players have perfect recall, these two types of strategies are essentially equivalent, meaning that any outcome that can be achieved with a mixed strategy can also be achieved with a behavioral strategy, and vice versa. This equivalence, notably formalized in Kuhn's theorem , simplifies the analysis of such games. [ 4 ] It is a core component of how game theorists analyze extensive-form games.
The formal definition of perfect recall involves the concept of information sets in extensive-form games. It ensures that if a player reaches a certain information set, the player's past actions and information are consistent with all the nodes within that information set. Games with players possessing perfect recall are often easier to analyze than those where players do not. Conversely, a lack of perfect recall by a player can lead to situations where that player is unable to execute planned strategies, affecting game outcomes.
This game theory article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perfect_recall_(game_theory) |
A perfect ruler of length ℓ {\displaystyle \ell } is a ruler with integer markings a 1 = 0 < a 2 < ⋯ < a n = ℓ {\displaystyle a_{1}=0<a_{2}<\dots <a_{n}=\ell } , for which there exists an integer m {\displaystyle m} such that any positive integer k ≤ m {\displaystyle k\leq m} is uniquely expressed as the difference k = a i − a j {\displaystyle k=a_{i}-a_{j}} for some i , j {\displaystyle i,j} . This is referred to as an m {\displaystyle m} -perfect ruler.
An optimal perfect ruler is one of the smallest length for fixed values of m {\displaystyle m} and n {\displaystyle n} .
A 4-perfect ruler of length 7 {\displaystyle 7} is given by ( a 1 , a 2 , a 3 , a 4 ) = ( 0 , 1 , 3 , 7 ) {\displaystyle (a_{1},a_{2},a_{3},a_{4})=(0,1,3,7)} . To verify this, we need to show that every positive integer k ≤ 4 {\displaystyle k\leq 4} is uniquely expressed as the difference of two markings:
This article incorporates material from perfect ruler on PlanetMath , which is licensed under the Creative Commons Attribution/Share-Alike License .
This combinatorics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Perfect_ruler |
In general topology , a subset of a topological space is perfect if it is closed and has no isolated points . Equivalently: the set S {\displaystyle S} is perfect if S = S ′ {\displaystyle S=S'} , where S ′ {\displaystyle S'} denotes the set of all limit points of S {\displaystyle S} , also known as the derived set of S {\displaystyle S} . (Some authors do not consider the empty set to be perfect. [ 1 ] )
In a perfect set, every point can be approximated arbitrarily well by other points from the set: given any point of S {\displaystyle S} and any neighborhood of the point, there is another point of S {\displaystyle S} that lies within the neighborhood. Furthermore, any point of the space that can be so approximated by points of S {\displaystyle S} belongs to S {\displaystyle S} .
Note that the term perfect space is also used, incompatibly, to refer to other properties of a topological space, such as being a G δ space . As another possible source of confusion, also note that having the perfect set property is not the same as being a perfect set.
Examples of perfect subsets of the real line R {\displaystyle \mathbb {R} } are the empty set , all closed intervals , the real line itself, and the Cantor set . The latter is noteworthy in that it is totally disconnected .
Whether a set is perfect or not (and whether it is closed or not) depends on the surrounding space. For instance, the set S = [ 0 , 1 ] ∩ Q {\displaystyle S=[0,1]\cap \mathbb {Q} } is perfect as a subset of the space Q {\displaystyle \mathbb {Q} } but not perfect as a subset of the space R {\displaystyle \mathbb {R} } , since it fails to be closed in the latter.
Every topological space can be written in a unique way as the disjoint union of a perfect set and a scattered set . [ 2 ] [ 3 ]
Cantor proved that every closed subset of the real line can be uniquely written as the disjoint union of a perfect set and a countable set . This is also true more generally for all closed subsets of Polish spaces , in which case the theorem is known as the Cantor–Bendixson theorem .
Cantor also showed that every non-empty perfect subset of the real line has cardinality 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} , the cardinality of the continuum . These results are extended in descriptive set theory as follows: | https://en.wikipedia.org/wiki/Perfect_set |
Perfluoro(2-methyl-3-pentanone) is a fluorinated ketone with the structural formula CF 3 CF 2 C(=O)CF(CF 3 ) 2 , a fully-fluorinated analog of ethyl isopropyl ketone . It is used as an electronics coolant liquid and fire protection fluid sold commercially by 3M under brand names such as Novec 1230 , Novec 649 , and FK-5-1-12 . It is also known as "waterless water" or "dry water".
3M produces perfluoro(2-methyl-3-pentanone) under different brand names of Novec 1230 and Novec 649 . These two products have different purity grades (>99% and >99.9%, respectively) [ 1 ] intended for different industrial applications.
Novec 1230 is used as gaseous fire suppression agent in scenarios where water-based fire suppression (for example, from a fire sprinkler ) would be impractical or where it could damage expensive equipment or property, such as museums , server rooms , banks , clean rooms and hospitals . It functions by rapidly removing heat to extinguish a fire before it starts; also, its density enables it to displace air and thereby deprive the fire of oxygen. Novec 1230 can be used in both total/partial/localized flooding systems, and directional spray-type applications; it is also used in portable extinguishers for specialized applications. The Patent for Novec 1230 as fire extinguishant ended on July 19, 2020. [ 2 ] Since the expiry of the patent, multiple companies have brought equivalent products to market under the chemical name FK-5-1-12.
Recently, it has found active use in microencapsulated form [ 3 ] [ 4 ] in the manufacture of fire-extinguishing composite materials. [ 5 ] Samsung SDI is using this product to extinguish fires in the early stages of modular high-capacity storage systems (ESS) based on lithium-ion batteries for solar panels and electric vehicles . In August 2019, Samsung SDI officially announced [ 6 ] its investment of $ 169 million into fire-extinguishing composite materials based on microencapsulated Novec 1230. The firm later reported that UL9540A testing for this product was passed.
Novec 649 is a low-temperature heat-transfer fluid. It has been used as a full-immersion fluid in a proof of concept data center cooling system by Intel and SGI . [ 7 ] Due to its relatively low 49 °C (120.2 °F) boiling point, it is used as a heat transfer fluid in two-phase immersion cooling systems. Within these systems evaporative cooling is utilized to remove excess heat generated from immersed technology. The heat is then removed from the vaporous Novec 649 using a condensing loop typically running cold water. Novec 649 is also being considered to be used for cooling silicon photomultiplier (SiPM) sensors to −40 °C (−40 °F) in single-phase configuration as part of Large Hadron Collider’s high luminosity upgrade . [ 8 ]
Traditional perfluorocarbon (PFC) based compounds used for cooling, such as Fluorinert , display high global warming potentials (GWPs), typically 5,000 to 10,000 times that of CO 2 . [ 1 ] Novec 649 was chosen as a good drop-in replacement due to it having similar thermo-physical properties to Fluorinert FC-72 ( perfluorohexane , C6F14) while exhibiting a very low global warming potential of 1. [ 1 ] [ 9 ]
Novec 649/1230 does not deplete ozone ( ODP 0) and has a global warming potential of 1 (over 100 years), equivalent to that of carbon dioxide . [ 10 ] The Globally Harmonized System of Classification and Labeling of Chemicals (GHS) classifies this chemical as H412 - Harmful to aquatic life with long lasting effects. [ 11 ] Photolysis in sunlight, hydrolysis and hydration may be a significant sink of Novec 649/1230 in the environment. [ 12 ] It has very short estimated atmospheric lifetime of around 4 to 15 days. [ 13 ]
Novec 649/1230 is classified as a PFAS substance. In December 2022, 3M announced that it would cease production of all PFAS products by 2025, including Novec 649/1230. [ 14 ] It degrades to Trifluoroacetic acid (TFA) via photolytic degradation in sunlight. | https://en.wikipedia.org/wiki/Perfluoro(2-methyl-3-pentanone) |
Perfluorocarbon emulsions are emulsions containing either bubbles or droplets which have perfluorocarbons inside them. Some of them are commonly used in medicine as ultrasound contrast agents, and others have been studied for use as oxygen therapeutics.
The most common use of perfluorocarbon emulsions is as ultrasound contrast agents . In this application, microscopic bubbles containing perfluorocarbon gas are injected intravenously and flow through the bloodstream. [ 1 ] An ultrasound machine then sends soundwaves through a tissue of interest, and the bubbles reflect the soundwaves to a greater extent than the surrounding tissues, thereby giving the blood greater contrast on ultrasound viewers. This can allow greater visibility of the structure of an organ of interest, or a better indication of the level of blood perfusion or blood volume in an area of interest. [ 2 ] The bubbles persist in the blood stream with half-lives of minutes before the perfluorocarbon molecules leave the bubbles and enter the surrounding fluids, before eventually passing through the lungs where they are exhaled. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] Notable ultrasound contrast agents include Definity and Optison which are FDA approved, Sonazoid which is approved in Japan, and EchoGen which was formerly approved in Europe but never marketed. [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ]
Other perfluorocarbon emulsions have been tested as oxygen therapeutics. When perfluorocarbons are exposed to high concentrations of oxygen, large amounts of oxygen dissolve into the perfluorocarbons. If the perfluorocarbon/oxygen solution is then exposed to a low oxygen environment, then oxygen diffuses out of the solution. [ 13 ] Three different approaches sought to utilize this characteristic to improve oxygen delivery to tissue.
Early perfluorocarbon emulsions for oxygen delivery were developed as blood substitutes. They used large-molecule perfluorocarbons with boiling points higher than body temperature which were formed into liquid emulsion droplets. The emulsions were injected intravenously and circulated through the bloodstream, and the droplets picked up oxygen when passing through the lungs and offloaded oxygen when passing through the capillaries in other tissues. [ 13 ] The primary form of excretion of the perfluorocarbon was through the reticulo-endothelial system - the droplets would remain in the bloodstream until they were recognized by the immune system, would be taken up by phagocytes, and broken down thereby releasing the perfluorocarbon molecules which eventually pass through the lungs and be exhaled. [ 14 ] These high boiling point perfluorocarbons typically had half-lives measured in hours or days. [ 13 ] [ 15 ] Relatively large doses were required, but such doses could have side effects including pneumonia. [ 13 ] Despite these challenges, Fluosol-DA was approved by the FDA and was marketed as a blood substitute in the United States from 1989 through 1994 when it was withdrawn from the market due to poor sales. [ 16 ] Perftoran was approved in the Soviet Union in 1994 and remained in limited use in Russia at least as late as 2019. [ 17 ]
The second approach to oxygen delivery tested a perfluorocarbon emulsion not as a blood substitute, but rather as a cerebrospinal fluid (CSF) substitute. In order to increase oxygen delivery to the brains of patients that had reduced blood flow due to acute ischemic stroke, artificial CSF mixed with pre-oxygenated perfluorocarbon emulsion was continuously added into the skull by a ventricular catheter while CSF was continuously removed by a lumbar catheter. Animal studies in cats with acute ischemic stroke showed very strong results, so a clinical trial in four humans was conducted. All four patients survived for 30 days to 2 years before dying of other causes. Enrollment in the trial was slow however, which caused the funding for the project to be cut. [ 18 ]
A third approach to oxygen delivery is to move perfluorocarbon molecules into positions where they can enhance the flow of oxygen through the lower parts of the oxygen cascade . While it is difficult to observe the positioning of the perfluorocarbon molecules directly, molecules positioned in the right places between red blood cells and mitochondria may reduce resistance to oxygen flow. [ 19 ] [ 20 ] In cases where the oxygen tension at the mitochondria are very low, this would expose nearby red blood cells to lower oxygen tensions and cause them to offload more oxygen as described by the oxygen–hemoglobin dissociation curve . The most notable example is dodecafluoropentane emulsion (DDFPe, formerly EchoGen, now NanO 2 ). The drug is injected intravenously then the perfluorocarbon molecules spread widely before eventually passing through the lungs whey they are evaporated and exhaled. [ 21 ] [ 5 ] The drug showed very strong results in animal studies of acute ischemic stroke, heart attack and other indications. [ 22 ] [ 23 ] [ 24 ] [ 25 ] The drug was tested in a Phase Ib/II clinical trial in 24 patients who had reduced blood flow to the brain due to acute ischemic stroke, where it was intended to increase oxygen delivery to the brain to keep the tissue alive until blood flow could be normalized. The high dose group of patients in the clinical trial had improved functional independence compared to placebo, though the number of patients tested was small and there were confounding factors including differences in stroke severity, so larger clinical trials are needed to confirm the effect. [ 26 ] Another perfluorocarbon, perfluorooctyl bromide, has been shown in animal studies to collect in tumor tissue and increase oxygenation of those tumors, potentially by improving the flow of oxygen from red blood cells. [ 27 ] | https://en.wikipedia.org/wiki/Perfluorocarbon_emulsions |
Perfluorocarbon tracers (PFTs) are a range of perfluorocarbons used in flow tracers and other tracing applications. They are used by releasing the PFT at a certain point, and determining the concentration of that PFT at another set of points, allowing the flow from the source to the points to be determined.
PFTs are believed to be non-toxic [ 1 ] and chemically inert, clear, colourless liquids. They are non-flammable and nonradioactive compounds that do not occur in nature at all, so background levels are very low, but they can be detected at extremely low concentrations.
There is a range of PFTs available commercially, allowing the experimenter to release different PFTs at the same time. Cyclic perfluorocarbons, such as perfluoromethylhexane and perfluoro-1,3-dimethylcyclohexane , are generally believed to be better than acyclic ones as they can be detected at lower levels.
The PFT can be released in a variety of ways, depending on the application, and may be as simple as spraying it into the air. Samples are then collected at set times and locations, and either taken to a laboratory for analysis, or analysed in the field.
Analysis of the samples typically involves three parts; preparation, chromatography and detection. Preparation involves removal of other impurities, for example, mixing with hydrogen then passing over a catalyst to convert oxygen to water, which is then removed with silica gel . The sample is then admitted to a gas chromatograph . This separates the different PFTs, so a concentration value can be determined for each one.
There are two ways in which the PFTs are then detected; using an electron capture detector or negative ion mass spectrometry . Both techniques involve bombarding the sample with electrons, and measuring the negative ions produced. Perfluorocarbons have a particularly high affinity for electrons, so are detected in low concentrations.
Alternatively, the chromatography can be omitted, and the different PFTs determined from their different masses in the mass spectrum.
PFTs can be detected in concentrations as low as 1 part in 10 15 by volume (1 femtolitre in a litre). [ 2 ]
Oil reservoirs are routinely mapped by injecting a PFT down one borehole and measuring the concentration at adjacent boreholes. In this way, geologists can build up an image of the reservoir.
Traditional underground high-tension cables are constructed either with internal oil ducts or channels or by the use of a pipe through which the insulated conductor is installed. In either design, the system is then filled with pressurised, de-gassed oil. The oil's primary function is to improve the insulating properties of the cable; but occasionally, leaks can occur through cable joints, oil system fittings or cable sheath damage. The leak is initially identified by the loss of liquid from the system, and its location involves engineers digging up the road, freezing a section of the cable and seeing if the level is still going down, then choosing a new point to dig and re-freeze, which could take several holes to isolate the leak. If a PFT is injected into the oil, there will be a relatively high concentration of PFT above the leak, which can be pin-pointed to within a few feet, requiring only a single hole to be dug right where the leak is. [ 3 ]
PFTs have been used to follow air movement, for tracing the flow of pollutants, for example, the Big Bend Regional Aerosol and Visibility Observational study, [ 4 ] measuring the effectiveness of ventilation and studying the possible effects of terrorist attacks (for example in New York ). [ 5 ]
PFTs have even been used to track ransom money after a kidnapping. [ 6 ] | https://en.wikipedia.org/wiki/Perfluorocarbon_tracer |
Perfluorodecyltrichlorosilane , also known as FDTS , is a colorless liquid chemical with molecular formula C 10 H 4 Cl 3 F 17 Si . FDTS molecules form self-assembled monolayers . They form covalent silicon–oxygen bonds to free hydroxyl (–OH) groups, such as the surfaces of glass, ceramics, or silica .
Due to its heavily fluorinated tail group, a FDTS monolayer reduces surface energy . Deposition of a FDTS monolayer is achieved by a relatively simple process, also known as molecular vapor deposition (MVD) It usually deposits from a vapor phase, at room to near-to-room temperatures (50 °C) and is thus compatible with most substrates. The process is usually carried out in a vacuum chamber and assisted by the presence of water vapor. Treated surfaces have water repellent and friction reducing properties.
For this reason, a FDTS monolayer is often applied to movable microparts of microelectromechanical systems ( MEMS ). [ 2 ] A FDTS monolayer reduces surface energy and prevents sticking, so they are used to coat micro- and nano-features on stamps for a nanoimprint lithography which is becoming a method of choice for making electronics, organic photodiodes , microfluidics and other.
Reduced surface energy is helpful for reduction of ejection force and demolding of polymer parts in an injection molding and FDTS coating was applied [ 3 ] onto some metallic injection molding molds and inserts. | https://en.wikipedia.org/wiki/Perfluorodecyltrichlorosilane |
Perfluorohexane ( C 6 F 14 ), or tetradecafluorohexane , is a fluorocarbon . It is a derivative of hexane in which all the hydrogen atoms are replaced by fluorine atoms. It is used in one formulation of the electronic cooling liquid/insulator Fluorinert for low-temperature applications due to its low boiling point of 56 °C and freezing point of −90 °C. It is odorless and colorless. Unlike typical hydrocarbons, the structure features a helical carbon backbone. [ 1 ] In medical imaging it is used as a contrast agent.
Because it is biologically inert and chemically stable, perfluorohexane has attracted attention in medicine. Like other fluorocarbons, perfluorohexane dissolves gases, including oxygen from the air, to a higher concentration than ordinary organic solvents. This effect is attributed to the weak intermolecular forces between perfluorohexane molecules, which allows "space" for gas molecules to partition into the liquid. Animals can be submerged in a bath of oxygenated perfluorohexane without drowning, as there is sufficient oxygen available in the solvent to allow respiration to continue. This effect has led to the experimental use of perfluorohexane in treating burn victims, as their lungs can be filled with either perfluorohexane vapor or in extreme cases liquid perfluorohexane, allowing breathing to continue without the problems normally seen with pulmonary edema that sometimes occur when the inside of the lungs have been burnt e.g. by inhalation of hot smoke. [ 2 ] [ 3 ] Research was particularly active on the topic of partial liquid ventilation (PLV) in the 1990s and early 2000s, however, perfluorohexane and other perfluorocarbons showed no significant improvement of patient outcomes in clinical trials. [ 4 ]
Perfluorohexane has extremely high global warming potential (GWP) of 9,300. This leads to a need to find low GWP alternative. Novec 649 was considered a good drop-in replacement in many applications due to its similar thermo-physical properties and having a global warming potential of 1. [ 5 ] | https://en.wikipedia.org/wiki/Perfluorohexane |
Perfluorohexanesulfonic acid ( PFHxS ) ( conjugate base perfluorohexanesulfonate ) is a synthetic chemical compound . It is one of many compounds collectively known as per- and polyfluoroalkyl substances (PFASs). It is an anionic fluorosurfactant and a persistent organic pollutant with bioaccumulative properties. Although the use of products containing PFHxS and other PFASs have been banned or are being phased out in many jurisdictions, it remains ubiquitous in many environments and within the general population, and is one of the most commonly detected PFASs. [ 4 ]
PFHxS, its salts and isomers are anthropogenic chemicals that do not occur naturally. It is used as a surfactant and protective coating in applications such as aqueous firefighting foams, textile coating, metal plating and in polishing agents. [ 5 ] [ 6 ] PFHxS production is slowly being phased out since 3M stopped producing C 6 fluorotelomers in 2002, but production by other companies may be ongoing. [ 4 ] Between 1958 and 2015, an estimated 120-1022 metric tonnes of PFHxS were produced. [ 6 ] PFHxS was also used as replacement for PFOS after the Stockholm Convention on persistent organic pollutants restricted the use of PFOS. [ 5 ] The exact quantity of PFHxS produced or in production is difficult to estimate, as production volumes and relevant formulation information is often not publicly available. PFHxS may also be formed as an impurity of PFOS production, or as a breakdown product of larger PFASs. [ 7 ]
PFHxS has a six carbon fluorocarbon chain that is both hydrophobic and lipophobic. Its sulfonic acid functional group imparts polarity, and allows it to interact with other polar compounds. Due to the strength of its carbon-fluorine bonds , it persists in the environment and in living organisms.
In humans, PFHxS binds to blood albumin , [ 8 ] and relatively little PFHxS is found in the liver compared to longer chain PFASs such as PFOS. [ 9 ] The half-life of PFHxS in adult blood serum is 5.3 years (4.7 years for women and 7.4 years for men). [ 10 ] The half-life of PFASs in human blood generally decreases with decreasing backbone (CF 2 ) length. However, PFHxS is an unusual exception in that its half-life is greater than both longer and shorter chain equivalents such as PFOS or PFBS . [ 10 ]
Data from the 2003-2004 National Health and Nutrition Examination Survey in the United States found the average serum concentration of PFHxS in the general US population to be 1.9 μg/L, with the 10th and 90th percentiles being 0.7 and 8.3 μg/L, respectively. Some studies reported serum PFHxS concentrations in the United States to be gradually decreasing since at least 1999. [ 11 ] [ 12 ] Nevertheless, evidence of exposure can be detected amongst people with historic exposure. Serum concentrations of PFHxS were elevated amongst a cohort of Australian firefighters with occupational exposure to PFHxS (mean = 33 μg/L) compared to the general Australian population (mean = 3.2 μg/L), and were significantly correlated with serum PFOS concentrations. [ 13 ] As with PFOS, serum PFHxS concentrations are lower amongst women and people who reported blood donation. [ 13 ] [ 14 ]
There is limited evidence for a relationship between PFHxS exposure and various health outcomes. However, contributions from PFHxS specifically are difficult to isolate, as most studies in humans and higher order organisms investigate exposure to a complex mixture of PFASs, of which PFHxS is just one component.
A number of jurisdictions have guidelines or limits for the concentration of PFHxS in water, in diets, and in the environment. There are fewer regulations on PFHxS compared to PFOS and PFOA. This reflects the relative lack of epidemiological and toxicological information on the human health effects of exposure to PFHxS. [ 4 ]
PFHxS, its salts and related compounds have been recommended to be added to Annex A of the United Nations Stockholm Convention on Persistent Organic Pollutants . The decision was initially scheduled to be made in June 2021. [ 15 ] Due to the COVID-19 pandemic , the decision at the conference of parties was deferred to June 2022, where the parties agreed to list PFHxS, its salts and related compounds in Annex a without specific exemptions. [ 16 ] Upon entry into force, nations party to the convention are legally bound to take act to cease production and use of PFHxS. Several hundred salts and precursors of PFHxS fall within the scope of the restriction. [ 17 ]
Food Standards Australia New Zealand found insufficient evidence to justify a tolerable daily intake (TDI) for PFHxS specifically. Therefore, the TDI level for PFOS (0.02 μg/kg) was adapted as the TDI for the sum of PFOS and PFHxS. Australia uses a drinking water guideline value of 0.07 μg/L for the sum of PFHxS and PFOS. In comparison, the drinking water guideline value for PFOA is 0.56 μg/L. [ 18 ]
A new EU drinking water directive issued in 2020 adopted PFAS limit values. The limit values are 0.1 μg/L for the sum of 20 PFASs including PFHxS, and 0.5 μg/L for the sum of all PFASs. This directive is binding for all EU member nations. It is a minimum directive, and member states can elect to adopt stricter regulations. [ 19 ]
The Danish EPA has established a drinking water and groundwater limit value of 2 ng/L for the sum of 4 PFASs; , PFHxS, PFOS , PFOA , and perfluorononanoic acid (PFNA). [ 20 ]
The Swedish National Food Agency recommends a drinking water limit of 0.09 μg/L for the sum of 11 PFASs (PFBS, PFHxS, PFOS, 6:2 FTSA, PFBA, PFPeA, PFHxA, PFHpA, PFOA, PFNA and PFDA). If PFASs are found above this limit in drinking water, immediate action is recommended to reduce the PFAS concentration in the drinking water to as far below the action level as possible. If PFASs is found above 900 ng/L in drinking water, the advice is to avoid drinking the water or preparing food with the water until the concentration drops to below 90 ng/L, and to contact the Swedish Food Agency. [ 19 ]
In 2018, a preliminary drinking water limit value of 0.48 μg/L was adopted for PFHxS. In comparison, the preliminary limit value for the sum of PFOS and PFOA is 0.07 μg/L. [ 4 ]
As of 2019, there is no federal limit or guideline value for PFHxS. The United States Environmental Protection Agency (EPA) is developing toxicity values for PFHxS, as well as PFBA, PFHxA, PFNA and PFDA. [ 21 ] [ 22 ] Meanwhile, some states have adopted their own guideline values for PFHxS. For example, Minnesota recommends a guidance value of 0.027 μg/L for PFHxS, [ 23 ] and Michigan has a screening level of 0.084 μg/L for PFHxS. [ 4 ]
In 2020, Michigan adopted drinking water standards for 5 previously unregulated PFASs including PFHxS, setting a maximum contaminant level (MCL) of 51 parts per trillion (ppt) or 0.051 μg/L. [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Perfluorohexanesulfonic_acid |
Perfluorooctanesulfonic acid ( PFOS ) ( conjugate base perfluorooctanesulfonate ) is a chemical compound having an eight- carbon fluorocarbon chain and a sulfonic acid functional group , and thus it is a perfluorosulfonic acid and a perfluoroalkyl substance (PFAS). It is an anthropogenic (man-made) fluorosurfactant , now regarded as a global pollutant . PFOS was the key ingredient in Scotchgard , a fabric protector made by 3M , and related stain repellents. The acronym "PFOS" refers to the parent sulfonic acid and to various salts of perfluorooctanesulfonate. These are all colorless or white, water-soluble solids. Although of low acute toxicity, PFOS has attracted much attention for its pervasiveness and environmental impact. It was added to Annex B of the Stockholm Convention on Persistent Organic Pollutants in May 2009. [ 4 ]
In 1949, 3M began producing PFOS-based compounds by electrochemical fluorination . [ 5 ] In 1968, organofluorine compounds were detected in the blood serum of consumers, and in 1976, perfluorooctanoic acid (PFOA) or a related compound such as PFOS were suggested as components. [ 6 ] [ 7 ] [ 8 ] In 1997, 3M detected PFOS in blood from global blood banks, [ 9 ] although the company's internal documents indicate knowledge of this decades earlier, dating from the 1970s. [ 10 ] In 1999, the U.S. Environmental Protection Agency began investigating perfluorinated compounds after receiving data on the global distribution and toxicity of PFOS, the key ingredient in Scotchgard . [ 11 ] For these reasons, and USEPA pressure, [ 12 ] the primary American producer of PFOS, 3M , announced, in May 2000, the phaseout of the production of PFOS, PFOA, and PFOS-related products. [ 13 ] [ 10 ] Most other manufacturers (particularly, those in Europe) phased out the production of PFOS and perfluorooctanoic acid (PFOA) in 2000 and 2006, respectively. A shorter-chain PFOS ( perfluorohexanesulfonic acid , PFHxS), was included in Annex A to the Stockholm Convention in 2022. [ 14 ]
Currently, most of PFOS and PFOS-related chemicals are produced in China. [ 15 ]
The main method used for the industrial scale production of PFOS is electrochemical fluorination (ECF). [ 16 ] ECF is an electrolysis method whereby the precursor of octanesulfonyl fluoride is electrolyzed in a solution of hydrogen fluoride to give perfluorooctanesulfonyl fluoride . This production method also results in shorter chain perfluoroalkyl substances being formed. [ citation needed ] PFOS predominates in the resultant mixture. A distinct isomer ratio has been observed in PFOS produced by ECF, in the order of 70% linear PFOS, 25% branched and 5% terminal; this is not a function of the production process but rather that the precursor also exhibits this isomer ratio. ECF was the means by which 3M produced PFOS up until May 2000 when the company announced a phaseout of fluorosurfactants .
Although 89 constitutional isomers of PFOS are possible, [ 17 ] environmental samples usually consist of a mixture of the linear isomer and 10 branched isomers. [ 18 ]
Telomerisation involves constructing the PFOS molecule using short chain (often 2-carbon) precursors and adding a sulfonate group as a final step. This production process results in 100% linear PFOS. This production method, whilst cleaner and resulting in a much purer product than ECF, is not known to have been widely used except for the production of reagent grade PFOS and analytical standards. [ citation needed ]
Perfluorooctylsulfonyl compounds degrade to PFOS. [ 19 ] Examples include N -methyl perfluorooctane sulfonamidoethanol [ de ] ( N -MeFOSE), a carpet stain repellent, and N -ethyl perfluorooctane sulfonamidoethanol [ de ] ( N -EtFOSE), a paper treatment. [ 20 ] Also perfluorooctanesulfonamide is a precursor. [ 21 ] About 50 precursors were named in the 2004 proposed Canadian ban on PFOS. [ 22 ]
PFOS virtually does not degrade under environmental conditions and is thus highly persistent. Waste water treatment plants are also unable to degrade PFOS. [ 23 ] On the other hand, precursors are transformed to PFOS in waste water treatment plants. [ 24 ]
The C 8 F 17 subunit of PFOS is hydrophobic and lipophobic , like other fluorocarbons , while the sulfonic acid / sulfonate group adds polarity. PFOS is an exceptionally stable compound in industrial applications and in the environment because of the effect of aggregate carbon–fluorine bonds . PFOS is a fluorosurfactant that lowers the surface tension of water more than that of hydrocarbon surfactants .
Perfluorooctanesulfonic acid was usually used as the sodium or potassium salts .
The most important emission sources of PFOS have been metal plating and fire-fighting foams. [ 25 ] Because of concerns about PFOS, F-53B has been used as a replacement for mist suppression in metal plating. [ 26 ]
Because of its chemical properties, PFOS will remain in the body for several years. It is estimated that it takes 4 years for half of this substance to be eliminated from the body. [ 27 ]
PFOS is detected in the blood serum of almost all people in the U.S., but concentrations have been decreasing over time. In contrast, PFOS blood levels appear to be rising in China [ 28 ] where PFOS production continues. A study of ca. 2000 teenagers from 9 European countries with most samples collected in years 2016-2018 found higher blood concentrations of several PFOS’s in those, who consumed more seafood, eggs or offal , as well as in those from North and West (versus the South and East) Europe. Within the same country, boys had a higher PFOS concentrations than girls. A typical PFOS blood concentration range in this study was 1,500–2,500 ppb . [ 29 ]
Much higher levels of blood PFOS (12,830 ppb ) have been reported in people with occupational exposure [ 30 ] —or possibly 1,656 parts per billion [ 31 ] —in a consumer. Occupationally exposed individuals may have an average level of PFOS over 1000 parts per billion, and a small segment of individuals in the upper range of the general population may be over the 91.5 parts per billion level. [ 32 ]
PFOS exposure has been demonstrated as early as fetal development during pregnancy since PFOS can easily pass through the placenta . [ 33 ] It has been shown that fetal exposure to PFOS is quite prevalent and has been shown to be detected in greater than 99% of umbilical cord serum samples. [ 34 ]
PFOS has been detected in U.S. freshwater fish , [ 35 ] [ 36 ] as well as in municipal wastewater [ 37 ] and drinking water samples, [ 38 ] worldwide, at concentrations ranging between few ng/L and some μg/L.
A variety of wildlife species have had PFOS levels measured in egg , liver , kidney , serum , and plasma samples and some of the highest recorded values as of January 2006 are listed below. [ 39 ]
Despite the global wide-ranging restriction, PFOS concentrations in air continued to increase at many monitoring stations between 2009 and 2017. [ 41 ]
There is a growing body of research investigating the health effects of PFOS in humans and animals, including the reproductive, developmental, liver, kidney, thyroid, and immunological effects. [ 42 ] According to a 2002 report by the Environmental Directorate of the OECD , "PFOS is persistent, bioaccumulative, and toxic to mammalian species." [ 43 ]
Several studies have focused on pregnancy outcomes in infants and mothers who are exposed to PFOS during pregnancy. For developing offspring, exposure to PFOS occurs through the placenta. [ 33 ] While the impact of PFOS compounds on fetal development continues to be an ongoing investigation, findings have demonstrated a relationship between PFOS exposure in pregnant mothers and negative birth outcomes. [ 44 ]
There has been some evidence to suggest that PFOS levels in pregnant women have been associated with preeclampsia , preterm labor , low birth weight and gestational diabetes . [ 45 ] [ 46 ] Although, the strongest association is between PFOS levels with preterm birth and preeclampsia. [ 46 ] [ 47 ] There has been some evidence to suggest that PFOS impairs fetal growth during pregnancy, although findings have been inconsistent. [ 46 ]
The specific physiological mechanisms behind adverse pregnancy outcomes with PFOS exposure remain unclear. One proposed cause has to do with PFOS impairment on placental blood flow. [ 42 ] This mechanism could help explain several of the pregnancy-related outcomes from PFOS exposure including such as intrauterine growth development, low birth weight, preterm birth labor, and preeclampsia. Additional physiological mechanisms may include disruption in inflammatory signals during pregnancy, decreased trophoblast signaling and trophoblast migration. [ 48 ] Additionally, PFOS exposure has been shown to be related to the downregulation genes corresponding to growth factors, pregnancy-related signal transducers, and maternal hormones. [ 49 ] PFOS impact on thyroid hormone regulation also has the potential to impact several birth outcomes. [ 50 ] [ 51 ]
PFOS has been measured in breastmilk and is estimated to contribute the greatest level of PFOS exposure in infants. Specifically, the duration of breastfeeding has been shown to be associated with increases in PFOS in infants. [ 52 ] Some evidence has shown that breastmilk accounts for more than 94% of the PFOS exposure in infants up to six months old. [ 53 ] The Agency for Toxic Substances and Disease Registry (ATSDR) concluded that breastfeeding benefits continue to outweigh potential risks associated with PFOS in breastmilk. [ 54 ]
Increased levels of PFOS have been shown to accumulate in thyroid gland cells and have been associated with altered thyroid hormone levels in adults. [ 55 ] [ 56 ] Appropriate levels of thyroid hormone during pregnancy are critical for a developing fetus as this hormone is involved with brain development and body growth. [ 57 ] Studies have demonstrated a relationship between PFOS exposure and thyroid dysfunction during pregnancy resulting in altered thyroid hormone levels in both the mother and the fetus. [ 58 ] [ 59 ]
PFOS has been associated with increased risk of abnormal levels of cholesterol . [ 60 ] [ 61 ] [ 62 ] Specifically, epidemiological studies in humans have reported an association between increased PFOS levels and the total cholesterol and low density lipoprotein (LDL) cholesterol. [ 63 ]
Serum levels of PFOS were found to be associated with increased risk of chronic kidney disease in the general US population. [ 64 ] "This association was independent of confounders such as age, sex, race/ethnicity, body mass index , diabetes, hypertension, and serum cholesterol level." [ 64 ]
Research demonstrating the association between PFOS and cancer is still ongoing. A few studies have demonstrated an elevated risk for prostate and bladder cancer, however, there were notable limitations in the design and analysis of these studies. [ 46 ] As of November 2023, the International Agency for Research on Cancer (IARC) has classified PFOS as possibly carcinogenic to humans (Group 2b) based on “strong” mechanistic evidence. [ 65 ] The Division of Cancer Epidemiology & Genetics (DCEG) is currently investigating the association of several PFAS compounds and cancers including kidney cancer, testicular cancer, prostate cancer, ovarian and endometrial cancer, thyroid cancer, non-hodgkins lymphoma, and childhood leukemia. [ 66 ]
The levels observed in wild animals are considered sufficient to "alter health parameters". [ 67 ] [ 68 ]
PFOS affects the immune system of male mice at a blood serum concentration of 91.5 parts per billion , raising the possibility that highly exposed people and wildlife are immunocompromised . [ 32 ] Chicken eggs dosed at 1 milligram per kilogram (or 1 part per million) of egg weight developed into juvenile chickens with an average of ~150 parts per billion in blood serum—and showed brain asymmetry and decreased immunoglobulin levels. [ 69 ]
It was added to Annex B of the Stockholm Convention on Persistent Organic Pollutants in May 2009. [ 4 ] Originally, parties agreed on acceptable proposes (time-unlimited exemptions) for the following uses—in addition to a range of specific exemptions (time-limited): [ 70 ]
In 2019, it was decided to only keep one acceptable purpose: [ 71 ]
In 2023, the Government of Canada is considering addressing PFAS as a class rather than as individual substances or in smaller groups. A report to conclude that PFAS as a class are harmful to human health and the environment, and to define risk management aspects and alternatives to PFAs, is under development. "Per-and polyfluoroalkyl substances (PFAS)"
Based on an OECD study on PFOS [ 43 ] and a risk assessment by Europe's Scientific Committee on Health and Environmental Risks [ 72 ] the European Union practically banned the use of PFOS in finished and semi-finished products in 2006 (maximum content of PFOS: 0.005% by weight). [ 73 ] However, PFOS use for industrial applications (e.g. photolithography, mist suppressants for hard chromium plating, hydraulic fluids for aviation) was exempted.
In 2009 this directive was incorporated into the REACH regulation. [ 74 ] In the summer of 2010 PFOS was added to the regulation on persistent organic pollutants and the threshold was lowered to max. 0.001% by weight (10 mg/kg). [ 75 ]
In 2018 the State of Michigan established a legally enforceable groundwater cleanup level of 70 ppt for both PFOA and PFOS. [ 76 ]
In 2020 the Michigan Department of Environment, Great Lakes, and Energy (EGLE) adopted stricter drinking water standards in the form of maximum contaminant levels (MCLs), lowering acceptable levels from the 2018 enforceable groundwater cleanup levels of 70 ppt to 8 ppt for PFOA and 16 ppt for PFOS and adding MCLs for 5 previously unregulated PFAS compounds PFNA , PFHxA , PFHxS , PFBS , and HFPO-DA . [ 77 ] [ 78 ]
In 2020, a California bill was passed banning PFOS and the following salts as an intentionally added ingredient from cosmetics: ammonium perfluorooctane sulfonate, diethanolamine perfluorooctane sulfonate, lithium perfluorooctane sulfonate and potassium perfluorooctane sulfonate. [ 79 ]
In March 2021 the U.S. EPA announced that it will develop national drinking water standards for PFOA and PFOS. [ 80 ]
In October 2021 the EPA proposed to designate PFOA and PFOS as hazardous substances in its PFAS Strategic Roadmap. [ 81 ] [ 82 ] In September 2022 the EPA proposed to designate as hazardous substances under the Superfund Comprehensive Environmental Response, Compensation, and Liability Act of 1980 (CERCLA). | https://en.wikipedia.org/wiki/Perfluorooctanesulfonic_acid |
Perfluorooctanesulfonyl fluoride ( POSF ) is a synthetic perfluorinated compound with a sulfonyl fluoride functional group . It is used to make perfluorooctanesulfonic acid (PFOS) and PFOS-based compounds. These compounds have a variety of industrial and consumer uses, but POSF-derived substances ultimately degrade to form PFOS.
Because of environmental concerns over PFOS, 3M ceased POSF use in 2002 and global production plummeted. However, Chinese production grew after 3M's phaseout. As of May 2009, POSF and PFOS are listed as persistent organic pollutants (POPs) included in Annex B of the Stockholm Convention .
POSF is synthesized by electrochemical fluorination of octanesulfonyl fluoride in anhydrous hydrogen fluoride by the equation : [ 2 ]
This reaction results in a 25% yield for POSF, less than that for shorter perfluorosulfonyl fluorides. [ 2 ] The POSF obtained is impure as it is a mixture of linear and branched isomers , with ~70% linear. [ 2 ] POSF can also be obtained by ECF of the sulfonyl halide octanesulfonyl chloride . [ 2 ]
In 1949, 3M began producing POSF by electrochemical fluorination (ECF). [ 3 ] From 1966 to the 1990s, 3M production increased to meet demand for POSF-based compounds. [ 3 ] In 1999, 3M reported POSF was its most highly produced fluorochemical. [ 4 ] [ better source needed ] Before 2000, 3M was the largest global producer of POSF (mainly at their Decatur, AL and Antwerp facilities) and global production peaked at ~4500 tonnes per year. [ 3 ]
In 1999, the U.S. Environmental Protection Agency began investigating perfluorinated compounds after receiving data on the global distribution and toxicity of PFOS, the key ingredient in Scotchgard . [ 5 ] For these reasons, and USEPA pressure, [ 6 ] the primary American producer of PFOS, 3M, announced, in May 2000, the phaseout of the production of PFOS, PFOA , and PFOS-related products. [ 7 ] 3M stated that they would have made the same decision regardless of USEPA pressure. [ 8 ]
Immediately after the 2000–2002 3M phaseout, production plummeted, but dominant and growing production shifted to China. [ 9 ] In 2004 Chinese production of PFOS-based compounds was estimated to be <50 tonnes . [ 9 ] In 2005 global production was estimated to be between 73 and 162 tonnes, [ 10 ] and by 2006 Chinese production was estimated at >200 tonnes. [ 9 ] Total historical global production was estimated at ~120,000 tonnes in 2009. [ 3 ]
Most, if not all industrially synthesized perfluorooctanesulfonyl derivatives, such as PFOS, have POSF as their precursor. [ 2 ]
POSF and POSF-based polymers degrade to form PFOS [ 11 ] which is not known to degrade by any environmental processes. [ 6 ] POSF hydrolysis in water , however, occurs slowly. [ 2 ]
POSF reacts with bases such as potassium hydroxide to form PFOS salts: [ 2 ]
Upon treatment with sulfuric acid the sulfonic acid PFOS tetra hydrate is obtained. [ 2 ]
POSF also reacts with ammonia to form perfluorooctanesulfonamide : [ 2 ]
Sulfonamides and sulfonamidoethanols synthesized from POSF can in turn react to form a variety of different functional groups for different applications and products. [ 12 ]
Because of multiple carbon–fluorine bonds , POSF-derivatives have chemical properties that are hydrophobic ("water-afraid"), lipophobic ("fat-afraid"), and surface tension lowering (as fluorosurfactants ). [ 4 ] The main uses of chemical substances derived from POSF were: [ 3 ]
Until 2019, the Stockholm Convention listed a variety of acceptable purposes and specific exemptions for POSF derivatives including
At the Fourth Conference of Parties, decision SC-4/17 put POSF, along with PFOS, in the Stockholm Convention on Persistent Organic Pollutants (Annex B) in May 2009. [ 14 ] [ 15 ] As such, POSF is not "banned" but has approved uses and exemptions—along with a program (SC-4/19) in Annex B that encourages reduced production. [ 16 ] [ 17 ]
The POSF degradation product, PFOS, is the dominant perfluorinated compound detected in biomonitoring studies, [ 18 ] where concentrations that have been detected are considered sufficient to "alter health parameters". [ 19 ] [ 20 ] | https://en.wikipedia.org/wiki/Perfluorooctanesulfonyl_fluoride |
Perfluorooctanoic acid ( PFOA ; conjugate base perfluorooctanoate ; also known colloquially as C8 , from its chemical formula C 8 HF 15 O 2 ) is a perfluorinated carboxylic acid produced and used worldwide as an industrial surfactant in chemical processes and as a chemical precursor. PFOA is considered a surfactant, or fluorosurfactant, due to its chemical structure, which consists of a perfluorinated, n -heptyl "tail group" and a carboxylic acid "head group". The head group can be described as hydrophilic while the fluorocarbon tail is both hydrophobic and lipophobic . [ 6 ]
The International Agency for Research on Cancer (IARC) has classified PFOA as carcinogenic to humans. [ 7 ] PFOA is one of many synthetic organofluorine compounds collectively known as per- and polyfluoroalkyl substances (PFASs). Many PFAS such as PFOS , PFOA are a concern because they do not break down via natural processes and are commonly described as persistent organic pollutants or "forever chemicals". [ 8 ] They can also move through soils and contaminate drinking water sources and can build up ( bioaccumulate ) in fish and wildlife. [ 8 ] Residues have been detected in humans and wildlife. [ 8 ] [ 9 ]
PFOA is used in several industrial applications, including carpeting, upholstery, apparel, floor wax, textiles, fire fighting foam and sealants. PFOA serves as a surfactant in the emulsion polymerization of fluoropolymers and as a chemical precursor for the synthesis of perfluoroalkyl-substituted compounds, polymers, and polymeric materials. PFOA has been manufactured since the 1940s in industrial quantities. [ 10 ] It is also formed by the degradation of precursors such as some fluorotelomers . PFOA is used as a surfactant because it can lower the surface tension of water more than hydrocarbon surfactants while having exceptional stability due to having perfluoroalkyl tail group. [ 6 ] [ 11 ] The stability of PFOA is desired industrially but is a cause of concern environmentally.
The primary manufacturer of perfluorooctanesulfonic acid (PFOS), 3M , began a production phase-out in 2002 in response to concerns expressed by the U.S. Environmental Protection Agency (EPA). [ 12 ] : 2 Eight other companies agreed to gradually phase out the manufacturing of the chemical by 2015. [ 12 ] : 3
By 2014, EPA had listed PFOA and perfluorooctanesulfonates ( salts of perfluorooctanesulfonic acid, PFOS) as emergent contaminants :
PFOA and PFOS are extremely persistent in the environment and resistant to typical environmental degradation processes. [They] are widely distributed across the higher trophic levels and are found in soil, air and groundwater at sites across the United States. The toxicity, mobility and bioaccumulation potential of PFOS and PFOA pose potential adverse effects for the environment and human health. [ 12 ] : 1
In 2024 EPA published drinking water regulations for PFOA and five other PFAS. [ 13 ]
3M (then the Minnesota Mining and Manufacturing Company) began producing PFOA by electrochemical fluorination in 1947. [ 2 ] Starting in 1951, DuPont purchased PFOA from 3M for use in the manufacturing of specific fluoropolymers —commercially branded as Teflon—but DuPont internally referred to PFOA as C8. [ 14 ] [ 15 ] [ 16 ]
In 1968, organofluorine content was detected in the blood serum of consumers, and in 1976 it was suggested to be PFOA or a related compound such as PFOS . [ 17 ] [ 18 ] [ 19 ]
In 1999, EPA ordered companies to examine the effects of perfluorinated chemicals after receiving data on the global distribution and toxicity of PFOS. [ 20 ] For these reasons, and EPA pressure, [ 21 ] in May 2000, 3M announced the phaseout of the production of PFOA, PFOS, and PFOS-related products—the company's best-selling repellent. [ 22 ] 3M stated that they would have made the same decision regardless of EPA pressure. [ 23 ]
Because of the 3M phaseout, in 2002, DuPont built its own plant in Fayetteville, North Carolina , to manufacture the chemical. [ 24 ] The chemical has received attention due to litigation from the PFOA-contaminated community around DuPont's Washington Works facility in Washington, West Virginia , along with EPA focus. In 2004, ChemRisk —an "industry risk assessor" that had been contracted by Dupont, reported that over 1.7 million pounds of C8 had been "dumped, poured and released" into the environment from Dupont's Parkersburg, West Virginia-based Washington Works plant between 1951 and 2003. [ 25 ]
Research on PFOA has demonstrated ubiquity, animal-based toxicity, and some associations with human health parameters and potential health effects. Additionally, advances in analytical chemistry in recent years have allowed the routine detection of low- and sub- parts per billion levels of PFOA in a variety of substances. [ 19 ] In 2013, Gore-Tex eliminated the use of PFOAs in the manufacture of its weatherproof functional fabrics. [ 26 ] Major companies producing PFOA signed with the Global PFOA Stewardship Program with the goal of elimination of PFOA by 2015. [ 27 ] Since then it has been eliminated from the production of non-stick materials used in cookware. GenX has been introduced as a replacement for PFOA, but in a 2015 study which tested the effects on rats, GenX caused many of the same health problems as PFOA, but required much higher concentrations. This is because GenX (C3) is a short chain alternative to PFOA. GenX also has a significantly shorter half-life than PFOA so it is not as bio-persistent as PFOA or other long chain perfluorinated chemicals. [ 28 ]
In the Autumn of 2000, lawyer Robert Bilott , a partner at Taft Stettinius & Hollister , won a court order forcing DuPont to share all documentation related to PFOA. This included 110,000 files, consisting of confidential studies and reports conducted by DuPont scientists over decades. By 1993, DuPont understood that "PFOA caused cancerous testicular, pancreatic and liver tumors in lab animals" and the company began to investigate alternatives. However, because products manufactured with PFOA were such an integral part of DuPont's earnings, $1 billion in annual profit, they chose to continue using PFOA. [ 14 ] Bilott learned that both "3M and DuPont had been conducting secret medical studies on PFOA for more than four decades", and by 1961 DuPont was aware of hepatomegaly in mice fed with PFOA. [ 14 ] [ 29 ] [ 30 ]
Bilott exposed how DuPont had been knowingly polluting water with PFOAs in Parkersburg, West Virginia , since the 1980s. [ 14 ] In the 1980s and 1990s, researchers investigated the toxicity of PFOA. [ 30 ] Regarding a secret agreement between 3M and the government of Jersey (UK) to not perform group testing of residents and to help 3M avoid a class action, Billott told The Guardian : “I’ve not seen something like this where there’s an agreement to try to help the company against claims by others, Particularly if it’s something affecting public health and safety or research.” [ 31 ]
For his work in the exposure of the contamination, Bilott received several awards including The Right Livelihood Award in 2017. [ 32 ] In film, this battle with DuPont has been depicted in the documentary The Devil We Know [ 33 ] and the legal thriller Dark Waters .
PFOA has two main synthesis routes, electrochemical fluorination (ECF) and telomerization . [ 2 ] The ECF route sees octanoyl chloride (the acid chloride of octanoic acid ) reacted with hydrofluoric acid . [ 34 ] Multiple products are formed by ECF with the target acid fluoride F(CF 2 ) 7 COF being produced as only 10–15% of the yield, while the main products are perfluorinated cyclic ether isomers , including FC-75 . [ 34 ] This acid fluoride is hydrolyzed to yield PFOA as a mixture of straight-chain (78%), terminally branched (13%), and internally branched (9%) molecules, because ECF induces rearrangements in the carbon tail of the acid chloride. [ 34 ] ECF also results in production wastes. [ 35 ] 3M synthesized ECF PFOA at their Cottage Grove, Minnesota facility from 1947 to 2002 and was the world's largest producer. [ 2 ] [ 35 ] ECF production continues on a smaller scale in Europe and Asia. [ 2 ]
PFOA is also synthesized by the telomerization represented below, where the telogen is the organoiodine compound and the taxogen is the tetrafluoroethylene . [ 34 ] [ 36 ] Each step is an addition reaction where the carbon-iodine bond of the telogen is added across the carbon-carbon double bond of the unsaturated taxogen, resulting in the formation of a new telogen.
The product is oxidized by SO 3 to form PFOA. [ 34 ] Since each addition produces a new teleomer, fluorotelomers like these form with varying length chains containing an even number of carbon atoms, depending on reaction conditions. Typically, most products within will contain between two and six taxogens (that is, from CF 3 (CF 2 ) 5 I to CF 3 (CF 2 ) 13 I). [ 34 ] After oxidation, distillation is used to separate PFOA from the other perfluorinated carboxylic acids. [ 34 ] The telomerization synthesis of PFOA was pioneered by DuPont , [ 34 ] and is not well suited to the laboratory. [ 36 ] PFOA formed by telomerization is completely linear, in contrast to the mixture of structures formed by ECF.
PFOA has widespread applications. In 1976, PFOA was reported as a water and oil repellent "in fabrics and leather and in the production of floor waxes and waxed papers "; [ 37 ] however, it is believed that paper is no longer treated with perfluorinated compounds , but with fluorotelomers with less than 0.1% PFOA. [ 38 ] The compound is also used in " insulators for electric wires , planar etching of fused silica ", [ 36 ] fire fighting foam , [ 2 ] [ 39 ] and outdoor clothing. [ 40 ] As a protonated species, the acid form of PFOA was the most widely used perfluorocarboxylic acid used as a reactive intermediate in the production of fluoroacrylic esters. [ 41 ] [ 42 ]
As a salt , its dominant use is as an emulsifier for the emulsion polymerization of fluoropolymers such as PTFE, polyvinylidene fluoride , and fluoroelastomers . [ 44 ] [ 45 ] For this use, 3M subsidiary Dyneon has a replacement emulsifer [ 46 ] despite DuPont stating PFOA is an "essential processing aid". [ 47 ] In the past PFOA was used in the production of Gore-Tex [ 48 ] as it is PTFE-based. In PTFE processing, PFOA is in aqueous solution and forms micelles that contain tetrafluoroethylene and the growing polymer . [ 49 ] PFOA can be used to stabilize fluoropolymer and fluoroelastomer suspensions before further industrial processing and in ion-pair reversed-phase liquid chromatography it can act as an extraction agent. [ 50 ] PFOA also finds uses in electronic products and as an industrial fluorosurfactant . [ 48 ] [ 11 ]
In a 2009 EPA study of 116 products, purchased between March 2007 and May 2008 and found to contain at least 0.01% fluorine by weight, the concentrations of PFOA were determined. [ 51 ] Concentrations shown below range from not detected, or ND, (with the detection limit in parentheses) to 6750 with concentrations in nanograms of PFOA per gram of sample ( parts per billion ) unless stated otherwise.
PFOA contaminates every continent . [ 52 ] Two of the most common types (PFOS and PFOA) were phased out of production in the United States (US) in 2002 and 2015 respectively, but are still present in some imported products. PFOA and PFOS are found in every American person's blood stream in the parts per billion range, though those concentrations have decreased by 70% for PFOA and 84% for PFOS between 1999 and 2014, which coincides with the end of the production and phase out of PFOA and PFOS in the US. [ 53 ] PFOA has been detected in the central Pacific Ocean at low parts per quadrillion ranges, and at low parts per trillion (ppt) levels in coastal waters . [ 54 ] Due to the surfactant nature of PFOA, it has been found to concentrate in the top layers of ocean water. [ 55 ] PFOA is detected widely in surface waters , and is present in numerous mammals, fish, and bird species. [ 52 ] PFOA is in the blood or vital organs of Atlantic salmon, swordfish, striped mullet, gray seals, common cormorants, Alaskan polar bears, brown pelicans, sea turtles, sea eagles, Midwestern bald eagles, California sea lions and Laysan albatrosses on Sand Island, a wildlife refuge on Midway Atoll, in the middle of the North Pacific Ocean, about halfway between North America and Asia. [ 14 ] Because PFAS are ubiquitous in households, consumer products, food, and the environment generally, some trace levels reflecting this ubiquitous broad use of these compounds will make their way into the wastewater and solid waste streams. [ 56 ]
However, wildlife has much less PFOA than humans, unlike PFOS [ 57 ] and other longer perfluorinated carboxylic acids ; [ 58 ] in wildlife, PFOA is not as bioaccumulative as longer perfluorinated carboxylic acids. [ 59 ] Municipal wastewater and landfill leachates are considered as important sources of PFOA to the environment. [ 60 ] [ 61 ]
Most industrialized nations have average PFOA blood serum levels ranging from 2 to 8 parts per billion ; [ 62 ] the highest consumer sub-population identified was in Korea—with about 60 parts per billion . [ 57 ] In Peru , [ 63 ] Vietnam , [ 64 ] and Afghanistan [ 65 ] blood serum levels have been recorded to be below one part per billion. In 2003–2004 99.7% of Americans had detectable PFOA in their serum with an average of about 4 parts per billion, [ 66 ] and concentrations of PFOA in US serum have declined by 25% in recent years. [ 67 ] Despite a decrease in PFOA, the longer perfluorinated carboxylic acid PFNA is increasing in the blood of US consumers. [ 66 ] PFAS are also found in paper mill residuals, digestates, composts, and soils. Given the ubiquity of PFAS, and the comparative background levels which may be found in wastewater, biosolids, and leachates, setting requirements near analytical detection limits on these sources may not provide a discernable benefit to protecting public health. [ 56 ]
PFOA is released directly from industrial sites. For example, the estimate for the DuPont Washington Works facility is a total PFOA emissions of 80,000 pounds ( lbs ) in 2000 and 1,700 pounds in 2004. [ 15 ] A 2006 study, with two of four authors being DuPont employees, estimated about 80% of historical perfluorocarboxylate emissions were released to the environment from fluoropolymer manufacture and use. [ 2 ] PFOA can be measured in water from industrial sites other than fluorochemical plants. PFOA has also been detected in emissions from the carpet industry , [ 68 ] paper [ 69 ] and electronics industries. [ 70 ] The most important emission sources are carpet and textile protection products, as well as fire-fighting foams. [ 71 ]
PFOA can form as a breakdown product from a variety of precursor molecules. In fact, the main products of the fluorotelomer industry, fluorotelomer-based polymers, have been shown to degrade to form PFOA and related compounds, with half-lives of decades, both biotically [ 72 ] and by simple abiotic reaction with water. [ 73 ] It has been argued that fluorotelomer-based polymers already produced might be major sources of PFOA globally for decades to come. [ 73 ] Other precursors that degrade to PFOA include 8:2 fluorotelomer alcohol (F(CF 2 ) 8 CH 2 CH 2 OH), polyfluoroalkyl phosphate surfactants (PAPS), [ 74 ] and possibly N -EtFOSE alcohol (F(CF 2 ) 8 SO 2 N(Et)CH 2 CH 2 OH). [ 52 ] [ 75 ] When PTFE (Teflon) is degraded by heat ( pyrolysis ) it can form PFOA as a minor product. [ 76 ] [ 77 ] The Organisation for Economic Co-operation and Development (OECD) has compiled a list of 615 chemicals that have the potential to break down into perfluorocarboxylic acids (PFCA) including PFOA. [ 78 ] However, not all 615 have the potential to break down to form PFOA.
A majority of waste water treatment plants (WWTPs) that have been tested output more PFOA than is input, and this increased output has been attributed to the biodegradation of fluorotelomer alcohols. [ 79 ] A current PFOA precursor concern are fluorotelomer -based polymers; fluorotelomer alcohols attached to hydrocarbon backbones via ester linkages may detach and be free to biodegrade to PFOA. [ 80 ]
Food , [ 81 ] drinking water , [ 82 ] outdoor air , indoor air, [ 83 ] dust , and food packagings [ 84 ] are all implicated as sources of PFOA to people. [ 74 ] However, it is unclear which exposure routes dominate [ 85 ] because of data gaps. When water is a source, blood levels are approximately 100 times higher than drinking water levels. [ 86 ] [ 87 ]
People who lived in the PFOA-contaminated area around DuPont's Washington Works facility were found to have higher levels of PFOA in their blood from drinking water. The highest PFOA levels in drinking water were found in the Little Hocking water system, with an average concentration of 3.55 parts per billion during 2002–2005. [ 15 ] Individuals who drank more tap water, ate locally grown fruits and vegetables, or ate local meat, were all associated with having higher PFOA levels. Residents who used water carbon filter systems had lower PFOA levels.
In Jersey, UK, 18% of residents of an area were found to have elevated levels of PFOA, downstream from 3M fire retardant tests in weekly fire-service practice from the 1960s to the mid 1990s. [ 31 ] Bloodletting is used for these residents at a cost of $4500 per patient. The potatoes of the island were found to contain 10x the EU limit of PFOS.
PFOA is also formed as an unintended byproduct in the production of fluorotelomers [ 88 ] and is present in finished goods treated with fluorotelomers, including those intended for food contact. Fluorotelomers are applied to food contact papers because they are lipophobic : they prevent oil from soaking into the paper from fatty foods. Also, fluorotelomers can be metabolized into PFOA. [ 89 ] In a U.S. Food and Drug Administration (USFDA) study, lipophobic fluorotelomer-based paper coatings (which can be applied to food contact paper in the concentration range of 0.4%) were found to contain 88,000–160,000 parts per billion PFOA before application, while the oil from microwave popcorn bags contained 6–290 parts per billion PFOA after heating. [ 90 ] Toxicologists estimate that microwave popcorn could account for about 20% of the PFOA levels measured in an individual consuming 10 bags a year if 1% of the fluorotelomers are metabolized to PFOA. [ 89 ]
In 2008 as news stories began to raise concerns about PFOA in microwaved popcorn, Dan Turner, DuPont's global public relations chief, said, "I serve microwave popcorn to my three-year-old." Five years later, journalist Peter Laufer wrote to Turner to ask if his child was still eating microwave popcorn. "I am not going to comment on such a personal inquiry", Turner replied. [ 91 ] [ 92 ]
Fluorotelomer coatings are used in fast food wrappers, candy wrappers, and pizza box liners. [ 93 ] PAPS, a type of paper fluorotelomer coating, and PFOA precursor, is also used in food contact papers. [ 74 ]
Despite DuPont's assertion that "cookware coated with DuPont Teflon non-stick coatings does not contain PFOA", [ 94 ] residual PFOA was also detected in finished PTFE products including PTFE cookware (4–75 parts per billion). [ 90 ] However, PFOA levels ranged from undetectable (<1.5) to 4.3 parts per billion in a more recent study. [ 51 ] Also, non-stick cookware is heated—which should volatilize PFOA; PTFE products that are not heated, such as PTFE sealant tape, had higher (1800 parts per billion) levels detected. [ 95 ] Overall, PTFE cookware is considered an insignificant exposure pathway to PFOA. [ 96 ] [ 97 ]
PFOA and PFOS were detected in "very high" (low parts per million ) levels in agricultural fields for grazing beef cattle [ 85 ] and crops [ 98 ] around Decatur, Alabama . [ 99 ] The approximately 5000 acres of land were fertilized with "treated municipal sewage sludge , or biosolids ". [ 85 ] PFOA was also detected in fodder grass grown in these soils [ 100 ] and the blood of the cattle feeding on this grass. [ 101 ] The water treatment plant received process wastewater from a nearby perfluorochemical manufacturing plant. 3M says they managed their own wastes, but Daikin America "discharged process wastewater to the municipal waste treatment plant". [ 85 ] If traced to meat, it would be the first time perfluorochemicals were traced from sludge to food. [ 85 ] However, the USDA reported—with a detection limits of 20 parts per billion—non-detectable levels for both PFOA and PFOS in cattle muscle tissue. [ 102 ]
PFOA is frequently found in household dust, making it an important exposure route for adults, but more substantially, children. Children have higher exposures to PFOA through dust compared to adults. [ 103 ] Hand-to-mouth contact and proximity to high concentrations of dust make them more susceptible to ingestion, and increases PFOA exposure. [ 104 ] One study showed significant positive associations were recognized between dust ingestion and PFOA serum concentrations. [ 103 ] However, an alternate study found exposure due to dust ingestion was associated with minimal risk. [ 105 ]
In 2024 it was reported that a brand of menstrual pad was found to contain PFOA. [ 106 ]
In April 2024 EPA issued a final drinking water rule for PFOA, PFOS, GenX, PFBS, PFNA, and PFHxS. Public water systems must remove these six PFAS to near-zero levels by 2027. Grant funding is available from EPA to assist utilities in water testing and development of treatment systems. [ 13 ] [ 107 ] [ 108 ] [ 109 ]
The State of New Jersey published drinking water standards for PFOA and PFOS in 2020. [ 110 ] A standard for PFNA was published in 2018. This was the first state to publish PFAS standards in the absence of federal regulations. [ 111 ] See U.S. state government actions .
In 2018 the State of New York adopted drinking water standards of 10 ppt for PFOA and 10 ppt for PFOS, the most stringent such standards in the United States. The standards apply to public water systems and took effect in 2019 after a public comment period. [ 112 ]
Using information gained through a Freedom of Information Act request, in May 2018 it was learned that January 2018 emails between the EPA , the Office of Management and Budget , the Department of Defense , and the Department of Health and Human Services showed an effort to suppress the release of a draft report on the toxicology of PFOS and PFOA done by the Agency for Toxic Substances and Disease Registry . The report found that these chemicals endanger human health at a far lower level than EPA has previously called safe. [ 113 ] After media accounts of the effort surfaced, the regional EPA administrator for Colorado denied that EPA had anything to do with suppressing the report. [ 114 ] The report was released on June 21, 2018. [ 82 ]
The new ATSDR analysis derives provisional Minimal Risk Levels (MRLs) of 3x10 −6 mg/kg/day for PFOA and 2x10 −6 mg/kg/day for PFOS during intermediate exposure. [ 115 ] The European Food Safety Authority opinion sets a provisional tolerable weekly intake (TWI) of 6 x10 −6 mg/kg body weight per week for PFOA. [ 116 ]
An attempt to regulate PFOA in food packaging occurred in the US state of California in 2008. A bill, sponsored by State Senator Ellen Corbett and the Environmental Working Group , was passed in the house and senate that would have banned PFOA, PFOS , and seven or more related fluorinated carbon compounds in food packaging starting in 2010, [ 117 ] [ 118 ] but the bill was vetoed by Governor Schwarzenegger . [ 119 ] The bill would have affected fluorochemical manufacturers outside of the state. Schwarzenegger said the compound should be reviewed by the newly established, and more comprehensive, state program. [ 119 ]
Fluorotelomer -based products have been shown to degrade to PFOA over periods of decades; [ 72 ] [ 73 ] these studies could lead EPA to require DuPont and others to reformulate products with a value over $1 billion. [ 120 ]
PFOA is a possible carcinogen , a possible liver toxicant, a possible developmental toxicant, and a possible immune system toxicant, and also exerts hormonal effects including alteration of thyroid hormone levels at very high concentrations. [ 45 ] Animal studies show developmental toxicity from reduced birth size, physical developmental delays, endocrine disruption , and neonatal mortality . [ 52 ] [ 121 ] PFOA alters lipid metabolism . [ 52 ]
In 2008, PFOA has been described as a member of a group of "classic non-genotoxic carcinogens". [ 122 ] However, a provisional German assessment notes that a 2005 study found PFOA to be genotoxic via a peroxisome proliferation pathway that produced oxygen radicals in HepG2 cells, and a 2006 study demonstrated the induction and suppression of a broad range of genes ; therefore, it states that the indirect genotoxic (and thus carcinogenic) potential of PFOA cannot be dismissed. [ 123 ] As of November 2023, the International Agency for Research on Cancer (IARC) has classified PFOA as carcinogenic to humans (Group 1) based on “sufficient” evidence for cancer in animals and “strong” mechanistic evidence in exposed humans. [ 7 ]
An additional study has shown PFOA to be developmentally toxic, hepatotoxic, immunotoxic, and to have negative effects of thyroid hormone production. [ 45 ]
PFOA is resistant to degradation by natural processes such as metabolism , hydrolysis , photolysis , or biodegradation [ 41 ] and has been found to persist in the environment. [ 85 ] PFOA is found in environmental and biological fluids as the anion perfluorooctanoate. [ 124 ] PFOA can be absorbed from ingestion and can penetrate skin . [ 17 ] The acid headgroup of PFOA enables binding to proteins with fatty acid or hormone substrates such as serum albumin , liver fatty acid-binding protein, and the nuclear receptors PPARα [ 45 ] and possibly CAR . [ 125 ]
In animals, PFOA is mainly present in the liver , blood , and kidneys . [ 17 ] PFOA does not accumulate in fat tissue , unlike traditional organohalogen persistent organic pollutants . [ 59 ] In humans, PFOA has an average elimination half-life of about three years. [ 126 ] [ 127 ] [ 128 ] Because of this long half-life, [ 129 ] PFOA has the potential to bioaccumulate .
The levels of PFOA exposure in humans vary widely. While an average American might have 3 or 4 parts per billion of PFOA present in their blood serum, [ 130 ] individuals occupationally exposed to PFOA have had blood serum levels over 100,000 parts per billion (100 parts per million or 0.01%) recorded. [ 131 ] While no amount of PFOA in humans is legally recognized as harmful, DuPont was "not satisfied" with data showing their Chinese workers accumulated an average of about 2,250 parts per billion of PFOA in their blood from a starting average of around 50 parts per billion less than a year prior. [ 24 ]
Single cross-sectional studies on consumers have been published noting multiple associations. Blood serum levels of PFOA were associated with an increased time to pregnancy—or " infertility "—in a 2009 study. [ 132 ] PFOA exposure was associated with decreased semen quality , [ 133 ] increased serum alanine aminotransferase levels, [ 134 ] and increased occurrence of thyroid disease . [ 129 ] In a study of 2003–2004 US samples, a higher (9.8 milligram per deciliter ) total cholesterol level was observed when the highest quartile was compared to the lowest. [ 135 ] Along with other related compounds, PFOA exposure was associated with an increased risk of attention deficit hyperactivity disorder (ADHD) in a study of US children aged 12–15. [ 136 ] In a paper presented at the 2009 annual meeting of the International Society of Environmental Epidemiology, [ 137 ] PFOA appeared to act as an endocrine disruptor by a potential mechanism on breast maturation in young girls. [ 138 ] A C8 Science Panel status report noted an association between exposure in girls and a later onset of puberty . [ 139 ]
PFOA exposure on thyroid function has also been a topic of concern, and has found to negatively impact thyroid stimulating hormone even at low levels when exposed during fetal development. [ 140 ] PFOA is also shown to have obesogenic effects, and an experimental study found a positive correlation to low-dose prenatal exposure of PFOA and prevalence of overweight and high waist circumference in females at age 20. [ 141 ] A correlation between in utero PFOA exposure and mental performance has yet to be established, as many studies have resulted in insignificant results. For example, a study conducted near Parkersburg, West Virginia did not find a significant association between in utero PFOA exposure and performance of math skills or reading performance in children ages 6 to 12 living in the PFOA-contaminated water district. [ 142 ] Based on a cohort study conducted in the Mid-Ohio Valley, no clear association was found between prenatal exposure to PFOA and birth defects, although a possible association with brain defects was observed and requires further research and assessment. [ 143 ]
Extrapolated epidemiological data suggests a slight association between PFOA exposure and low birth weight. [ 144 ] This was consistent based on blood levels of PFOA metabolites regardless of the geographic residence of subjects. [ 144 ] Generally, the findings among human fetuses exposed to the chemical were considerably less drastic than what was seen in mice studies. [ 144 ] Because of this, studies linking exposure to low birth weight can be considered inconclusive. [ 144 ] PFOA exposure in the Danish general population was not associated with an increased risk of prostate , bladder , pancreatic , or liver cancer . [ 145 ] Maternal PFOA levels were not associated with an offspring's increased risk of hospitalization due to infectious diseases, [ 146 ] behavioral and motor coordination problems, [ 147 ] or delays in reaching developmental milestones. [ 148 ]
In 2010, the three members of the C8 Science Panel [ 149 ] published a review of the epidemiological evidence on PFOA exposure in Environmental Health Perspectives . [ 127 ] Insufficient evidence exists to conclude PFOA causes adverse health effects in humans, but consistent evidence exists on associations with higher cholesterol and uric acid. Whether or not these potential effects result in an increase in cardiovascular disease is unknown. [ 150 ] Further data on the 69,030 member cohort [ 151 ] that is being studied by the panel is scheduled for release through 2012. [ 152 ] [ obsolete source ] A 2011 epidemiological study demonstrated "probable link" between PFOA and kidney cancer, testicular cancer, thyroid disease, high cholesterol, pre-eclampsia and ulcerative colitis. [ 14 ] [ 153 ]
Facial birth defects, an effect observed in rat offspring, occurred with the children of two out of seven female DuPont employees from the Washington Works facility from 1979 to 1981. [ 30 ] [ 154 ] Bucky Bailey is one of the affected individuals; DuPont, however, does not accept any liability from the toxicity of PFOA. [ 155 ] While 3M sent DuPont results from a study that showed birth defects to rats administered PFOA and DuPont moved the women out of the Teflon production unit, [ 30 ] subsequent animal testing led DuPont to conclude there was no reproductive risk to women, and they were returned to the production unit. [ 156 ] However, data released in March 2009 on the community around DuPont's Washington Works plant showed "a modest, imprecise indication of an elevation in risk ... above the 90th percentile ... based on 12 cases in the uppermost category", which was deemed "suggestive of a possible relationship" between PFOA exposure and birth defects. [ 157 ] [ 158 ]
PFOA was proposed for listing under the Stockholm Convention on Persistent Organic Pollutants in 2015, and on May 10, 2019, PFOA, its salts, and PFOA-related compounds were added to Annex A of the Stockholm Convention by the Conference of the Parties. [ 159 ] Several hundred salts and precursors of PFOA fall within the scope of the restriction. [ 160 ] [ 161 ] A few specific exemptions remained. Among them is a time-bound exemption for PFOA in fire-fighting foam.
DuPont has used PFOA for over 50 years at its Washington Works plant. Area residents sued DuPont in August 2001 and claimed DuPont released PFOA in excess of their community guideline of 1 part per billion resulting in lower property values and increased risk of illness. [ 30 ] The class was certified by Wood Circuit Court Judge George W. Hill. [ 162 ] As part of the settlement, DuPont has paid for blood tests and health surveys of residents believed to be affected. [ 163 ] Participants numbered 69,030 in the study, which was reviewed by three epidemiologists —the C8 Science Panel—to determine if any health effects are the likely result of exposure.
On December 13, 2005, DuPont announced a settlement with the EPA in which DuPont would pay US$ 10.25 million in fines and an additional US$6.25 million for two supplemental environmental projects without any admission of liability. [ 164 ]
On September 30, 2008, Chief Judge Joseph R. Goodwin of the United States District Court for the Southern District of West Virginia denied the certification of a class of Parkersburg residents exposed to PFOA from DuPont's facility because they did not "show the common individual injuries needed to certify a class action". [ 165 ] On September 28, 2009, Judge Goodwin dismissed the claims of those residents except for medical monitoring. [ 162 ] [ 166 ] By 2015, more than three thousand plaintiffs have filed personal-injury lawsuits against DuPont. [ 14 ] In 2017, DuPont reached a $670.7 million cash settlement [ 167 ] related to 3,550 personal injury lawsuits tied to PFOA contamination of drinking water in the Parkersburg area. Chemours, which was spun off from DuPont in 2015, agreed to pay half the settlement. Both companies denied any wrongdoing.
The government of Jersey signed a confidential agreement with 3M in 2005, agreeing to not pursue legal claims for £2.6m. Jersey must assist 3M in the defense of future claims.
A source told the Guardian that Jersey needed 3M’s permission to proceed with blood tests to avoid 3M punitive measures. “The state got an agreement to do individual blood tests, but not screening, as that could be the first step towards a possible class action lawsuit.” [ 31 ]
In 2002, a panel of toxicologists, including several from EPA, proposed a level of 150 ppb for drinking water in the PFOA contaminated area around DuPont's Washington Works plant. This initially proposed level was much higher than any known environmental concentration [ 48 ] and was over 2,000 times the level EPA eventually settled on for the drinking water health advisory.
In July 2004, EPA filed a suit against DuPont alleging "widespread contamination" of PFOA near the Parkersburg, West Virginia plant "at levels exceeding the company's community exposure guidelines;" the suit also alleged that "DuPont had—over a 20 year period—repeatedly failed to submit information on adverse effects (in particular, information on liver enzyme alterations and birth defects in offspring of female Parkersburg workers)." [ 30 ]
In October 2005, a USFDA study was published revealing PFOA and PFOA precursor chemicals in food contact and PTFE products. [ 90 ]
On January 25, 2006, EPA announced a voluntary program with several chemical companies to reduce PFOA and PFOA precursor emissions by the year 2015. [ 168 ]
On February 15, 2005, EPA's Science Advisory Board (SAB) voted to recommended that PFOA should be considered a "likely human carcinogen ". [ 169 ]
On May 26, 2006, EPA's SAB addressed a letter to Administrator Stephen L. Johnson . Three-quarters of advisers thought the stronger "likely to be carcinogenic" descriptor was warranted, in opposition to EPA's own PFOA hazard descriptor of "suggestive evidence of carcinogenicity, but not sufficient to assess human carcinogenic potential". [ 170 ]
On November 21, 2006, EPA ordered DuPont to offer alternative drinking water or treatment for public or private water users living near DuPont's Washington Works plant in West Virginia (and in Ohio), if the level of PFOA detected in drinking water is equal to or greater than 0.5 parts per billion. This measure sharply lowered the previous action level of 150 parts per billion that was established in March 2002. [ 171 ]
According to a May 23, 2007, Environmental Science & Technology Online article, U.S. Food and Drug Administration research regarding food contact papers as a potential source of PFOA to humans is ongoing. [ 74 ]
In November 2007, the Centers for Disease Control and Prevention (CDC) published data on PFOA concentrations comparing 1999–2000 vs. 2003–2004 NHANES samples. [ 66 ]
In October 2021 the EPA proposed to designate PFOA and PFOS as hazardous substances in its PFAS Strategic Roadmap. [ 172 ] [ 173 ] In September 2022 the EPA proposed to designate as hazardous substances under the Superfund Comprehensive Environmental Response, Compensation, and Liability Act of 1980 (CERCLA).
In 2024 EPA published drinking water regulations for PFOA and five other PFAS. [ 13 ]
In 2007 the New Jersey Department of Environmental Protection (NJDEP) announced that it found PFOA at "elevated levels in the system's drinking water near DuPont's massive Chambers Works chemical plant". [ 174 ]
In 2018 the state published a drinking water standard for PFNA. Public water systems in New Jersey are required to meet a maximum contaminant level (MCL) standard of 13 ppt. [ 111 ] [ 175 ]
In 2019 New Jersey filed lawsuits against the owners of two plants that had manufactured PFASs (the Chambers Works and the Parlin plant in Sayreville ), and two plants that were cited for water pollution from other chemicals. The companies cited are DuPont, Chemours and 3M. [ 176 ]
In 2020 the NJDEP set a PFOA standard at 14 ppt and a PFOS standard at 13 ppt. [ 110 ]
In 2018 the New York State Department of Health adopted drinking water standards of 10 ppt for PFOA and 10 ppt for PFOS, effective in 2019 after a public comment period. [ 112 ]
In November 2017, the Michigan PFAS Action Response Team (MPART) was created to address growing pollution concerns after multiple sites contaminated by PFAS were identified. MPART is a multi-agency team tasked with investigating PFAS contamination sites and sources in the state, protecting drinking water, enhancing interagency communication and keeping the public informed. [ 177 ]
In January 2018, Michigan established a legally enforceable groundwater cleanup level of 70 ppt for both PFOA and PFOS. Two science advisory committees were also created and joined MPART to "coordinate and review medical and environmental health, PFAS science and develop evidence-based recommendations". [ 178 ]
In August 2020, the Michigan Department of Environment, Great Lakes, and Energy adopted stricter drinking water standards in the form of MCLs , lowering acceptable levels from the 2018 enforceable groundwater cleanup levels of 70 ppt to 8 ppt for PFOA and 16 ppt for PFOS and adding MCLs for 5 previously unregulated PFAS compounds PFNA, PFHxA , PFHxS , PFBS , and HFPO-DA . [ 179 ] [ 180 ]
In 2007, the Minnesota Department of Health lowered its Health Based Value for PFOA in drinking water from 1.0 ppb to 0.5 ppb, [ 181 ] where "the sources are landfilled industrial wastes from a 3M manufacturing plant". [ 174 ]
PFOA contaminated waste was incorporated into soil improver and spread on agricultural land in Germany, leading to PFOA drinking water contamination of up to 0.519 parts per billion . [ 182 ] [ 183 ] The German Federal Environmental Agency issued guidelines for the sum of PFOA and PFOS concentrations in drinking water: 0.1 parts per billion for precaution and 0.3 parts per billion for a threshold. [ 184 ] Residents were found to have a 6–8 factor increase of PFOA serum levels over unexposed Germans, with average PFOA concentrations in the 22–27 parts per billion range. [ 52 ] An expert panel concluded that "concentrations were considered too low to cause overt adverse health effects in the exposed population". [ 184 ]
In the Netherlands, after questions by members of Parliament, the minister of Environment ordered a study into the potential exposure to PFOA of people living in the vicinity of the DuPont factory in Dordrecht . The report was published in March 2016 and concluded that "prior to 2002 residents were exposed to levels of PFOA at which health effects could not be ruled out". [ 185 ] As a result of this, the government commissioned several further studies, including blood tests and measurements in drinking water.
PFOA was identified as a PBT substance in the EU in 2013. It was then included in the candidate list of substances of very high concern . In 2017, PFOA, its salts and PFOA-related substances were added to annex XVII (restriction) of the REACH Regulation . [ 186 ]
The EU adopted the listing of PFOA in Annex A of the Stockholm Convention with Commission Delegated Regulation (EU) 2020/784 of 8 April 2020 and introduced a limit value of 0,025 mg/kg for PFOA including its salts, and at 1 mg/kg for the individual PFOA-related compounds or a combination of those compounds. [ 187 ] They also included some specific exemptions. Among them is a time-bound exemption for PFOA in fire-fighting foam.
On August 10, 2016, Australian litigation funder IMF Bentham announced an agreement to fund a class action led by the law firm Gadens against the Australian Department of Defence for economic losses to homeowners, fishers, and farmers resulting from the use of aqueous film forming foam (containing PFOA) at RAAF Base Williamtown . [ 188 ] | https://en.wikipedia.org/wiki/Perfluorooctanoic_acid |
Perfluorotributylamine ( PFTBA ), also referred to as FC43, is an organic compound with the chemical formula N(CF 2 CF 2 CF 2 CF 3 ) 3 . It is a colorless liquid. A molecule of this chemical compound consists of three butyl groups connected to one nitrogen atom , in which all of the hydrogen atoms are replaced with fluorine atoms. The compound is produced for the electronics industry, along with other perfluoroalkylamines. The high degree of fluorination significantly reduces the basicity of the central amine due to electron-withdrawing effects. [ 1 ]
It is prepared by electrofluorination of tributylamine using hydrogen fluoride as solvent and source of fluorine: [ 2 ]
The compound has two commercial uses.
It is used as an ingredient in Fluosol , artificial blood. This application exploits the high solubility of oxygen and carbon dioxide in the solvent, as well as the low viscosity and toxicity. [ 3 ] It is also a component of Fluorinert coolant liquids. CPUs of some computers are immersed in this liquid to facilitate cooling. [ 2 ]
The compound is used as a calibrant [ 4 ] in gas chromatography when the analytical technique uses mass spectrometry as a detector to identify and quantify chemical compounds in gases or liquids. When undergoing ionization in the mass spectrometer, the compound decomposes in a repeatable pattern to form fragments of specific masses, which can be used to tune the mass response and accuracy of the mass spectrometer. Most commonly used ions are those with approximate mass of 69, 131, 219, 414 and 502 atomic mass units .
Fluorofluids are generally of very low toxicity, so much that they have been evaluated as synthetic blood. [ 2 ]
It is a greenhouse gas with warming properties more than 7,000 times that of carbon dioxide over a 100-year period, [ 5 ] [ 6 ] and, as such, is one of the most potent greenhouse gasses ever discovered. [ 7 ] Its concentration in the atmosphere is approximately 0.18 parts per trillion. The compound can persist in the atmosphere for up to 500 years. | https://en.wikipedia.org/wiki/Perfluorotributylamine |
In March 2013, Lockheed Martin announced that it was developing a family of membranes made from graphene , under the trademark Perforene .
The most promising application is seawater desalination . With holes as small as one nanometer in diameter, the membranes would trap sodium, chlorine and other ions, while allowing water molecules to pass through easily. [ citation needed ] Performance expectations (relative to the use of reverse osmosis membranes) include:
In addition to the desalination industry, Lockheed Martin plans to market Perforene variants in the following fields:
The product was not expected to be released until 2020.
Bruce Sterling commented for Wired , "if this graphene vaporware actually worked out in practice, we’d have to forgive Lockheed Martin for everything else they’ve ever done — plus maybe even give them Nobels and McMansion palaces in former deserts." [ 3 ]
The Water Desalination Report evaluated Lockheed Martin's claims that it had developed a membrane that will desalinate water “at a fraction of the cost of industry-standard RO systems” as "ridiculous and very premature." [ 4 ] | https://en.wikipedia.org/wiki/Perforene |
Performance-Based Building Design is an approach to the design of any complexity of building, from single-detached homes up to and including high-rise apartments and office buildings. A building constructed in this way is required to meet certain measurable or predictable performance requirements, such as energy efficiency or seismic load, without a specific prescribed method by which to attain those requirements. This is in contrast to traditional prescribed building codes , which mandate specific construction practises, such as stud size and distance between studs in wooden frame construction . [ 1 ] Such an approach provides the freedom to develop tools and methods to evaluate the entire life cycle of the building process, from the business dealings, to procurement , through construction and the evaluation of results.
One of the first implementations of performance-based building design requirements was in Hammurabi's Code (c. 1795 to 1750 BC), where is stated that "a house should not collapse and kill anybody". This concept is also described in Vitruvius 's "De architectura libri decem" (" The Ten Books of Architecture ") in first century BC.In modern times, the first definition of performance-based building design was introduced in 1965 in France by Blachère with the Agrément system [ 2 ]
Despite this, the building process remained relatively conventional for the next 50 years, based solely on experience and codes, regulations prescribed by law which stifled innovations and change. The prescription approach is a technical procedure based on past experience which consists of comparing the proposed design with standardized codes, so no simulation or verification tools are needed for the design and building process.
A new approach began to emerge during the second half of the 20th century, when many local building markets began to show that they needed greater flexibility in the procurement procedures to facilitate the exchange of building goods between countries and to improve the speed of procedures and innovations in the building process. This innovative approach to the procurement, design, contracting, management and maintenance of buildings was performance-based building design (PBBD).
Most recently the clearest definition of performance based building approach was explained in 1982 by the CIB W60 Commission in the report n.64, where Gibson stated that "first and foremost, the performance approach is [...] the practice of thinking and working in terms of ends rather than means.[ …] It is concerned with what a building or building product is required to do, and not with prescribing how it is to be constructed". [ 3 ]
Many research establishments have studied the implementation of PBBD during the last fifty years. [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] A majority of areas of building design remain open to innovation.
During 1998-2001, the CIB Board and Programme Committee initiated the Proactive Programme on Performance-Based Building [ 11 ] [ 12 ] in order to practically implement technical developments of performance-based building. This programme was followed by the establishment of the Performance-Based Building (PeBBu), running from October 2001 to October 2005, thanks to funds from the European Commission (EC) Fifth Framework Programme .
The PeBBu Network had a broad and varied programme, a set of activities and produced many papers to aid in the implementation of such vision.
PeBBu Thematic Network was managed by the CIB General Secretariat (International Council for Research and Innovation in Building Construction), particularly by the CIB Development Foundation (CIBdf). The PeBBu Network started working in 2001 and completed in 2005. In the PeBBu Network 73 organisations, included CIBdf (coordinating contractor), BBRI (Belgium), VTT (Finland), CSTB (France), EGM (Netherlands), TNO (Netherlands), BRE (UK), cooperated to this project bringing people together to share their work, their information and knowledge. The objectives of the Network was to stimulate and facilitate international dissemination and implementation of Performance Based Building in building and construction sector, maximising the contribution to this by the international Research and Development community. The PeBBu Thematic Network result is described and explained in 26 final reports which included three reports with an overall PBB scope, a multitude of research reports from the PeBBu Domains, User Platforms and Regional Platforms, a Final Management report and four practice reports for providing practical support to the actual application of PBB concept in building and construction sector.
A conceptual framework for implementing a PBB market was identified while reviewing various viewpoints during the compilation of the 2nd International State of the Art Report for the PeBBu Thematic Network (Becker and Foliente 2005). The building facility is a multi-component system with a generally very long life cycle. The system's design agenda as a whole, and the more specific design objectives of its parts, originate from relevant user requirements. These requirements evolve into a comprehensive set of Performance Requirements that should be established by a large number of stakeholders (the users, entrepreneur/owner, regulatory framework, design team, and manufacturers).
The main steps in a Performance Based Building Design process are:
In a Performance-based approach, the focus of all decisions, is on the required performance-in-use and on the evaluations and testing of building asset. Performance Based Building (PBB) is focused on performance required in use for the business processes and the needs of the users, and then on the evaluations and verification of building assets result. The Performance approach can be used whether the process is about an existing or new assets. It is applicable to the procurement of constructed assets and to any phase of the whole life cycle Building Process, such as strategic planning , asset management , briefing/programming, design and construction, operation and maintenance, management and use, renovations and alterations, codes, regulations and standards. It includes many topics and criteria, which can be categorized as physical, functional, environmental, financial, economical, psychological, social, facilities, and other more. These criteria are related to singular project, according to the context and the situation.
Performance concept is based on two key characteristics:
The Performance concept requires two languages: the language of demand requirements and the language of the required performance which should have a capability to fulfill the demand. It is important to recognize that these languages are different. Szigeti and Davis (Performance Based Building: Conceptual Framework, 2005) explain that "the dialog between client and supplier can be described as two halves of a "hamburger bun", with the statement of the requirement in functional or performance language (FC - functional concept) matched to a solution (SC - solution concept) in more technical language, and the matching, verification / validation that needs to occur in between".
In a recent paper Ang, Groosman, and Scholten (2005) explain that the functional concept represents the set of unquantified objectives and scopes to be satisfied by the supply solutions, related to performance requirements. The solution concept represents technical realization that satisfies at least the required performance. Design decision is a development of a solution concept.
Building performance evaluation is the process of systematically comparing and matching the performance in use of building assets with explicitly documented or implicitly criteria for their expected performance. In the PBB approach is essential matching and comparing demand and supply. It can be done by using a validation method, by measurement, calculation, or testing. Tools and methods are used to permit some form of measurement of testing of the requirements, and the relating measurement of the capability of assets to perform.
There are many types of in-depth specialized technical evaluations and audits. These validations generally require time, a major effort by the customer group, and a high level of funding. Normally, the most valuable methods and tools are comprehensive scans which are performance based and include metrics that can easily be measured without lab-type instruments. Evaluations and reviews, are integral part of asset and portfolio management, design, construction, commissioning. Evaluations can be used for different purposes, depending on the requirements being considered, for example they could be used in support of funding decisions, they could include a condition assessment to ensure that the level of degradation or the obsolescence is known, they could include an assessment of the utilization or an assessment of the capability of the product result to perform functional expected requirements. Such evaluations can be used at any time during the life cycle of the asset. PBB evaluations should be done in a routine manner, really the evaluations are often done only as part of Commissioning or shortly thereafter, or when there is a problem.
There are two different kinds of performance verifications. Performance evaluations rate the physical asset according to a set of existing criteria and indicators of capability, and match the results against the required levels of performance. The Occupant Satisfaction Surveys record the perceptions of the users, usually through a scale of satisfaction measurements. Both types of evaluations complement each other.
Innovative decision-support methodologies are taking place in building sector. There are some tools explicitly based on the demand and supply concepts and other ones which employ standardized performance metrics that for the first time link facility condition to the functional requirements of organizations and their customers. Projects can be planned, prioritize, and budgeted using a multi-criteria approach, that is transparent, comprehensive and auditable. One of the methodologies that can be used is a gap analysis based on calibrated scales that measure both the levels of requirements and the capability of the asset that is either already used, or being designed, or offer to be bought, or leased. Such methodology is an ASTM and American National (ANSI) standard and is currently being considered as an ISO standard. It is particularly useful when the information about the "gap", if any, can be presented in support of funding decisions and actions.
There are a large number of verification methodologies, (e.g. POEs, CRE-FM), and all of these need to refer back to explicit statements of requirements to be able to compare with expected performance. To evaluate the result of a building asset against the expected performance requirements it is necessary to fix some tools used during the process. These tools are the reference of whole life cycle building process, so organizations use 'key performance indicators (KPI)' to prove that they are meeting the targets that have been set by senior management. At the same time performance measurement (PM) becomes central to managing organizations, their operations and logistic support. These methodologies include the feedback loop that links a facility in use to the requirements and capabilities that are compared and matched whenever decisions are needed.
A prescriptive approach describes the way a building asset must be constructed, rather than the end result of the building process, and is related to the type and quality of materials used, the method of construction, and the workmanship. This type of approach is strictly mandated by a combination of law, codes, standards, and regulations, and is based on past experience and consolidated know-how. The content of prescriptive codes and standards is usually a consequence of an accident causing injury or death which requires a remedy to avoid a repeat, as a consequence of some hazardous situation, or as a consequence of some recognized social need. In many countries, in both the public and private sector, research is taking place into a different set of codes, methods and tools based on performance criteria to complement the traditional prescriptive codes. In the 1970s, this search produced the "Nordic Model" (NKB 1978), which constituted the reference model of next performance-based codes. This model links easily to one of the key characteristics of the Performance approach, the dialog between the why, the what and the how.
Using a Performance Based approach does not preclude the use of prescriptive specifications. Although the benefits of the adopting of a PBBD approach are significant, it is recognized that employing a performance-based approach at any stage in the building process is more complex and expensive than using the simpler prescriptive route. So, the application of this approach should not be regarded as an end in itself. When simple building are concerned or well proven technologies are used, the use of prescriptive codes results more effective, efficient, faster, or less costly, so prescriptive specifications will continue to be useful in many situations.
At the same time for the complex projects use of the performance based route at every stage is indispensable, in particular during design and evaluation phases.
It is not likely that a facility will be planned, procured, delivered, maintained, used and renovated using solely Performance Based documents at each step of the way, down the supply chain, to the procurement of products and materials, because there is not yet enough experience with the Performance Based Building approach. At the same time the prescriptive approach can bring to stifle changes and innovations, so best way to set building process is blending both different approaches.
The Statements of Requirements represents a reference for the whole life cycle management of facilities, they are the core of the conceptual framework came up from the PeBBu Thematic Network. They constitute the key to implementation of the PBB in the construction sector.
The SoRs is a document prepared by clients, or in the verbal statements communicated to supplies, it is based on the user functional needs. These user requirements are converted into performance requirements, which can be explicit or implicit. Such document should include information about what is essential to the client. SoRs will take different forms depending on the kind of client and what is being procured, at what phase of the Life Cycle or where in the supply chain a document is being used. The SoRs should be, dynamic, not static, and should include more and more details as projects proceed. This document should be prepared at different levels of granularity, how detailed the documentation is at each stage depends on the complexity of the project and on the procurement route chosen for the project.
The SoRs represent a very important part of a continuous process of communication between clients (demand) and their project team (supply), they will be updated and managed using computerized tools and will contain all requirements throughout the life of the facility. This process is called "briefing" in UK and Commonwealth English, and "programming" in American English. An SoR is normally prepared for any project, whether it is a PBB project or not. Assembling such a document usually leads to a more appropriate match between the needs of clients and users and the constructed assets. Statements of Requirements have to be very carefully stated so that it is easy to verify that a proposed solution can meet those requirements.
High level statement of requirements need to be paired with indicators of capability so design solutions can be evaluated before they are built in order to avoid mistakes. In the SoRs it is important to take into account some design aspect like flexibility indicators because constructed assets need for change during their life cycle, uses and activities can change very rapidly, so it is essential to test different solutions way that the spaces might be used according to anticipate changes. SoRs, as understood in ISO 9000, include not only what the client requires and is prepared to pay for, but also the process and indicators that will provide the means to verify, and validate, that the product or service delivered meets those stated requirements.
As part of the worldwide movement to implement a PBB approach and to develop tools that will make it easier to shift to PBB, the International Alliance for Interoperability (IAI) set up projects to map the processes that are part of Whole Life Cycle Management as Portfolio and Asset Management: Performance (PAMPeR) and Early Design" (ED). The IAI efforts are complemented by many other efforts to create standards for the information to be captured and analyzed to verify performance-in-use.
Performance requirements translate user requirements in more precise quantitative measurable and technical terms, usually for a specific purpose.
Supply team prepares a document that includes, objectives and goals, performance requirements and criteria. It is important to include "indicators of performance" in the way that it can be measured the results against explicit requirements, whether qualitative or quantitative. Performance indicators need to be easily understood by the users and the evaluators. To validate the indicators and verify that required performance-in-use has been achieved it is necessary using appropriate methods and tools. Levels of performance requirements can be stated as part of the preparation of SoRs, as part of project programs, or as part of requests for proposals and procurement contracts. It is preferable adopting a flexible approach to the expression and comparison of performance levels, so required and achieved performance can be expressed not as single values but as bands between upper and lower limits. In consequence, in performance terms the criteria can be expressed as graduated scales, divided into broad bands.
In the building and construction industry, until 25–30 years old, prescriptive codes, regulations and standards made innovation and change difficult and costly to implement, and created technical restrictions to trade. These concerns have been the major drivers towards the use of a Performance Based approach to codes, regulations and standards. Performance-based building regulations have been implemented or are being developed in many countries but they have not yet reached their full potential. In part, this can be attributed to the fact that the overall regulatory system has not yet been fully addressed, and gaps exist in several key areas. Bringing the regulatory and non-regulatory models together is probably the best way to work. This is shown in the "Total Performance System Models" diagram (Meacham, et al. 2002), that maps the flow of decision making from society and business objectives to construction solutions.
The difference between the regulatory and non-regulatory parts of the Total Performance System Models is that the first one is mandated by codes and regulations based on the law, while those other functional requirements, included in Statements of Requirements, are an integral part of what the client requires and is willing to pay for.
For procurements in the public sector and for publicly traded corporations, it's important that the decisions and choices are transparent and explicit, regardless of the specific procurement route. All procurement processes can be either Prescriptive or Performance Based. Design-Build, Public Private Partnerships (PPP), private finance initiative (PFI) and similar procurement procedures are particularly suited to the use of a strong Performance Based Building application. If the expected performance are not stated explicitly and verifiably then these procurement methods will likely be more subject to disappointments and legal problems. To get the benefits from these procurement approaches, it is essential to organize the services of the supply chain in order to get innovative, less costly, or better solutions by shifting decisions about "how" to the integrated team. | https://en.wikipedia.org/wiki/Performance-based_building_design |
Performance-enhancing proxies ( PEPs ) are network agents designed to improve the end-to-end performance of some communication protocols . PEP standards are defined in RFC 3135 (PEPs intended to mitigate link-related degradations) and RFC 3449 (TCP performance implications of network path asymmetry).
Available PEP implementations use different methods to enhance performance.
There are a range of different types of PEPs. Each is used to solve a link related problem. Some common types include:
Split TCP is typically used to solve TCP problems with large round-trip delay times . A typical system uses Split TCP PEPs to improve TCP performance over a satellite link . Split TCP functions by breaking the end-to-end connection into multiple connections and using different parameters to transfer data across the different legs. The end systems use standard TCP with no modifications, and do not need to know of the existence of the PEPs in between. Split TCP intercepts TCP connections from the end systems and terminates them. This allows the end systems to run unmodified and can overcome some problems with TCP window sizes on the end systems being set too low for satellite communications.
Ack filtering or decimation is used on highly asymmetric links. In asymmetric links the upstream and downstream rates vary widely. A common example is satellite broadband where a downstream satellite link provides significantly greater bandwidths than the upstream dialup modem link. In this scenario, the speed at which the modem can return TCP acknowledgements can be a limiting factor. As TCP acknowledgements are cumulatively acknowledged some can be decimated or filtered to improve performance.
The Snoop proxy [ 2 ] is an example of an integrated proxy. It is designed to hide interference or collision-based packet loss over a wireless link. Snoop proxies detect losses by monitoring TCP transmissions for duplicate acknowledgements. When duplicate TCP acknowledgements, indicating a packet loss, are received by Snoop, they will be silently dropped and lost data packet will be retransmitted. The TCP sender should have no knowledge of the loss. This should prevent TCP senders from unnecessarily reducing the TCP window.
D-Proxy [ 3 ] [ 4 ] is also designed to hide interference or collision based packet loss over a wireless link. D-Proxy is a new distributed TCP proxy, requiring a proxy on either side of the lossy link. Like Snoop, it uses TCP sequence numbers to detect lost packets. However, it has a proactive approach, monitoring the TCP sequence numbers on data packets rather than acknowledgements. When packet loss occurs, the TCP stream will be temporarily buffered until the missing packet can be recovered and re-sequenced. | https://en.wikipedia.org/wiki/Performance-enhancing_proxy |
Performance Analyzer is a commercial utility software for software performance analysis for x86 or SPARC machines. It has both a graphical user interface [ 2 ] and a command line interface . It is available for both Linux and Solaris operating systems. It can profile C, C++, and Java . [ 3 ]
Performance Analyzer is available as part of Oracle Developer Studio . It has visualization capabilities, can read out hardware performance counters , [ 4 ] thread synchronization, memory allocations and I/O, and specifically supports Java, OpenMP , MPI , and the Solaris kernel.
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Performance_Analyzer |
The PR ( performance rating , P-rating , or Pentium rating ) system was a figure of merit developed by AMD , Cyrix , IBM Microelectronics and SGS-Thomson in the mid-1990s as a method of comparing their x86 processors to those of rival Intel . The idea was to consider instructions per cycle (IPC) in addition to the clock speed, so that the processors become comparable with Intel's Pentium that had a higher clock speed with overall lower IPC. [ 1 ] [ 2 ]
The first use of the PR system was in 1995, when AMD used it to assert that their AMD 5x86 processor was as fast as a Pentium running at 75 MHz. The designation "P75" was added to the chip to denote this. [ 3 ] : 3 Later that year, Cyrix also adopted the PR system for its 6x86 [ 1 ] and 6x86MX line of processors. [ citation needed ] These processors were faster than Pentiums of the same speed in some benchmarks, so Cyrix gave them a Performance Rating faster than their clock speed. [ 3 ] Some AMD K5 models also use the PR system.
AMD initially branded its AMD K6 processors with a "PR2" rating but dropped this after consumer confusion. [ 4 ] AMD revived the branding for its Athlon XP , which was released in 2001. The efficient Athlon XP chips could perform better than similarly-clocked chips from Intel's competing Pentium 4 line-up, which depended on high clock speeds to overcome their low IPC. As a result, AMD believed consumers would be swayed by the megahertz myth . [ 5 ] These chips were rated against the Athlon Thunderbird but were popularly compared to the Pentium 4. As a result, the branding became colloquially known as a "Pentium Rating". [ 3 ] : 6 Maximum PC criticized this as making it more difficult for power users to differentiate between the various Athlon XP chips. For example, two chips could be given the same "PR" branding but have much different engineering ( cache size, bus speed, etc), which would affect their performance at different tasks. [ 6 ] | https://en.wikipedia.org/wiki/Performance_Rating |
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