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Molecular models of DNA structures are representations of the molecular geometry and topology of deoxyribonucleic acid ( DNA ) molecules using one of several means, with the aim of simplifying and presenting the essential, physical and chemical, properties of DNA molecular structures either in vivo or in vitro . These representations include closely packed spheres ( CPK models) made of plastic, metal wires for skeletal models , graphic computations and animations by computers, artistic rendering. Computer molecular models also allow animations and molecular dynamics simulations that are very important for understanding how DNA functions in vivo .
The more advanced, computer-based molecular models of DNA involve molecular dynamics simulations and quantum mechanics computations of vibro-rotations, delocalized molecular orbitals (MOs), electric dipole moments , hydrogen-bonding , and so on. DNA molecular dynamics modeling involves simulating deoxyribonucleic acid ( DNA ) molecular geometry and topology changes with time as a result of both intra- and inter- molecular interactions of DNA. Whereas molecular models of DNA molecules such as closely packed spheres (CPK models) made of plastic or metal wires for skeletal models are useful representations of static DNA structures, their usefulness is very limited for representing complex DNA dynamics. Computer molecular modeling allows both animations and molecular dynamics simulations that are very important to understand how DNA functions in vivo .
From the very early stages of structural studies of DNA by X-ray diffraction and biochemical means, molecular models such as the Watson-Crick nucleic acid double helix model were successfully employed to solve the 'puzzle' of DNA structure, and also find how the latter relates to its key functions in living cells. The first high quality X-ray diffraction patterns
of A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953. [ 1 ] Rosalind Franklin made the critical observation that DNA exists in two distinct forms, A and B, and produced the sharpest pictures of both through X-ray diffraction technique. [ 2 ] The first calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand, [ 3 ] and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick. [ 4 ]
Structural information is generated from X-ray diffraction studies of oriented DNA fibers with the help of molecular models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.
The first reports of a double helix molecular model of B-DNA structure were made by James Watson and Francis Crick in 1953. [ 5 ] [ 6 ] That same year, Maurice F. Wilkins,
A. Stokes and H.R. Wilson, reported the first X-ray patterns
of in vivo B-DNA in partially oriented salmon sperm heads. [ 7 ]
The development of the first correct double helix molecular model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the nucleotide base-pairing ([A---T]; [C---G]), or Chargaff's rules . [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] Although such initial studies of DNA structures with the help of molecular models were essentially static, their consequences for explaining the in vivo functions of DNA were significant in the areas of protein biosynthesis and the quasi-universality of the genetic code. Epigenetic transformation studies of DNA in vivo were however much slower to develop despite their importance for embryology, morphogenesis and cancer research. Such chemical dynamics and biochemical reactions of DNA are much more complex than the molecular dynamics of DNA physical interactions with water, ions and proteins/enzymes in living cells.
An old standing dynamic problem is how DNA "self-replication" takes place in living cells that should involve transient uncoiling of supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongated biopolymer molecules called fibers or chains (that are made of repeating nucleotide units of four basic types, attached to deoxyribose and phosphate groups), its molecular structure in vivo undergoes dynamic configuration changes that involve dynamically attached water molecules and ions. Supercoiling, packing with histones in chromosome structures, and other such supramolecular aspects also involve in vivo DNA topology which is even more complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especially challenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers, DNA often exists in multiple stable geometries (that is, it exhibits conformational isomerism ) and configurational, quantum states which are close to each other in energy on the potential energy surface of the DNA molecule.
Such varying molecular geometries can also be computed, at least in principle, by employing ab initio quantum chemistry methods that can attain high accuracy for small molecules, although claims that acceptable accuracy can be also achieved for polynuclelotides, and DNA conformations, were recently made on the basis of vibrational circular dichroism (VCD) spectral data. Such quantum geometries define an important class of ab initio molecular models of DNA which exploration has barely started, especially related to results obtained by VCD in solutions. More detailed comparisons with such ab initio quantum computations are in principle obtainable through 2D-FT NMR spectroscopy and relaxation studies of polynucleotide solutions or specifically labeled DNA, as for example with deuterium labels.
In an interesting twist of roles, the DNA molecule was proposed to be used for quantum computing via DNA. Both DNA nanostructures and DNA computing biochips have been built.
The chemical structure of DNA is insufficient to understand the complexity of the 3D structures of DNA. In contrast, animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. The DNA model shown (far right) is a space-filling, or CPK , model of the DNA double helix. Animated molecular models, such as the wire, or skeletal, type shown at the top of this article, allow one to visually explore the three-dimensional (3D) structure of DNA. Another type of DNA model is the space-filling, or CPK, model.
The hydrogen bonding dynamics and proton exchange is very different by many orders of magnitude between the two systems of fully hydrated DNA and water molecules in ice. Thus, the DNA dynamics is complex, involving nanosecond and several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time scale, and that of proton exchange in ice is on the millisecond time scale. The proton exchange rates in DNA and attached proteins may vary from picosecond to nanosecond, minutes or years, depending on the exact locations of the exchanged protons in the large biopolymers.
A simple harmonic oscillator 'vibration' is only an oversimplified dynamic representation of the longitudinal vibrations of the DNA intertwined helices which were found to be anharmonic rather than harmonic as often assumed in quantum dynamic simulations of DNA.
The structure of DNA shows a variety of forms, both double-stranded and single-stranded. The mechanical properties of DNA, which are directly related to its structure, are a significant problem for cells . Every process which binds or reads DNA is able to use or modify the mechanical properties of DNA for purposes of recognition, packaging and modification. The extreme length (a chromosome may contain a 10 cm long DNA strand), relative rigidity and helical structure of DNA has led to the evolution of histones and of enzymes such as topoisomerases and helicases to manage a cell's DNA. The properties of DNA are closely related to its molecular structure and sequence, particularly the weakness of the hydrogen bonds and electronic interactions that hold strands of DNA together compared to the strength of the bonds within each strand.
Experimental methods which can directly measure the mechanical properties of DNA are relatively new, and high-resolution visualization in solution is often difficult. Nevertheless, scientists have uncovered large amount of data on the mechanical properties of this polymer, and the implications of DNA's mechanical properties on cellular processes is a topic of active current research.
The DNA found in many cells can be macroscopic in length: a few centimetres long for each human chromosome. Consequently, cells must compact or package DNA to carry it within them. In eukaryotes this is carried by spool-like proteins named histones , around which DNA winds. It is the further compaction of this DNA-protein complex which produces the well known mitotic eukaryotic chromosomes .
In the late 1970s, alternate non-helical models of DNA structure were briefly considered as a potential solution to problems in DNA replication in plasmids and chromatin . However, the models were set aside in favor of the double-helical model due to subsequent experimental advances such as X-ray crystallography of DNA duplexes, and later the nucleosome core particle , and the discovery of topoisomerases . Such non-double-helical models are not currently accepted by the mainstream scientific community. [ 14 ] [ 15 ]
After DNA has been separated and purified by standard biochemical methods, one has a sample in a jar much like in the figure at the top of this article. Below are the main steps involved in generating structural information from X-ray diffraction studies of oriented DNA fibers that are drawn from the hydrated DNA sample with the help of molecular models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.
A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant amounts (e.g., larger than a few percent) of partial disordering of molecular arrangements. Limiting cases of the paracrystal model are nanostructures , such as glasses , liquids , etc., that may possess only local ordering and no global order. A simple example of a paracrystalline lattice is shown in the following figure for a silica glass:
Liquid crystals also have paracrystalline rather than crystalline structures.
Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one despite the relatively rigid DNA double helix stabilized by parallel hydrogen bonds between the nucleotide base-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular models omit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamic behaviors of B-DNA in vivo . The physical and mathematical analysis of X-ray [ 16 ] [ 17 ] and spectroscopic data for paracrystalline B-DNA is thus far more complex than that of crystalline, A-DNA X-ray diffraction patterns. The paracrystal model is also important for DNA technological applications such as DNA nanotechnology . Novel methods that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now also being developed. [ 18 ]
There are various uses of DNA molecular modeling in Genomics and Biotechnology research applications, from DNA repair to PCR and DNA nanostructures . Two-dimensional DNA junction arrays have been visualized by Atomic force microscopy . [ 19 ]
DNA molecular modeling has various uses in genomics and biotechnology , with research applications ranging from DNA repair to PCR and DNA nanostructures. These include computer molecular models of molecules as varied as RNA polymerase, an E. coli, bacterial DNA primase template suggesting very complex dynamics at the interfaces between the enzymes and the DNA template, and molecular models of the mutagenic, chemical interaction of potent carcinogen molecules with DNA. These are all represented in the gallery below.
Technological application include a DNA biochip and DNA nanostructures designed for DNA computing and other dynamic applications of DNA nanotechnology . [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] The image at right is of self-assembled DNA nanostructures. The DNA "tile" structure in this image consists of four branched junctions oriented at 90° angles. Each tile consists of nine DNA oligonucleotides as shown; such tiles serve as the primary "building block" for the assembly of the DNA nanogrids shown in the AFM micrograph.
Quadruplex DNA may be involved in certain cancers. [ 26 ] [ 27 ] Images of quadruplex DNA are in the gallery below. | https://en.wikipedia.org/wiki/Molecular_models_of_DNA |
Molecular motors are natural (biological) or artificial molecular machines that are the essential agents of movement in living organisms. In general terms, a motor is a device that consumes energy in one form and converts it into motion or mechanical work ; for example, many protein -based molecular motors harness the chemical free energy released by the hydrolysis of ATP in order to perform mechanical work. [ 1 ] In terms of energetic efficiency, this type of motor can be superior to currently available man-made motors. One important difference between molecular motors and macroscopic motors is that molecular motors operate in the thermal bath , an environment in which the fluctuations due to thermal noise are significant.
Some examples of biologically important molecular motors: [ 2 ]
A recent study has also shown that certain enzymes, such as Hexokinase and Glucose Oxidase, are aggregating or fragmenting during catalysis. This changes their hydrodynamic size that can affect enhanced diffusion measurements. [ 14 ]
There are two major families of molecular motors that transport organelles throughout the cell. These families include the dynein family and the kinesin family. Both have very different structures from one another and different ways of achieving a similar goal of moving organelles around the cell. These distances, though only few micrometers, are all preplanned out using microtubules. [ 16 ]
Because the motor events are stochastic , molecular motors are often modeled with the Fokker–Planck equation or with Monte Carlo methods . These theoretical models are especially useful when treating the molecular motor as a Brownian motor .
In experimental biophysics , the activity of molecular motors is observed with many different experimental approaches, among them:
Many more techniques are also used. As new technologies and methods are developed, it is expected that knowledge of naturally occurring molecular motors will be helpful in constructing synthetic nanoscale motors.
Recently, chemists and those involved in nanotechnology have begun to explore the possibility of creating molecular motors de novo. [ 17 ] These synthetic molecular motors currently suffer many limitations that confine their use to the research laboratory. However, many of these limitations may be overcome as our understanding of chemistry and physics at the nanoscale increases. One step toward understanding nanoscale dynamics was made with the study of catalyst diffusion in the Grubb's catalyst system. [ 18 ] Other systems like the nanocars , while not technically motors, are also illustrative of recent efforts towards synthetic nanoscale motors.
Other non-reacting molecules can also behave as motors. This has been demonstrated by using dye molecules that move directionally in gradients of polymer solution through favorable hydrophobic interactions. [ 19 ] Another recent study has shown that dye molecules, hard and soft colloidal particles are able to move through gradient of polymer solution through excluded volume effects. [ 20 ] | https://en.wikipedia.org/wiki/Molecular_motor |
Molecular nanotechnology ( MNT ) is a technology based on the ability to build structures to complex, atomic specifications by means of mechanosynthesis . [ 1 ] This is distinct from nanoscale materials .
Based on Richard Feynman 's vision of miniature factories using nanomachines to build complex products ( including additional nanomachines ), this advanced form of nanotechnology (or molecular manufacturing [ 2 ] ) would make use of positionally-controlled mechanosynthesis guided by molecular machine systems.
MNT would involve combining physical principles demonstrated by biophysics , chemistry , other nanotechnologies, and the molecular machinery of life, with the systems engineering principles found in modern macroscale factories.
While conventional chemistry uses inexact processes obtaining inexact results, and biology exploits inexact processes to obtain definitive results, molecular nanotechnology would employ original definitive processes to obtain definitive results. The desire in molecular nanotechnology would be to balance molecular reactions in positionally-controlled locations and orientations to obtain desired chemical reactions and then to build systems by further assembling the products of these reactions.
A roadmap for the development of MNT is an objective of a broadly based technology project led by Battelle (the manager of several U.S. National Laboratories) and the Foresight Institute . [ 3 ] The roadmap was originally scheduled for completion by late 2006 but was released in January 2008. [ 4 ] The Nanofactory Collaboration [ 5 ] is a more focused ongoing effort involving 23 researchers from 10 organizations and 4 countries that is developing a practical research agenda [ 6 ] specifically aimed at positionally-controlled diamond mechanosynthesis and diamondoid nanofactory development. In August 2005, a task force consisting of 50+ international experts from various fields was organized by the Center for Responsible Nanotechnology to study the societal implications of molecular nanotechnology. [ 7 ]
Any sort of material designed and engineered at the nanometer scale for a specific task is a smart material . If materials could be designed to respond differently to various molecules, for example, artificial drugs could recognize and render inert specific viruses . Self-healing structures would repair small tears in a surface naturally in the same way as human skin.
A nanosensor would resemble a smart material, involving a small component within a larger machine that would react to its environment and change in some fundamental, intentional way. A very simple example: a photosensor might passively measure the incident light and discharge its absorbed energy as electricity when the light passes above or below a specified threshold, sending a signal to a larger machine. Such a sensor would supposedly cost less [ according to whom? ] and use less power than a conventional sensor, and yet function usefully in all the same applications — for example, turning on parking lot lights when it gets dark.
While smart materials and nanosensors both exemplify useful applications of MNT, they pale in comparison with the complexity of the technology most popularly associated with the term: the replicating nanorobot .
MNT nanofacturing is popularly linked with the idea of swarms of coordinated nanoscale robots working together, a popularization of an early proposal by K. Eric Drexler in his 1986 discussions of MNT , but superseded in 1992 . In this early proposal, sufficiently capable nanorobots would construct more nanorobots in an artificial environment containing special molecular building blocks.
Critics have doubted both the feasibility of self-replicating nanorobots and the feasibility of control if self-replicating nanorobots could be achieved: they cite the possibility of mutations removing any control and favoring reproduction of mutant pathogenic variations. Advocates address the first doubt by pointing out that the first macroscale autonomous machine replicator, made of Lego blocks , was built and operated experimentally in 2002. [ 8 ] While there are sensory advantages present at the macroscale compared to the limited sensorium available at the nanoscale, proposals for positionally controlled nanoscale mechanosynthetic fabrication systems employ dead reckoning of tooltips combined with reliable reaction sequence design to ensure reliable results, hence a limited sensorium is no handicap; similar considerations apply to the positional assembly of small nanoparts. Advocates address the second doubt by arguing that bacteria are (of necessity) evolved to evolve, while nanorobot mutation could be actively prevented by common error-correcting techniques. Similar ideas are advocated in the Foresight Guidelines on Molecular Nanotechnology, [ 9 ] and a map of the 137-dimensional replicator design space [ 10 ] recently published by Freitas and Merkle provides numerous proposed methods by which replicators could, in principle, be safely controlled by good design.
However, the concept of suppressing mutation raises the question: How can design evolution occur at the nanoscale without a process of random mutation and deterministic selection? Critics argue that MNT advocates have not provided a substitute for such a process of evolution in this nanoscale arena where conventional sensory-based selection processes are lacking. The limits of the sensorium available at the nanoscale could make it difficult or impossible to winnow successes from failures. Advocates argue that design evolution should occur deterministically and strictly under human control, using the conventional engineering paradigm of modeling, design, prototyping, testing, analysis, and redesign. [ citation needed ]
In any event, since 1992 technical proposals for MNT do not include self-replicating nanorobots, and recent ethical guidelines put forth by MNT advocates prohibit unconstrained self-replication. [ 9 ] [ 11 ]
One of the most important applications of MNT would be medical nanorobotics or nanomedicine , an area pioneered by Robert Freitas in numerous books [ 12 ] and papers. [ 13 ] The ability to design, build, and deploy large numbers of medical nanorobots would, at a minimum, make possible the rapid elimination of disease and the reliable and relatively painless recovery from physical trauma. Medical nanorobots might also make possible the convenient correction of genetic defects, and help to ensure a greatly expanded lifespan. More controversially, medical nanorobots might be used to augment natural human capabilities . One study has reported on how conditions like tumors, arteriosclerosis , blood clots leading to stroke, accumulation of scar tissue and localized pockets of infection can possibly be addressed by employing medical nanorobots. [ 14 ] [ 15 ]
Another proposed application of molecular nanotechnology is " utility fog " [ 16 ] – in which a cloud of networked microscopic robots (simpler than molecular assemblers ) would change its shape and properties to form macroscopic objects and tools in accordance with software commands. Rather than modify the current practices of consuming material goods in different forms, utility fog would simply replace many physical objects.
Yet another proposed application of MNT would be phased-array optics (PAO). [ 17 ] However, this appears to be a problem addressable by ordinary nanoscale technology. PAO would use the principle of phased-array millimeter technology but at optical wavelengths. This would permit duplicating any sort of optical effect, but virtually. Users could request holograms, sunrises and sunsets, or floating lasers as desired. PAO systems were described in BC Crandall's Nanotechnology: Molecular Speculations on Global Abundance in the Brian Wowk article Phased-Array Optics . [ 17 ]
Molecular manufacturing is a potential future subfield of nanotechnology that would make it possible to build complex structures at atomic precision. [ 18 ] Molecular manufacturing requires significant advances in nanotechnology, but once achieved could produce highly advanced products at low costs and in large quantities in nanofactories weighing a kilogram or more. [ 18 ] [ 19 ] When nanofactories gain the ability to produce other nanofactories production may only be limited by relatively abundant factors such as input materials, energy and software. [ 19 ]
The products of molecular manufacturing could range from cheaper, mass-produced versions of known high-tech products to novel products with added abilities in many areas of application. Some applications that have been suggested are advanced smart materials , nanosensors, medical nanorobots, and space travel. [ 18 ] Further, molecular manufacturing could be used to cheaply produce highly advanced, durable weapons, which is an area of special concern regarding the impact of nanotechnology. [ 19 ] Being equipped with compact computers and motors these could be increasingly autonomous and have a large range of abilities. [ 19 ]
According to Chris Phoenix and Mike Treder from the Center for Responsible Nanotechnology, and Anders Sandberg from the Future of Humanity Institute , molecular manufacturing is the application of nanotechnology that poses the most significant global catastrophic risk . [ 19 ] [ 20 ] Several nanotechnology researchers state that the bulk of risk from nanotechnology comes from the potential to lead to war, arms races and destructive global government. [ 19 ] [ 20 ] [ 21 ] Several reasons have been suggested why the availability of nanotech weaponry may with significant likelihood lead to unstable arms races (compared to e.g. nuclear arms races): (1) A large number of players may be tempted to enter the race since the threshold for doing so is low; [ 19 ] (2) the ability to make weapons with molecular manufacturing will be cheap and easy to hide; [ 19 ] (3) therefore lack of insight into the other parties' abilities can tempt players to arm out of caution or to launch preemptive strikes; [ 19 ] [ 22 ] (4) molecular manufacturing may reduce dependency on international trade, [ 19 ] a potential peace-promoting factor; [ 23 ] (5) wars of aggression may pose a smaller economic threat to the aggressor since manufacturing is cheap and humans may not be needed on the battlefield. [ 19 ]
Since self-regulation by all state and non-state actors seems hard to achieve, [ 24 ] measures to mitigate war-related risks have mainly been proposed in the area of international cooperation . [ 19 ] [ 25 ] International infrastructure may be expanded giving more sovereignty to the international level. This could help coordinate efforts for arms control. [ 26 ] International institutions dedicated specifically to nanotechnology (perhaps analogously to the International Atomic Energy Agency IAEA ) or general arms control may also be designed. [ 25 ] One may also jointly progress in differential technological development on defensive technologies, a policy that players should usually favour. [ 19 ] The Center for Responsible Nanotechnology also suggest some technical restrictions. [ 27 ] Improved transparency regarding technological abilities may be another important facilitator for arms-control. [ 28 ]
A grey goo is another catastrophic scenario, which was proposed by Eric Drexler in his 1986 book Engines of Creation , [ 29 ] has been analyzed by Freitas in "Some Limits to Global Ecophagy by Biovorous Nanoreplicators, with Public Policy Recommendations" [ 30 ] and has been a theme in mainstream media and fiction. [ 31 ] [ 32 ] This scenario involves tiny self-replicating robots that consume the entire biosphere using it as a source of energy and building blocks. Nanotech experts including Drexler now discredit the scenario. According to Chris Phoenix a "So-called grey goo could only be the product of a deliberate and difficult engineering process, not an accident". [ 33 ] With the advent of nano-biotech, a different scenario called green goo has been forwarded. Here, the malignant substance is not nanobots but rather self-replicating biological organisms engineered through nanotechnology.
Nanotechnology (or molecular nanotechnology to refer more specifically to the goals discussed here) will let us continue the historical trends in manufacturing right up to the fundamental limits imposed by physical law. It will let us make remarkably powerful molecular computers. It will let us make materials over fifty times lighter than steel or aluminium alloy but with the same strength. We'll be able to make jets, rockets, cars or even chairs that, by today's standards, would be remarkably light, strong, and inexpensive. Molecular surgical tools, guided by molecular computers and injected into the blood stream could find and destroy cancer cells or invading bacteria, unclog arteries, or provide oxygen when the circulation is impaired.
Nanotechnology will replace our entire manufacturing base with a new, radically more precise, radically less expensive, and radically more flexible way of making products. The aim is not simply to replace today's computer chip making plants, but also to replace the assembly lines for cars, televisions, telephones, books, surgical tools, missiles, bookcases, airplanes, tractors, and all the rest. The objective is a pervasive change in manufacturing, a change that will leave virtually no product untouched. Economic progress and military readiness in the 21st Century will depend fundamentally on maintaining a competitive position in nanotechnology.
[ 34 ]
Despite the current early developmental status of nanotechnology and molecular nanotechnology, much concern surrounds MNT's anticipated impact on economics [ 35 ] [ 36 ] and on law . Whatever the exact effects, MNT, if achieved, would tend to reduce the scarcity of manufactured goods and make many more goods (such as food and health aids) manufacturable.
MNT should make possible nanomedical abilities to cure any medical condition not already cured by advances in other areas. Good health would be common, and poor health of any form would be as rare as smallpox and scurvy are today. Even cryonics would be feasible, as cryopreserved tissue could be fully repaired.
Molecular nanotechnology is one of the technologies that some analysts believe could lead to a technological singularity , in which technological growth has accelerated to the point of having unpredictable effects. Some effects could be beneficial, while others could be detrimental, such as the utilization of molecular nanotechnology by an unfriendly artificial general intelligence . [ 37 ] Some feel that molecular nanotechnology would have daunting risks. [ 38 ] It conceivably could enable cheaper and more destructive conventional weapons . Also, molecular nanotechnology might permit weapons of mass destruction that could self-replicate, as viruses and cancer cells do when attacking the human body. Commentators generally agree that, in the event molecular nanotechnology were developed, its self-replication should be permitted only under very controlled or "inherently safe" conditions.
A fear exists that nanomechanical robots, if achieved, and if designed to self-replicate using naturally occurring materials (a difficult task), could consume the entire planet in their hunger for raw materials, [ 39 ] or simply crowd out natural life, out-competing it for energy (as happened historically when blue-green algae appeared and outcompeted earlier life forms). Some commentators have referred to this situation as the " grey goo " or " ecophagy " scenario. K. Eric Drexler considers an accidental "grey goo" scenario extremely unlikely and says so in later editions of Engines of Creation .
In light of this perception of potential danger, the Foresight Institute , founded by Drexler, has prepared a set of guidelines [ 40 ] for the ethical development of nanotechnology. These include the banning of free-foraging self-replicating pseudo-organisms on the Earth's surface, at least, and possibly in other places.
The feasibility of the basic technologies analyzed in Nanosystems has been the subject of a formal scientific review by U.S. National Academy of Sciences, and has also been the focus of extensive debate on the internet and in the popular press.
In 2006, U.S. National Academy of Sciences released the report of a study of molecular manufacturing as part of a longer report, A Matter of Size: Triennial Review of the National Nanotechnology Initiative [ 41 ] The study committee reviewed the technical content of Nanosystems , and in its conclusion states that no current theoretical analysis can be considered definitive regarding several questions of potential system performance, and that optimal paths for implementing high-performance systems cannot be predicted with confidence. It recommends experimental research to advance knowledge in this area:
A section heading in Drexler's Engines of Creation reads [ 42 ] "Universal Assemblers", and the following text speaks of multiple types of assemblers which, collectively, could hypothetically "build almost anything that the laws of nature allow to exist." Drexler's colleague Ralph Merkle has noted that, contrary to widespread legend, [ 43 ] Drexler never claimed that assembler systems could build absolutely any molecular structure. The endnotes in Drexler's book explain the qualification "almost": "For example, a delicate structure might be designed that, like a stone arch, would self-destruct unless all its pieces were already in place. If there were no room in the design for the placement and removal of a scaffolding, then the structure might be impossible to build. Few structures of practical interest seem likely to exhibit such a problem, however."
In 1992, Drexler published Nanosystems: Molecular Machinery, Manufacturing, and Computation , [ 44 ] a detailed proposal for synthesizing stiff covalent structures using a table-top factory. Diamondoid structures and other stiff covalent structures, if achieved, would have a wide range of possible applications, going far beyond current MEMS technology. An outline of a path was put forward in 1992 for building a table-top factory in the absence of an assembler. Other researchers have begun advancing tentative, alternative proposed paths [ 5 ] for this in the years since Nanosystems was published.
In 2004 Richard Jones wrote Soft Machines (nanotechnology and life), a book for lay audiences published by Oxford University . In this book he describes radical nanotechnology (as advocated by Drexler) as a deterministic/mechanistic idea of nano engineered machines that does not take into account the nanoscale challenges such as wetness , stickiness , Brownian motion , and high viscosity . He also explains what is soft nanotechnology or more appropriately biomimetic nanotechnology which is the way forward, if not the best way, to design functional nanodevices that can cope with all the problems at a nanoscale. One can think of soft nanotechnology as the development of nanomachines that uses the lessons learned from biology on how things work, chemistry to precisely engineer such devices and stochastic physics to model the system and its natural processes in detail.
Several researchers, including Nobel Prize winner Dr. Richard Smalley (1943–2005), [ 45 ] attacked the notion of universal assemblers, leading to a rebuttal from Drexler and colleagues, [ 46 ] and eventually to an exchange of letters. [ 47 ] Smalley argued that chemistry is extremely complicated, reactions are hard to control, and that a universal assembler is science fiction. Drexler and colleagues, however, noted that Drexler never proposed universal assemblers able to make absolutely anything, but instead proposed more limited assemblers able to make a very wide variety of things. They challenged the relevance of Smalley's arguments to the more specific proposals advanced in Nanosystems . Also, Smalley argued that nearly all of modern chemistry involves reactions that take place in a solvent (usually water ), because the small molecules of a solvent contribute many things, such as lowering binding energies for transition states. Since nearly all known chemistry requires a solvent, Smalley felt that Drexler's proposal to use a high vacuum environment was not feasible. However, Drexler addresses this in Nanosystems by showing mathematically that well designed catalysts can provide the effects of a solvent and can fundamentally be made even more efficient than a solvent/ enzyme reaction could ever be. It is noteworthy that, contrary to Smalley's opinion that enzymes require water, "Not only do enzymes work vigorously in anhydrous organic media, but in this unnatural milieu they acquire remarkable properties such as greatly enhanced stability, radically altered substrate and enantiomeric specificities, molecular memory, and the ability to catalyse unusual reactions." [ 48 ]
For the future, some means have to be found for MNT design evolution at the nanoscale which mimics the process of biological evolution at the molecular scale. Biological evolution proceeds by random variation in ensemble averages of organisms combined with culling of the less-successful variants and reproduction of the more-successful variants, and macroscale engineering design also proceeds by a process of design evolution from simplicity to complexity as set forth somewhat satirically by John Gall : "A complex system that works is invariably found to have evolved from a simple system that worked. . . . A complex system designed from scratch never works and can not be patched up to make it work. You have to start over, beginning with a system that works." [ 49 ] A breakthrough in MNT is needed which proceeds from the simple atomic ensembles which can be built with, e.g., an STM to complex MNT systems via a process of design evolution. A handicap in this process is the difficulty of seeing and manipulation at the nanoscale compared to the macroscale which makes deterministic selection of successful trials difficult; in contrast biological evolution proceeds via action of what Richard Dawkins has called the "blind watchmaker" [ 50 ] comprising random molecular variation and deterministic reproduction/extinction.
At present in 2007 the practice of nanotechnology embraces both stochastic approaches (in which, for example, supramolecular chemistry creates waterproof pants) and deterministic approaches wherein single molecules (created by stochastic chemistry) are manipulated on substrate surfaces (created by stochastic deposition methods) by deterministic methods comprising nudging them with STM or AFM probes and causing simple binding or cleavage reactions to occur. The dream of a complex, deterministic molecular nanotechnology remains elusive. Since the mid-1990s, thousands of surface scientists and thin film technocrats have latched on to the nanotechnology bandwagon and redefined their disciplines as nanotechnology. This has caused much confusion in the field and has spawned thousands of "nano"-papers on the peer reviewed literature. Most of these reports are extensions of the more ordinary research done in the parent fields.
The feasibility of Drexler's proposals largely depends, therefore, on whether designs like those in Nanosystems could be built in the absence of a universal assembler to build them and would work as described. Supporters of molecular nanotechnology frequently claim that no significant errors have been discovered in Nanosystems since 1992. Even some critics concede [ 51 ] that "Drexler has carefully considered a number of physical principles underlying the 'high level' aspects of the nanosystems he proposes and, indeed, has thought in some detail" about some issues.
Other critics claim, however, that Nanosystems omits important chemical details about the low-level 'machine language' of molecular nanotechnology. [ 52 ] [ 53 ] [ 54 ] [ 55 ] They also claim that much of the other low-level chemistry in Nanosystems requires extensive further work, and that Drexler's higher-level designs therefore rest on speculative foundations. Recent such further work by Freitas and Merkle [ 56 ] is aimed at strengthening these foundations by filling the existing gaps in the low-level chemistry.
Drexler argues that we may need to wait until our conventional nanotechnology improves before solving these issues: "Molecular manufacturing will result from a series of advances in molecular machine systems, much as the first Moon landing resulted from a series of advances in liquid-fuel rocket systems. We are now in a position like that of the British Interplanetary Society of the 1930s which described how multistage liquid-fueled rockets could reach the Moon and pointed to early rockets as illustrations of the basic principle." [ 57 ] However, Freitas and Merkle argue [ 58 ] that a focused effort to achieve diamond mechanosynthesis (DMS) can begin now, using existing technology, and might achieve success in less than a decade if their "direct-to-DMS approach is pursued rather than a more circuitous development approach that seeks to implement less efficacious nondiamondoid molecular manufacturing technologies before progressing to diamondoid".
To summarize the arguments against feasibility: First, critics argue that a primary barrier to achieving molecular nanotechnology is the lack of an efficient way to create machines on a molecular/atomic scale, especially in the absence of a well-defined path toward a self-replicating assembler or diamondoid nanofactory. Advocates respond that a preliminary research path leading to a diamondoid nanofactory is being developed. [ 6 ]
A second difficulty in reaching molecular nanotechnology is design. Hand design of a gear or bearing at the level of atoms might take a few to several weeks. While Drexler, Merkle and others have created designs of simple parts, no comprehensive design effort for anything approaching the complexity of a Model T Ford has been attempted. Advocates respond that it is difficult to undertake a comprehensive design effort in the absence of significant funding for such efforts, and that despite this handicap much useful design-ahead has nevertheless been accomplished with molecular design software and editing tools that have been developed, e.g., at Nanorex, [ 59 ] or the newer Molecular Science and Engineering Platform One (MSEP.one). [ 60 ] [ 61 ]
In the latest report A Matter of Size: Triennial Review of the National Nanotechnology Initiative [ 41 ] put out by the National Academies Press in December 2006 (roughly twenty years after Engines of Creation was published), no clear way forward toward molecular nanotechnology could yet be seen, as per the conclusion on page 108 of that report: "Although theoretical calculations can be made today, the eventually attainable
range of chemical reaction cycles, error rates, speed of operation, and thermodynamic
efficiencies of such bottom-up manufacturing systems cannot be reliably
predicted at this time. Thus, the eventually attainable perfection and complexity of
manufactured products, while they can be calculated in theory, cannot be predicted
with confidence. Finally, the optimum research paths that might lead to systems
which greatly exceed the thermodynamic efficiencies and other capabilities of
biological systems cannot be reliably predicted at this time. Research funding that
is based on the ability of investigators to produce experimental demonstrations
that link to abstract models and guide long-term vision is most appropriate to
achieve this goal." This call for research leading to demonstrations is welcomed by groups such as the Nanofactory Collaboration who are specifically seeking experimental successes in diamond mechanosynthesis. [ 62 ] The "Technology Roadmap for Productive Nanosystems " [ 63 ] aims to offer additional constructive insights.
It is perhaps interesting to ask whether or not most structures consistent with physical law can in fact be manufactured. Advocates assert that to achieve most of the vision of molecular manufacturing it is not necessary to be able to build "any structure that is compatible with natural law." Rather, it is necessary to be able to build only a sufficient (possibly modest) subset of such structures—as is true, in fact, of any practical manufacturing process used in the world today, and is true even in biology. In any event, as Richard Feynman once said, "It is scientific only to say what's more likely or less likely, and not to be proving all the time what's possible or impossible." [ 64 ]
There is a growing body of peer-reviewed theoretical work on synthesizing diamond by mechanically removing/adding hydrogen atoms [ 65 ] and depositing carbon atoms [ 66 ] [ 67 ] [ 68 ] [ 69 ] [ 70 ] [ 71 ] (a process known as mechanosynthesis ). This work is slowly permeating the broader nanoscience community and is being critiqued. For instance, Peng et al. (2006) [ 72 ] (in the continuing research effort by Freitas, Merkle and their collaborators) reports that the most-studied mechanosynthesis tooltip motif (DCB6Ge) successfully places a C 2 carbon dimer on a C(110) diamond surface at both 300 K (room temperature) and 80 K ( liquid nitrogen temperature), and that the silicon variant (DCB6Si) also works at 80 K but not at 300 K. Over 100,000 CPU hours were invested in this latest study. The DCB6 tooltip motif, initially described by Merkle and Freitas at a Foresight Conference in 2002, was the first complete tooltip ever proposed for diamond mechanosynthesis and remains the only tooltip motif that has been successfully simulated for its intended function on a full 200-atom diamond surface.
The tooltips modeled in this work are intended to be used only in carefully controlled environments (e. g., vacuum). Maximum acceptable limits for tooltip translational and rotational misplacement errors are reported in Peng et al. (2006) -- tooltips must be positioned with great accuracy to avoid bonding the dimer incorrectly. Peng et al. (2006) reports that increasing the handle thickness from 4 support planes of C atoms above the tooltip to 5 planes decreases the resonance frequency of the entire structure from 2.0 THz to 1.8 THz. More importantly, the vibrational footprints of a DCB6Ge tooltip mounted on a 384-atom handle and of the same tooltip mounted on a similarly constrained but much larger 636-atom "crossbar" handle are virtually identical in the non-crossbar directions. More computed studies modeling still bigger handle structures are welcome, but the ability to precisely position SPM tips to the requisite atomic accuracy has been repeatedly demonstrated experimentally at low temperature, [ 73 ] [ 74 ] or even at room temperature [ 75 ] [ 76 ] constituting a basic existence proof for this capability.
Further research [ 77 ] to consider additional tooltips will require time-consuming computational chemistry and difficult laboratory work.
A working nanofactory would require a variety of well-designed tips for different reactions, and detailed analyses of placing atoms on more complicated surfaces. Although this appears a challenging problem given current resources, many tools will be available to help future researchers: Moore's law predicts further increases in computer power, semiconductor fabrication techniques continue to approach the nanoscale, and researchers grow ever more skilled at using proteins , ribosomes and DNA to perform novel chemistry. | https://en.wikipedia.org/wiki/Molecular_nanotechnology |
Molecular oncology is an interdisciplinary medical specialty at the interface of medicinal chemistry and oncology that refers to the investigation of the chemistry of cancer and tumors at the molecular scale. Also the development and application of molecularly targeted therapies .
Molecular oncology has identified genes that are involved in the development of cancer. Cancer arises as an abnormality in genomic control, either due to the activation of oncogenes or loss of functioning tumor-suppressor genes. Oncogenes result in an uncontrolled increase in cell proliferation; tumor-suppressor genes act as a brake, leading the cell cycle to stop and promote cell death when necessary. [ 1 ] The research combined diverse techniques ranging from genomics , computational biology , tumour imaging , in vitro and in vivo functional models to study biological and clinical phenotypes . The proteins produced by these genes may serve as targets for novel chemotherapy drugs and other cancer treatments, or imaging scans. Scientists use a range of techniques to validate the role of the novel candidate genes in the development of cancer. The ultimate aim is to translate these findings into improved treatment options for cancer patients. [ 2 ]
There are many different genes being researched for possible cancer therapies. Among the most studied are the p53 gene and the PTEN gene . [ 3 ] These genes are major regulators of the cell cycle and other pathways involved in cellular and genomic integrity. By halting the cell cycle, these genes ensure that genetically damaged cells are not passing on that damage to daughter cells. The cell cycle may be paused and if the damage is severe enough, the p53 and PTEN gene pathways may signal for the death of the damaged cells. [ 4 ] Both the p53 and PTEN genes are classified as tumor suppressors because their pathways oversee the repair of cells that may replicate out of control with damaged genetic material, eventually leading to cancer growth if not kept in check. [ 5 ] Mutations in these genes are seen in more than half of human cancers. [ 3 ]
Immune gene therapy is a targeted approach to cancer therapy where actual immune cells of the patient and their genes are manipulated to produce an anti-tumor response. [ 6 ] The body's own immune system is used to attack the tumor cells, therefore the immune system can naturally attack the specific cancer cells again to in the future if necessary. [ 7 ] Many types of immunotherapies exist including bone marrow transplants, antibody therapies, and various manipulations of host immune cells to target and kill cancer cells. Cellular receptors , antigens, and cofactor molecules are some such cellular manipulations to target cancer cells. [ 6 ]
Chimeric antigen receptor T cell immunotherapy (CAR-T), possibly combined with cytokines and checkpoint inhibitors , are a regularly used form of immune gene therapy. [ 6 ] CAR-T involves manipulation of a patient's natural T cells to express a chimeric antigen receptor. This receptor, now on millions of the patient's T cells, recognizes cancerous cells that express specific antigens . [ 6 ] Usually, the T cell antigen receptor is inactive but when the receptor recognizes a certain cancerous antigen, the physical structure of the T cell changes to destroy the cancer cell. [ 8 ] This is a method of cancer treatment that works on the cellular and molecular level.
Some regulatory proteins , specifically immune checkpoint inhibitors , have been found to reduce the ability of T cells to multiply within the body. [ 8 ] In order to optimize the efficacy of CAR-T gene therapy, these checkpoint inhibitors can be blocked to stimulate a robust anti-tumor immune response, spearheaded by the CAR-T cells. [ 8 ] There are various known inhibitory receptors on the CAR-T cell; through manipulation of these receptors and the molecules that bind them, expression of the CAR-T cell can be amplified. [ 8 ]
CAR-T cells can also be combined with cytokines to improve the efficacy of the immunotherapy method. [ 8 ] Cytokines are messenger molecules that can act on themselves, nearby cells, or distant cells. [ 8 ] The signal pathways of these cytokines can be used to enhance CAR-T anti-tumor characteristics. [ 8 ] For example, Interleukin 2 (IL2) is a cytokine that acts as a growth factor for various immune system cells, including T cells. In regards to gene therapy, IL2 can be used to increase replication and dispersing of CAR-T cells throughout the body. [ 8 ]
There is room for improvement with this gene therapy approach. Firstly, the antigens of interest expressed on the cancer cells may sometimes be expressed on regular body cells, too. [ 6 ] This means the body's T cells will attack its own healthy cells instead of the cancer cells when the antigen is lacking specificity with just the cancer cell. [ 6 ] A possible solution to this problem is to include two different antigen receptors on the CAR-T cells to make them even more specific. [ 6 ] The second issue with the CAR-T immunotherapy approach is that it can cause cytokine release syndrome . This is when an excess of pro-inflammatory factors are released by the immune system and can cause unpleasant side effects for the patient like nausea and a high fever . [ 6 ]
In the past few decades, gene therapy has emerged as a targeted way to treat cancer. Gene therapy introduces foreign genetic sequences to diseased cells in order to change the expression of these cancerous cells that are functioning with severely damaged genomes. [ 6 ] Cancer cells do not behave like normal cells, so the methods for ridding the body of these cells are more complicated. Manipulation of the pathways controlled by certain genes and their regulators are a large branch of cancer research. | https://en.wikipedia.org/wiki/Molecular_oncology |
In chemistry , a molecular orbital ( / ɒr b ə d l / ) is a mathematical function describing the location and wave-like behavior of an electron in a molecule . This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital [ a ] were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions . [ 2 ] At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.
In an isolated atom , the orbital electrons' location is determined by functions called atomic orbitals . When multiple atoms combine chemically into a molecule by forming a valence chemical bond , the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödinger equation for the electrons in the field of the molecule's atomic nuclei . They are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods.
Molecular orbitals are of three types: bonding orbitals which have an energy lower than the energy of the atomic orbitals which formed them, and thus promote the chemical bonds which hold the molecule together; antibonding orbitals which have an energy higher than the energy of their constituent atomic orbitals, and so oppose the bonding of the molecule, and non-bonding orbitals which have the same energy as their constituent atomic orbitals and thus have no effect on the bonding of the molecule.
A molecular orbital (MO) can be used to represent the regions in a molecule where an electron occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the Schrödinger equation for the electrons in the electric field of the molecule's atomic nuclei . However calculating the orbitals directly from this equation is far too intractable a problem. Instead they are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom. A molecular orbital can specify the electron configuration of a molecule: the spatial distribution and energy of one (or one pair of) electron(s). Most commonly a MO is represented as a linear combination of atomic orbitals (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory .
Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the same orbital, the Pauli principle demands that they have opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see configuration interaction ).
Molecular orbitals are, in general, delocalized throughout the entire molecule. Moreover, if the molecule has symmetry elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries. In other words, the application of a symmetry operation S (e.g., a reflection, rotation, or inversion) to molecular orbital ψ results in the molecular orbital being unchanged or reversing its mathematical sign: S ψ = ±ψ. In planar molecules, for example, molecular orbitals are either symmetric ( sigma ) or antisymmetric ( pi ) with respect to reflection in the molecular plane. If molecules with degenerate orbital energies are also considered, a more general statement that molecular orbitals form bases for the irreducible representations of the molecule's symmetry group holds. [ 4 ] The symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from (and complementary to) valence bond theory , in which bonds are viewed as localized electron pairs, with allowance for resonance to account for delocalization.
In contrast to these symmetry-adapted canonical molecular orbitals, localized molecular orbitals can be formed by applying certain mathematical transformations to the canonical orbitals. The advantage of this approach is that the orbitals will correspond more closely to the "bonds" of a molecule as depicted by a Lewis structure. As a disadvantage, the energy levels of these localized orbitals no longer have physical meaning. (The discussion in the rest of this article will focus on canonical molecular orbitals. For further discussions on localized molecular orbitals, see: natural bond orbital and sigma-pi and equivalent-orbital models .)
Molecular orbitals arise from allowed interactions between atomic orbitals , which are allowed if the symmetries (determined from group theory ) of the atomic orbitals are compatible with each other. Efficiency of atomic orbital interactions is determined from the overlap (a measure of how well two orbitals constructively interact with one another) between two atomic orbitals, which is significant if the atomic orbitals are close in energy. Finally, the number of molecular orbitals formed must be equal to the number of atomic orbitals in the atoms being combined to form the molecule.
For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the " Linear combination of atomic orbitals molecular orbital method " ansatz . Here, the molecular orbitals are expressed as linear combinations of atomic orbitals . [ 5 ]
Molecular orbitals were first introduced by Friedrich Hund [ 6 ] [ 7 ] and Robert S. Mulliken [ 8 ] [ 9 ] in 1927 and 1928. [ 10 ] [ 11 ] The linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones . [ 12 ] His ground-breaking paper showed how to derive the electronic structure of the fluorine and oxygen molecules from quantum principles. This qualitative approach to molecular orbital theory is part of the start of modern quantum chemistry .
Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation . For simple diatomic molecules, the wavefunctions obtained are represented mathematically by the equations
where Ψ {\displaystyle \Psi } and Ψ ∗ {\displaystyle \Psi ^{*}} are the molecular wavefunctions for the bonding and antibonding molecular orbitals, respectively, ψ a {\displaystyle \psi _{a}} and ψ b {\displaystyle \psi _{b}} are the atomic wavefunctions from atoms a and b, respectively, and c a {\displaystyle c_{a}} and c b {\displaystyle c_{b}} are adjustable coefficients. These coefficients can be positive or negative, depending on the energies and symmetries of the individual atomic orbitals. As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and, as a consequence, molecular orbitals are formed between the two atoms. The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals. [ 13 ]
When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding.
Bonding MOs :
Antibonding MOs :
Nonbonding MOs :
The type of interaction between atomic orbitals can be further categorized by the molecular-orbital symmetry labels σ (sigma), π (pi), δ (delta), φ (phi), γ (gamma) etc. These are the Greek letters corresponding to the atomic orbitals s, p, d, f and g respectively. The number of nodal planes containing the internuclear axis between the atoms concerned is zero for σ MOs, one for π, two for δ, three for φ and four for γ.
A MO with σ symmetry results from the interaction of either two atomic s-orbitals or two atomic p z -orbitals. An MO will have σ-symmetry if the orbital is symmetric with respect to the axis joining the two nuclear centers, the internuclear axis. This means that rotation of the MO about the internuclear axis does not result in a phase change. A σ* orbital, sigma antibonding orbital, also maintains the same phase when rotated about the internuclear axis. The σ* orbital has a nodal plane that is between the nuclei and perpendicular to the internuclear axis. [ 14 ]
A MO with π symmetry results from the interaction of either two atomic p x orbitals or p y orbitals. An MO will have π symmetry if the orbital is asymmetric with respect to rotation about the internuclear axis. This means that rotation of the MO about the internuclear axis will result in a phase change. There is one nodal plane containing the internuclear axis, if real orbitals are considered.
A π* orbital, pi antibonding orbital, will also produce a phase change when rotated about the internuclear axis. The π* orbital also has a second nodal plane between the nuclei. [ 14 ] [ 15 ] [ 16 ] [ 17 ]
A MO with δ symmetry results from the interaction of two atomic d xy or d x 2 -y 2 orbitals. Because these molecular orbitals involve low-energy d atomic orbitals, they are seen in transition-metal complexes. A δ bonding orbital has two nodal planes containing the internuclear axis, and a δ* antibonding orbital also has a third nodal plane between the nuclei.
Theoretical chemists have conjectured that higher-order bonds, such as phi bonds corresponding to overlap of f atomic orbitals, are possible. There is no known example of a molecule purported to contain a phi bond.
For molecules that possess a center of inversion ( centrosymmetric molecules ) there are additional labels of symmetry that can be applied to molecular orbitals.
Centrosymmetric molecules include:
Non-centrosymmetric molecules include:
If inversion through the center of symmetry in a molecule results in the same phases for the molecular orbital, then the MO is said to have gerade (g) symmetry, from the German word for even.
If inversion through the center of symmetry in a molecule results in a phase change for the molecular orbital, then the MO is said to have ungerade (u) symmetry, from the German word for odd.
For a bonding MO with σ-symmetry, the orbital is σ g (s' + s'' is symmetric), while an antibonding MO with σ-symmetry the orbital is σ u , because inversion of s' – s'' is antisymmetric.
For a bonding MO with π-symmetry the orbital is π u because inversion through the center of symmetry for would produce a sign change (the two p atomic orbitals are in phase with each other but the two lobes have opposite signs), while an antibonding MO with π-symmetry is π g because inversion through the center of symmetry for would not produce a sign change (the two p orbitals are antisymmetric by phase). [ 14 ]
The qualitative approach of MO analysis uses a molecular orbital diagram to visualize bonding interactions in a molecule. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity (only 2 electrons, having opposite spins, per orbital; place as many unpaired electrons on one energy level as possible before starting to pair them). For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding (although is still necessary for a quantitative approach).
Some properties:
The general procedure for constructing a molecular orbital diagram for a reasonably simple molecule can be summarized as follows:
1. Assign a point group to the molecule.
2. Look up the shapes of the SALCs.
3. Arrange the SALCs of each molecular fragment in order of energy, noting first whether they stem from s , p , or d orbitals
(and put them in the order s < p < d ), and then their number of internuclear nodes.
4. Combine SALCs of the same symmetry type from the two fragments, and from N SALCs form N molecular orbitals.
5. Estimate the relative energies of the molecular orbitals from considerations of overlap and relative energies of the parent orbitals, and draw the levels on a molecular orbital energy level diagram (showing the origin of the orbitals).
6. Confirm, correct, and revise this qualitative order by carrying out a molecular orbital calculation by using commercial software. [ 18 ]
Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p x and the p y atomic orbitals result in two degenerate bonding orbitals (of low energy) and two degenerate antibonding orbitals (of high energy). [ 13 ]
In an ionic bond, oppositely charged ions are bonded by electrostatic attraction . [ 19 ] It is possible to describe ionic bonds with molecular orbital theory by treating them as extremely polar bonds . Their bonding orbitals are very close in energy to the atomic orbitals of the anion . They are also very similar in character to the anion's atomic orbitals, which means the electrons are completely shifted to the anion. In computer diagrams, the orbitals are centered on the anion's core. [ 20 ]
The bond order, or number of bonds, of a molecule can be determined by combining the number of electrons in bonding and antibonding molecular orbitals. A pair of electrons in a bonding orbital creates a bond, whereas a pair of electrons in an antibonding orbital negates a bond. For example, N 2 , with eight electrons in bonding orbitals and two electrons in antibonding orbitals, has a bond order of three, which constitutes a triple bond.
Bond strength is proportional to bond order—a greater amount of bonding produces a more stable bond—and bond length is inversely proportional to it—a stronger bond is shorter.
There are rare exceptions to the requirement of molecule having a positive bond order. Although Be 2 has a bond order of 0 according to MO analysis, there is experimental evidence of a highly unstable Be 2 molecule having a bond length of 245 pm and bond energy of 10 kJ/mol. [ 14 ] [ 21 ]
The highest occupied molecular orbital and lowest unoccupied molecular orbital are often referred to as the HOMO and LUMO, respectively. The difference of the energies of the HOMO and LUMO is called the HOMO-LUMO gap. This notion is often the matter of confusion in literature and should be considered with caution. Its value is usually located between the fundamental gap (difference between ionization potential and electron affinity) and the optical gap. In addition, HOMO-LUMO gap can be related to a bulk material band gap or transport gap, which is usually much smaller than fundamental gap. [ citation needed ]
Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H 2 , He 2 , and Li 2 , all of which containing symmetric orbitals. [ 14 ]
As a simple MO example, consider the electrons in a hydrogen molecule, H 2 (see molecular orbital diagram ), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:
The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H 2 molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (hence more stable) than two free hydrogen atoms. This is called a covalent bond . The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms. [ citation needed ]
On the other hand, consider the hypothetical molecule of He 2 with the atoms labeled He' and He". As with H 2 , the lowest energy atomic orbitals are the 1s' and 1s", and do not transform according to the symmetries of the molecule, while the symmetry adapted atomic orbitals do. The symmetric combination—the bonding orbital—is lower in energy than the basis orbitals, and the antisymmetric combination—the antibonding orbital—is higher. Unlike H 2 , with two valence electrons, He 2 has four in its neutral ground state. Two electrons fill the lower-energy bonding orbital, σ g (1s), while the remaining two fill the higher-energy antibonding orbital, σ u *(1s). Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms; without a stable bond holding the atoms together, the molecule would not be expected to exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists (the molecule has one bound state supported by the Van der Waals potential). [ citation needed ]
Dilithium Li 2 is formed from the overlap of the 1s and 2s atomic orbitals (the basis set) of two Li atoms. Each Li atom contributes three electrons for bonding interactions, and the six electrons fill the three MOs of lowest energy, σ g (1s), σ u *(1s), and σ g (2s). Using the equation for bond order, it is found that dilithium has a bond order of one, a single bond. [ 22 ]
Considering a hypothetical molecule of He 2 , since the basis set of atomic orbitals is the same as in the case of H 2 , we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H 2 + 2 He, so the molecule is very unstable and exists only briefly before decomposing into hydrogen and helium. In general, we find that atoms such as He that have full energy shells rarely bond with other atoms. Except for short-lived Van der Waals complexes , there are very few noble gas compounds known. [ citation needed ]
While MOs for homonuclear diatomic molecules contain equal contributions from each interacting atomic orbital, MOs for heteronuclear diatomics contain different atomic orbital contributions. Orbital interactions to produce bonding or antibonding orbitals in heteronuclear diatomics occur if there is sufficient overlap between atomic orbitals as determined by their symmetries and similarity in orbital energies. [ citation needed ]
In hydrogen fluoride HF overlap between the H 1s and F 2s orbitals is allowed by symmetry but the difference in energy between the two atomic orbitals prevents them from interacting to create a molecular orbital. Overlap between the H 1s and F 2p z orbitals is also symmetry allowed, and these two atomic orbitals have a small energy separation. Thus, they interact, leading to creation of σ and σ* MOs and a molecule with a bond order of 1. Since HF is a non-centrosymmetric molecule, the symmetry labels g and u do not apply to its molecular orbitals. [ 23 ]
To obtain quantitative values for the molecular energy levels , one needs to have molecular orbitals that are such that the configuration interaction (CI) expansion converges fast towards the full CI limit. The most common method to obtain such functions is the Hartree–Fock method , which expresses the molecular orbitals as eigenfunctions of the Fock operator . One usually solves this problem by expanding the molecular orbitals as linear combinations of Gaussian functions centered on the atomic nuclei (see linear combination of atomic orbitals and basis set (chemistry) ). The equation for the coefficients of these linear combinations is a generalized eigenvalue equation known as the Roothaan equations , which are in fact a particular representation of the Hartree–Fock equation. There are a number of programs in which quantum chemical calculations of MOs can be performed, including Spartan . [ citation needed ]
Simple accounts often suggest that experimental molecular orbital energies can be obtained by the methods of ultra-violet photoelectron spectroscopy for valence orbitals and X-ray photoelectron spectroscopy for core orbitals. This, however, is incorrect as these experiments measure the ionization energy, the difference in energy between the molecule and one of the ions resulting from the removal of one electron. Ionization energies are linked approximately to orbital energies by Koopmans' theorem . While the agreement between these two values can be close for some molecules, it can be very poor in other cases. [ citation needed ] | https://en.wikipedia.org/wiki/Molecular_orbital |
A molecular orbital diagram , or MO diagram , is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. [ 1 ] [ 2 ] [ 3 ] A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals , although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen , dioxygen , and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane . MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.
Qualitative MO theory was introduced in 1928 by Robert S. Mulliken [ 4 ] [ 5 ] and Friedrich Hund . [ 6 ] A mathematical description was provided by contributions from Douglas Hartree in 1928 [ 7 ] and Vladimir Fock in 1930. [ 8 ]
Molecular orbital diagrams are diagrams of molecular orbital (MO) energy levels , shown as short horizontal lines in the center, flanked by constituent atomic orbital (AO) energy levels for comparison, with the energy levels increasing from the bottom to the top. Lines, often dashed diagonal lines, connect MO levels with their constituent AO levels. Degenerate energy levels are commonly shown side by side. Appropriate AO and MO levels are filled with electrons by the Pauli Exclusion Principle, symbolized by small vertical arrows whose directions indicate the electron spins . The AO or MO shapes themselves are often not shown on these diagrams. For a diatomic molecule , an MO diagram effectively shows the energetics of the bond between the two atoms, whose AO unbonded energies are shown on the sides. For simple polyatomic molecules with a "central atom" such as methane ( CH 4 ) or carbon dioxide ( CO 2 ), a MO diagram may show one of the identical bonds to the central atom. For other polyatomic molecules, an MO diagram may show one or more bonds of interest in the molecules, leaving others out for simplicity. Often even for simple molecules, AO and MO levels of inner orbitals and their electrons may be omitted from a diagram for simplicity.
In MO theory molecular orbitals form by the overlap of atomic orbitals . Because σ bonds feature greater overlap than π bonds , σ bonding and σ* antibonding orbitals feature greater energy splitting (separation) than π and π* orbitals. The atomic orbital energy correlates with electronegativity as more electronegative atoms hold their electrons more tightly, lowering their energies. Sharing of molecular orbitals between atoms is more important when the atomic orbitals have comparable energy; when the energies differ greatly the orbitals tend to be localized on one atom and the mode of bonding becomes ionic . A second condition for overlapping atomic orbitals is that they have the same symmetry.
Two atomic orbitals can overlap in two ways depending on their phase relationship (or relative signs for real orbitals ). The phase (or sign) of an orbital is a direct consequence of the wave-like properties of electrons. In graphical representations of orbitals, orbital phase is depicted either by a plus or minus sign (which has no relationship to electric charge ) or by shading one lobe. The sign of the phase itself does not have physical meaning except when mixing orbitals to form molecular orbitals.
Two same-sign orbitals have a constructive overlap forming a molecular orbital with the bulk of the electron density located between the two nuclei. This MO is called the bonding orbital and its energy is lower than that of the original atomic orbitals. A bond involving molecular orbitals which are symmetric with respect to any rotation around the bond axis is called a sigma bond ( σ -bond). If the phase cycles once while rotating round the axis, the bond is a pi bond ( π -bond). Symmetry labels are further defined by whether the orbital maintains its original character after an inversion about its center; if it does, it is defined gerade , g . If the orbital does not maintain its original character, it is ungerade , u .
Atomic orbitals can also interact with each other out-of-phase which leads to destructive cancellation and no electron density between the two nuclei at the so-called nodal plane depicted as a perpendicular dashed line. In this anti-bonding MO with energy much higher than the original AO's, any electrons present are located in lobes pointing away from the central internuclear axis. For a corresponding σ -bonding orbital, such an orbital would be symmetrical but differentiated from it by an asterisk as in σ* . For a π -bond, corresponding bonding and antibonding orbitals would not have such symmetry around the bond axis and be designated π and π* , respectively.
The next step in constructing an MO diagram is filling the newly formed molecular orbitals with electrons. Three general rules apply:
The filled MO highest in energy is called the highest occupied molecular orbital (HOMO) and the empty MO just above it is then the lowest unoccupied molecular orbital (LUMO). The electrons in the bonding MO's are called bonding electrons and any electrons in the antibonding orbital would be called antibonding electrons . The reduction in energy of these electrons is the driving force for chemical bond formation. Whenever mixing for an atomic orbital is not possible for reasons of symmetry or energy, a non-bonding MO is created, which is often quite similar to and has energy level equal or close to its constituent AO, thus not contributing to bonding energetics. The resulting electron configuration can be described in terms of bond type, parity and occupancy for example dihydrogen 1σ g 2 . Alternatively it can be written as a molecular term symbol e.g. 1 Σ g + for dihydrogen. Sometimes, the letter n is used to designate a non-bonding orbital.
For a stable bond, the bond order defined as
bond order = ( number of electrons in bonding MOs ) − ( number of electrons in antibonding MOs ) 2 {\displaystyle \ {\mbox{bond order}}={\frac {({\mbox{number of electrons in bonding MOs}})-({\mbox{number of electrons in antibonding MOs}})}{2}}}
must be positive.
The relative order in MO energies and occupancy corresponds with electronic transitions found in photoelectron spectroscopy (PES). In this way it is possible to experimentally verify MO theory. In general, sharp PES transitions indicate nonbonding electrons and broad bands are indicative of bonding and antibonding delocalized electrons. Bands can resolve into fine structure with spacings corresponding to vibrational modes of the molecular cation (see Franck–Condon principle ). PES energies are different from ionisation energies which relates to the energy required to strip off the n th electron after the first n − 1 electrons have been removed. MO diagrams with energy values can be obtained mathematically using the Hartree–Fock method . The starting point for any MO diagram is a predefined molecular geometry for the molecule in question. An exact relationship between geometry and orbital energies is given in Walsh diagrams .
The phenomenon of s-p mixing occurs when molecular orbitals of the same symmetry formed from the combination of 2s and 2p atomic orbitals are close enough in energy to further interact, which can lead to a change in the expected order of orbital energies. [ 9 ] When molecular orbitals are formed, they are mathematically obtained from linear combinations of the starting atomic orbitals. Generally, in order to predict their relative energies, it is sufficient to consider only one atomic orbital from each atom to form a pair of molecular orbitals, as the contributions from the others are negligible. For instance, in dioxygen the 3σ g MO can be roughly considered to be formed from interaction of oxygen 2p z AOs only. It is found to be lower in energy than the 1π u MO, both experimentally and from more sophisticated computational models, so that the expected order of filling is the 3σ g before the 1π u . [ 10 ] Hence the approximation to ignore the effects of further interactions is valid.
However, experimental and computational results for homonuclear diatomics from Li 2 to N 2 and certain heteronuclear combinations such as CO and NO show that the 3σ g MO is higher in energy than (and therefore filled after) the 1π u MO. [ 11 ] This can be rationalised as the first-approximation 3σ g has a suitable symmetry to interact with the 2σ g bonding MO formed from the 2s AOs. As a result, the 2σ g is lowered in energy, whilst the 3σ g is raised. For the aforementioned molecules this results in the 3σ g being higher in energy than the 1π u MO, which is where s-p mixing is most evident. Likewise, interaction between the 2σ u * and 3σ u * MOs leads to a lowering in energy of the former and a raising in energy of the latter. [ 9 ] However this is of less significance than the interaction of the bonding MOs.
A diatomic molecular orbital diagram is used to understand the bonding of a diatomic molecule . MO diagrams can be used to deduce magnetic properties of a molecule and how they change with ionization . They also give insight to the bond order of the molecule, how many bonds are shared between the two atoms. [ 12 ]
The energies of the electrons are further understood by applying the Schrödinger equation to a molecule. Quantum Mechanics is able to describe the energies exactly for single electron systems but can be approximated precisely for multiple electron systems using the Born-Oppenheimer Approximation , such that the nuclei are assumed stationary. The LCAO-MO method is used in conjunction to further describe the state of the molecule. [ 13 ]
Diatomic molecules consist of a bond between only two atoms . They can be broken into two categories: homonuclear and heteronuclear. A homonuclear diatomic molecule is one composed of two atoms of the same element . Examples are H 2 , O 2 , and N 2 . A heteronuclear diatomic molecule is composed of two atoms of two different elements. Examples include CO , HCl , and NO .
The smallest molecule, hydrogen gas exists as dihydrogen (H-H) with a single covalent bond between two hydrogen atoms. As each hydrogen atom has a single 1s atomic orbital for its electron , the bond forms by overlap of these two atomic orbitals. In the figure the two atomic orbitals are depicted on the left and on the right. The vertical axis always represents the orbital energies . Each atomic orbital is singly occupied with an up or down arrow representing an electron.
Application of MO theory for dihydrogen results in having both electrons in the bonding MO with electron configuration 1σ g 2 . The bond order for dihydrogen is (2-0)/2 = 1. The photoelectron spectrum of dihydrogen shows a single set of multiplets between 16 and 18 eV (electron volts). [ 14 ]
The dihydrogen MO diagram helps explain how a bond breaks. When applying energy to dihydrogen, a molecular electronic transition takes place when one electron in the bonding MO is promoted to the antibonding MO. The result is that there is no longer a net gain in energy.
The superposition of the two 1s atomic orbitals leads to the formation of the σ and σ* molecular orbitals. Two atomic orbitals in phase create a larger electron density, which leads to the σ orbital. If the two 1s orbitals are not in phase, a node between them causes a jump in energy, the σ* orbital. From the diagram you can deduce the bond order , how many bonds are formed between the two atoms. For this molecule it is equal to one. Bond order can also give insight to how close or stretched a bond has become if a molecule is ionized. [ 12 ]
Dihelium (He-He) is a hypothetical molecule and MO theory helps to explain why dihelium does not exist in nature. The MO diagram for dihelium looks very similar to that of dihydrogen, but each helium has two electrons in its 1s atomic orbital rather than one for hydrogen, so there are now four electrons to place in the newly formed molecular orbitals.
The only way to accomplish this is by occupying both the bonding and antibonding orbitals with two electrons, which reduces the bond order ((2−2)/2) to zero and cancels the net energy stabilization. However, by removing one electron from dihelium, the stable gas-phase species He + 2 ion is formed with bond order 1/2.
Another molecule that is precluded based on this principle is diberyllium . Beryllium has an electron configuration 1s 2 2s 2 , so there are again two electrons in the valence level. However, the 2s can mix with the 2p orbitals in diberyllium, whereas there are no p orbitals in the valence level of hydrogen or helium. This mixing makes the antibonding 1σ u orbital slightly less antibonding than the bonding 1σ g orbital is bonding, with a net effect that the whole configuration has a slight bonding nature. This explains the fact that the diberyllium molecule exists and has been observed in the gas phase. [ 15 ] [ 16 ] The slight bonding nature explains the low dissociation energy of only 59 kJ·mol −1 . [ 15 ]
MO theory correctly predicts that dilithium is a stable [ clarification needed ] molecule with bond order 1 (configuration 1σ g 2 1σ u 2 2σ g 2 ). The 1s MOs are completely filled and do not participate in bonding.
Dilithium is a gas-phase molecule with a much lower bond strength than dihydrogen because the 2s electrons are further removed from the nucleus. In a more detailed analysis [ 17 ] which considers the environment of each orbital due to all other electrons, both the 1σ orbitals have higher energies than the 1s AO and the occupied 2σ is also higher in energy than the 2s AO (see table 1).
The MO diagram for diboron (B-B, electron configuration 1σ g 2 1σ u 2 2σ g 2 2σ u 2 1π u 2 ) requires the introduction of an atomic orbital overlap model for p orbitals . The three dumbbell -shaped p-orbitals have equal energy and are oriented mutually perpendicularly (or orthogonally ). The p-orbitals oriented in the z-direction (p z ) can overlap end-on forming a bonding (symmetrical) σ orbital and an antibonding σ* molecular orbital. In contrast to the sigma 1s MO's, the σ 2p has some non-bonding electron density at either side of the nuclei and the σ* 2p has some electron density between the nuclei.
The other two p-orbitals, p y and p x , can overlap side-on. The resulting bonding orbital has its electron density in the shape of two lobes above and below the plane of the molecule. The orbital is not symmetric around the molecular axis and is therefore a pi orbital . The antibonding pi orbital (also asymmetrical) has four lobes pointing away from the nuclei. Both p y and p x orbitals form a pair of pi orbitals equal in energy ( degenerate ) and can have higher or lower energies than that of the sigma orbital.
In diboron the 1s and 2s electrons do not participate in bonding but the single electrons in the 2p orbitals occupy the 2πp y and the 2πp x MO's resulting in bond order 1. Because the electrons have equal energy (they are degenerate) diboron is a diradical and since the spins are parallel the molecule is paramagnetic .
In certain diborynes the boron atoms are excited and the bond order is 3.
Like diboron, dicarbon (C-C electron configuration :1σ g 2 1σ u 2 2σ g 2 2σ u 2 1π u 4 ) is a reactive gas-phase molecule. The molecule can be described as having two pi bonds but without a sigma bond. [ 18 ]
With nitrogen, we see the two molecular orbitals mixing and the energy repulsion. This is the reasoning for the rearrangement from a more familiar diagram. The σ from the 2p is more non-bonding due to mixing, and same with the 2s σ. This also causes a large jump in energy in the 2p σ* orbital.
The bond order of diatomic nitrogen is three, and it is a diamagnetic molecule. [ 12 ]
The bond order for dinitrogen (1σ g 2 1σ u 2 2σ g 2 2σ u 2 1π u 4 3σ g 2 ) is three because two electrons are now also added in the 3σ MO. The MO diagram correlates with the experimental photoelectron spectrum for nitrogen. [ 19 ] The 1σ electrons can be matched to a peak at 410 eV (broad), the 2σ g electrons at 37 eV (broad), the 2σ u electrons at 19 eV (doublet), the 1π u 4 electrons at 17 eV (multiplets), and finally the 3σ g 2 at 15.5 eV (sharp).
Oxygen has a similar setup to H 2 , but now we consider 2s and 2p orbitals. When creating the molecular orbitals from the p orbitals, the three atomic orbitals split into three molecular orbitals, a singly degenerate σ and a doubly degenerate π orbital. Another property we can observe by examining molecular orbital diagrams is the magnetic property of diamagnetic or paramagnetic . If all the electrons are paired, there is a slight repulsion and it is classified as diamagnetic. If unpaired electrons are present, it is attracted to a magnetic field, and therefore paramagnetic. Oxygen is an example of a paramagnetic diatomic. The bond order of diatomic oxygen is two. [ 12 ]
MO treatment of dioxygen is different from that of the previous diatomic molecules because the pσ MO is now lower in energy than the 2π orbitals. This is attributed to interaction between the 2s MO and the 2p z MO. [ 20 ] Distributing 8 electrons over 6 molecular orbitals leaves the final two electrons as a degenerate pair in the 2pπ* antibonding orbitals resulting in a bond order of 2. As in diboron, these two unpaired electrons have the same spin in the ground state, which is a paramagnetic diradical triplet oxygen . The first excited state has both HOMO electrons paired in one orbital with opposite spins, and is known as singlet oxygen .
The bond order decreases and the bond length increases in the order O + 2 (112.2 pm), O 2 (121 pm), O − 2 (128 pm) and O 2− 2 (149 pm). [ 20 ]
In difluorine two additional electrons occupy the 2pπ* with a bond order of 1. In dineon Ne 2 (as with dihelium) the number of bonding electrons equals the number of antibonding electrons and this molecule does not exist.
Dimolybdenum ( Mo 2 ) is notable for having a sextuple bond . This involves two sigma bonds (4d z 2 and 5s), two pi bonds (using 4d xz and 4d yz ), and two delta bonds (4d x 2 − y 2 and 4d xy ). Ditungsten ( W 2 ) has a similar structure. [ 21 ] [ 22 ]
Table 1 gives an overview of MO energies for first row diatomic molecules calculated by the Hartree-Fock-Roothaan method , together with atomic orbital energies.
In heteronuclear diatomic molecules, mixing of atomic orbitals only occurs when the electronegativity values are similar. In carbon monoxide (CO, isoelectronic with dinitrogen) the oxygen 2s orbital is much lower in energy than the carbon 2s orbital and therefore the degree of mixing is low. The electron configuration 1σ 2 1σ* 2 2σ 2 2σ* 2 1π 4 3σ 2 is identical to that of nitrogen. The g and u subscripts no longer apply because the molecule lacks a center of symmetry.
In hydrogen fluoride (HF), the hydrogen 1s orbital can mix with fluorine 2p z orbital to form a sigma bond because experimentally the energy of 1s of hydrogen is comparable with 2p of fluorine. The HF electron configuration 1σ 2 2σ 2 3σ 2 1π 4 reflects that the other electrons remain in three lone pairs and that the bond order is 1.
The more electronegative atom is the more energetically excited because it more similar in energy to its atomic orbital. This also accounts for the majority of the electron negativity residing around the more electronegative molecule. Applying the LCAO-MO method allows us to move away from a more static Lewis structure type approach and actually account for periodic trends that influence electron movement. Non-bonding orbitals refer to lone pairs seen on certain atoms in a molecule. A further understanding for the energy level refinement can be acquired by delving into quantum chemistry; the Schrödinger equation can be applied to predict movement and describe the state of the electrons in a molecule. [ 13 ] [ 23 ]
Nitric oxide is a heteronuclear molecule that exhibits mixing. The construction of its MO diagram is the same as for the homonuclear molecules. It has a bond order of 2.5 and is a paramagnetic molecule. The energy differences of the 2s orbitals are different enough that each produces its own non-bonding σ orbitals. Notice this is a good example of making the ionized NO + stabilize the bond and generate a triple bond, also changing the magnetic property to diamagnetic. [ 12 ]
Hydrogen fluoride is another example of a heteronuclear molecule. It is slightly different in that the π orbital is non-bonding, as well as the 2s σ. From the hydrogen, its valence 1s electron interacts with the 2p electrons of fluorine. This molecule is diamagnetic and has a bond order of one.
Carbon dioxide , CO 2 , is a linear molecule with a total of sixteen bonding electrons in its valence shell . Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.
For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the Schrödinger equation . [ 24 ] In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different. [ 25 ]
Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p x , p y , and p z . With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, pi bond ( π ) [ 26 ] or generates no phase change, known as a sigma bond ( σ ). [ 27 ] Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade , g , or if the atomic orbital does not maintain its original character, ungerade , u . The final symmetry-labeled atomic orbital is now known as an irreducible representation.
Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur. [ 28 ] Strong mixing of the oxygen 2s atomic orbital is not to be expected and are non-bonding degenerate molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the nonbonding (no change), bonding (lower than either parent orbital energy) and antibonding (higher energy than either parent atomic orbital energy) molecular orbitals.
For nonlinear molecules, the orbital symmetries are not σ or π but depend on the symmetry of each molecule. Water ( H 2 O ) is a bent molecule (105°) with C 2v molecular symmetry . The possible orbital symmetries are listed in the table below. For example, an orbital of B 1 symmetry (called a b 1 orbital with a small b since it is a one-electron function) is multiplied by -1 under the symmetry operations C 2 (rotation about the 2-fold rotation axis) and σ v '(yz) (reflection in the molecular plane). It is multiplied by +1(unchanged) by the identity operation E and by σ v (xz) (reflection in the plane bisecting the H-O-H angle).
The oxygen atomic orbitals are labeled according to their symmetry as a 1 for the 2s orbital and b 1 (2p x ), b 2 (2p y ) and a 1 (2p z ) for the three 2p orbitals. The two hydrogen 1s orbitals are premixed to form a 1 (σ) and b 2 (σ*) MO.
Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water:
In agreement with this description the photoelectron spectrum for water shows a sharp peak for the nonbonding 1b 1 MO (12.6 eV) and three broad peaks for the 3a 1 MO (14.7 eV), 1b 2 MO (18.5 eV) and the 2a 1 MO (32.2 eV). [ 29 ] The 1b 1 MO is a lone pair, while the 3a 1 , 1b 2 and 2a 1 MO's can be localized to give two O−H bonds and an in-plane lone pair. [ 30 ] This MO treatment of water does not have two equivalent rabbit ear lone pairs. [ 31 ]
Hydrogen sulfide (H 2 S) too has a C 2v symmetry with 8 valence electrons but the bending angle is only 92°. As reflected in its photoelectron spectrum as compared to water the 5a 1 MO (corresponding to the 3a 1 MO in water) is stabilised (improved overlap) and the 2b 2 MO (corresponding to the 1b 2 MO in water) is destabilized (poorer overlap). | https://en.wikipedia.org/wiki/Molecular_orbital_diagram |
In chemistry , molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics . It was proposed early in the 20th century. The MOT explains the paramagnetic nature of O 2 , which valence bond theory cannot explain.
In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms , but are treated as moving under the influence of the atomic nuclei in the whole molecule. [ 1 ] Quantum mechanics describes the spatial and energetic properties of electrons as molecular orbitals that surround two or more atoms in a molecule and contain valence electrons between atoms.
Molecular orbital theory revolutionized the study of chemical bonding by approximating the states of bonded electrons – the molecular orbitals – as linear combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation .
Molecular orbital theory and valence bond theory are the foundational theories of quantum chemistry .
In the LCAO method, each molecule has a set of molecular orbitals . It is assumed that the molecular orbital wave function ψ j can be written as a simple weighted sum of the n constituent atomic orbitals χ i , according to the following equation: [ 2 ]
ψ j = ∑ i = 1 n c i j χ i . {\displaystyle \psi _{j}=\sum _{i=1}^{n}c_{ij}\chi _{i}.}
One may determine c ij coefficients numerically by substituting this equation into the Schrödinger equation and applying the variational principle . The variational principle is a mathematical technique used in quantum mechanics to build up the coefficients of each atomic orbital basis. A larger coefficient means that the orbital basis is composed more of that particular contributing atomic orbital – hence, the molecular orbital is best characterized by that type. This method of quantifying orbital contribution as a linear combination of atomic orbitals is used in computational chemistry . An additional unitary transformation can be applied on the system to accelerate the convergence in some computational schemes. Molecular orbital theory was seen as a competitor to valence bond theory in the 1930s, before it was realized that the two methods are closely related and that when extended they become equivalent.
Molecular orbital theory is used to interpret ultraviolet–visible spectroscopy (UV–VIS). Changes to the electronic structure of molecules can be seen by the absorbance of light at specific wavelengths. Assignments can be made to these signals indicated by the transition of electrons moving from one orbital at a lower energy to a higher energy orbital. The molecular orbital diagram for the final state describes the electronic nature of the molecule in an excited state.
There are three main requirements for atomic orbital combinations to be suitable as approximate molecular orbitals.
Molecular orbital theory was developed in the years after valence bond theory had been established (1927), primarily through the efforts of Friedrich Hund , Robert Mulliken , John C. Slater , and John Lennard-Jones . [ 4 ] MO theory was originally called the Hund-Mulliken theory. [ 5 ] According to physicist and physical chemist Erich Hückel , the first quantitative use of molecular orbital theory was the 1929 paper of Lennard-Jones . [ 6 ] [ 7 ] This paper predicted a triplet ground state for the dioxygen molecule which explained its paramagnetism [ 8 ] (see Molecular orbital diagram § Dioxygen ) before valence bond theory, which came up with its own explanation in 1931. [ 9 ] The word orbital was introduced by Mulliken in 1932. [ 5 ] By 1933, the molecular orbital theory had been accepted as a valid and useful theory. [ 10 ]
Erich Hückel applied molecular orbital theory to unsaturated hydrocarbon molecules starting in 1931 with his Hückel molecular orbital (HMO) method for the determination of MO energies for pi electrons , which he applied to conjugated and aromatic hydrocarbons. [ 11 ] [ 12 ] This method provided an explanation of the stability of molecules with six pi-electrons such as benzene .
The first accurate calculation of a molecular orbital wavefunction was that made by Charles Coulson in 1938 on the hydrogen molecule. [ 13 ] By 1950, molecular orbitals were completely defined as eigenfunctions (wave functions) of the self-consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent. [ 14 ] This rigorous approach is known as the Hartree–Fock method for molecules although it had its origins in calculations on atoms. In calculations on molecules, the molecular orbitals are expanded in terms of an atomic orbital basis set , leading to the Roothaan equations . [ 15 ] This led to the development of many ab initio quantum chemistry methods . In parallel, molecular orbital theory was applied in a more approximate manner using some empirically derived parameters in methods now known as semi-empirical quantum chemistry methods . [ 15 ]
The success of Molecular Orbital Theory also spawned ligand field theory , which was developed during the 1930s and 1940s as an alternative to crystal field theory .
Molecular orbital (MO) theory uses a linear combination of atomic orbitals (LCAO) to represent molecular orbitals resulting from bonds between atoms. These are often divided into three types, bonding , antibonding , and non-bonding . A bonding orbital concentrates electron density in the region between a given pair of atoms, so that its electron density will tend to attract each of the two nuclei toward the other and hold the two atoms together. [ 16 ] An anti-bonding orbital concentrates electron density "behind" each nucleus (i.e. on the side of each atom which is farthest from the other atom), and so tends to pull each of the two nuclei away from the other and actually weaken the bond between the two nuclei. Electrons in non-bonding orbitals tend to be associated with atomic orbitals that do not interact positively or negatively with one another, and electrons in these orbitals neither contribute to nor detract from bond strength. [ 16 ]
Molecular orbitals are further divided according to the types of atomic orbitals they are formed from. Chemical substances will form bonding interactions if their orbitals become lower in energy when they interact with each other. Different bonding orbitals are distinguished that differ by electron configuration (electron cloud shape) and by energy levels .
The molecular orbitals of a molecule can be illustrated in molecular orbital diagrams .
Common bonding orbitals are sigma (σ) orbitals which are symmetric about the bond axis and pi (π) orbitals with a nodal plane along the bond axis. Less common are delta (δ) orbitals and phi (φ) orbitals with two and three nodal planes respectively along the bond axis. Antibonding orbitals are signified by the addition of an asterisk. For example, an antibonding pi orbital may be shown as π*.
Bond order is the number of chemical bonds between a pair of atoms. The bond order of a molecule can be calculated by subtracting the number of electrons in anti-bonding orbitals from the number of bonding orbitals, and the resulting number is then divided by two. A molecule is expected to be stable if it has bond order larger than zero. It is adequate to consider the valence electron to determine the bond order. Because (for principal quantum number n > 1) when MOs are derived from 1s AOs, the difference in number of electrons in bonding and anti-bonding molecular orbital is zero. So, there is no net effect on bond order if the electron is not the valence one.
Bond order = 1 2 ( Number of electrons in bonding MO − Number of electrons in anti-bonding MO ) {\displaystyle {\text{Bond order}}={\frac {1}{2}}({\text{Number of electrons in bonding MO}}-{\text{Number of electrons in anti-bonding MO}})}
From bond order, one can predict whether a bond between two atoms will form or not. For example, the existence of He 2 molecule. From the molecular orbital diagram, the bond order is 1 2 ( 2 − 2 ) = 0 {\textstyle {\frac {1}{2}}(2-2)=0} . That means, no bond formation will occur between two He atoms which is seen experimentally. It can be detected under very low temperature and pressure molecular beam and has binding energy of approximately 0.001 J/mol. [ 17 ] (The helium dimer is a van der Waals molecule .)
Besides, the strength of a bond can also be realized from bond order (BO). For example:
For H 2 : Bond order is 1 2 ( 2 − 0 ) = 1 {\textstyle {\frac {1}{2}}(2-0)=1} ; bond energy is 436 kJ/mol.
For H 2 + : Bond order is 1 2 ( 1 − 0 ) = 1 2 {\textstyle {\frac {1}{2}}(1-0)={\frac {1}{2}}} ; bond energy is 171 kJ/mol.
As the bond order of H 2 + is smaller than H 2 , it should be less stable which is observed experimentally and can be seen from the bond energy.
For almost every covalent molecule that exists, we can now draw the Lewis structure, predict the electron-pair geometry, predict the molecular geometry, and come close to predicting bond angles. However, one of the most important molecules we know, the oxygen molecule O 2 , presents a problem with respect to its Lewis structure.
The electronic structure of O 2 adheres to all the rules governing Lewis theory. There is an O=O double bond, and each oxygen atom has eight electrons around it. However, this picture is at odds with the magnetic behavior of oxygen. By itself, O 2 is not magnetic, but it is attracted to magnetic fields. Thus, when we pour liquid oxygen past a strong magnet, it collects between the poles of the magnet and defies gravity. Such attraction to a magnetic field is called paramagnetism , and it arises in molecules that have unpaired electrons. And yet, the Lewis structure of O 2 indicates that all electrons are paired. How do we account for this discrepancy?
Molecular orbital diagram of oxygen molecule:
Atomic number of oxygen – 8
Electronic configuration – 1s²2s²2p 4
Electronic configuration of oxygen molecule;
ó1s² < *ó1s² < ó2s² < *ó2s² , [ π2px² = π2py²] < ó 2pz² < [*π2px¹ =*π2py¹] < *ó2pz
Bond order of O 2 = (Bonding electrons − Anti bonding electrons) / 2
= (10 − 6) / 2 = 2
O 2 has unpaired electrons, hence it is paramagnetic. [ 18 ]
Magnetic susceptibility measures the force experienced by a substance in a magnetic field. When we compare the weight of a sample to the weight measured in a magnetic field, paramagnetic samples that are attracted to the magnet will appear heavier because of the force exerted by the magnetic field. We can calculate the number of unpaired electrons based on the increase in weight.
Experiments show that each O 2 molecule has two unpaired electrons. The Lewis-structure model does not predict the presence of these two unpaired electrons. Unlike oxygen, the apparent weight of most molecules decreases slightly in the presence of an inhomogeneous magnetic field. Materials in which all of the electrons are paired are diamagnetic and weakly repel a magnetic field. Paramagnetic and diamagnetic materials do not act as permanent magnets. Only in the presence of an applied magnetic field do they demonstrate attraction or repulsion.
Water, like most molecules, contains all paired electrons. Living things contain a large percentage of water, so they demonstrate diamagnetic behavior. If you place a frog near a sufficiently large magnet, it will levitate.
Molecular orbital theory (MO theory) provides an explanation of chemical bonding that accounts for the paramagnetism of the oxygen molecule. It also explains the bonding in a number of other molecules, such as violations of the octet rule and more molecules with more complicated bonding (beyond the scope of this text) that are difficult to describe with Lewis structures. Additionally, it provides a model for describing the energies of electrons in a molecule and the probable location of these electrons. Unlike valence bond theory, which uses hybrid orbitals that are assigned to one specific atom, MO theory uses the combination of atomic orbitals to yield molecular orbitals that are delocalized over the entire molecule rather than being localized on its constituent atoms. MO theory also helps us understand why some substances are electrical conductors, others are semiconductors, and still others are insulators.
Molecular orbital theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the behavior of an electron in a molecule is still described by a wave function, Ψ , analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital ( Ψ 2 ) . Like an atomic orbital, a molecular orbital is full when it contains two electrons with opposite spin. [ 19 ]
MOT provides a global, delocalized perspective on chemical bonding . In MO theory, any electron in a molecule may be found anywhere in the molecule, since quantum conditions allow electrons to travel under the influence of an arbitrarily large number of nuclei, as long as they are in eigenstates permitted by certain quantum rules. Thus, when excited with the requisite amount of energy through high-frequency light or other means, electrons can transition to higher-energy molecular orbitals. For instance, in the simple case of a hydrogen diatomic molecule, promotion of a single electron from a bonding orbital to an antibonding orbital can occur under UV radiation. This promotion weakens the bond between the two hydrogen atoms and can lead to photodissociation, the breaking of a chemical bond due to the absorption of light.
Molecular orbital theory is used to interpret ultraviolet–visible spectroscopy (UV–VIS). Changes to the electronic structure of molecules can be seen by the absorbance of light at specific wavelengths. Assignments can be made to these signals indicated by the transition of electrons moving from one orbital at a lower energy to a higher energy orbital. The molecular orbital diagram for the final state describes the electronic nature of the molecule in an excited state.
Although in MO theory some molecular orbitals may hold electrons that are more localized between specific pairs of molecular atoms, other orbitals may hold electrons that are spread more uniformly over the molecule. Thus, overall, bonding is far more delocalized in MO theory, which makes it more applicable to resonant molecules that have equivalent non-integer bond orders than valence bond theory . This makes MO theory more useful for the description of extended systems.
Robert S. Mulliken , who actively participated in the advent of molecular orbital theory, considers each molecule to be a self-sufficient unit. He asserts in his article:
...Attempts to regard a molecule as consisting of specific atomic or ionic units held together by discrete numbers of bonding electrons or electron-pairs are considered as more or less meaningless, except as an approximation in special cases, or as a method of calculation […]. A molecule is here regarded as a set of nuclei, around each of which is grouped an electron configuration closely similar to that of a free atom in an external field, except that the outer parts of the electron configurations surrounding each nucleus usually belong, in part, jointly to two or more nuclei.... [ 20 ]
An example is the MO description of benzene , C 6 H 6 , which is an aromatic hexagonal ring of six carbon atoms and three double bonds. In this molecule, 24 of the 30 total valence bonding electrons – 24 coming from carbon atoms and 6 coming from hydrogen atoms – are located in 12 σ (sigma) bonding orbitals, which are located mostly between pairs of atoms (C–C or C–H), similarly to the electrons in the valence bond description. However, in benzene the remaining six bonding electrons are located in three π (pi) molecular bonding orbitals that are delocalized around the ring. Two of these electrons are in an MO that has equal orbital contributions from all six atoms. The other four electrons are in orbitals with vertical nodes at right angles to each other. As in the VB theory, all of these six delocalized π electrons reside in a larger space that exists above and below the ring plane. All carbon–carbon bonds in benzene are chemically equivalent. In MO theory this is a direct consequence of the fact that the three molecular π orbitals combine and evenly spread the extra six electrons over six carbon atoms.
In molecules such as methane , CH 4 , the eight valence electrons are found in four MOs that are spread out over all five atoms. It is possible to transform the MOs into four localized sp 3 orbitals. Linus Pauling, in 1931, hybridized the carbon 2s and 2p orbitals so that they pointed directly at the hydrogen 1s basis functions and featured maximal overlap. However, the delocalized MO description is more appropriate for predicting ionization energies and the positions of spectral absorption bands . When methane is ionized, a single electron is taken from the valence MOs, which can come from the s bonding or the triply degenerate p bonding levels, yielding two ionization energies. In comparison, the explanation in valence bond theory is more complicated. When one electron is removed from an sp 3 orbital, resonance is invoked between four valence bond structures, each of which has a single one-electron bond and three two-electron bonds. Triply degenerate T 2 and A 1 ionized states (CH 4 + ) are produced from different linear combinations of these four structures. The difference in energy between the ionized and ground state gives the two ionization energies.
As in benzene, in substances such as beta carotene , chlorophyll , or heme , some electrons in the π orbitals are spread out in molecular orbitals over long distances in a molecule, resulting in light absorption in lower energies (the visible spectrum ), which accounts for the characteristic colours of these substances. [ 21 ] This and other spectroscopic data for molecules are well explained in MO theory, with an emphasis on electronic states associated with multicenter orbitals, including mixing of orbitals premised on principles of orbital symmetry matching. [ 16 ] The same MO principles also naturally explain some electrical phenomena, such as high electrical conductivity in the planar direction of the hexagonal atomic sheets that exist in graphite . This results from continuous band overlap of half-filled p orbitals and explains electrical conduction. MO theory recognizes that some electrons in the graphite atomic sheets are completely delocalized over arbitrary distances, and reside in very large molecular orbitals that cover an entire graphite sheet, and some electrons are thus as free to move and therefore conduct electricity in the sheet plane, as if they resided in a metal. | https://en.wikipedia.org/wiki/Molecular_orbital_theory |
Molecular paleontology refers to the recovery and analysis of DNA , proteins , carbohydrates , or lipids , and their diagenetic products from ancient human, animal, and plant remains. [ 1 ] [ 2 ] The field of molecular paleontology has yielded important insights into evolutionary events, species' diasporas , the discovery and characterization of extinct species .
In shallow time , advancements in the field of molecular paleontology have allowed scientists to pursue evolutionary questions on a genetic level rather than relying on phenotypic variation alone. By applying molecular analytical techniques to DNA in recent animal remains, one can quantify the level of relatedness between any two organisms for which DNA has been recovered. [ 3 ] Using various biotechnological techniques such as DNA isolation , amplification , and sequencing [ 4 ] scientists have been able to acquire and expand insights into the divergence and evolutionary history of countless recently extinct organisms. In February 2021, scientists reported, for the first time, the sequencing of DNA from animal remains , a mammoth in this instance, over a million years old, the oldest DNA sequenced to date. [ 5 ] [ 6 ]
In deep time , compositional heterogeneities in carbonaceous remains of a diversity of animals , ranging in age from the Neoproterozoic to the Recent , have been linked to biological signatures encoded in modern biomolecules via a cascade of oxidative fossilization reactions. [ 7 ] [ 8 ] [ 9 ] [ 10 ] The macromolecular composition of carbonaceous fossils, some Tonian in age, [ 11 ] preserve biological signatures reflecting original biomineralization , tissue types, metabolism , and relationship affinities ( phylogeny ). [ 9 ]
The study of molecular paleontology is said to have begun with the discovery by Abelson of 360 million year old amino acids preserved in fossil shells. [ 12 ] However, Svante Pääbo is often the one considered to be the founder of the field of molecular paleontology. [ 13 ]
The field of molecular paleontology has had several major advances since the 1950s and is a continuously growing field. Below is a timeline showing notable contributions that have been made.
mid-1950s: Abelson found preserved amino acids in fossil shells that were about 360 million years old. Produced idea of comparing fossil amino acid sequences with existing organism so that molecular evolution could be studied. [ 12 ]
1970s: Fossil peptides are studied by amino acid analysis . [ 14 ] Start to use whole peptides and immunological methods . [ 15 ]
Late 1970s: Palaeobotanists (can also be spelled as Paleobotanists) studied molecules from well-preserved fossil plants. [ 16 ]
1984: The first successful DNA sequencing of an extinct species, the quagga , a zebra-like species. [ 1 ]
1991: Published article on the successful extraction of proteins from the fossil bone of a dinosaur, specifically the Seismosaurus . [ 17 ]
2005: Scientists resurrect extinct 1918 influenza virus . [ 18 ]
2006: Neanderthals nuclear DNA sequence segments begin to be analyzed and published. [ 23 ]
2007: Scientists synthesize entire extinct human endogenous retrovirus (HERV-K) from scratch. [ 19 ]
2010: A new species of early hominid, the Denisovans , discovered from mitochondrial and nuclear genomes recovered from bone found in a cave in Siberia. Analysis showed that the Denisovan specimen lived approximately 41,000 years ago, and shared a common ancestor with both modern humans and Neanderthals approximately 1 million years ago in Africa. [ 20 ]
2013: The first entire Neanderthal genome is successfully sequenced. More information can be found at the Neanderthal genome project . [ 21 ]
2013: A 400,000-year-old specimen with remnant mitochondrial DNA sequenced and is found to be a common ancestor to Neanderthals and Denisovans, Homo heidelbergensis . [ 22 ]
2013: Mary Schweitzer and colleagues propose the first chemical mechanism explaining the potential preservation of vertebrate cells and soft tissues into the fossil record. The mechanism proposes that free oxygen radicals, potentially produced by redox-active iron, induce biomolecule crosslinking. This crosslinking mechanism is somewhat analogous to the crosslinking that occurs during histological tissue fixation, such as with formaldehyde. The authors also suggest the source of iron to be the hemoglobin from the deceased organism. [ 24 ]
2015: A 110,000-year-old fossil tooth containing DNA from Denisovans was reported. [ 25 ] [ 26 ]
2018: Molecular paleobiologists link polymers of N-, O-, S-heterocycle composition (AGEs/ALEs, as referred to in the cited publication, Wiemann et al. 2018) in carbonaceous fossil remains mechanistically to structural biomolecules in original tissues. Through oxidative crosslinking, a process similar to the Maillard reaction , nucleophilic amino acid residues condense with Reactive Carbonyl Species derived from lipids and sugars . [ 8 ] The processes of biomolecule fossilization, identified via Raman spectroscopy of modern and fossil tissues, experimental modelling, and statistical data evaluation, include Advanced Glycosylation and Advanced Lipoxidation . [ 8 ]
2019: An independent laboratory of Molecular Paleontologists confirms the transformation of biomolecules through Advanced Glycosylation and Lipoxidation during fossilization. [ 10 ] The authors use Synchrotron Fourier-Transform Infrared spectroscopy .
2020: Wiemann and colleagues identify biological signatures reflecting original biomineralization , tissue types, metabolism , and relationship affinity ( phylogeny ) in preserved compositional heterogeneities of a diversity of carbonaceous animal fossils. [ 9 ] This is the first large-scale analysis of fossils ranging in age from the Neoproterozoic to the Recent , and the first published record of biological signals found in complex organic matter. [ 9 ] The authors rely on statistical analyses of a uniquely large Raman spectroscopy data set.
2021: Geochemists find tissue type signals in the composition of carbonaceous fossils dating back to the Tonian , [ 11 ] and apply these signals to identify epibionts . The authors use Raman spectroscopy .
2022: Raman spectroscopy data revealing patterns in the fossilization of structural biomolecules have been replicated with Fourier-Transform Infrared spectroscopy and a diversity of different Raman instruments, filters, and excitation sources. [ 27 ]
2023: The first in-depth chemical description of how original, biological cells and tissues fossilize is published. Importantly, the study shows that the free oxygen radical hypothesis (proposed by Mary Schweitzer and colleagues in 2013) is in many cases identical to the AGE/ALE formation hypothesis (proposed by Jasmina Wiemann and colleagues in 2018). The combined hypotheses, along with thermal maturation and carbonization , form a loose framework for biological cell and tissue fossilization. [ 7 ]
The first successful DNA sequencing of an extinct species was in 1984, from a 150-year-old museum specimen of the quagga, a zebra-like species. [ 1 ] Mitochondrial DNA (also known as mtDNA) was sequenced from desiccated muscle of the quagga, and was found to differ by 12 base substitutions from the mitochondrial DNA of a mountain zebra. It was concluded that these two species had a common ancestor 3-4 million years ago, which is consistent with known fossil evidence of the species. [ 28 ]
The Denisovans of Eurasia , a hominid species related to Neanderthals and humans, was discovered as a direct result of DNA sequencing of a 41,000-year-old specimen recovered in 2008. Analysis of the mitochondrial DNA from a retrieved finger bone showed the specimen to be genetically distinct from both humans and Neanderthals. Two teeth and a toe bone were later found to belong to different individuals with the same population. Analysis suggests that both the Neanderthals and Denisovans were already present throughout Eurasia when modern humans arrived. [ 21 ] In November 2015, scientists reported finding a fossil tooth containing DNA from Denisovans, and estimated its age at 110,000-years-old. [ 25 ] [ 26 ]
The mtDNA from the Denisovan finger bone differs from that of modern humans by 385 bases ( nucleotides ) in the mtDNA strand out of approximately 16,500, whereas the difference between modern humans and Neanderthals is around 202 bases. In contrast, the difference between chimpanzees and modern humans is approximately 1,462 mtDNA base pairs. [ 20 ] This suggested a divergence time around one million years ago. The mtDNA from a tooth bore a high similarity to that of the finger bone, indicating they belonged to the same population. [ 29 ] From a second tooth, an mtDNA sequence was recovered that showed an unexpectedly large number of genetic differences compared to that found in the other tooth and the finger, suggesting a high degree of mtDNA diversity. These two individuals from the same cave showed more diversity than seen among sampled Neanderthals from all of Eurasia, and were as different as modern-day humans from different continents. [ 30 ]
Isolation and sequencing of nuclear DNA has also been accomplished from the Denisova finger bone. This specimen showed an unusual degree of DNA preservation and low level of contamination. They were able to achieve near-complete genomic sequencing, allowing a detailed comparison with Neanderthal and modern humans. From this analysis, they concluded, in spite of the apparent divergence of their mitochondrial sequence, the Denisova population along with Neanderthal shared a common branch from the lineage leading to modern African humans. The estimated average time of divergence between Denisovan and Neanderthal sequences is 640,000 years ago, and the time between both of these and the sequences of modern Africans is 804,000 years ago. They suggest the divergence of the Denisova mtDNA results either from the persistence of a lineage purged from the other branches of humanity through genetic drift or else an introgression from an older hominin lineage. [ 29 ]
Homo heidelbergensis was first discovered in 1907 near Heidelberg, Germany and later also found elsewhere in Europe, Africa, and Asia. [ 31 ] [ 32 ] However it was not until 2013 that a specimen with retrievable DNA was found, in a ~400,000 year old femur found in the Sima de los Huesos Cave in Spain. The femur was found to contain both mtDNA and nuclear DNA. Improvements in DNA extraction and library preparation techniques allowed for mtDNA to be successfully isolated and sequenced, however the nuclear DNA was found to be too degraded in the observed specimen, and was also contaminated with DNA from an ancient cave bear ( Ursus deningeri ) present in the cave. [ 33 ] The mtDNA analysis found a surprising link between the specimen and the Denisovans, and this finding raised many questions. Several scenarios were proposed in a January 2014 paper titled "A mitochondrial genome sequence of a hominin from Sima de los Huesos", elucidating the lack of convergence in the scientific community on how Homo heidelbergensis is related to other known hominin groups. One plausible scenario that the authors proposed was that the H. heidelbergensis was an ancestor to both Denisovans and Neanderthals. [ 33 ] Completely sequenced nuclear genomes from both Denisovans and Neanderthals suggest a common ancestor approximately 700,000 years ago, and one leading researcher in the field, Svante Paabo, suggests that perhaps this new hominin group is that early ancestor. [ 22 ]
Molecular paleontology techniques applied to fossils have contributed to the discovery and characterization of several new species, including the Denisovans and Homo heidelbergensis . We have been able to better understand the path that humans took as they populated the earth, and what species were present during this diaspora .
It is now possible to revive extinct species using molecular paleontology techniques. This was first accomplished via cloning in 2003 with the Pyrenean ibex , a type of wild goat that became extinct in 2000. Nuclei from the Pyrenean ibex's cells were injected into goat eggs emptied of their own DNA, and implanted into surrogate goat mothers. [ 34 ] The offspring lived only seven minutes after birth, due to defects in its lungs. Other cloned animals have been observed to have similar lung defects. [ 35 ]
There are many species that have gone extinct as a direct result of human activity. Some examples include the dodo , the great auk , the Tasmanian tiger , the Chinese river dolphin , and the passenger pigeon . An extinct species can be revived by using allelic replacement [ 36 ] of a closely related species that is still living. By only having to replace a few genes within an organism, instead of having to build the extinct species' genome from scratch, it could be possible to bring back several species in this way, even Neanderthals. [ citation needed ]
The ethics surrounding the re-introduction of extinct species are very controversial. Critics of bringing extinct species back to life contend that it would divert limited money and resources from protecting the world's current biodiversity problems. [ 37 ] With current extinction rates approximated to be 100 to 1,000 times the background extinction rate, [ 38 ] it is feared that a de-extinction program might lessen public concerns over the current mass extinction crisis, if it is believed that these species can simply be brought back to life. As the editors of a Scientific American article on de-extinction pose: Should we bring back the woolly mammoth only to let elephants become extinct in the meantime? [ 37 ] The main driving factor for the extinction of most species in this era (post 10,000 BC) is the loss of habitat, and temporarily bringing back an extinct species will not recreate the environment they once inhabited. [ 39 ]
Proponents of de-extinction, such as George Church , speak of many potential benefits. Reintroducing an extinct keystone species, such as the woolly mammoth , could help re-balance the ecosystems that once depended on them. Some extinct species could create broad benefits for the environments they once inhabited, if returned. For example, woolly mammoths may be able to slow the melting of the Russian and Arctic tundra in several ways such as eating dead grass so that new grass can grow and take root, and periodically breaking up the snow, subjecting the ground below to the arctic air. These techniques could also be used to reintroduce genetic diversity in a threatened species, or even introduce new genes and traits to allow the animals to compete better in a changing environment. [ 40 ]
When a new potential specimen is found, scientists normally first analyze for cell and tissue preservation using histological techniques , and test the conditions for the survivability of DNA. They will then attempt to isolate a DNA sample using the technique described below, and conduct a PCR amplification of the DNA to increase the amount of DNA available for testing. This amplified DNA is then sequenced. Care is taken to verify that the sequence matches the phylogenetic traits of the organism. [ 1 ] When an organism dies, a technique called amino acid dating can be used to age the organism. It inspects the degree of racemization of aspartic acid , leucine , and alanine within the tissue. As time passes, the D/L ratio (where "D" and "L" are mirror images of each other) increase from 0 to 1. [ 41 ] In samples where the D/L ratio of aspartic acid is greater than 0.08, ancient DNA sequences can not be retrieved (as of 1996). [ 42 ]
Mitochondrial DNA (mtDNA) is separate from one's nuclear DNA. It is present in organelles called mitochondria in each cell . Unlike nuclear DNA , which is inherited from both parents and rearranged every generation, an exact copy of mitochondrial DNA gets passed down from mother to her sons and daughters. The benefits of performing DNA analysis with Mitochondrial DNA is that it has a far smaller mutation rate than nuclear DNA, making tracking lineages on the scale of tens of thousands of years much easier. Knowing the base mutation rate for mtDNA, [ 43 ] (in humans this rate is also known as the Human mitochondrial molecular clock ) one can determine the amount of time any two lineages have been separated. Another advantage of mtDNA is that thousands of copies of it exist in every cell, whereas only two copies of nuclear DNA exist in each cell. [ 44 ] All eukaryotes , a group which includes all plants, animals, and fungi, have mtDNA. [ 45 ] A disadvantage of mtDNA is that only the maternal line is represented. For example, a child will inherit 1/8 of its DNA from each of its eight great-grandparents, however it will inherit an exact clone of its maternal great-grandmother's mtDNA. This is analogous to a child inheriting only his paternal great-grandfather's last name, and not a mix of all of the eight surnames.
There are many things to consider when isolating a substance. First, depending upon what it is and where it is located, there are protocols that must be carried out in order to avoid contamination and further degradation of the sample. [ 4 ] Then, handling of the materials is usually done in a physically isolated work area and under specific conditions (i.e. specific Temperature, moisture, etc...) also to avoid contamination and further loss of sample. [ 4 ]
Once the material has been obtained, depending on what it is, there are different ways to isolate and purify it. DNA extraction from fossils is one of the more popular practices and there are different steps that can be taken to get the desired sample. [ 4 ] DNA extracted from amber-entombed fossils can be taken from small samples and mixed with different substances, centrifuged , incubated, and centrifuged again. [ 46 ] On the other hand, DNA extraction from insects can be done by grinding the sample, mixing it with buffer, and undergoing purification through glass fiber columns. [ 47 ] In the end, regardless of how the sample was isolated for these fossils, the DNA isolated must be able to undergo amplification . [ 4 ] [ 46 ] [ 47 ]
The field of molecular paleontology benefited greatly from the invention of the polymerase chain reaction(PCR) , which allows one to make billions of copies of a DNA fragment from just a single preserved copy of the DNA. One of the biggest challenges up until this point was the extreme scarcity of recovered DNA because of degradation of the DNA over time. [ 1 ]
DNA sequencing is done to determine the order of nucleotides and genes. [ 48 ] There are many different materials from which DNA can be extracted. In animals, the mitochondrial chromosome can be used for molecular study. Chloroplasts can be studied in plants as a primary source of sequence data. [ 48 ]
In the end, the sequences generated are used to build evolutionary trees . [ 48 ] Methods to match data sets include: maximum probability , minimum evolution (also known as neighbor-joining ) which searches for the tree with shortest overall length, and the maximum parsimony method which finds the tree requiring the fewest character-state changes. [ 48 ] The groups of species defined within a tree can also be later evaluated by statistical tests, such as the bootstrap method , to see if they are indeed significant. [ 48 ]
Ideal environmental conditions for preserving DNA where the organism was desiccated and uncovered are difficult to come by, as well as maintaining their condition until analysis. Nuclear DNA normally degrades rapidly after death by endogenous hydrolytic processes , [ 42 ] by UV radiation, [ 1 ] and other environmental stressors.
Also, interactions with the organic breakdown products of surrounding soil have been found to help preserve biomolecular materials. [ 49 ] However, they have also created the additional challenge of being able to separate the various components in order to be able to conduct the proper analysis on them. [ 50 ] Some of these breakdowns have also been found to interfere with the action of some of the enzymes used during PCR. [ 49 ]
Finally, one of the largest challenge in extracting ancient DNA, particularly in ancient human DNA, is in contamination during PCR. Small amounts of human DNA can contaminate the reagents used for extraction and PCR of ancient DNA. These problems can be overcome by rigorous care in the handling of all solutions as well as the glassware and other tools used in the process. It can also help if only one person performs the extractions, to minimize different types of DNA present. [ 42 ] | https://en.wikipedia.org/wiki/Molecular_paleontology |
Molecular pathological epidemiology ( MPE , also molecular pathologic epidemiology ) is a discipline combining epidemiology and pathology . It is defined as "epidemiology of molecular pathology and heterogeneity of disease". [ 1 ] Pathology and epidemiology share the same goal of elucidating etiology of disease, and MPE aims to achieve this goal at molecular, individual and population levels. Typically, MPE utilizes tissue pathology resources and data within existing epidemiology studies. Molecular epidemiology broadly encompasses MPE and conventional-type molecular epidemiology with the use of traditional disease designation systems.
Data from The Cancer Genome Atlas projects indicate that disease evolution is an inherently heterogeneous process. [ 2 ] [ 3 ] Each patient has a unique disease process (“the unique disease principle”), considering the uniqueness of the exposome and its unique influence on molecular pathologic process. [ 2 ] This concept has been adopted in clinical medicine along with precision medicine and personalized medicine . [ citation needed ]
In MPE, investigators dissect interrelationships between exposures (e.g., environmental, dietary, lifestyle and genetic factors); alterations in cellular or extracellular molecules (disease molecular signatures); and disease evolution and progression. [ 2 ] Investigators can analyze genome , methylome , epigenome , metabolome , transcriptome , proteome , microbiome , immunity and interactome . A putative risk factor can be linked to specific molecular signatures. [ citation needed ]
MPE research enables identification of a new biomarker for potential clinical utility, using large-scale population-based data (e.g., PIK3CA mutation in colorectal cancer to select patients for aspirin therapy). [ 1 ] The MPE approach can be used following a genome-wide association study (GWAS), termed "GWAS-MPE approach". [ 4 ] Detailed disease endpoint phenotyping can be conducted by means of molecular pathology or surrogate histopathology or immunohistochemistry analysis of diseased tissues and cells within GWAS. [ 5 ] [ 6 ]
As an alternative approach, potential risk variants identified by GWAS can be examined in combination with molecular pathology analysis on diseased tissues. [ 7 ] [ 8 ] [ 9 ] [ 10 ] This GWAS-MPE approach can give not only more precise effect estimates, even larger effects, for specific molecular subtypes of the disease, but also insights into pathogenesis by linking genetic variants to molecular pathologic signatures of disease. [ 4 ] Since molecular diagnostics is becoming routine clinical practice, molecular pathology data can aid epidemiologic research. [ citation needed ]
MPE began as analysis of risk factors (e.g., smoking) and molecular pathological findings (e.g., KRAS G12C oncogene mutations in lung carcinoma). [ citation needed ]
Studies to examine the relationship between an exposure and molecular pathological signatures of disease (particularly, cancer) became increasingly common throughout the 1990s and early 2000s. [ 11 ]
The use of molecular pathology in epidemiology lacked standardized methodologies and guidelines as well as interdisciplinary experts and training programs. [ 12 ] MPE research required a new conceptual framework and methodologies ( epidemiological method ) because MPE examines heterogeneity in an outcome variable. [ 13 ]
The term "molecular pathological epidemiology" was used by Shuji Ogino and Meir Stampfer in 2010. [ 14 ] Specific principles of MPE developed following 2010. The MPE paradigm is in widespread use globally, [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ excessive citations ] and has been a subject of international conferences. [ 26 ] [ 27 ] [ 28 ] The International Molecular Pathological Epidemiology (MPE) Meeting Series, which was established in 2013, has been open to the research community around the world, and five meetings were held through 2021. [ 29 ] [ 30 ] [ 31 ] [ 32 ] | https://en.wikipedia.org/wiki/Molecular_pathological_epidemiology |
Molecular phenotyping describes the technique of quantifying pathway reporter genes, i.e. pre-selected genes that are modulated specifically by metabolic and signaling pathways , in order to infer activity of these pathways. [ 1 ] [ 2 ]
In most cases, molecular phenotyping quantifies changes of pathway reporter gene expression to characterize modulation of pathway activities induced by perturbations such as therapeutic agents or stress in a cellular system in vitro . In such contexts, measurements at early time points are often more informative than later observations because they capture the primary response to the perturbation by the cellular system. [ 3 ] Integrated with quantified changes of phenotype induced by the perturbation, molecular phenotyping can identify pathways that contribute to the phenotypic changes.
Currently molecular phenotyping uses RNA sequencing and mRNA expression to infer pathway activities. Other technologies and readouts such as mass spectrometry and protein abundance or phosphorylation levels can be potentially used as well. [ 4 ]
Current data suggest that by quantifying pathway reporter gene expression , molecular phenotyping is able to cluster compounds based on pathway profiles and dissect associations between pathway activities and disease phenotypes simultaneously. [ 5 ] Furthermore, molecular phenotyping can be applicable to compounds with a range of binding specificities and is able to triage false positives derived from high-content screening assays. Furthermore, molecular phenotyping allows integration of data derived from in vitro and in vivo models as well as patient data into the drug discovery process. [ citation needed ] | https://en.wikipedia.org/wiki/Molecular_phenotyping |
Molecular phylogenetics ( / m ə ˈ l ɛ k j ʊ l ər ˌ f aɪ l oʊ dʒ ə ˈ n ɛ t ɪ k s , m ɒ -, m oʊ -/ [ 1 ] [ 2 ] ) is the branch of phylogeny that analyzes genetic, hereditary molecular differences, predominantly in DNA sequences, to gain information on an organism's evolutionary relationships. From these analyses, it is possible to determine the processes by which diversity among species has been achieved. The result of a molecular phylogenetic analysis is expressed in a phylogenetic tree . Molecular phylogenetics is one aspect of molecular systematics , a broader term that also includes the use of molecular data in taxonomy and biogeography . [ 3 ] [ 4 ] [ 5 ]
Molecular phylogenetics and molecular evolution correlate. Molecular evolution is the process of selective changes (mutations) at a molecular level (genes, proteins, etc.) throughout various branches in the tree of life (evolution). Molecular phylogenetics makes inferences of the evolutionary relationships that arise due to molecular evolution and results in the construction of a phylogenetic tree. [ 6 ]
The theoretical frameworks for molecular systematics were laid in the 1960s in the works of Emile Zuckerkandl , Emanuel Margoliash , Linus Pauling , and Walter M. Fitch . [ 7 ] Applications of molecular systematics were pioneered by Charles G. Sibley ( birds ), Herbert C. Dessauer ( herpetology ), and Morris Goodman ( primates ), followed by Allan C. Wilson , Robert K. Selander , and John C. Avise (who studied various groups). Work with protein electrophoresis began around 1956. Although the results were not quantitative and did not initially improve on morphological classification, they provided tantalizing hints that long-held notions of the classifications of birds , for example, needed substantial revision. In the period of 1974–1986, DNA–DNA hybridization was the dominant technique used to measure genetic difference. [ 8 ]
Early attempts at molecular systematics were also termed chemotaxonomy and made use of proteins, enzymes , carbohydrates , and other molecules that were separated and characterized using techniques such as chromatography . These have been replaced in recent times largely by DNA sequencing , which produces the exact sequences of nucleotides or bases in either DNA or RNA segments extracted using different techniques. In general, these are considered superior for evolutionary studies, since the actions of evolution are ultimately reflected in the genetic sequences. At present, it is still a long and expensive process to sequence the entire DNA of an organism (its genome ). However, it is quite feasible to determine the sequence of a defined area of a particular chromosome . Typical molecular systematic analyses require the sequencing of around 1000 base pairs . At any location within such a sequence, the bases found in a given position may vary between organisms. The particular sequence found in a given organism is referred to as its haplotype . In principle, since there are four base types, with 1000 base pairs, we could have 4 1000 distinct haplotypes. However, for organisms within a particular species or in a group of related species, it has been found empirically that only a minority of sites show any variation at all, and most of the variations that are found are correlated, so that the number of distinct haplotypes that are found is relatively small. [ 9 ]
In a molecular systematic analysis, the haplotypes are determined for a defined area of genetic material ; a substantial sample of individuals of the target species or other taxon is used; however, many current studies are based on single individuals. Haplotypes of individuals of closely related, yet different, taxa are also determined. Finally, haplotypes from a smaller number of individuals from a definitely different taxon are determined: these are referred to as an outgroup . The base sequences for the haplotypes are then compared. In the simplest case, the difference between two haplotypes is assessed by counting the number of locations where they have different bases: this is referred to as the number of substitutions (other kinds of differences between haplotypes can also occur, for example, the insertion of a section of nucleic acid in one haplotype that is not present in another). The difference between organisms is usually re-expressed as a percentage divergence , by dividing the number of substitutions by the number of base pairs analysed: the hope is that this measure will be independent of the location and length of the section of DNA that is sequenced.
An older and superseded approach was to determine the divergences between the genotypes of individuals by DNA–DNA hybridization . The advantage claimed for using hybridization rather than gene sequencing was that it was based on the entire genotype, rather than on particular sections of DNA. Modern sequence comparison techniques overcome this objection by the use of multiple sequences.
Once the divergences between all pairs of samples have been determined, the resulting triangular matrix of differences is submitted to some form of statistical cluster analysis , and the resulting dendrogram is examined in order to see whether the samples cluster in the way that would be expected from current ideas about the taxonomy of the group. Any group of haplotypes that are all more similar to one another than any of them is to any other haplotype may be said to constitute a clade , which may be visually represented as the figure displayed on the right demonstrates. Statistical techniques such as bootstrapping and jackknifing help in providing reliability estimates for the positions of haplotypes within the evolutionary trees.
Every living organism contains deoxyribonucleic acid ( DNA ), ribonucleic acid ( RNA ), and proteins . In general, closely related organisms have a high degree of similarity in the molecular structure of these substances, while the molecules of organisms distantly related often show a pattern of dissimilarity. Conserved sequences, such as mitochondrial DNA, are expected to accumulate mutations over time, and assuming a constant rate of mutation, provide a molecular clock for dating divergence. Molecular phylogeny uses such data to build a "relationship tree" that shows the probable evolution of various organisms. With the invention of Sanger sequencing in 1977, it became possible to isolate and identify these molecular structures. [ 10 ] [ 11 ] High-throughput sequencing may also be used to obtain the transcriptome of an organism, allowing inference of phylogenetic relationships using transcriptomic data .
The most common approach is the comparison of homologous sequences for genes using sequence alignment techniques to identify similarity. Another application of molecular phylogeny is in DNA barcoding , wherein the species of an individual organism is identified using small sections of mitochondrial DNA or chloroplast DNA . Another application of the techniques that make this possible can be seen in the very limited field of human genetics, such as the ever-more-popular use of genetic testing to determine a child's paternity , as well as the emergence of a new branch of criminal forensics focused on evidence known as genetic fingerprinting .
There are several methods available for performing a molecular phylogenetic analysis. One method, including a comprehensive step-by-step protocol on constructing a phylogenetic tree, including DNA/Amino Acid contiguous sequence assembly, multiple sequence alignment , model-test (testing best-fitting substitution models), and phylogeny reconstruction using Maximum Likelihood and Bayesian Inference, is available at Nature Protocol. [ 12 ]
Another molecular phylogenetic analysis technique has been described by Pevsner and shall be summarized in the sentences to follow (Pevsner, 2015). A phylogenetic analysis typically consists of five major steps. The first stage comprises sequence acquisition. The following step consists of performing a multiple sequence alignment, which is the fundamental basis of constructing a phylogenetic tree. The third stage includes different models of DNA and amino acid substitution. Several models of substitution exist. A few examples include Hamming distance , the Jukes and Cantor one-parameter model, and the Kimura two-parameter model (see Models of DNA evolution ). The fourth stage consists of various methods of tree building, including distance-based and character-based methods. The normalized Hamming distance and the Jukes-Cantor correction formulas provide the degree of divergence and the probability that a nucleotide changes to another, respectively. Common tree-building methods include unweighted pair group method using arithmetic mean ( UPGMA ) and Neighbor joining , which are distance-based methods, Maximum parsimony , which is a character-based method, and Maximum likelihood estimation and Bayesian inference , which are character-based/model-based methods. UPGMA is a simple method; however, it is less accurate than the neighbor-joining approach. Finally, the last step comprises evaluating the trees. This assessment of accuracy is composed of consistency, efficiency, and robustness. [ 13 ]
MEGA (molecular evolutionary genetics analysis) is an analysis software that is user-friendly and free to download and use. This software is capable of analyzing both distance-based and character-based tree methodologies. MEGA also contains several options one may choose to utilize, such as heuristic approaches and bootstrapping. Bootstrapping is an approach that is commonly used to measure the robustness of topology in a phylogenetic tree, which demonstrates the percentage each clade is supported after numerous replicates. In general, a value greater than 70% is considered significant. The flow chart displayed on the right visually demonstrates the order of the five stages of Pevsner's molecular phylogenetic analysis technique that have been described. [ 13 ]
Molecular systematics is an essentially cladistic approach: it assumes that classification must correspond to phylogenetic descent, and that all valid taxa must be monophyletic . This is a limitation when attempting to determine the optimal tree(s), which often involves bisecting and reconnecting portions of the phylogenetic tree(s).
The recent discovery of extensive horizontal gene transfer among organisms provides a significant complication to molecular systematics, indicating that different genes within the same organism can have different phylogenies. HGTs can be detected and excluded using a number of phylogenetic methods (see Inferring horizontal gene transfer § Explicit phylogenetic methods ).
In addition, molecular phylogenies are sensitive to the assumptions and models that go into making them. Firstly, sequences must be aligned; then, issues such as long-branch attraction , saturation , and taxon sampling problems must be addressed. This means that strikingly different results can be obtained by applying different models to the same dataset. [ 14 ] [ 15 ] The tree-building method also brings with it specific assumptions about tree topology, evolution speeds, and sampling. The simplistic UPGMA assumes a rooted tree and a uniform molecular clock, both of which can be incorrect. [ 13 ] | https://en.wikipedia.org/wiki/Molecular_phylogenetics |
Molecular physics is the study of the physical properties of molecules and molecular dynamics . The field overlaps significantly with physical chemistry , chemical physics , and quantum chemistry . It is often considered as a sub-field of atomic, molecular, and optical physics . Research groups studying molecular physics are typically designated as one of these other fields. Molecular physics addresses phenomena due to both molecular structure and individual atomic processes within molecules. Like atomic physics , it relies on a combination of classical and quantum mechanics to describe interactions between electromagnetic radiation and matter. Experiments in the field often rely heavily on techniques borrowed from atomic physics , such as spectroscopy and scattering .
In a molecule, both the electrons and nuclei experience similar-scale forces from the Coulomb interaction . However, the nuclei remain at nearly fixed locations in the molecule while the electrons move significantly. This picture of a molecule is based on the idea that nucleons are much heavier than electrons, so will move much less in response to the same force. Neutron scattering experiments on molecules have been used to verify this description. [ 1 ]
When atoms join into molecules, their inner electrons remain bound to their original nucleus while the outer valence electrons are distributed around the molecule. The charge distribution of these valence electrons determines the electronic energy level of a molecule, and can be described by molecular orbital theory , which closely follows the atomic orbital theory used for single atoms. Assuming that the momenta of the electrons are on the order of ħ / a (where ħ is the reduced Planck constant and a is the average internuclear distance within a molecule, ~ 1 Å), the magnitude of the energy spacing for electronic states can be estimated at a few electron volts . This is the case for most low-lying molecular energy states, and corresponds to transitions in the visible and ultraviolet regions of the electromagnetic spectrum . [ 1 ] [ 2 ]
In addition to the electronic energy levels shared with atoms, molecules have additional quantized energy levels corresponding to vibrational and rotational states. Vibrational energy levels refer to motion of the nuclei about their equilibrium positions in the molecule. The approximate energy spacing of these levels can be estimated by treating each nucleus as a quantum harmonic oscillator in the potential produced by the molecule, and comparing its associated frequency to that of an electron experiencing the same potential. The result is an energy spacing about 100× smaller than that for electronic levels. In agreement with this estimate, vibrational spectra show transitions in the near infrared (about 1–5 μm ). [ 2 ] Finally, rotational energy states describe semi-rigid rotation of the entire molecule and produce transition wavelengths in the far infrared and microwave regions (about 100-10,000 μm in wavelength ). These are the smallest energy spacings, and their size can be understood by comparing the energy of a diatomic molecule with internuclear spacing ~ 1 Å to the energy of a valence electron (estimated above as ~ ħ / a ). [ 1 ]
Actual molecular spectra also show transitions which simultaneously couple electronic, vibrational, and rotational states. For example, transitions involving both rotational and vibrational states are often referred to as rotational-vibrational or rovibrational transitions. Vibronic transitions combine electronic and vibrational transitions, and rovibronic transitions combine electronic, rotational, and vibrational transitions. Due to the very different frequencies associated with each type of transition, the wavelengths associated with these mixed transitions vary across the electromagnetic spectrum. [ 2 ]
In general, the goals of molecular physics experiments are to characterize shape and size, electric and magnetic properties, internal energy levels, and ionization and dissociation energies for molecules. In terms of shape and size, rotational spectra and vibrational spectra allow for the determination of molecular moments of inertia , which allows for calculations of internuclear distances in molecules. X-ray diffraction allows determination of internuclear spacing directly, especially for molecules containing heavy elements. [ 2 ] All branches of spectroscopy contribute to determination of molecular energy levels due to the wide range of applicable energies (ultraviolet to microwave regimes).
Within atomic, molecular, and optical physics, there are numerous studies using molecules to verify fundamental constants and probe for physics beyond the Standard Model . Certain molecular structures are predicted to be sensitive to new physics phenomena, such as parity [ 3 ] and time-reversal [ 4 ] violation. Molecules are also considered a potential future platform for trapped ion quantum computing , as their more complex energy level structure could facilitate higher efficiency encoding of quantum information than individual atoms. [ 5 ] From a chemical physics perspective, intramolecular vibrational energy redistribution experiments use vibrational spectra to determine how energy is redistributed between different quantum states of a vibrationally excited molecule. [ 6 ] | https://en.wikipedia.org/wiki/Molecular_physics |
A molecular probe is a group of atoms or molecules used in molecular biology or chemistry to study the properties of other molecules or structures. If some measurable property of the molecular probe used changes when it interacts with the analyte (such as a change in absorbance ), the interactions between the probe and the analyte can be studied. This makes it possible to indirectly study the properties of compounds and structures which may be hard to study directly.
The choice of molecular probe will depend on which compound or structure is being studied as well as on what property is of interest. Radioactive DNA or RNA sequences are used in molecular genetics to detect the presence of a complementary sequence by molecular hybridization . [ 1 ]
There are two main classes of antibodies
Both classes of probes provide a secondary form of identification that indicate binding has successfully occurred, typically fluorescence. Molecular probes also often contain two components, a receptor that recognizes the target molecule, and a reporter/fluorophore that emits light upon excitation. [ 3 ]
The goal of covalently bound probes is to cause an irreversible covalent link to form between the probe and the target molecule, so that when the fluorophore is used to identify the molecule, it is physically attached to the target molecule. Proteins are a common target of molecular probes, and can either be targeted through specific amino acids, or through their active site.
For molecular probes that interact with the active site, what often occurs is the receptor portion of the probe is typically a ligand, with an electrophilic or nucleophilic functional group attached to the ligand that can then covalently bind to an amino acid in the active site, so that the fluorophore can be directly linked to the target protein. An example of this, Pablo Martin-Gago Et. Al designed a Woodward Reagent K probe, that reacts with a neighbouring glutamic acid in the active site of PDE6δ, after the ligand portion of the molecule bound to the Active site. [ 4 ] This allows for the fluorophore attached to the probe to be identified by researchers, after successfully binding to the protein.
Another application of this is with photo-reactive molecules that can bind after being excited by light, which has been worked on by Dr. Michael Taylor’s lab group at the University of Arizona. Pyridinium and Pyrimidinium salts are a pertinent example of this, as when they are activated by 427 nm light and 467 nm light respectively, they form a reactive fluorophore that then binds to the amino acid tryptophan. [ 5 ]
The goal of non-covalent is to design a receptor that maximizes the amount of intramolecular reactions.
A class of probes that achieve this are “Alexa” probes. This class of probes contains hundreds of different antibodies that are designed to bind tightly to the target molecule or protein, allowing for further reactions to be conducted, or for attached fluorophores to be recognized through fluorescence detection at their specified wavelength. [ 6 ]
The main purpose of these class of molecules is to perform secondary experiments after labeling in order to detect the levels of the targeted proteins, or to attach other functional groups to that molecule. This is used primarily in drug research, as if a given molecular probe allows for you to detect levels of a given protein, or to image the location of a protein, experiments can be conducted to determine how a certain drug affects levels of the target protein, such as analyzing levels of growth factors like HER2 and VEGF to determine the effectiveness of a cancer drug. This can also lessen the cost of drug research, as it can allow for previous testing to see if a lead molecule would even bind to a given protein without having to go past pre-clinical testing. [ 7 ] | https://en.wikipedia.org/wiki/Molecular_probe |
A molecular processor is a processor that is based on a molecular [ 1 ] [ 2 ] platform rather than on an inorganic semiconductor in integrated circuit format.
Molecular processors are currently in their infancy and currently only a few exist. At present a basic molecular processor is any biological or chemical system that uses a complementary DNA (cDNA) template to form a long chain amino acid molecule. A key factor that differentiates molecular processors is "the ability to control output" of protein or peptide concentration as a function of time. Simple formation of a molecule becomes the task of a chemical reaction, bioreactor or other polymerization technology. Current molecular processors take advantage of cellular processes to produce amino acid based proteins and peptides. The formation of a molecular processor currently involves integrating cDNA into the genome and should not replicate and re-insert, or be defined as a virus after insertion. Current molecular processors are replication incompetent, non-communicable and cannot be transmitted from cell to cell, animal to animal or human to human. All must have a method to terminate if implanted. The most effective methodology for insertion of cDNA (template with control mechanism) uses capsid technology to insert a payload into the genome. A viable molecular processor is one that dominates cellular function by re-task and or reassignment but does not terminate the cell. It will continuously produce protein or produce on demand and have method to regulate dosage if qualifying as a "drug delivery" molecular processor. Potential applications range from up-regulation of functional CFTR in cystic fibrosis and hemoglobin in sickle cell anemia to angiogenesis in cardiovascular stenosis to account for protein deficiency (used in gene therapy.)
A vector inserted to form a molecular processor is described in part. The objective was to promote angiogenesis, blood vessel formation and improve cardiovasculature. Vascular endothelial growth factor (VEGF) [ 3 ] and enhanced green fluorescent protein (EGFP) cDNA was ligated to either side of an internal ribosomal re-entry site (IRES) to produce inline production of both the VEGF and EGFP proteins. After in vitro insertion and quantification [ 4 ] of integrating units (IUs), engineered cells produce a bioluminescent marker and a chemotactic growth factor. In this instance, increased fluorescence of EGFP is used to show VEGF production in individual cells with active molecular processors. The production was exponential in nature and regulated through use of an integrating promoter, cell numbers, the number of integrated units (IUs) of molecular processors and or cell numbers. The measure the molecular processors efficacy was performed by FC/FACS to indirectly measure VEGF through fluorescence intensity. Proof of functional molecular processing was quantified by ELISA to show VEGF effect through chemotactic and angiogenesis models. The result involved directed assembly and coordination of endothelial cells for tubule formation [ 5 ] by engineered cells on endothelial cells. The research goes on to show implantation and VEGF with dosage capabilities to promote revascularization, validating mechanisms of molecular processor control. [ 6 ] | https://en.wikipedia.org/wiki/Molecular_processor |
Molecular promiscuity indicates the ability of a molecule to bind to interact with one or more other classes and subtypes of molecules, in synergistic or antagonistic ways. These interactions may involve multiple paracrine , endocrine and autocrine features. [ 1 ] [ 2 ] [ 3 ]
This chemical reaction article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_promiscuity |
A Molecular propeller is a molecule that can propel fluids when rotated, due to its special shape that is designed in analogy to macroscopic propellers : [ 1 ] [ 2 ] it has several molecular-scale blades attached at a certain pitch angle around the circumference of a shaft , aligned along the rotational axis.
The molecular propellers designed in the group of Prof. Petr Král from the University of Illinois at Chicago have their blades formed by planar aromatic molecules and the shaft is a carbon nanotube . [ 3 ] Molecular dynamics simulations show that these propellers can serve as efficient pumps in the bulk and at the surfaces of liquids. Their pumping efficiency depends on the chemistry of the interface between the blades and the liquid. For example, if the blades are hydrophobic , water molecules do not bind to them, and the propellers can pump them well. If the blades are hydrophilic , water molecules form hydrogen bonds with the atoms in the polar blades. This can largely block the flow of other water molecules around the blades and significantly slow down their pumping.
Molecular propellers can be rotated by molecular motors that can be driven by chemical, biological, optical and electrical means, [ 4 ] [ 5 ] [ 6 ] or various ratchet -like mechanisms. [ 7 ] Nature realizes most biological activities with a large number of highly sophisticated molecular motors, such as myosin , kinesin , and ATP synthase . [ 8 ] For example, rotary molecular motors attached to protein-based tails called flagella can propel bacteria.
In a similar way, the assembly of a molecular propeller and a molecular motor can form a nanoscale machine that can pump fluids or perform locomotion . [ 9 ] Future applications of these nanosystems range from novel analytical tools in physics and chemistry, drug delivery and gene therapy in biology and medicine, advanced nanofluidic lab-on-a-chip techniques, to tiny robots performing various activities at the nanoscale or microscale. | https://en.wikipedia.org/wiki/Molecular_propeller |
Molecular properties include the chemical properties , physical properties , and structural properties of molecules , including drugs . Molecular properties typically do not include pharmacological or biological properties of a chemical compound . [ 1 ] [ 2 ]
This chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_property |
Molecular risk assessment is a procedure in which biomarkers (for example, biological molecules or changes in tumor cell DNA ) are used to estimate a person's risk for developing cancer . Specific biomarkers may be linked to particular types of cancer.
This article incorporates public domain material from Dictionary of Cancer Terms . U.S. National Cancer Institute .
This oncology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_risk_assessment |
Molecular scale electronics , also called single-molecule electronics , is a branch of nanotechnology that uses single molecules, or nanoscale collections of single molecules, as electronic components . Because single molecules constitute the smallest stable structures imaginable [ citation needed ] , this miniaturization is the ultimate goal for shrinking electrical circuits .
The field is often termed simply as " molecular electronics ", but this term is also used to refer to the distantly related field of conductive polymers and organic electronics , which uses the properties of molecules to affect the bulk properties of a material. A nomenclature distinction has been suggested so that molecular materials for electronics refers to this latter field of bulk applications, while molecular scale electronics refers to the nanoscale single-molecule applications treated here. [ 1 ] [ 2 ]
Conventional electronics have traditionally been made from bulk materials. Ever since their invention in 1958, the performance and complexity of integrated circuits has undergone exponential growth , a trend named Moore’s law , as feature sizes of the embedded components have shrunk accordingly. As the structures shrink, the sensitivity to deviations increases. In a few technology generations, the composition of the devices must be controlled to a precision of a few atoms [ 3 ] for the devices to work. With bulk methods growing increasingly demanding and costly as they near inherent limits, the idea was born that the components could instead be built up atom by atom in a chemistry lab (bottom up) versus carving them out of bulk material ( top down ). This is the idea behind molecular electronics, with the ultimate miniaturization being components contained in single molecules.
In single-molecule electronics, the bulk material is replaced by single molecules. Instead of forming structures by removing or applying material after a pattern scaffold, the atoms are put together in a chemistry lab. In this way, billions of billions of copies are made simultaneously (typically more than 10 20 molecules are made at once) while the composition of molecules are controlled down to the last atom. The molecules used have properties that resemble traditional electronic components such as a wire , transistor or rectifier .
Single-molecule electronics is an emerging field, and entire electronic circuits consisting exclusively of molecular sized compounds are still very far from being realized. [ citation needed ] However, the unceasing demand for more computing power, along with the inherent limits of lithographic methods as of 2016 [update] , make the transition seem unavoidable. Currently, the focus is on discovering molecules with interesting properties and on finding ways to obtain reliable and reproducible contacts between the molecular components and the bulk material of the electrodes. [ citation needed ]
Molecular electronics operates at distances of less than 100 nanometers. The miniaturization down to single molecules brings the scale down to a regime where quantum mechanics effects are important. In conventional electronic components, electrons can be filled in or drawn out more or less like a continuous flow of electric charge . In contrast, in molecular electronics the transfer of one electron alters the system significantly. For example, when an electron has been transferred from a source electrode to a molecule, the molecule gets charged up, which makes it far harder for the next electron to transfer (see also Coulomb blockade ). The significant amount of energy due to charging must be accounted for when making calculations about the electronic properties of the setup, and is highly sensitive to distances to conducting surfaces nearby.
The theory of single-molecule devices is especially interesting since the system under consideration is an open quantum system in nonequilibrium (driven by voltage). In the low bias voltage regime, the nonequilibrium nature of the molecular junction can be ignored, and the current-voltage traits of the device can be calculated using the equilibrium electronic structure of the system. However, in stronger bias regimes a more sophisticated treatment is required, as there is no longer a variational principle . In the elastic tunneling case (where the passing electron does not exchange energy with the system), the formalism of Rolf Landauer can be used to calculate the transmission through the system as a function of bias voltage, and hence the current. In inelastic tunneling, an elegant formalism based on the non-equilibrium Green's functions of Leo Kadanoff and Gordon Baym , and independently by Leonid Keldysh was advanced by Ned Wingreen and Yigal Meir . This Meir-Wingreen formulation has been used to great success in the molecular electronics community to examine the more difficult and interesting cases where the transient electron exchanges energy with the molecular system (for example through electron-phonon coupling or electronic excitations).
Further, connecting single molecules reliably to a larger scale circuit has proven a great challenge, and constitutes a significant hindrance to commercialization.
Common for molecules used in molecular electronics is that the structures contain many alternating double and single bonds (see also Conjugated system ). This is done because such patterns delocalize the molecular orbitals, making it possible for electrons to move freely over the conjugated area.
The sole purpose of molecular wires is to electrically connect different parts of a molecular electrical circuit. As the assembly of these and their connection to a macroscopic circuit is still not mastered, the focus of research in single-molecule electronics is primarily on the functionalized molecules: molecular wires are characterized by containing no functional groups and are hence composed of plain repetitions of a conjugated building block. Among these are the carbon nanotubes that are quite large compared to the other suggestions but have shown very promising electrical properties.
The main problem with the molecular wires is to obtain good electrical contact with the electrodes so that electrons can move freely in and out of the wire.
Single-molecule transistors are fundamentally different from the ones known from bulk electronics. The gate in a conventional (field-effect) transistor determines the conductance between the source and drain electrode by controlling the density of charge carriers between them, whereas the gate in a single-molecule transistor controls the possibility of a single electron to jump on and off the molecule by modifying the energy of the molecular orbitals. One of the effects of this difference is that the single-molecule transistor is almost binary: it is either on or off . This opposes its bulk counterparts, which have quadratic responses to gate voltage.
It is the quantization of charge into electrons that is responsible for the markedly different behavior compared to bulk electronics. Because of the size of a single molecule, the charging due to a single electron is significant and provides means to turn a transistor on or off (see Coulomb blockade ). For this to work, the electronic orbitals on the transistor molecule cannot be too well integrated with the orbitals on the electrodes. If they are, an electron cannot be said to be located on the molecule or the electrodes and the molecule will function as a wire.
A popular group of molecules, that can work as the semiconducting channel material in a molecular transistor, is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb blockade mechanism when placed between the source and drain electrode in an appropriate way. [ 4 ] Fullerenes work by the same mechanism and have also been commonly used.
Semiconducting carbon nanotubes have also been demonstrated to work as channel material but although molecular, these molecules are sufficiently large to behave almost as bulk semiconductors .
The size of the molecules, and the low temperature of the measurements being conducted, makes the quantum mechanical states well defined. Thus, it is being researched if the quantum mechanical properties can be used for more advanced purposes than simple transistors (e.g. spintronics ).
Physicists at the University of Arizona , in collaboration with chemists from the University of Madrid , have designed a single-molecule transistor using a ring-shaped molecule similar to benzene . Physicists at Canada's National Institute for Nanotechnology have designed a single-molecule transistor using styrene. Both groups expect (the designs were experimentally unverified as of June 2005 [update] ) their respective devices to function at room temperature, and to be controlled by a single electron. [ 5 ]
Molecular rectifiers are mimics of their bulk counterparts and have an asymmetric construction so that the molecule can accept electrons in one end but not the other. The molecules have an electron donor (D) in one end and an electron acceptor (A) in the other. This way, the unstable state D + – A − will be more readily made than D − – A + . The result is that an electric current can be drawn through the molecule if the electrons are added through the acceptor end, but less easily if the reverse is attempted.
One of the biggest problems with measuring on single molecules is to establish reproducible electrical contact with only one molecule and doing so without shortcutting the electrodes. Because the current photolithographic technology is unable to produce electrode gaps small enough to contact both ends of the molecules tested (on the order of nanometers), alternative strategies are applied.
One way to produce electrodes with a molecular sized gap between them is break junctions, in which a thin electrode is stretched until it breaks. Another is electromigration . Here a current is led through a thin wire until it melts and the atoms migrate to produce the gap. Further, the reach of conventional photolithography can be enhanced by chemically etching or depositing metal on the electrodes.
Probably the easiest way to conduct measurements on several molecules is to use the tip of a scanning tunneling microscope (STM) to contact molecules adhered at the other end to a metal substrate. [ 7 ]
A popular way to anchor molecules to the electrodes is to make use of sulfur 's high chemical affinity to gold . In these setups, the molecules are synthesized so that sulfur atoms are placed strategically to function as crocodile clips connecting the molecules to the gold electrodes. Though useful, the anchoring is non-specific and thus anchors the molecules randomly to all gold surfaces. Further, the contact resistance is highly dependent on the precise atomic geometry around the site of anchoring and thereby inherently compromises the reproducibility of the connection.
To circumvent the latter issue, experiments has shown that fullerenes could be a good candidate for use instead of sulfur because of the large conjugated π-system that can electrically contact many more atoms at once than one atom of sulfur. [ 8 ]
In polymers , classical organic molecules are composed of both carbon and hydrogen (and sometimes additional compounds such as nitrogen, chlorine or sulphur). They are obtained from petrol and can often be synthesized in large amounts. Most of these molecules are insulating when their length exceeds a few nanometers. However, naturally occurring carbon is conducting, especially graphite recovered from coal or encountered otherwise. From a theoretical viewpoint, graphite is a semi-metal , a category in between metals and semi-conductors. It has a layered structure, each sheet being one atom thick. Between each sheet, the interactions are weak enough to allow an easy manual cleavage.
Tailoring the graphite sheet to obtain well defined nanometer-sized objects remains a challenge. However, by the close of the twentieth century, chemists were exploring methods to fabricate extremely small graphitic objects that could be considered single molecules. After studying the interstellar conditions under which carbon is known to form clusters, Richard Smalley 's group (Rice University, Texas) set up an experiment in which graphite was vaporized via laser irradiation. Mass spectrometry revealed that clusters containing specific magic numbers of atoms were stable, especially those clusters of 60 atoms. Harry Kroto , an English chemist who assisted in the experiment, suggested a possible geometry for these clusters – atoms covalently bound with the exact symmetry of a soccer ball. Coined buckminsterfullerenes , buckyballs, or C 60 , the clusters retained some properties of graphite, such as conductivity. These objects were rapidly envisioned as possible building blocks for molecular electronics.
When trying to measure electronic traits of molecules, artificial phenomena can occur that can be hard to distinguish from truly molecular behavior. [ 9 ] Before they were discovered, these artifacts have mistakenly been published as being features pertaining to the molecules in question.
Applying a voltage drop on the order of volts across a nanometer sized junction results in a very strong electrical field. The field can cause metal atoms to migrate and eventually close the gap by a thin filament, which can be broken again when carrying a current. The two levels of conductance imitate molecular switching between a conductive and an isolating state of a molecule.
Another encountered artifact is when the electrodes undergo chemical reactions due to the high field strength in the gap. When the voltage bias is reversed, the reaction will cause hysteresis in the measurements that can be interpreted as being of molecular origin.
A metallic grain between the electrodes can act as a single electron transistor by the mechanism described above, thus resembling the traits of a molecular transistor. This artifact is especially common with nanogaps produced by the electromigration method.
In their treatment of so-called donor-acceptor complexes in the 1940s, Robert Mulliken and Albert Szent-Györgyi advanced the concept of charge transfer in molecules. They subsequently further refined the study of both charge transfer and energy transfer in molecules. Likewise, a 1974 paper from Mark Ratner and Ari Aviram illustrated a theoretical molecular rectifier . [ 10 ]
In 1988, Aviram described in detail a theoretical single-molecule field-effect transistor . Further concepts were proposed by Forrest Carter of the Naval Research Laboratory , including single-molecule logic gates . A wide range of ideas were presented, under his aegis, at a conference entitled Molecular Electronic Devices in 1988. [ 11 ] These were theoretical constructs and not concrete devices. The direct measurement of the electronic traits of individual molecules awaited the development of methods for making molecular-scale electrical contacts. This was no easy task. Thus, the first experiment directly-measuring the conductance of a single molecule was only reported in 1995 on a single C 60 molecule by C. Joachim and J. K. Gimzewsky in their seminal Physical Review Letter paper and later in 1997 by Mark Reed and co-workers on a few hundred molecules. Since then, this branch of the field has advanced rapidly. Likewise, as it has grown possible to measure such properties directly, the theoretical predictions of the early workers have been confirmed substantially.
The concept of molecular electronics was published in 1974 when Aviram and Ratner suggested an organic molecule that could work as a rectifier. [ 12 ] Having both huge commercial and fundamental interest, much effort was put into proving its feasibility, and 16 years later in 1990, the first demonstration of an intrinsic molecular rectifier was realized by Ashwell and coworkers for a thin film of molecules.
The first measurement of the conductance of a single molecule was realised in 1994 by C. Joachim and J. K. Gimzewski and published in 1995 (see the corresponding Phys. Rev. Lett. paper). This was the conclusion of 10 years of research started at IBM TJ Watson, using the scanning tunnelling microscope tip apex to switch a single molecule as already explored by A. Aviram, C. Joachim and M. Pomerantz at the end of the 1980s (see their seminal Chem. Phys. Lett. paper during this period). The trick was to use a UHV Scanning Tunneling microscope to allow the tip apex to gently touch the top of a single C 60 molecule adsorbed on an Au(110) surface. A resistance of 55 MOhms was recorded along with a low voltage linear I-V. The contact was certified by recording the I-z current distance property, which allows measurement of the deformation of the C 60 cage under contact. This first experiment was followed by the reported result using a mechanical break junction method to connect two gold electrodes to a sulfur-terminated molecular wire by Mark Reed and James Tour in 1997. [ 13 ]
The scanning tunneling microscope (STM) and later the atomic force microscope (AFM) have facilitated manipulating single-molecule electronics. Also, theoretical advances in molecular electronics have facilitated further understanding of non-adiabatic charge transfer events at electrode-electrolyte interfaces. [ 14 ] [ 15 ]
A single-molecule amplifier was implemented by C. Joachim and J.K. Gimzewski in IBM Zurich. This experiment, involving one C 60 molecule, demonstrated that one such molecule can provide gain in a circuit via intramolecular quantum interference effects alone.
A collaboration of researchers at Hewlett-Packard (HP) and University of California, Los Angeles (UCLA), led by James Heath, Fraser Stoddart, R. Stanley Williams, and Philip Kuekes, has developed molecular electronics based on rotaxanes and catenanes .
Work is also occurring on the use of single-wall carbon nanotubes as field-effect transistors. Most of this work is being done by International Business Machines ( IBM ).
Some specific reports of a field-effect transistor based on molecular self-assembled monolayers were shown to be fraudulent in 2002 as part of the Schön scandal . [ 16 ]
The Aviram-Ratner model for a unimolecular rectifier has been confirmed experimentally. [ 17 ] [ 18 ] [ 19 ] Many rectifying molecules have so far been identified, and the number and efficiency of these systems is growing rapidly.
Supramolecular electronics is a new field involving electronics at a supramolecular level.
An important issue in molecular electronics is the determination of the resistance of a single molecule (both theoretical and experimental). For example, Bumm, et al. used STM to analyze a single molecular switch in a self-assembled monolayer to determine how conductive such a molecule can be. [ 20 ] Another problem faced by this field is the difficulty of performing direct characterization since imaging at the molecular scale is often difficult in many experimental devices. | https://en.wikipedia.org/wiki/Molecular_scale_electronics |
In chemistry and materials science , molecular self-assembly is the process by which molecules adopt a defined arrangement without guidance or management from an outside source. There are two types of self-assembly : intermolecular and intramolecular . Commonly, the term molecular self-assembly refers to the former, while the latter is more commonly called folding .
Molecular self-assembly is a key concept in supramolecular chemistry . [ 6 ] [ 7 ] [ 8 ] This is because assembly of molecules in such systems is directed through non-covalent interactions (e.g., hydrogen bonding , metal coordination, hydrophobic forces , van der Waals forces , pi-stacking interactions , and/or electrostatic) as well as electromagnetic interactions. Common examples include the formation of colloids , biomolecular condensates , micelles , vesicles , liquid crystal phases, and Langmuir monolayers by surfactant molecules. [ 9 ] Further examples of supramolecular assemblies demonstrate that a variety of different shapes and sizes can be obtained using molecular self-assembly. [ 10 ]
Molecular self-assembly allows the construction of challenging molecular topologies . One example is Borromean rings , interlocking rings wherein removal of one ring unlocks each of the other rings. DNA has been used to prepare a molecular analog of Borromean rings . [ 11 ] More recently, a similar structure has been prepared using non-biological building blocks. [ 12 ]
Molecular self-assembly underlies the construction of biologic macromolecular assemblies and biomolecular condensates in living organisms, and so is crucial to the function of cells . It is exhibited in the self-assembly of lipids to form the membrane , the formation of double helical DNA through hydrogen bonding of the individual strands, and the assembly of proteins to form quaternary structures . Molecular self-assembly of incorrectly folded proteins into insoluble amyloid fibers is responsible for infectious prion -related neurodegenerative diseases. Molecular self-assembly of nanoscale structures plays a role in the growth of the remarkable β-keratin lamellae / setae / spatulae structures used to give geckos the ability to climb walls and adhere to ceilings and rock overhangs . [ 13 ] [ 14 ]
When multiple copies of a polypeptide encoded by a gene self-assemble to form a complex, this protein structure is referred to as a "multimer". [ 15 ] Genes that encode multimer-forming polypeptides appear to be common. When a multimer is formed from polypeptides produced by two different mutant alleles of a particular gene, the mixed multimer may exhibit greater functional activity than the unmixed multimers formed by each of the mutants alone. In such a case, the phenomenon is referred to as intragenic complementation . [ 16 ] Jehle pointed out that, when immersed in a liquid and intermingled with other molecules, charge fluctuation forces favor the association of identical molecules as nearest neighbors. [ 17 ]
Molecular self-assembly is an important aspect of bottom-up approaches to nanotechnology . Using molecular self-assembly, the final (desired) structure is programmed in the shape and functional groups of the molecules. Self-assembly is referred to as a 'bottom-up' manufacturing technique in contrast to a 'top-down' technique such as lithography where the desired final structure is carved from a larger block of matter. In the speculative vision of molecular nanotechnology , microchips of the future might be made by molecular self-assembly. An advantage to constructing nanostructure using molecular self-assembly for biological materials is that they will degrade back into individual molecules that can be broken down by the body.
DNA nanotechnology is an area of current research that uses the bottom-up, self-assembly approach for nanotechnological goals. DNA nanotechnology uses the unique molecular recognition properties of DNA and other nucleic acids to create self-assembling branched DNA complexes with useful properties. [ 18 ] DNA is thus used as a structural material rather than as a carrier of biological information, to make structures such as complex 2D and 3D lattices (both tile-based as well as using the " DNA origami " method) and three-dimensional structures in the shapes of polyhedra . [ 19 ] These DNA structures have also been used as templates in the assembly of other molecules such as gold nanoparticles [ 20 ] and streptavidin proteins. [ 21 ]
The spontaneous assembly of a single layer of molecules at interfaces is usually referred to as two-dimensional self-assembly. One of the common examples of such assemblies are Langmuir-Blodgett monolayers and multilayers of surfactants. Non-surface active molecules can assemble into ordered structures as well. Early direct proofs showing that non-surface active molecules can assemble into higher-order architectures at solid interfaces came with the development of scanning tunneling microscopy and shortly thereafter. [ 22 ] Eventually two strategies became popular for the self-assembly of 2D architectures, namely self-assembly following ultra-high-vacuum deposition and annealing and self-assembly at the solid-liquid interface. [ 23 ] The design of molecules and conditions leading to the formation of highly-crystalline architectures is considered today a form of 2D crystal engineering at the nanoscopic scale . | https://en.wikipedia.org/wiki/Molecular_self-assembly |
A molecular sensor or chemosensor is a molecular structure (organic or inorganic complexes) that is used for sensing of an analyte to produce a detectable change or a signal . [ 1 ] [ 2 ] [ 3 ] [ 4 ] The action of a chemosensor, relies on an interaction occurring at the molecular level, usually involves the continuous monitoring of the activity of a chemical species in a given matrix such as solution, air, blood, tissue, waste effluents, drinking water, etc. The application of chemosensors is referred to as chemosensing, which is a form of molecular recognition . All chemosensors are designed to contain a signalling moiety and a recognition moiety , that is connected either directly to each other or through a some kind of connector or a spacer. [ 5 ] [ 6 ] [ 7 ] The signalling is often optically based electromagnetic radiation , giving rise to changes in either (or both) the ultraviolet and visible absorption or the emission properties of the sensors. Chemosensors may also be electrochemically based. Small molecule sensors are related to chemosensors. These are traditionally, however, considered as being structurally simple molecules and reflect the need to form chelating molecules for complexing ions in analytical chemistry . Chemosensors are synthetic analogues of biosensors , the difference being that biosensors incorporate biological receptors such as antibodies, aptamers or large biopolymers.
Chemosensors describes molecule of synthetic origin that signal the presence of matter or energy. A chemosensor can be considered as type of an analytical device. Chemosensors are used in everyday life and have been applied to various areas such as in chemistry, biochemistry, immunology, physiology, etc. and within medicine in general, such as in critical care analysis of blood samples. Chemosensors can be designed to detect/signal a single analyte or a mixture of such species in solution. [ 4 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] This can be achieved through either a single measurement or through the use of continuous monitoring. The signalling moiety acts as a signal transducer , converting the information (recognition event between the chemosensor and the analyte) into an optical response in a clear and reproducible manner.
Most commonly, the change (the signal) is observed by measuring the various physical properties of the chemosensor, such as the photo-physical properties seen in the absorption or emission , where different wavelengths of the electromagnetic spectrum are used. [ 12 ] [ 13 ] Consequently, most chemosensors are described as being either colorimetric ( ground state ) or luminescent ( excited state , fluorescent or phosphorescent ). Colorimetric chemosensors give rise to changes in their absorption properties (recorded using ultraviolet–visible spectroscopy ), such as in absorption intensity and wavelength or in chirality (using circularly polarized light , and CD spectroscopy ). [ 14 ]
In contrast, then in the case of luminescent chemosensors, the detection of an analyte, using fluorescence spectroscopy , gives rise to spectral changes in the fluorescence excitation or in the emission spectra, which are recorded using a fluorimeter . [ 15 ] Such changes can also occur in other excited state properties such as in the excited state life-time(s), quantum yield of fluorescence, and polarisation, etc. of the chemosensor. Fluorescence detection can be achieved at a low concentration (below ~ 10-6 M) with most fluorescence spectrometers. This offers the advantage of using the sensors directly within fibre optic systems. Examples of the use of chemosensors are to monitor blood content, drug concentrations, etc., as well as in environmental samples. Ions and molecules occur in abundance in biological and environmental systems where they are involved/effete biological and chemical processes. [ 16 ] The development of molecular chemosensors as probes for such analytes is an annual multibillion-dollar business involving both small SMEs as well as large pharmaceutical and chemical companies.
Chemosensors were first used to describe the combination of a molecular recognition with some form of reporter so the presence of a guest can be observed (also referred to as the analyte, cf. above). [ 17 ] Chemosensors are designed to contain a signalling moiety and a molecular recognition moiety (also called the binding site or a receptor). Combining both of these components can be achieved in a number of ways, such as integrated, twisted or spaced. Chemosensors are consider as major component of the area of molecular diagnostics , within the discipline of supramolecular chemistry , which relies on molecular recognition . In terms of supramolecular chemistry, chemosensing is an example of host–guest chemistry , where the presence of a guest (the analyte) at the host site (the sensor) gives rise to recognition event (e.g. sensing) that can be monitored in real time. This requires the binding of the analyte to the receptor, using all kinds of binding interactions such as hydrogen bonding , dipole - and electrostatic interactions , solvophobic effect, metal chelation, etc. The recognition/binding moiety is responsible for selectivity and efficient binding of the guest/analyte, which depend on ligand topology, characteristics of the target (ionic radius, size of molecule, chirality, charge, coordination number and hardness, etc.) and the nature of the solvent (pH, ionic strength, polarity). Chemosensors are normally developed to be able to interact with the target species in reversible manner, which is a prerequisite for continuous monitoring.
Optical signalling methods (such as fluorescence ) are sensitive and selective, and provide a platform for real-time response, and local observation. As chemosensors are designed to be both targeting (i.e. can recognize and bind a specific species) and sensitive to various concentration ranges, they can be used to observed real-live events on the cellular level. As each molecule can give rise to a signal/readout, that can be selectively measured, chemosensors are often said to be non-invasive and consequently have attracted significant attentions for their applications within biological matter, such as within living cells. Many examples of chemosensors have been developed for observing cellular function and properties, including monitoring ion flux concentrations and transports within cells such as Ca(II), Zn(II), Cu(II) and other physiologically important cations [ 18 ] and anions, [ 19 ] as well as biomolecules. [ 20 ] [ 21 ]
The design of ligands for the selective recognition of suitable guests such as metal cations [ 22 ] and anions [ 23 ] [ 24 ] has been an important goal of supramolecular chemistry. The term supramolecular analytical chemistry has recently been coined to describe the application of molecular sensors to analytical chemistry. [ 25 ] Small molecule sensors are related to chemosensors. However, these are traditionally considered as being structurally simple molecules and reflect the need to form chelating molecules for complexing ions in analytical chemistry.
While chemosensors were first defined in the 1980s, the first example of such a fluorescent chemosensor can be documented to be that of Friedrich Goppelsroder , who in 1867, developed a method for the determination/sensing of aluminium ion, using fluorescent ligand/chelate. This and subsequent work by others, gave birth to what is considered as modern analytical chemistry.
In the 1980s the development of chemosensing was achieved by Anthony W. Czarnik, [ 26 ] [ 27 ] [ 28 ] A. Prasanna de Silva [ 29 ] [ 30 ] [ 31 ] and Roger Tsien , [ 32 ] [ 33 ] [ 34 ] in the book Fluorescent Chemosensors for Ion and Molecule Recognition . They focused on the analysis of various types of luminescent probes for ions and molecules in solutions and within biological cells, for real-time applications. [ 35 ] Czarnik introduced the term ‘chemosensor’ to describe synthetic compounds capable of binding to analytes and providing a reversible signaling response. [ 36 ] Tsien went on to studying and developing this area of research further by developing and studding fluorescent proteins for applications in biology, such as green fluorescent proteins (GFP) for which he was awarded the Nobel Prize in Chemistry in 2008. The work of Lynn Sousa in the late 1970s, on the detection of alkali metal ions, possibly resulting in one of the first examples of the use of supramolecular chemistry in fluorescent sensing design, [ 37 ] as well as that of J.-M. Lehn , H. Bouas-Laurent and co-workers at Université Bordeaux I, France. [ 38 ] The development of PET sensing of transition metal ions was developed by L. Fabbrizzi, among others. [ 39 ]
In chemosensing, the use of fluorophore connected to the receptor via a covalent spacer is now commonly referred to as fluorophores-spacer-receptor principle. In such systems, the sensing event is normally described as being due to changes in the photophysical properties of the chemosensor systems due to chelation induced enhanced fluorescence (CHEF), [ 26 ] [ 27 ] [ 28 ] and photoinduced electron transfer (PET), [ 29 ] [ 30 ] [ 31 ] mechanisms. In principle the two mechanisms are based on the same idea; the communication pathway is in the form of a through-space electron transfer from the electron rich receptors to the electron deficient fluorophores (through space). This results in fluorescence quenching (active electron transfer), and the emission from the chemosensor is 'switched off,' for both mechanisms in the absence of the analytes. However, upon forming a host–guest complex between the analyte and receptor, the communication pathway is broken and the fluorescence emission from the fluorophores is enhanced, or 'switched on'. In other words, the fluorescence intensity and quantum yield are enhanced upon analyte recognition.
The fluorophores-receptor can also be integrated within the chemosensor. This leads to changes in the emission wavelength, which often results in change in colour. When the sensing event results in the formation of a signal that is visible to the naked eye, such sensors are normally referred to as colorimetric . Many examples of colorimetric chemosensors for ions such as fluoride have been developed. [ 40 ] A pH indicator can be consider as a colorimetric chemosensors for protons. Such sensors have been developed for other cations, as well as anions and larger organic and biological molecules, such as proteins and carbohydrates. [ 41 ]
Chemosensors are nano-sized molecules and for application in vivo need to be non-toxic. A chemosensor must be able to give a measurable signal in direct response to the analyte recognition. Hence, the signal response is directly related to the magnitude of the sensing event (and, in turn concentration of the analyte). While the signalling moiety acts as a signal transducer, converting the recognition event into an optical response. The recognition moiety is responsible for binding to the analyte in a selective and reversible manner. If the binding sites are 'irreversible chemical reactions,' the indicators are described as fluorescent chemodosimeters, or fluorescent probes .
An active communication pathway has to be open between the two moieties for the sensor to operate. In colorimetric chemosensors, this usually relies on the receptor and transducer to be structurally integrated. In luminescent/fluorescent chemosensing these two parts can be 'spaced' out or connected with a covalent spacer. The communication pathway is through electron transfer or energy transfer for such fluorescent chemosensors. The effectiveness of the host–guest recognition between the receptor and the analyte depends on several factors, including the design of the receptor moiety, which is objective is to match as much the nature of the structural nature of the target analyte, as well as the nature of the environment that the sensing event occurs within (e.g. the type of media, i.e. blood, saliva, urine, etc. in biological samples). An extension to this approach is the development of molecular beacons , which are oligonucleotide hybridization probes based on fluorescence signalling where the recognition or the sensing event is communicated through enhancement or reduction in luminescence through the use of Förster resonance energy transfer (FRET) mechanism.
All chemosensors are designed to contain a signalling moiety and a recognition moiety. These are integrated directly or connected with a short covalent spacer depending on the mechanism involved in the signalling event. The chemosensor can be based on self-assembly of the sensor and the analyte. An example of such a design are the (indicator) displacement assays IDA. [ 42 ] IDA sensor for anions such as citrate or phosphate ions have been developed whereby these ions can displace a fluorescent indicator in an indicator-host complex. [ 5 ] The so-called UT taste chip (University of Texas) is a prototype electronic tongue and combines supramolecular chemistry with charge-coupled devices based on silicon wafers and immobilized receptor molecules.
Most examples of chemosensors for ions , such as those of alkali metal ions (Li+, Na+, K+, etc.) and alkali earth metal ions (Mg2+, Ca2+, etc.) are designed so that the excited state of the fluorophore component of the chemosensor is quenched by an electron transfer when the sensor is not complexed to these ions. No emission is thus observed, and the sensor is sometimes referred to as being 'switched off'. By complexing the sensor with a cation, the conditions for electron transfer are altered so that the quenching process is blocked, and fluorescence emission is 'switched on'. The probability of PET is governed by the overall free energy of the system (the Gibbs free energy ΔG). The driving force for PET is represented by ΔGET, the overall changes in the free energy for the electron transfer can be estimated using the Rehm-Weller equation. [ 43 ] Electron transfer is distance dependent and decreases with increasing spacer length. Quenching by electron transfer between uncharged species leads to the formation of a radical ion pair. This is sometimes referred to as being the primary electron transfer. The possible electron transfer, which takes place after the PET, is referred to as the 'secondary electron transfer'. Chelation Enhancement Quenching (CHEQ) is the opposite effect seen for CHEF. [ 44 ] In CHEQ, a reduction is observed in fluorescent emission of the chemosensor in comparison to that seen the originally for the 'free' sensor upon host–guest formation. As electron transfer is directional, such systems have also been described by the PET principle, being described as an enhancement in PET from the receptor to the fluorophore with enhanced degree of quenching. Such an effect has been demonstrated for the sensing of anions such as carboxylates and fluorides. [ 45 ]
A large number of examples of chemosensors have been developed by scientists in physical, life and environmental sciences. The advantages of fluorescence emission being 'switched on' from 'off' upon the recognition event enabling the chemosensors to be compared to 'beacons in the night'. As the process is reversible, the emission enhancement is concentration dependent, only becoming 'saturated' at high concentrations (fully bound receptor). Hence, a correlation can be made between luminescence (intensity, quantum yield and in some cases lifetime) and the analyte concentration. Through careful design, and evaluation of the nature of the communication pathway, similar sensors based on the use of 'on-off' switching, or 'on-off-on,' or 'off-on-off' switching have been designed. The incorporation of chemosensors onto surfaces, such as quantum dots , nanoparticles , or into polymers is also a fast-growing area of research. [ 46 ] [ 47 ] [ 48 ] Fluorescence sensing has also been combined with electrochemical techniques, conferring the advantages of both methods. [ 49 ] Other examples of chemosensors that work on the principle of switching fluorescent emission either on or off include, Förster resonance energy transfer (FRET), internal charge transfer (ICT), twisted internal charge transfer (TICT), metal-based emission (such as in lanthanide luminescence), [ 50 ] [ 51 ] and excimer and exciplex emission and aggregation-induced emission (AIE). [ 52 ] [ 53 ] Chemosensors were one of the first examples of molecules that could result in switching between 'on' or 'off' states through the use of external stimuli and as such can be classed as synthetic molecular machine , to which the Nobel Prize in Chemistry was awarded to in 2016 to Jean-Pierre Sauvage , Fraser Stoddart and Bernard L. Feringa .
The application of these same design principles used in chemosensing also paved the way for the development of molecular logic gates mimics (MLGMs), [ 54 ] [ 55 ] being first proposed using PET based fluorescent chemosensors by de Silva and co-workers in 1993. [ 56 ] Molecules have been made to operate in accordance with Boolean algebra that performs a logical operation based on one or more physical or chemical inputs. The field has advanced from the development of simple logic systems based on a single chemical input to molecules capable of carrying out complex and sequential operations.
Chemosensors have been incorporated through surface functionalization onto particles and beads such as metal based nanoparticles , quantum dots , carbon-based particles and into soft materials such as polymers to facilitate their various applications.
Other receptors are sensitive not to a specific molecule but to a molecular compound class, these chemosensors are used in array- (or microarray) based sensors. Array-based sensors utilize analyte binding by the differential receptors. One example is the grouped analysis of several tannic acids that accumulate in ageing Scotch whisky in oak barrels. The grouped results demonstrated a correlation with the age but the individual components did not. A similar receptor can be used to analyze tartrates in wine.
The application of chemosensors in cellular imaging is particularly promising as most biological process are now monitored by using imaging technologies such as confocal fluorescence and super resolution microscopy , among others.
The compound saxitoxin is a neurotoxin found in shellfish and a chemical weapon. An experimental sensor for this compound is again based on PET. Interaction of saxitoxin with the sensor's crown ether moiety kills its PET process towards the fluorophore and fluorescence is switched from off to on. [ 4 ] The unusual boron moiety causes the fluorescence to occur in the visible light part of the electromagnetic spectrum.
Chemosensors also have applications in chemistry, biochemistry, immunology, physiology, medicine and landmine detection. [ 57 ] In 2003, Czarnik outlined a way to use chemosensors to track glucose levels in diabetic patients which, along with contributions from others, created an FDA-approved implantable continuous glucose monitor. [ 58 ] [ 59 ] | https://en.wikipedia.org/wiki/Molecular_sensor |
A molecular shuttle in supramolecular chemistry is a special type of molecular machine capable of shuttling molecules or ions from one location to another. This field is of relevance to nanotechnology in its quest for nanoscale electronic components and also to biology where many biochemical functions are based on molecular shuttles. Academic interest also exists for synthetic molecular shuttles, the first prototype reported in 1991 based on a rotaxane . [ 1 ]
This device is based on a molecular thread composed of an ethyleneglycol chain interrupted by two arene groups acting as so-called stations . The terminal units (or stoppers ) on this wire are bulky triisopropylsilyl groups. The bead is a tetracationic cyclophane based on two bipyridine groups and two para-phenylene groups. The bead is locked to one of the stations by pi-pi interactions but since the activation energy for migration from one station to the other station is only 13 kcal / mol (54 kJ /mol) the bead shuttles between them. The stoppers prevent the bead from slipping from the thread. Chemical synthesis of this device is based on molecular self-assembly from a preformed thread and two bead fragments (32% chemical yield ).
In certain molecular switches the two stations are non-degenerate. | https://en.wikipedia.org/wiki/Molecular_shuttle |
A molecular sieve is a material with pores (voids or holes), having uniform size comparable to that of individual molecules , linking the interior of the solid to its exterior. These materials embody the molecular sieve effect , the preferential sieving of molecules larger than the pores. [ a ] Many kinds of materials exhibit some molecular sieves, but zeolites dominate the field. Zeolites are almost always aluminosilicates , or variants where some or all of the Si or Al centers are replaced by similarly charged elements. [ 2 ]
The diameters of the pores that comprise molecular sieves are similar in size to small molecules. Large molecules cannot enter or be adsorbed , while smaller molecules can. As a mixture of molecules migrates through the stationary bed of porous, semi-solid substance referred to as a sieve (or matrix), the components of the highest molecular weight (which are unable to pass into the molecular pores) leave the bed first, followed by successively smaller molecules. Most of molecular sieves are aluminosilicates ( zeolites ) with Si/Al molar ratio less than 2, but there are also examples of activated charcoal and silica gel . [ 2 ] [ 3 ] [ 4 ]
The pore diameter of a molecular sieve is measured in ångströms (Å) or nanometres (nm). According to IUPAC notation, microporous materials have pore diameters of less than 2 nm (20 Å) and macroporous materials have pore diameters of greater than 50 nm (500 Å); the mesoporous category thus lies in the middle with pore diameters between 2 and 50 nm (20–500 Å). [ 5 ]
The sieving properties of molecular sieves are classified as
Some molecular sieves are used in size-exclusion chromatography , a separation technique that sorts molecules based on their size.
Another important use is as a desiccant . They are often utilized in the petrochemical industry for drying gas streams. For example, in the liquid natural gas (LNG) industry, the water content of the gas needs to be reduced to less than 1 ppmv to prevent blockages caused by ice or methane clathrate .
In the laboratory, molecular sieves are used to dry solvent. "Sieves" have proven to be superior to traditional drying techniques, which often employ aggressive desiccants . [ 7 ]
Under the term zeolites, molecular sieves are used for a wide range of catalytic applications. They catalyze isomerisation , alkylation , and epoxidation , and are used in large scale industrial processes, including hydrocracking and fluid catalytic cracking . [ 8 ]
They are also used in the filtration of air supplies for breathing apparatus, for example those used by scuba divers and firefighters . In such applications, air is supplied by an air compressor and is passed through a cartridge filter which, depending on the application, is filled with molecular sieve and/or activated carbon , finally being used to charge breathing air tanks. [ 9 ] Such filtration can remove particulates and compressor exhaust products from the breathing air supply.
The U.S. FDA has as of April 1, 2012, approved sodium aluminosilicate for direct contact with consumable items under 21 CFR 182.2727. [ 10 ] Prior to this approval the European Union had used molecular sieves with pharmaceuticals and independent testing suggested that molecular sieves meet all government requirements but the industry had been unwilling to fund the expensive testing required for government approval. [ 11 ]
Methods for regeneration of molecular sieves include pressure change (as in oxygen concentrators), heating and purging with a carrier gas (as when used in ethanol dehydration), or heating under high vacuum. Regeneration temperatures range from 175 °C (350 °F) to 315 °C (600 °F) depending on molecular sieve type. [ 12 ] In contrast, silica gel can be regenerated by heating it in a regular oven to 120 °C (250 °F) for two hours. However, some types of silica gel will "pop" when exposed to enough water. This is caused by breakage of the silica spheres when contacting the water. [ 13 ]
3A molecular sieves are produced by cation exchange of potassium for sodium in 4A molecular sieves (See below)
3A molecular sieves do not adsorb molecules with diameters are larger than 3 Å. The characteristics of these molecular sieves include fast adsorption speed, frequent regeneration ability, good crushing resistance and pollution resistance . These features can improve both the efficiency and lifetime of the sieve. 3A molecular sieves are the necessary desiccant in petroleum and chemical industries for refining oil, polymerization, and chemical gas-liquid depth drying.
3A molecular sieves are used to dry a range of materials, such as ethanol , air, refrigerants , natural gas and unsaturated hydrocarbons . The latter include cracking gas, acetylene , ethylene , propylene and butadiene .
3A molecular sieves are stored at room temperature, with a relative humidity not more than 90%. They are sealed under reduced pressure, being kept away from water, acids and alkalis.
For the production of 4A sieve, typically aqueous solutions of sodium silicate and sodium aluminate are combined at 80 °C. The product is "activated" by "heating" at 400 °C [ 15 ] 4A sieves serve as the precursor to 3A and 5A sieves through cation exchange of sodium for potassium (for 3A) or calcium (for 5A) [ 16 ] [ 17 ]
The main use of zeolitic molecular sieves is in laundry detergents. In 2001, an estimated 1200 kilotons of zeolite A were produced for this purpose, which entails water softening . [ 2 ]
4A molecular sieves are widely used to dry laboratory solvents. They can absorb water and other species with a critical diameter less than 4 Å such as NH 3 , H 2 S, SO 2 , CO 2 , C 2 H 5 OH, C 2 H 6 , and C 2 H 4 .
Some molecular sieves are used to assist detergents as they can produce demineralized water through calcium ion exchange, remove and prevent the deposition of dirt. They are widely used to replace phosphorus . The 4A molecular sieve plays a major role to replace sodium tripolyphosphate as detergent auxiliary in order to mitigate the environmental impact of the detergent. It also can be used as a soap forming agent and in toothpaste .
Molecular sieves are available in diverse shape and sizes. Spherical beads have advantage over other shapes as they offer lower pressure drop and are mechanically robust. | https://en.wikipedia.org/wiki/Molecular_sieve |
A molecular solid is a solid consisting of discrete molecules . The cohesive forces that bind the molecules together are van der Waals forces , dipole–dipole interactions , quadrupole interactions , π–π interactions , hydrogen bonding , halogen bonding , London dispersion forces , and in some molecular solids, coulombic interactions . [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] Van der Waals, dipole interactions, quadrupole interactions, π–π interactions, hydrogen bonding, and halogen bonding (2–127 kJ mol −1 ) [ 10 ] are typically much weaker than the forces holding together other solids: metallic ( metallic bonding , 400–500 kJ mol −1 ), [ 4 ] ionic ( Coulomb’s forces , 700–900 kJ mol −1 ), [ 4 ] and network solids ( covalent bonds , 150–900 kJ mol −1 ). [ 4 ] [ 10 ]
Intermolecular interactions typically do not involve delocalized electrons , unlike metallic and certain covalent bonds. Exceptions are charge-transfer complexes such as the tetrathiafulvane-tetracyanoquinodimethane (TTF-TCNQ), a radical ion salt . [ 5 ] These differences in the strength of force (i.e. covalent vs. van der Waals) and electronic characteristics (i.e. delocalized electrons) from other types of solids give rise to the unique mechanical , electronic , and thermal properties of molecular solids. [ 3 ] [ 4 ] [ 5 ] [ 8 ]
Molecular solids are poor electrical conductors , [ 4 ] [ 5 ] although some, such as TTF-TCNQ are semiconductors (ρ = 5 x 10 2 Ω −1 cm −1 ). [ 5 ] They are still substantially less than the conductivity of copper (ρ = 6 x 10 5 Ω −1 cm −1 ). [ 8 ] Molecular solids tend to have lower fracture toughness ( sucrose , K Ic = 0.08 MPa m 1/2 ) [ 11 ] than metal ( iron , K Ic = 50 MPa m 1/2 ), [ 11 ] ionic ( sodium chloride , K Ic = 0.5 MPa m 1/2 ), [ 11 ] and covalent solids ( diamond , K Ic = 5 MPa m 1/2 ). [ 12 ] Molecular solids have low melting (T m ) and boiling (T b ) points compared to metal (iron), ionic (sodium chloride), and covalent solids (diamond). [ 4 ] [ 5 ] [ 8 ] [ 13 ] Examples of molecular solids with low melting and boiling temperatures include argon , water , naphthalene , nicotine , and caffeine (see table below). [ 13 ] [ 14 ] The constituents of molecular solids range in size from condensed monatomic gases [ 15 ] to small molecules (i.e. naphthalene and water) [ 16 ] [ 17 ] to large molecules with tens of atoms (i.e. fullerene with 60 carbon atoms). [ 18 ]
Molecular solids may consist of single atoms, diatomic , and/or polyatomic molecules . [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] The intermolecular interactions between the constituents dictate how the crystal lattice of the material is structured. [ 19 ] [ 20 ] [ 21 ] All atoms and molecules can partake in van der Waals and London dispersion forces ( sterics ). It is the lack or presence of other intermolecular interactions based on the atom or molecule that affords materials unique properties. [ 19 ]
Argon, is a noble gas that has a full octet , no charge , and is nonpolar . [ 3 ] [ 4 ] [ 7 ] [ 8 ] These characteristics make it unfavorable for argon to partake in metallic, covalent, and ionic bonds as well as most intermolecular interactions. [ 3 ] [ 4 ] [ 7 ] [ 8 ] It can though partake in van der Waals and London dispersion forces. [ 3 ] [ 4 ] These weak self-interactions are isotropic and result in the long-range ordering of the atoms into face centered cubic packing when cooled below -189.3. [ 13 ] Similarly iodine, a linear diatomic molecule has a net dipole of zero and can only partake in van der Waals interactions that are fairly isotropic. [ 3 ] [ 4 ] [ 7 ] [ 8 ] This results in the bipyramidal symmetry .
For acetone dipole-dipole interactions are a major driving force behind the structure of its crystal lattice. The negative dipole is caused by oxygen. Oxygen is more electronegative than carbon and hydrogen, [ 13 ] causing a partial negative (δ-) and positive charge (δ+) on the oxygen and remainder of the molecule, respectively. [ 3 ] [ 5 ] The δ- orienttowards the δ+ causing the acetone molecules to prefer to align in a few configurations in a δ- to δ+ orientation (pictured left). The dipole-dipole and other intermolecular interactions align to minimize energy in the solid state and determine the crystal lattice structure.
A quadrupole, like a dipole, is a permanent pole but the electric field of the molecule is not linear as in acetone, but in two dimensions. [ 25 ] Examples of molecular solids with quadrupoles are octafluoronaphthalene and naphthalene . [ 17 ] [ 25 ] Naphthalene consists of two joined conjugated rings. The electronegativity of the atoms of this ring system and conjugation cause a ring current resulting in a quadrupole. For naphthalene, this quadrupole manifests in a δ- and δ+ accumulating within and outside the ring system, respectively. [ 4 ] [ 5 ] [ 6 ] [ 10 ] [ 25 ] Naphthalene assembles through the coordination of δ- of one molecules to the δ+ of another molecule. [ 4 ] [ 5 ] [ 6 ] This results in 1D columns of naphthalene in a herringbone configuration. These columns then stack into 2D layers and then 3D bulk materials. Octafluoronaphthalene follows this path of organization to build bulk material except the δ- and δ+ are on the exterior and interior of the ring system, respectively. [ 5 ]
A hydrogen bond is a specific dipole where a hydrogen atom has a partial positive charge (δ+) to due a neighboring electronegative atom or functional group . [ 9 ] [ 10 ] Hydrogen bonds are amongst the strong intermolecular interactions know other than ion-dipole interactions . [ 10 ] For intermolecular hydrogen bonds the δ+ hydrogen interacts with a δ- on an adjacent molecule. Examples of molecular solids that hydrogen bond are water, amino acids , and acetic acid. [ 3 ] [ 5 ] [ 8 ] [ 10 ] For acetic acid, the hydrogen (δ+) on the alcohol moiety of the carboxylic acid hydrogen bonds with other the carbonyl moiety (δ-) of the carboxylic on the adjacent molecule. This hydrogen bond leads a string of acetic acid molecules hydrogen bonding to minimize free energy . [ 10 ] [ 26 ] These strings of acetic acid molecules then stack together to build solids.
A halogen bond is when an electronegative halide participates in a noncovalent interaction with a less electronegative atom on an adjacent molecule. [ 10 ] [ 28 ] Examples of molecular solids that halogen bond are hexachlorobenzene [ 11 ] [ 29 ] and a cocrystal of bromine 1,4-dioxane . [ 27 ] For the second example, the δ- bromine atom in the diatomic bromine molecule is aligning with the less electronegative oxygen in the 1,4-dioxane. The oxygen in this case is viewed as δ+ compared to the bromine atom. This coordination results in a chain-like organization that stack into 2D and then 3D. [ 27 ]
Coulombic interactions are manifested in some molecular solids. A well-studied example is the radical ion salt TTF-TCNQ with a conductivity of 5 x 10 2 Ω −1 cm −1 , [ 5 ] much closer to copper (ρ = 6 x 10 5 Ω −1 cm −1 ) [ 8 ] than many molecular solids. [ 31 ] [ 18 ] [ 30 ] The coulombic interaction in TTF-TCNQ stems from the large partial negative charge (δ = -0.59) on the cyano- moiety on TCNQ at room temperature. [ 5 ] For reference, a completely charged molecule δ = ±1. [ 5 ] This partial negative charge leads to a strong interaction with the thio- moiety of the TTF. The strong interaction leads to favorable alignment of these functional groups adjacent to each other in the solid state. [ 5 ] [ 30 ] While π-π interactions cause the TTF and TCNQ to stack in separate columns. [ 10 ] [ 30 ]
One form of an element may be a molecular solid, but another form of that same element may not be a molecular solid. [ 3 ] [ 4 ] [ 5 ] For example, solid phosphorus can crystallize as different allotropes called "white", "red", and "black" phosphorus. White phosphorus forms molecular crystals composed of tetrahedral P 4 molecules. [ 32 ] Heating at ambient pressure to 250 °C or exposing to sunlight converts white phosphorus to red phosphorus where the P 4 tetrahedra are no longer isolated, but connected by covalent bonds into polymer-like chains. [ 33 ] Heating white phosphorus under high (GPa) pressures converts it to black phosphorus which has a layered, graphite -like structure. [ 34 ] [ 35 ]
The structural transitions in phosphorus are reversible: upon releasing high pressure, black phosphorus gradually converts into the red phosphorus, and by vaporizing red phosphorus at 490 °C in an inert atmosphere and condensing the vapor, covalent red phosphorus can be transformed into the molecular solid, white phosphorus. [ 36 ]
Similarly, yellow arsenic is a molecular solid composed of As 4 units. [ 37 ] Some forms of sulfur and selenium are composed of S 8 (or Se 8 ) units and are molecular solids at ambient conditions, but converted into covalent allotropes having atomic chains extending throughout the crystal. [ 38 ] [ 39 ]
Since molecular solids are held together by relatively weak forces they tend to have low melting and boiling points, low mechanical strength, low electrical conductivity, and poor thermal conductivity. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] it will Also, depending on the structure of the molecule the intermolecular forces may have directionality leading to anisotropy of certain properties. [ 4 ] [ 5 ] [ 8 ]
The characteristic melting point of metals and ionic solids is ~ 1000 °C and greater, while molecular solids typically melt closer to 300 °C (see table), thus many corresponding substances are either liquid (ice) or gaseous (oxygen) at room temperature. [ 4 ] [ 6 ] [ 7 ] [ 8 ] [ 40 ] This is due to the elements involved, the molecules they form, and the weak intermolecular interactions of the molecules.
Allotropes of phosphorus are useful to further demonstrate this structure-property relationship. White phosphorus, a molecular solid, has a relatively low density of 1.82 g/cm 3 and melting point of 44.1 °C; it is a soft material which can be cut with a knife. When it is converted to the covalent red phosphorus, the density goes to 2.2–2.4 g/cm 3 and melting point to 590 °C, and when white phosphorus is transformed into the (also covalent) black phosphorus, the density becomes 2.69–3.8 g/cm 3 and melting temperature ~200 °C. Both red and black phosphorus forms are significantly harder than white phosphorus. [ 43 ]
Molecular solids can be either ductile or brittle , or a combination depending on the crystal face stressed. [ 5 ] [ 11 ] Both ductile and brittle solids undergo elastic deformation till they reach the yield stress. [ 8 ] [ 11 ] Once the yield stress is reached, ductile solids undergo a period of plastic deformation and eventually fracture. Brittle solids fracture promptly after passing the yield stress. [ 8 ] [ 11 ] Due to the asymmetric structure of most molecules or the presence of functional groups capable of forming specific interactions (e.g. hydrogen bonds , halogen bonds ), many molecular solids have directional intermolecular forces. [ 11 ] This phenomenon can lead to anisotropic mechanical properties. Typically, a molecular solid is ductile when it has isotropic intermolecular interactions. This allows for dislocation between layers of the crystal much like metals. [ 5 ] [ 8 ] [ 11 ] For example, plastic crystals are soft, resemble waxes and are easily deformed.
One example of a ductile molecular solid, that can be bent 180°, is hexachlorobenzene (HCB). [ 11 ] [ 29 ] In this example the π-π interactions between the benzene cores are stronger than the halogen interactions of the chlorides. This difference leads to its flexibility . [ 11 ] [ 29 ] This flexibility is anisotropic; to bend HCB to 180° you must stress the [001] face of the crystal. [ 29 ] Another example of a flexible molecular solid is 2-(methylthio)nicotinic acid (MTN). [ 11 ] [ 29 ] MTN is flexible due to its strong hydrogen bonding and π-π interactions creating a rigid set of dimers that dislocate along the alignment of their terminal methyls. [ 29 ] When stressed on the [010] face this crystal will bend 180°. [ 29 ] Note, not all ductile molecular solids bend 180°, and some may have more than one bending face. [ 29 ]
Molecular solids are generally insulators. [ 5 ] [ 18 ] This large band gap (compared to germanium at 0.7 eV) [ 8 ] is due to the weak intermolecular interactions, which result in low charge carrier mobility . Some molecular solids exhibit electrical conductivity, such as TTF-TCNQ with ρ = 5 x 10 2 Ω −1 cm −1 but in such cases orbital overlap is evident in the crystal structure. Fullerenes, which are insulating, become conducting or even superconducting upon doping. [ 44 ]
The thermal properties of molecular solids (as, for instance, specific heat capacity, thermal expansion, and thermal conductance to name a few) are determined by the intra- and intermolecular vibrations of the atoms and molecules of the molecular solid. [ 3 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] In molecular solids the transitions of an electron contribute negligibly to thermal properties compared to the vibrational contribution. [ 5 ] [ 8 ] | https://en.wikipedia.org/wiki/Molecular_solid |
A Molecular spring is a device or part of a biological system based on molecular mechanics and is associated with molecular vibration .
Any molecule can be deformed in several ways - A-A bond length, A-A-A angle, A-A-A-A torsion angle.
Deformed molecules store energy, which can be released and cause mechanical work as the molecules return into their optimal geometrical conformation .
The term molecular string is usually used in nano-science and molecular biology, however theoretically also macroscopic molecular springs can be considered, if it is manufactured. Such a device composed for example of arranged ultra-high molecular mass polymer fibres ( Helicene , Polyacetylene ) could store extraordinary (0.1-10MJ/kg in comparison to 0.0003MJ/kg of clockwork spring) amount of energy which can be stored and released almost instantly, with high energy conversion efficiency . The amount of energy storable in molecular spring is limited by the value of deformation the molecule can withstand until it undergoes chemical change . Manufacturing of such macroscopic device is however out of reach of contemporary technology, because of difficulties of synthesis and molecular arrangement of such long polymer molecules. In addition, the force needed to draw molecular string to its maximum length could be impractically high - comparable to the tensile strength of particular polymer molecule (~100GPa for some carbon compounds)
This nanotechnology-related article is a stub . You can help Wikipedia by expanding it .
This molecular physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_spring |
A molecular switch is a molecule that can be switched between two or more stable or metastable states with the use of any external (exogenous) or internal (endogenous) stimuli, such as changes in pH, light, temperature, an electric current, a microenvironment, or in the presence of ions , and other ligands . [ 1 ] [ 2 ] In some cases, a combination of stimuli is required. [ 1 ] Molecular switches are reversible . They have been considered for a wide area of possible applications, but the main uses are in photochromic lenses and windows. [ 1 ]
Biological stimuli are endogenous form of stimuli. [ 3 ] [ 4 ] This involves variation in the physiological changes around the cells, such as variable pH, presence of oxidative or reductive species, and enzymes . [ 5 ] In cellular biology , proteins act as intracellular signaling molecules by activating another protein in a signaling pathway. In order to do this, proteins act as molecular switches by toggling between active and inactive states. [ 6 ]
For example, phosphorylation of proteins can be used to activate or inactivate proteins. The external signal flipping the molecular switch could be a protein kinase , which adds a phosphate group to the protein, or a protein phosphatase , which removes phosphate groups. [ 7 ] Normal tissues and diseased tissues have different pH, so current approaches of effective drug delivery systems (DDS) include the use of this difference in pH as an endogenous stimulus. Such DDS offer a huge advantage over the conventional therapeutic drug release methods as they selectively release drug cargo at a specific physiological pH. [ 8 ] For instance, a study by Shi et al . proposed a pH-responsive/enzyme-cascade-reactive nanoplatform for antibacterial applications. [ 9 ] Many artificial nucleic acid-based switches have opened up new opportunities in nucleic-acid nanoscience and RNA/DNA biochemistry . [ 1 ]
The ability of some compounds to change color in function of the pH was known since the sixteenth century. [ 10 ] This effect was even known before the development of acid-base theory . Those are found in a wide range of plants like roses, cornflowers, primroses and violets. Robert Boyle was the first person to describe this effect, employing plant juices (in the forms of solution and impregnated paper). [ 11 ] This effect is the result of structural or electronic changes in molecules upon interaction with protons and is called acidochromism. Acidochromic molecules are most commonly used as pH indicators such as phenolphthalein , methyl orange , and methyl red . Their acidic and basic forms have different colors. When an acid or a base is added, the equilibrium between the two forms is displaced. [ 12 ]
Examples in the literature of molecular switches with reversible pH response are spiropyran , [ 13 ] hydrazones , [ 14 ] Donor-Acceptor-Steenhouse Aduucts (DASA), [ 15 ] heptamethine–oxonol dyes, [ 16 ] etc.
Spiropyran, SP changes its color from blue in the presence of acid such as TFA ( trifluroacetic acid ) to colorless ring opened form called merocyanine, MC while under alkaline conditions reverts it back to the ring closed, SP form. [ 17 ] They are called dual responsive switches since light can also be used to trigger the isomerization. [ 18 ] There mechanism of isomerization is shown in the figure above. Due to their easy synthesis and excellent optical stability, they are widely used in bioimaging and pH sensing. [ 19 ]
An interesting example of pH-responsive molecular switches is shown by Yin's group, who developed pH sensors made up of the spiropyran-based fluorescent probe that can be used for precise and rapid pH detection by making their pH paper strips. Their probe also incorporates indole salts as nucleophilic addition sites that react with OH − ions (hydroxide ions) in different pH environments. [ 20 ] A 2022 report by Wang et al. shows the spiropyran-based cellulose nanocrystals useful for pH sensors. [ 21 ]
Acidochromic behavior of hydrazones (C=N-N-) is attributed to their tautomerization under an acidic or basic conditions. [ 22 ] This linkage is useful in drug delivery (DDS) due to their faster hydrolysis rate in an acidic environment. [ 23 ]
Acid can also help to tune the physical state of the switch. In 2022, Quintard and coworkers have shown the sol- gel transition of various amines using trichloroacetic acid (TCA) as fuel to create new types of time-controlled smart materials. [ 24 ]
These property changes enable azobenzenes to be used in various applications. In particular, azobenzenes incorporated into crown ethers give switchable receptors and azobenzenes in monolayers can provide light-controlled changes in surface properties. [ 27 ]
The molecules that isomerize when exposed to light of suitable wavelength are called photoswitches . Members of this class include azobenzenes , diarylethenes, dithienylethenes , fulgides, stilbenes , norbornadiene , spiropyrans, hydrazones , indigoids, [ 37 ] diazocines, [ 38 ] and phenoxynaphthacene quinones. [ 39 ]
The inspiration to study light-sensitive switches came from an understanding of retinal . In the dark, retinal exists primarily in an all-trans configuration, except for a cis bond at C-11. Upon exposure to light, it undergoes photoisomerization to an all-trans configuration.
Photo-induced structural, physical, or chemical changes can involve isomerization of bonds (cis <--> trans), electron transfer, proton transfer in the excited state, ring opening and closing mechanism. [ 40 ] These isomerizations affect optical properties. For example, the absorption maximum of (Z) -azobenzene is blue shifted with respect to ( E) -azobenzene. [ 1 ]
Many light-driven azo-based switches have been investigated. [ 41 ]
Chiroptical molecular switches are a specific subgroup with photochemical switching taking place between an enantiomers . In these compounds the "readout" is by circular dichroism . [ 42 ] Hindered alkenes can change their helicity (see: planar chirality ) as response to irradiation with right or left-handed circularly polarized light Chiroptical molecular switches that show directional motion are considered synthetic molecular motors . [ 43 ] When attached to the end of a helical poly (isocyanate) polymer, they can switch the helical sense of the polymer. [ 44 ]
Species that exist in more than one redox state are potential switches. When the optical properties of the redox state differ, then redox is sometimes called electrochromism . [ 45 ] For instance, Ferrocene , which is orange, oxidizes to the blue ferrocenium cation. [ 46 ]
Many fluorescence based sensors are based on redox couple mechanism of switches which in their oxidized form quenches the fluorescence of fluorophore while in reduced state does not, or vice versa. Some other examples include, biindeno[2,1-b]thiophenylidene (BTP), [ 47 ] viologens , napthelene diimides, [ 48 ] bipyridinium, [ 49 ] and metal-ligand redox complex. [ 50 ]
The first electrochemical sensors for selective binding of metal cations were designed using ferrocene. [ 51 ] Because of the high electrostatic repulsion metal cation (taken up by the receptor), the oxidation of ferrocene (Fc to Fc + ) becomes difficult while this becomes more easier with anion uptake since it has negative charge to stabilize the system by attractive interactions, hence shifts the redox potential of Fc cathodically i.e., towards less positive direction. Thus, different redox properties of Fc help to do the selective binding of ions. [ 46 ] Further, biindeno[2,1-b]thiophenylidene on oxidation converts from the neutral to charged form which leads to the increase in the conductivity of the molecule and hence, they are used as actuators or dopants to modify the surface properties of polymers or nanomaterials . [ 47 ]
In 2024, Prof. Ben Feringa and his group reported a helicene featuring an indenofluorene-bridged bisthioxanthylidene as a novel switch that undergoes a two-electron redox process allowing it to modulate its (anti)aromatic character reversibly. [ 52 ]
In thermal molecular switches, conformational or structural change is induced by the temperature . [ 53 ] The mechanism responsible for thermochromic behavior is the gain of planarity in overcrowded alkenes, keto-enol tautomerization , a change in the crystalline structure (mainly found in inorganic materials such as change of octahedral crystal structure to tetrahedral), [ 54 ] the formation of free radicals , and ring-opening reactions . [ 55 ] Some molecules show reversible color change when they are heated or cooled respectively. Examples of thermochromic organic molecules include crowded ethenes (e.g., bianthrone and dixanthylene), schiff bases , and spiro compounds.
In 1999, the first example of thermochromic dye was published, in which 2,6-diphenyl-4-(2,4,6-triphenylpyridinio)phenolate (DTPP) and an indicator dye, Cresol Red embedded in a polymer gel network, are shown to exhibit an outstanding thermochromism. [ 56 ] The contrasting thermal response of RNA and DNA at variable temperatures is an interesting phenomenon. Tashiro et al. (2005) made a biomolecular device using this property of DNA and RNA. [ 57 ] They attached a fluorophore ( 2-aminopurene ) to both DNA and RNA strands. The fluorescence signal of the fluorophore was turned "on" to "off" as the temperature changed from low to high for the DNA device and vice versa for the RNA device. Hence, successfully made reversible, thermoresponsive RNA- and DNA-based devices.
In 2011, Feng et al. reported a temperature-sensitive fluorescent triarylboron thermometer that shows high quantum yield and color change at a wide variety of temperatures. [ 58 ] Leuco dye (LD)-based thermochromic (TC) materials have been widely applied in energy storage, sensors, and optical memory storage. [ 59 ] A recent report in 2022 by Fei et al. demonstrated a four-input signal based optically controlled thermochromic switch. Azobenzene derivatives were used to lock the color developer and leuco dye at the required temperature. [ 60 ]
The first photochemical synthesis of crown ether via photochemical anthracene dimerization is described in 1978 by Desvergne & Bouas-Laurent. [ 61 ] [ 62 ] Although not strictly speaking switchable, the compound is able to take up cations after a photochemical trigger; reverse was not possible with light. Solvent (acetonitrile) gives back the open form.
Anthracene groups serve as photo-antennae can control the conformations of crown ethers, which in turn control their chemical reactivity. [ 63 ] Upon absorption of light, they cab trigger trans-cis isomerization of the azo group, which resulted in ring expansion. Thus, in the trans orm the crown binds preferentially to ammonium , lithium , and sodium ions, while in the cis form the preference is for potassium and rubidium (both larger ions in the same alkali metal group). In the dark, the reverse isomerization takes place. This device concept mimics the biochemical action of monensin and nigericin : in a biphasic system, ions are taken up, triggered by light in one phase and deposited in the other phase in the absence of light. [ 64 ]
Apart from the solution phase modulation of interactions among host and guest molecules, solid phase interactions for their practical applications in functional devices have also been explored. Host materials embedded on nanomaterials showed better surface activity and sensing capabilities, enabling applications in nanotechnology, biology, environmental, and energy technologies. [ 65 ]
Some of the most advanced molecular switches are based on mechanically-interlocked molecular architectures where the bistable states differ in the position of the macrocycle. [ 66 ] These systems enable dynamic and reversible switching between different states in response to external stimuli like light, pH, redox processes, or mechanical force because they are made up of several molecular components that are spatially entangled but not covalently bound. Also, they provide better stability to the system by interlocking the guest molecules at the specific site, as compared to free unprotected guest in host guest molecular switches.
In 1991, Stoddart [ 67 ] devised a molecular shuttle based on a rotaxane on which a molecular bead was able to shuttle between two docking stations situated on a molecular thread . Stoddart predicted that when the stations are dissimilar with each of the stations addressed by a different external stimulus the shuttle becomes a molecular machine. In 1993, Stoddart was scooped by supramolecular chemistry pioneer Fritz Vögtle who actually delivered a switchable molecule based not on a rotaxane but on a related catenane . [ 68 ] [ 69 ]
This compound is based on two ring systems: one ring holds the photoswichable azobenzene ring and two paraquat docking stations and the other ring is a polyether with to arene rings with binding affinity for the paraquat units. In this system NMR spectroscopy shows that in the azo trans-form the polyether ring is free to rotate around its partner ring but then when a light trigger activates the cis azo form this rotation mode is stopped.
Molecular shuttles were utilized in an experimental DRAM circuit . [ 70 ] The device consists of 400 bottom silicon nanowire electrodes (16 nanometer (nm) wide at 33 nm intervals) crossed by another 400 titanium top-nanowires with similar dimensions sandwiching a monolayer of a bistable rotaxane depicted below:
The hydrophilic diethylene glycol stopper on the left (gray) is specifically designed to anchor to the silicon wire (made hydrophilic by phosphorus doping) while the hydrophobic tetraarylmethane stopper on the right does the same to the likewise hydrophobic titanium wire. In the ground state of the switch, the paraquat ring is located around a tetrathiafulvalene unit (in red) but it moves to the dioxynaphthyl unit (in green) when the fulvalene unit is oxidized by application of a current. When the fulvalene is reduced back a metastable high conductance '1' state is formed which relaxes back to the ground state with a chemical half-life of around one hour. The problem of defects is circumvented by adopting a defect-tolerant architecture also found in the Teramac project. In this way a circuit is obtained consisting of 160,000 bits on an area the size of a white blood cell translating into 10 11 bits per square centimeter. | https://en.wikipedia.org/wiki/Molecular_switch |
Molecular tagging velocimetry ( MTV ) is a specific form of flow velocimetry , a technique for determining the velocity of currents in fluids such as air and water. [ 1 ] In its simplest form, a single "write" laser beam is shot once through the sample space. Along its path an optically induced chemical process is initiated, resulting in the creation of a new chemical species or in changing the internal energy state of an existing one, so that the molecules struck by the laser beam can be distinguished from the rest of the fluid. Such molecules are said to be "tagged".
This line of tagged molecules is now transported by the fluid flow. To obtain velocity information, images at two instances in time are obtained and analyzed (often by correlation of the image intensities) to determine the displacement. If the flow is three-dimensional or turbulent the line will not only be displaced, it will also be deformed.
There are three optical ways via which these tagged molecules can be visualized: fluorescence , phosphorescence and laser-induced fluorescence (LIF). In all three cases molecules relax to a lower state and their excess energy is released as photons . In fluorescence this energy decay occurs rapidly (within 10 − 7 {\displaystyle 10^{-7}} s to 10 − 9 {\displaystyle 10^{-9}} s at atmospheric pressure ), thus making "direct" fluorescence impractical for tagging. In phosphorescence the decay is slower, because the transition is quantum-mechanically forbidden .
In some "writing" schemes, the tagged molecule ends up in an excited state . If the molecule relaxes through phosphorescence, lasting long enough to see line displacement, this can be used to track the written line and no additional visualisation step is needed. If during tagging the molecule did not reach a phosphorescing state, or relaxed before the molecule was "read", a second step is needed. The tagged molecule is then excited using a second laser beam, employing a wavelength such that it specifically excites the tagged molecule. The molecule will fluoresce and this fluorescence is captured by means of a camera. This manner of visualisation is called laser induced fluorescence (LIF).
Optical techniques are frequently used in modern fluid velocimetry but most are opto-mechanical in nature. Opto-mechanical techniques do not rely on photonics alone for flow measurements but require macro-size seeding. The best known and often used examples are particle image velocimetry (PIV) and laser Doppler velocimetry (LDV). Within the field of all-optical techniques we can distinguish analogous techniques but using molecular tracers. In Doppler schemes, light quasi-elastically scatters off molecules and the velocity of the molecules convey a Doppler shift to the frequency of the scattered light . In molecular tagging techniques, like in PIV, velocimetry is based on visualizing the tracer displacements.
MTV techniques have proven to allow measurements of velocities in inhospitable environments, like jet engines , flames, high-pressure vessels, where it is difficult for techniques like Pitot , hot-wire velocimetry and PIV to work. The field of MTV is fairly young; the first demonstration of implementation emerged within the 1980s and the number of schemes developed and investigated for use in air is still fairly small. These schemes differ in the molecule that is created, whether seeding the flow with foreign molecules is necessary and what wavelength of light is being used.
The most thorough fluid mechanics studies in gas have been performed using the RELIEF scheme and the APART scheme. Both techniques can be used in ambient air without the need for additional seeding.
In RELIEF, excited oxygen is used as a tracer. The method takes advantage of quantum mechanical properties that prohibit relaxation of the molecule so that the excited oxygen has a relatively long lifetime.
APART is based on the "photosynthesis" of nitric oxide . Since NO is a stable molecule, patterns written with it can, in principle, be followed almost indefinitely.
Another well-developed and widely documented technique that yields extremely high accuracy is hydroxyl tagging velocimetry (HTV). It is based on photo-dissociation of water vapor followed by visualization of the resulting OH radical using LIF. HTV has been successfully demonstrated in many test conditions ranging from room air temperature flows to Mach 2 flows within a cavity.
In liquids, three MTV approaches have been classified: [ 2 ] MTV by direct phosphorescence (using a phosphorescent dye), absorbance (using a photochromic dye), and photoproduct fluorescence (typically using a caged dye ).
MTV based on direct phosphorescence is the easiest technique to implement because a single laser is needed to produce a luminescent excited molecular state. [ 3 ] The phosphorescence signal is generally weaker and harder to detect than fluorescence .
The second technique called MTV by absorbance relies on the reversible alteration of the fluorescence properties of a photochromic dye. The scheme showed good results in alcohol [ 4 ] and oils, [ 5 ] [ 6 ] but not in water in which typical dyes are not soluble.
The third variant of MTV was first deployed in liquids in 1995 [ 7 ] under the name "photoactivated nonintrusive tracking of molecular motion" (PHANTOMM). The PHANTOMM technique initially relied on a fluorescein-based caged dye excited by a blue laser. More recently, a rhodamine-based caged dye was successfully used with pulsed UV and green lasers. [ 8 ] | https://en.wikipedia.org/wiki/Molecular_tagging_velocimetry |
In molecular physics , the molecular term symbol is a shorthand expression of the group representation and angular momenta that characterize the state of a molecule , i.e. its electronic quantum state which is an eigenstate of the electronic molecular Hamiltonian . It is the equivalent of the term symbol for the atomic case. However, the following presentation is restricted to the case of homonuclear diatomic molecules, or other symmetric molecules with an inversion centre. For heteronuclear diatomic molecules, the u/g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian . In the case of less symmetric molecules the molecular term symbol contains the symbol of the group representation to which the molecular electronic state belongs.
It has the general form:
2 S + 1 Λ Ω , ( g / u ) ( + / − ) {\displaystyle {}^{2S+1}\!\Lambda _{\Omega ,(g/u)}^{(+/-)}}
where
For atoms, we use S , L , J and M J to characterize a given state . In linear molecules, however, the lack of spherical symmetry destroys the relationship [ L ^ 2 , H ^ ] = 0 {\displaystyle [{\hat {\mathbf {L} }}^{2},{\hat {H}}]=0} , so L ceases to be a good quantum number . A new set of operators have to be used instead: { S ^ 2 , S ^ z , L ^ z , J ^ z = S ^ z + L ^ z } {\displaystyle \{{\hat {\mathbf {S} }}^{2},{\hat {\mathbf {S} }}_{z},{\hat {\mathbf {L} }}_{z},{\hat {\mathbf {J} }}_{z}={\hat {\mathbf {S} }}_{z}+{\hat {\mathbf {L} }}_{z}\}} , where the z -axis is defined along the internuclear axis of the molecule. Since these operators commute with each other and with the Hamiltonian on the limit of negligible spin-orbit coupling, their eigenvalues may be used to describe a molecule state through the quantum numbers S , M S , M L and M J .
The cylindrical symmetry of a linear molecule ensures that positive and negative values of a given m ℓ {\displaystyle m_{\ell }} for an electron in a molecular orbital will be degenerate in the absence of spin-orbit coupling. Different molecular orbitals are classified with a new quantum number, λ, defined as
Following the spectroscopic notation pattern, molecular orbitals are designated by a lower case Greek letter: for λ = 0, 1, 2, 3,... orbitals are called σ, π, δ, φ... respectively, analogous to the Latin letters s, p, d, f used for atomic orbitals.
Now, the total z -projection of L can be defined as
As states with positive and negative values of M L are degenerate, we define
and a capital Greek letter is used to refer to each value: Λ = 0, 1, 2, 3... are coded as Σ, Π, Δ, Φ... respectively (analogous to S, P, D, F for atomic states).
The molecular term symbol is then defined as
and the number of electron degenerate states (under the absence of spin-orbit coupling) corresponding to this term symbol is given by:
Spin–orbit coupling lifts the degeneracy of the electronic states. This is because the z -component of spin interacts with the z -component of the orbital angular momentum, generating a total electronic angular momentum along the molecule axis J z . This is characterized by the M J quantum number, where
Again, positive and negative values of M J are degenerate, so the pairs ( M L , M S ) and (− M L , − M S ) are degenerate: {(1, 1/2), (−1, −1/2)}, and {(1, −1/2), (−1, 1/2)} represent two different degenerate states. These pairs are grouped together with the quantum number Ω, which is defined as the sum of the pair of values ( M L , M S ) for which M L is positive. Sometimes the equation
is used (often Σ is used instead of M S ). Note that although this gives correct values for Ω it could be misleading, as obtained values do not correspond to states indicated by a given pair of values ( M L , M S ). For example, a state with (−1, −1/2) would give an Ω value of Ω = |−1| + (−1/2) = 1/2, which is wrong. Choosing the pair of values with M L positive will give a Ω = 3/2 for that state.
With this, a level is given by
Note that Ω can have negative values and subscripts r and i represent regular (normal) and inverted multiplets, respectively. [ 1 ] For a 4 Π term there are four degenerate ( M L , M S ) pairs: {(1, 3/2), (−1, −3/2)}, {(1, 1/2), (−1, −1/2)}, {(1, −1/2), (−1, 1/2)}, {(1, −3/2), (−1, 3/2)}. These correspond to Ω values of 5/2, 3/2, 1/2 and −1/2, respectively.
Approximating the spin–orbit Hamiltonian to first order perturbation theory , the energy level is given by
where A is the spin–orbit constant. For 4 Π the Ω values 5/2, 3/2, 1/2 and −1/2 correspond to energies of 3 A /2, A /2, − A /2 and −3 A /2. Despite having the same magnitude of Ω, the levels Ω = ±1/2 have different energies and so are not degenerate. States with different energies are assigned different Ω values. For states with positive values of A (which are said to be regular ), increasing values of Ω correspond to increasing values of energies; on the other hand, with A negative (said to be inverted ) the energy order is reversed. Including higher-order effects can lead to a spin-orbital levels or energy that do not even follow the increasing value of Ω.
When Λ = 0 there is no spin–orbit splitting to first order in perturbation theory, as the associated energy is zero. So for a given S , all of its M S values are degenerate. This degeneracy is lifted when spin–orbit interaction is treated to higher order in perturbation theory, but still states with same | M S | are degenerate in a non-rotating molecule. We can speak of a 5 Σ 2 substate, a 5 Σ 1 substate or a 5 Σ 0 substate. Except for the case Ω = 0, these substates have a degeneracy of 2.
There are an infinite number of planes containing the internuclear axis and hence there are an infinite number of possible reflections. For any of these planes, molecular terms with Λ > 0 always have a state which is symmetric with respect to this reflection and one state that is antisymmetric. Rather than labelling those situations as, e.g., 2 Π ± , the ± is omitted.
For the Σ states, however, this two-fold degeneracy disappears, and all Σ states are either symmetric under any plane containing the internuclear axis, or antisymmetric. These two situations are labeled as Σ + or Σ − .
Taking the molecular center of mass as origin of coordinates, consider the change of all electrons' position from ( x i , y i , z i ) to (− x i , − y i , − z i ). If the resulting wave function is unchanged, it is said to be gerade (German for even) or have even parity ; if the wave function changes sign then it is said to be ungerade (odd) or have odd parity. For a molecule with a center of inversion, all orbitals will be symmetric or antisymmetric. [ 2 ] The resulting wavefunction for the whole multielectron system will be gerade if an even number of electrons are in ungerade orbitals, and ungerade if there are an odd number of electrons in ungerade orbitals, regardless of the number of electrons in gerade orbitals.
An alternative method for determining the symmetry of an MO is to rotate the orbital about the axis joining the two nuclei and then rotate the orbital about a line perpendicular to the axis. If the sign of the lobes remains the same, the orbital is gerade , and if the sign changes, the orbital is ungerade . [ 3 ]
In 1928 Eugene Wigner and E.E. Witmer proposed rules to determine the possible term symbols for diatomic molecular states formed by the combination of a pair of atomic states with given atomic term symbols . [ 4 ] [ 5 ] [ 6 ] For example, two like atoms in identical 3 S states can form a diatomic molecule in 1 Σ g + , 3 Σ u + , or 5 Σ g + states. For one like atom in a 1 S g state and one in a 1 P u state, the possible diatomic states are 1 Σ g + , 1 Σ u + , 1 Π g and 1 Π u . [ 5 ] The parity of an atomic term is g if the sum of the individual angular momentum is even, and u if the sum is odd.
Electronic states are also often identified by an empirical single-letter label. The ground state is labelled X, excited states of the same multiplicity (i.e., having the same spin quantum number) are labelled in ascending order of energy with capital letters A, B, C...; excited states having different multiplicity than the ground state are labelled with lower-case letters a, b, c...
In polyatomic molecules (but not in diatomic) it is customary to add a tilde (e.g. X ~ {\displaystyle {\tilde {X}}} , a ~ {\displaystyle {\tilde {a}}} ) to these empirical labels to prevent possible confusion with symmetry labels based on group representations. | https://en.wikipedia.org/wiki/Molecular_term_symbol |
Molecular tweezers , and molecular clips , are host molecules with open cavities capable of binding guest molecules. [ 3 ] The open cavity of the molecular tweezers may bind guests using non-covalent bonding, which includes hydrogen bonding , metal coordination , hydrophobic forces , van der Waals forces , π–π interactions , and/or electrostatic effects. These complexes are a subset of macrocyclic molecular receptors and their structure is that the two "arms" that bind the guest molecule between them are only connected at one end leading to a certain flexibility of these receptor molecules (induced fit model).
The term "molecular tweezers" was first used by Whitlock. [ 4 ] The class of hosts was developed and popularized by Zimmerman in the mid-1980s to early 1990s [ 5 ] [ 6 ] [ 7 ] and later by Klärner. [ 8 ]
Some molecular tweezers bind aromatic guests. [ 1 ] These molecular tweezers consist of a pair of anthracene arms held at a distance that allows aromatic guests to gain π–π interactions from both (see Figure). Other molecular tweezers feature a pair of tethered porphyrins . [ 9 ]
Yet another type of molecular tweezers binds fullerenes . [ 2 ] These " buckycatchers " are composed of two corannulene pincers that complement the surface of the convex fullerene guest (Figure 2). An association constant ( K a ) of 8,600 M −1 was calculated using 1 H NMR spectroscopy .
Stoermer and co-workers described clefts capable of capturing cyclohexane or chloroform molecules. Intriguingly, pi interactions played key roles in guest capture as well as cleft formation rate. [ 10 ]
Water-soluble phosphate-substituted molecular tweezers made of alternating phenyl and norbornenyl substituents bind to positively charged aliphatic side chains of basic amino acids, such as lysine and arginine (Figure 3). [ 11 ] [ 12 ] Similar compounds called "molecular clips", whose side walls are flat rather than convex, prefer to enclose flat pyridinium rings (for example the nicotinamide ring of NAD(P)+) between their plane naphthalene sidewalls (Figure 4). [ 13 ] These mutually exclusive binding modes make these compounds valuable tools for probing critical biological interactions of basic amino acid side chains in peptides and proteins as well as of NAD(P) + and similar cofactors. For example, both types of compounds inhibit the oxidation reactions of ethanol by alcohol dehydrogenase or of glucose-6-phosphate by glucose-6-phosphate dehydrogenase , [ 14 ] respectively.
The molecular tweezers, but not the clips, efficiently inhibit the formation of toxic oligomers and aggregates by amyloidogenic proteins associated with different diseases. Examples include the proteins involved in Alzheimer's disease – amyloid β-protein (Aβ) and tau; [ 15 ] [ 16 ] [ 17 ] α-synuclein, which is thought to cause Parkinson's disease and other synucleinopathies [ 18 ] [ 19 ] [ 20 ] [ 21 ] and is involved in spinal-cord injury ; [ 22 ] mutant huntingtin, which causes Huntington's disease; [ 23 ] islet amyloid polypeptide (amylin), which kills pancreatic β-cells in type-2 diabetes ; [ 24 ] transthyretin (TTR), which causes familial amyloid polyneuropathy, familial amyloid cardiomyopathy, and senile systemic amyloidosis; [ 25 ] aggregation-prone mutants of the tumor-suppressor protein p53 ; [ 26 ] and semen proteins whose aggregation enhances HIV infection. [ 27 ] Importantly, the molecular tweezers have been found to be effective and safe not only in the test tube but also in animal models of different diseases, [ 28 ] [ 29 ] suggesting that they may be developed as drugs against diseases caused by abnormal protein aggregation, all of which currently have no cure. They were also shown to destroy the membranes of enveloped viruses, such as HIV, herpes, and hepatitis C, [ 27 ] which makes them good candidates for development of microbicides.
The above examples show the potential reactivity and specificity of these molecules. The binding cavity between the side arms of the tweezer can evolve to bind to an appropriate guest with high specificity, depending on the configuration of the tweezer. That makes this overall class of macromolecule truly synthetic molecular receptors with important application to biology and medicine. [ 30 ] [ 31 ] [ 32 ] | https://en.wikipedia.org/wiki/Molecular_tweezers |
Molecular vapor deposition is the gas-phase reaction between surface reactive chemicals and an appropriately receptive surface. [ 1 ] [ 2 ]
Often bi-functional silanes are used in which one termination of the molecule is reactive. For example, a functional chlorosilane (R-Si-Cl 3 ) can react with surface hydroxyl groups (-OH) resulting a radicalized (R) deposition on the surface.
The advantage of a gas phase reaction over a comparable liquid phase process is the control of moisture from the ambient environment, which often results in cross polymerization of the silane leading to particulates on the treated surface. Often a heated sub-atmospheric vacuum chamber [ 3 ] is used to allow precise control of the reactants and water content. Additionally the gas phase process allows for easy treatment of complex parts since the coverage of the reactant is generally diffusion limited. Microelectromechanical Systems ( MEMS ) sensors often use molecular vapor deposition as a technique to address stiction and other parasitic issues relative to surface-to-surface interactions.
This nanotechnology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_vapor_deposition |
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
For a diatomic molecule A−B, the vibrational frequency in s −1 is given by ν = 1 2 π k / μ {\textstyle \nu ={\frac {1}{2\pi }}{\sqrt {k/\mu }}} , where k is the force constant in dyne/cm or erg/cm 2 and μ is the reduced mass given by 1 μ = 1 m A + 1 m B {\textstyle {\frac {1}{\mu }}={\frac {1}{m_{A}}}+{\frac {1}{m_{B}}}} . The vibrational wavenumber in cm −1 is ν ~ = 1 2 π c k / μ , {\textstyle {\tilde {\nu }}\;={\frac {1}{2\pi c}}{\sqrt {k/\mu }},} where c is the speed of light in cm/s.
Vibrations of polyatomic molecules are described in terms of normal modes , which are independent of each other, but each normal mode involves simultaneous vibrations of different parts of the molecule. In general, a non-linear molecule with N atoms has 3 N − 6 normal modes of vibration , but a linear molecule has 3 N − 5 modes, because rotation about the molecular axis cannot be observed. [ 1 ] A diatomic molecule has one normal mode of vibration, since it can only stretch or compress the single bond.
A molecular vibration is excited when the molecule absorbs energy, Δ E , corresponding to the vibration's frequency, ν , according to the relation Δ E = hν , where h is the Planck constant . A fundamental vibration is evoked when one such quantum of energy is absorbed by the molecule in its ground state . When multiple quanta are absorbed, the first and possibly higher overtones are excited.
To a first approximation, the motion in a normal vibration can be described as a kind of simple harmonic motion . In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first overtone has twice the frequency of the fundamental. In reality, vibrations are anharmonic and the first overtone has a frequency that is slightly lower than twice that of the fundamental. Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule, because the potential energy of the molecule is more like a Morse potential or more accurately, a Morse/Long-range potential .
The vibrational states of a molecule can be probed in a variety of ways. The most direct way is through infrared spectroscopy , as vibrational transitions typically require an amount of energy that corresponds to the infrared region of the spectrum. Raman spectroscopy , which typically uses visible light, can also be used to measure vibration frequencies directly. The two techniques are complementary and comparison between the two can provide useful structural information such as in the case of the rule of mutual exclusion for centrosymmetric molecules .
Vibrational excitation can occur in conjunction with electronic excitation in the ultraviolet-visible region. The combined excitation is known as a vibronic transition , giving vibrational fine structure to electronic transitions , particularly for molecules in the gas state .
Simultaneous excitation of a vibration and rotations gives rise to vibration–rotation spectra.
For a molecule with N atoms, the positions of all N nuclei depend on a total of 3 N coordinates , so that the molecule has 3 N degrees of freedom including translation , rotation and vibration. Translation corresponds to movement of the center of mass whose position can be described by 3 cartesian coordinates .
A nonlinear molecule can rotate about any of three mutually perpendicular axes and therefore has 3 rotational degrees of freedom. For a linear molecule , rotation about the molecular axis does not involve movement of any atomic nucleus, so there are only 2 rotational degrees of freedom which can vary the atomic coordinates. [ 2 ] [ 3 ]
An equivalent argument is that the rotation of a linear molecule changes the direction of the molecular axis in space, which can be described by 2 coordinates corresponding to latitude and longitude. For a nonlinear molecule, the direction of one axis is described by these two coordinates, and the orientation of the molecule about this axis provides a third rotational coordinate. [ 4 ]
The number of vibrational modes is therefore 3 N minus the number of translational and rotational degrees of freedom, or 3 N − 5 for linear and 3 N − 6 for nonlinear molecules. [ 2 ] [ 3 ] [ 4 ]
The coordinate of a normal vibration is a combination of changes in the positions of atoms in the molecule. When the vibration is excited the coordinate changes sinusoidally with a frequency ν , the frequency of the vibration.
Internal coordinates are of the following types, illustrated with reference to the planar molecule ethylene ,
In a rocking, wagging or twisting coordinate the bond lengths within the groups involved do not change. The angles do. Rocking is distinguished from wagging by the fact that the atoms in the group stay in the same plane.
In ethylene there are 12 internal coordinates: 4 C–H stretching, 1 C–C stretching, 2 H–C–H bending, 2 CH 2 rocking, 2 CH 2 wagging, 1 twisting. Note that the H–C–C angles cannot be used as internal coordinates as well as the H–C–H angle because the angles at each carbon atom cannot all increase at the same time.
Note that these coordinates do not correspond to normal modes (see § Normal coordinates ). In other words, they do not correspond to particular frequencies or vibrational transitions.
Within the CH 2 group, commonly found in organic compounds , the two low mass hydrogens can vibrate in six different ways which can be grouped as 3 pairs of modes: 1. symmetric and asymmetric stretching , 2. scissoring and rocking , 3. wagging and twisting . These are shown here:
(These figures do not represent the " recoil " of the C atoms, which, though necessarily present to balance the overall movements of the molecule, are much smaller than the movements of the lighter H atoms).
Symmetry–adapted coordinates may be created by applying a projection operator to a set of internal coordinates. [ 5 ] The projection operator is constructed with the aid of the character table of the molecular point group . For example, the four (un-normalized) C–H stretching coordinates of the molecule ethene are given by Q s 1 = q 1 + q 2 + q 3 + q 4 Q s 2 = q 1 + q 2 − q 3 − q 4 Q s 3 = q 1 − q 2 + q 3 − q 4 Q s 4 = q 1 − q 2 − q 3 + q 4 {\displaystyle {\begin{aligned}Q_{s1}&=q_{1}+q_{2}+q_{3}+q_{4}\\Q_{s2}&=q_{1}+q_{2}-q_{3}-q_{4}\\Q_{s3}&=q_{1}-q_{2}+q_{3}-q_{4}\\Q_{s4}&=q_{1}-q_{2}-q_{3}+q_{4}\end{aligned}}} where q 1 − q 4 {\displaystyle q_{1}-q_{4}} are the internal coordinates for stretching of each of the four C–H bonds.
Illustrations of symmetry–adapted coordinates for most small molecules can be found in Nakamoto. [ 6 ]
The normal coordinates, denoted as Q , refer to the positions of atoms away from their equilibrium positions, with respect to a normal mode of vibration. Each normal mode is assigned a single normal coordinate, and so the normal coordinate refers to the "progress" along that normal mode at any given time. Formally, normal modes are determined by solving a secular determinant, and then the normal coordinates (over the normal modes) can be expressed as a summation over the cartesian coordinates (over the atom positions). The normal modes diagonalize the matrix governing the molecular vibrations, so that each normal mode is an independent molecular vibration. If the molecule possesses symmetries, the normal modes "transform as" an irreducible representation under its point group . The normal modes are determined by applying group theory, and projecting the irreducible representation onto the cartesian coordinates. For example, when this treatment is applied to CO 2 , it is found that the C=O stretches are not independent, but rather there is an O=C=O symmetric stretch and an O=C=O asymmetric stretch:
When two or more normal coordinates belong to the same irreducible representation of the molecular point group (colloquially, have the same symmetry) there is "mixing" and the coefficients of the combination cannot be determined a priori . For example, in the linear molecule hydrogen cyanide , HCN, The two stretching vibrations are
The coefficients a and b are found by performing a full normal coordinate analysis by means of the Wilson GF method . [ 7 ]
Perhaps surprisingly, molecular vibrations can be treated using Newtonian mechanics to calculate the correct vibration frequencies. The basic assumption is that each vibration can be treated as though it corresponds to a spring. In the harmonic approximation the spring obeys Hooke's law : the force required to extend the spring is proportional to the extension. The proportionality constant is known as a force constant, k . The anharmonic oscillator is considered elsewhere. [ 8 ] F = − k Q {\displaystyle \mathrm {F} =-kQ} By Newton's second law of motion this force is also equal to a reduced mass , μ , times acceleration. F = μ d 2 Q d t 2 {\displaystyle \mathrm {F} =\mu {\frac {d^{2}Q}{dt^{2}}}} Since this is one and the same force the ordinary differential equation follows. μ d 2 Q d t 2 + k Q = 0 {\displaystyle \mu {\frac {d^{2}Q}{dt^{2}}}+kQ=0} The solution to this equation of simple harmonic motion is Q ( t ) = A cos ( 2 π ν t ) ; ν = 1 2 π k μ . {\displaystyle Q(t)=A\cos(2\pi \nu t);\ \ \nu ={1 \over {2\pi }}{\sqrt {k \over \mu }}.} A is the maximum amplitude of the vibration coordinate Q . It remains to define the reduced mass, μ . In general, the reduced mass of a diatomic molecule, AB, is expressed in terms of the atomic masses, m A and m B , as 1 μ = 1 m A + 1 m B . {\displaystyle {\frac {1}{\mu }}={\frac {1}{m_{A}}}+{\frac {1}{m_{B}}}.} The use of the reduced mass ensures that the centre of mass of the molecule is not affected by the vibration. In the harmonic approximation the potential energy of the molecule is a quadratic function of the normal coordinate. It follows that the force-constant is equal to the second derivative of the potential energy. k = ∂ 2 V ∂ Q 2 {\displaystyle k={\frac {\partial ^{2}V}{\partial Q^{2}}}}
When two or more normal vibrations have the same symmetry a full normal coordinate analysis must be performed (see GF method ). The vibration frequencies, ν i , are obtained from the eigenvalues , λ i , of the matrix product GF . G is a matrix of numbers derived from the masses of the atoms and the geometry of the molecule. [ 7 ] F is a matrix derived from force-constant values. Details concerning the determination of the eigenvalues can be found in. [ 9 ]
In the harmonic approximation the potential energy is a quadratic function of the normal coordinates. Solving the Schrödinger wave equation , the energy states for each normal coordinate are given by E n = h ( n + 1 2 ) ν = h ( n + 1 2 ) 1 2 π k m , {\displaystyle E_{n}=h\left(n+{1 \over 2}\right)\nu =h\left(n+{1 \over 2}\right){1 \over {2\pi }}{\sqrt {k \over m}},} where n is a quantum number that can take values of 0, 1, 2, ... In molecular spectroscopy where several types of molecular energy are studied and several quantum numbers are used, this vibrational quantum number is often designated as v . [ 10 ] [ 11 ]
The difference in energy when n (or v ) changes by 1 is therefore equal to h ν {\displaystyle h\nu } , the product of the Planck constant and the vibration frequency derived using classical mechanics. For a transition from level n to level n+1 due to absorption of a photon, the frequency of the photon is equal to the classical vibration frequency ν {\displaystyle \nu } (in the harmonic oscillator approximation).
See quantum harmonic oscillator for graphs of the first 5 wave functions, which allow certain selection rules to be formulated. For example, for a harmonic oscillator transitions are allowed only when the quantum number n changes by one, Δ n = ± 1 {\displaystyle \Delta n=\pm 1} but this does not apply to an anharmonic oscillator; the observation of overtones is only possible because vibrations are anharmonic . Another consequence of anharmonicity is that transitions such as between states n = 2 and n = 1 have slightly less energy than transitions between the ground state and first excited state. Such a transition gives rise to a hot band . To describe vibrational levels of an anharmonic oscillator, Dunham expansion is used.
When it comes to polyatomic molecules , it is common to solve the Schrödinger Equation using Watson's nuclear motion Hamiltonian . Similar as for diatomics, this can be done within the harmonic approximation as stated above. For the anharmonic calculation of vibrational spectra of polyatomic molecules, more sophisticated approaches are used. [ 12 ] Prominent examples in computational chemistry are 2nd order vibrational perturbation theory (VPT2) or vibrational configuration interaction theory (VCI) . [ 13 ]
In an infrared spectrum the intensity of an absorption band is proportional to the derivative of the molecular dipole moment with respect to the normal coordinate. [ 14 ] Likewise, the intensity of Raman bands depends on the derivative of polarizability with respect to the normal coordinate. There is also a dependence on the fourth-power of the wavelength of the laser used. | https://en.wikipedia.org/wiki/Molecular_vibration |
In ultrafiltration , the molecular weight cut-off or MWCO of a membrane refers to the lowest molecular weight of the solute (in daltons ) for which 90% of the solute is retained by (prevented from passing through) the membrane, [ 1 ] or the molecular weight of the molecule (e.g. globular protein ) that is 90% retained by the membrane.
This definition is not however standardized, and MWCOs can also be defined as the molecular weight at which 80% of the analytes (or solutes) are prohibited from membrane diffusion .
Commercially available microdialysis probes typically have molecular weight cutoffs that range from 1,000 to 300,000 Da, and larger thresholds of filtration are measured in μm . Microdialysis may also be used to separate nanoparticles from the solutions in which they were formed. In such a separation, the eluate will consist of non-complexed reactants and components.
Ultrafiltration membrane manufacturers commonly produce and offer MWCO's of 2k, 5k, 10k, 30k, 50k, 100k, and 1,000k. Devices offered range from laboratory focused centrifugal devices (100ul to 100ml) to laboratory and bioprocessing relevant tangential flow filtration (TFF) devices (50ml to hundreds of litres).
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molecular_weight_cut-off |
Molecular wires (or sometimes called molecular nanowires) are molecular chains that conduct electric current. They are the proposed building blocks for molecular
electronic devices. Their typical diameters are less than three nanometers, while their lengths may be macroscopic, extending to centimeters or more.
Most types of molecular wires are derived from organic molecules. One naturally occurring molecular wire is DNA . Prominent inorganic examples include polymeric materials such as Li 2 Mo 6 Se 6 [ 1 ] and Mo 6 S 9−x I x , [ 2 ] [ 3 ] [ 4 ] [Pd 4 (CO) 4 (OAc) 4 Pd(acac) 2 ], [ 5 ] and single-molecule extended metal atom chains (EMACs) which comprise strings of transition metal atoms directly bonded to each other. [ 6 ] Molecular wires containing paramagnetic inorganic moieties can exhibit Kondo peaks .
Molecular wires conduct electricity. They typically have non-linear current-voltage characteristics, and do not behave as simple ohmic conductors. The conductance follows typical power law behavior as a function of temperature or electric field, whichever is the greater, arising from their strong one-dimensional character. Numerous theoretical ideas have been used in an attempt to understand the conductivity of one-dimensional systems, where strong interactions between electrons lead to departures from normal metallic ( Fermi liquid ) behavior. Important concepts are those introduced by Tomonaga , Luttinger and Wigner . Effects caused by classical Coulomb repulsion (called Coulomb blockade ), interactions with vibrational degrees of freedom (called phonons ) and Quantum Decoherence [ 7 ] have also been found to be important in determining the properties of molecular wires.
Methods have been developed for the synthesis of diverse types of molecular wires (e.g. organic molecular wires and inorganic molecular wires). [ 8 ] The basic principle is to assemble repeating modules. Organic molecular wires are usually synthesized via transition metal -mediated cross-coupling reactions.
Organic molecular wires usually consist aromatic rings connected by ethylene group or acetylene groups. Transition metal-mediated cross-coupling reactions are used to connect simple building blocks together in a convergent fashion to build organic molecular wires. For example, a simple oligo (phenylene ethylnylene) type molecular wire (B) was synthesized starting from readily available 1-bromo-4-iodobenzene (A). [ 9 ] The final product was obtained through several steps of Sonogashira coupling reactions.
Other organic molecular wires include carbon nanotubes and DNA . Carbon nanotubes can be synthesized via various nano-technological approaches. DNA can be prepared by either step-wise DNA synthesis on solid-phase or by DNA-polymerase-catalyzed replication inside cells.
It was recently shown that pyridine and pyridine-derived polymers can form electronically conductive polyazaacetylene chains under simple ultraviolet irradiation, and that the common observation of "browning" of aged pyridine samples is due in part to the formation of molecular wires. The gels exhibited a transition between ionic conductivity and electronic conductivity on irradiation. [ 10 ]
One class of inorganic molecular wires consist of subunits related to Chevrel clusters . The synthesis of Mo 6 S 9−x I x was performed in sealed and vacuumed quartz ampoule at 1343 K. In Mo 6 S 9−x I x , the repeat units are Mo 6 S 9−x I x clusters, which are joined together by flexible sulfur or iodine bridges. [ 11 ]
Chains can also be produced from metallo-organic precursors. [ 12 ]
To be of use for connecting molecules, MWs need to self-assemble following well-defined routes and form reliable electrical contacts between them. To reproducibly self-assemble a complex circuit based on single molecules. Ideally, they would connect to diverse materials, such as gold metal surfaces (for connections to outside world), biomolecules (for nanosensors, nanoelectrodes, molecular switches) and most importantly, they must allow branching. The connectors should also be available of pre-determined diameter and length. They should also have covalent bonding to ensure reproducible transport and contact properties.
DNA-like molecules have specific molecular-scale recognition and can be used in molecular scaffold fabrication. Complex shapes have been demonstrated, but unfortunately metal coated DNA which is electrically conducting is too thick to connect to individual molecules. Thinner coated DNA lacks electronic connectivity and is unsuited for connecting molecular electronics components.
Some varieties of carbon nanotubes (CNTs) are conducting, and connectivity at their ends can be achieved by attachment of connecting groups. Unfortunately manufacturing CNTs with pre-determined properties is impossible at present, and the functionalized ends are typically not conducting, limiting their usefulness as molecular connectors. Individual CNTs can be soldered in an electron microscope, but the contact is not covalent and cannot be self-assembled.
Possible routes for the construction of larger functional circuits using Mo 6 S 9−x I x MWs have been demonstrated, either via gold nanoparticles as linkers, or by direct connection to thiolated molecules. The two approaches may lead to different possible applications. The use of GNPs offers the possibility of branching and construction of larger circuits.
Molecular wires can be incorporated into polymers , enhancing their mechanical and/or conducting properties. The enhancement of these properties relies on uniform dispersion of the wires into the host polymer. MoSI wires have been made in such composites, relying on their superior solubility within the polymer host compared to other nanowires or nanotubes. Bundles of wires can be used to enhance tribological properties of polymers, with applications in actuators and potentiometers. It has been recently proposed that twisted nanowires could work as electromechanical nanodevices (or torsion nanobalances ) to measure forces and torques at nanoscale with great precision. [ 14 ] | https://en.wikipedia.org/wiki/Molecular_wire |
In chemistry , molecularity is the number of molecules that come together to react in an elementary (single-step) reaction [ 1 ] and is equal to the sum of stoichiometric coefficients of reactants in the elementary reaction with effective collision ( sufficient energy ) and correct orientation. [ 2 ] Depending on how many molecules come together, a reaction can be unimolecular, bimolecular or even trimolecular.
The kinetic order of any elementary reaction or reaction step is equal to its molecularity, and the rate equation of an elementary reaction can therefore be determined by inspection, from the molecularity. [ 1 ]
The kinetic order of a complex (multistep) reaction, however, is not necessarily equal to the number of molecules involved. The concept of molecularity is only useful to describe elementary reactions or steps.
In a unimolecular reaction, a single molecule rearranges atoms, forming different molecules. [ 1 ] This is illustrated by the equation
where P {\displaystyle {\rm {P}}} refers to chemical product(s) . The reaction or reaction step is an isomerization if there is only one product molecule, or a dissociation if there is more than one product molecule.
In either case, the rate of the reaction or step is described by the first order rate law
where [ A ] {\displaystyle [{\rm {A]}}} is the concentration of species A, t {\displaystyle t} is time, and k r {\displaystyle k_{r}} is the reaction rate constant .
As can be deduced from the rate law equation, the number of A molecules that decay is proportional to the number of A molecules available. An example of a unimolecular reaction, is the isomerization of cyclopropane to propene:
Unimolecular reactions can be explained by the Lindemann-Hinshelwood mechanism.
In a bimolecular reaction, two molecules collide and exchange energy, atoms or groups of atoms. [ 1 ]
This can be described by the equation
A + B ⟶ P {\displaystyle {\ce {A + B -> P}}}
which corresponds to the second order rate law: d [ A ] d t = − k r [ A ] [ B ] {\displaystyle {\frac {d[{\ce {A}}]}{dt}}=-k_{r}{\ce {[A][B]}}} .
Here, the rate of the reaction is proportional to the rate at which the reactants come together. An example of a bimolecular
reaction is the S N 2 -type nucleophilic substitution of methyl bromide by hydroxide ion : [ 3 ]
CH 3 Br + OH − ⟶ CH 3 OH + Br − {\displaystyle {\ce {CH3Br + OH^- -> CH3OH + Br^-}}}
A termolecular [ 4 ] [ 5 ] (or trimolecular) [ 6 ] reaction in solutions or gas mixtures involves three reactants simultaneously colliding , with appropriate orientation and sufficient energy. [ 4 ] However the term trimolecular is also used to refer to three body association reactions of the type:
A + B → M C {\displaystyle {\ce {A + B ->[{\ce {M}}] C}}}
Where the M over the arrow denotes that to conserve energy and momentum a second reaction with a third body is required. After the initial bimolecular collision of A and B an energetically excited reaction intermediate is formed, then, it collides with a M body, in a second bimolecular reaction, transferring the excess energy to it. [ 7 ]
The reaction can be explained as two consecutive reactions:
A + B ⟶ AB ∗ {\displaystyle {\ce {A + B -> AB}}^{*}} AB ∗ + M ⟶ C + M {\displaystyle {\ce {AB}}^{*}{\ce {+ M -> C + M}}}
These reactions frequently have a pressure and temperature dependence region of transition between second and third order kinetics. [ 8 ]
Catalytic reactions are often three-component, but in practice a complex of the starting materials is first formed and the rate-determining step is the reaction of this complex into products, not an adventitious collision between the two species and the catalyst. For example, in hydrogenation with a metal catalyst, molecular dihydrogen first dissociates onto the metal surface into hydrogen atoms bound to the surface, and it is these monatomic hydrogens that react with the starting material, also previously adsorbed onto the surface.
Reactions of higher molecularity are not observed due to very small probability of simultaneous interaction between 4 or more molecules. [ 9 ] [ 4 ]
It is important to distinguish molecularity from order of reaction . The order of reaction is an empirical quantity determined by experiment from the rate law of the reaction. It is the sum of the exponents in the rate law equation. [ 10 ] Molecularity, on the other hand, is deduced from the mechanism of an elementary reaction, and is used only in context of an elementary reaction. It is the number of molecules taking part in this reaction.
This difference can be illustrated on the reaction between nitric oxide and hydrogen: [ 11 ]
2 NO + 2 H 2 ⟶ N 2 + 2 H 2 O , {\displaystyle {\ce {2NO + 2H2 -> N2 + 2H2O,}}}
where the observed rate law is v = k [ NO ] 2 [ H 2 ] {\displaystyle v=k{\ce {[NO]^2[H2]}}} , so that the reaction is third order . Since the order does not equal the sum of reactant stoichiometric coefficients, the reaction must involve more than one step. The proposed two-step mechanism [ 11 ] has a rate-limiting first step whose molecularity corresponds to the overall order of 3:
Slow: 2 NO + H 2 ⟶ N 2 + H 2 O 2 {\displaystyle {\ce {2 NO + H2 -> N2 + H2O2}}} Fast: H 2 O 2 + H 2 ⟶ 2 H 2 O {\displaystyle {\ce {H2O2 + H2 -> 2H2O}}}
On the other hand, the molecularity of this reaction is undefined, because it involves a mechanism of more than one step. However, we can consider the molecularity of the individual elementary reactions that make up this mechanism: the first step is trimolecular because it involves three reactant molecules, while the second step is bimolecular because it involves two reactant molecules. | https://en.wikipedia.org/wiki/Molecularity |
A molecularly imprinted polymer (MIP) is a polymer that has been processed using the molecular imprinting technique which leaves cavities in the polymer matrix with an affinity for a chosen "template" molecule. The process usually involves initiating the polymerization of monomers in the presence of a template molecule that is extracted afterwards, leaving behind complementary cavities. These polymers have affinity for the original molecule and have been used in applications such as chemical separations, catalysis, or molecular sensors. Published works on the topic date to the 1930s.
Molecular imprinting is the process of generating an impression within a solid or a gel, the size, shape and charge distribution of which corresponds to a template molecule (typically present during polymerisation). The result is a synthetic receptor capable of binding to a target molecule, which fits into the binding site with high affinity and specificity. The interactions between the polymer and the template are similar to those between antibodies and antigens , consisting of electrostatic interactions , hydrogen bonds , Van der Waals forces , and hydrophobic interactions .
One of the greatest advantages of artificial receptors over naturally occurring receptors is freedom of molecular design. Their frameworks are not restricted to proteins, and a variety of skeletons (e.g., carbon chains and fused aromatic rings) can be used. Thus, the stability, flexibility, and other properties are freely modulated according to need. Even functional groups that are not found in nature can be employed in these synthetic compounds. Furthermore, when necessary, the activity in response towards outer stimuli (photo-irradiation, pH change, electric or magnetic field, and others) can be provided by using appropriate functional groups.
In a molecular imprinting processes, one needs a 1) template, 2) functional monomer(s) 3) cross-linker , 4) radical or other polymerization initiator , 5) porogenic solvent and 6) extraction solvent. According to polymerization method and final polymer format one or some of the reagent can be avoided. [ 1 ]
There are two main methods for creating these specialized polymers. The first is known as self-assembly, which involves the formation of polymer by combining all elements of the MIP and allowing the molecular interactions to form the cross-linked polymer with the template molecule bound. The second method of formation of MIPs involves covalently linking the imprint molecule to the monomer. After polymerization, the monomer is cleaved from the template molecule. [ 2 ] The selectivity is greatly influenced by the kind and amount of cross-linking agent used in the synthesis of the imprinted polymer. The selectivity is also determined by the covalent and non-covalent interactions between the target molecule and monomer functional groups. The careful choice of functional monomer is another important choice to provide complementary interactions with the template and substrates. [ 3 ] In an imprinted polymer, the cross-linker fulfills three major functions: First of all, the cross-linker is important in controlling the morphology of the polymer matrix, whether it is gel-type, macroporous or a microgel powder. Secondly, it serves to stabilize the imprinted binding site. Finally, it imparts mechanical stability to the polymer matrix. From a polymerization point of view, high cross-link ratios are generally preferred in order to access permanently porous materials and in order to be able to generate materials with adequate mechanical stability.
The self-assembly method has advantages in the fact that it forms a more natural binding site, and also offers additional flexibility in the types of monomers that can be polymerized. The covalent method has its advantages in generally offering a high yield of homogeneous binding sites, but first requires the synthesis of a derivatized imprint molecule and may not imitate the "natural" conditions that could be present elsewhere. [ 4 ] Over the recent years, interest in the technique of molecular imprinting has increased rapidly, both in the academic community and in the industry. Consequently, significant progress has been made in developing polymerization methods that produce adequate MIP formats with rather good binding properties expecting an enhancement in the performance or in order to suit the desirable final application, such as beads, films or nanoparticles . One of the key issues that have limited the performance of MIPs in practical applications so far is the lack of simple and robust methods to synthesize MIPs in the optimum formats required by the application. Chronologically, the first polymerization method encountered for MIP was based on "bulk" or solution polymerization. This method is the most common technique used by groups working on imprinting especially due to its simplicity and versatility. It is used exclusively with organic solvents mainly with low dielectric constant and consists basically of mixing all the components (template, monomer, solvent and initiator) and subsequently polymerizing them. The resultant polymeric block is then pulverized, freed from the template, crushed and sieved to obtain particles of irregular shape and size between 20 and 50 μm.
Depending on the target (template) type and the final application of the MIP, MIPs are appeared in different formats such as nano/micro spherical particles, nanowires and thin film or membranes. They are produced with different polymerization techniques like bulk , precipitation , emulsion , suspension , dispersion , gelation , and multi-step swelling polymerization. Most of investigators in the field of MIP are making MIP with heuristic techniques such as hierarchical imprinting method. The technique for the first time was used for making MIP by Sellergren et al. [ 5 ] for imprinting small target molecules. With the same concept, Nematollahzadeh et al. [ 6 ] developed a general technique, so-called polymerization packed bed, to obtain hierarchically-structured, high capacity protein imprinted porous polymer beads by using silica porous particles for protein recognition and capture.
Solid-phase molecular imprinting has been recently developed as an alternative to traditional bulk imprinting, generating water-soluble nanoparticles. [ 7 ] [ 8 ] As the name implies, this technique requires the immobilisation of the target molecule on a solid support prior to performing polymerisation. This is analogous to solid-phase synthesis of peptides . The solid phase doubles as an affinity separation matrix, allowing the removal of low-affinity MIPs and overcoming many of the previously described limitations of MIPs:
MIP nanoparticles synthesised via this approach have found applications in various diagnostic assay and sensors. [ 9 ] [ 10 ] [ 11 ]
An adaptation of the solid-phase protocol was performed by Sullivan et al. who used a modified aptamer as a recognition macromonomer, encapsulated within a polymer nanoparticle scaffold. Producing the first truly aptamer-MIP hybrid (aptaMIP), improving target recognition. [ 12 ] [ 13 ]
Molecular modelling has become a convenient choice in MIP design and analysis, allowing rapid selection of monomers and optimization of polymer composition, with a range of different techniques being applied. [ 14 ] [ 15 ] The application of molecular modelling in this capacity is commonly attributed to Sergey Pletsky and his visiting diploma student Sreenath Subrahmanyam, who developed a method of automated screening of a large database of monomers against a given target or template with a molecular mechanics approach. [ 16 ] [ 17 ] [ 18 ] In recent years technological advances have permitted more efficient analysis of monomer-template interactions by quantum mechanical molecular modelling , providing more precise calculations of binding energies. [ 19 ] Molecular dynamics has also been applied for more detailed analysis of systems before polymerisation, [ 20 ] [ 21 ] and of the resulting polymer, [ 22 ] which by including more system components (initiator, cross-linkers, solvents) provides greater accuracy in predicting successful MIP synthesis than monomer-template interactions alone. [ 23 ] [ 24 ] Molecular modelling, particular molecular dynamics and the less common coarse-grained techniques , [ 25 ] can often also be integrated into greater theoretical models permitting thermodynamic analysis and kinetic data for mesoscopic analysis of imprinted polymer bulk monoliths and MIP nanoparticles. [ 26 ] [ 27 ]
Niche areas for application of MIPs are in sensors and separation. Despite the current good health of molecular imprinting in general, one difficulty which appears to remain to this day is the commercialization of molecularly imprinted polymers. Despite this, many patents (1035 patents, up to October 2018, according to the Scifinder data base) on molecular imprinting were held by different groups.
Fast and cost-effective molecularly imprinted polymer technique has applications in many fields of chemistry, biology and engineering, particularly as an affinity material for sensors, [ 28 ] detection of chemical, antimicrobial , and dye, residues in food, adsorbents for solid phase extraction , binding assays, artificial antibodies, chromatographic stationary phase, catalysis, drug development and screening, and byproduct removal in chemical reaction. [ 29 ] Molecular imprinted polymers pose this wide range of capabilities in extraction through highly specific micro-cavity binding sites. [ 30 ] [ 31 ] Due to the specific binding site created in a MIP this technique is showing promise in analytical chemistry as a useful method for solid phase extraction. [ 32 ] The capability for MIPs to be a cheaper easier production of antibody/enzyme like binding sites doubles the use of this technique as a valuable breakthrough in medical research and application. [ 33 ] Such possible medical applications include "controlled release drugs, drug monitoring devices, and biological receptor mimetics". [ 34 ] Beyond this MIPs show a promising future in the developing knowledge and application in food sciences. [ 35 ] [ 36 ]
The binding activity of MIPs can be lower compared than that of specific antibodies, even though examples have been reported of MIPs with comparable or better performance to commercially produced antibodies. [ 37 ] [ 38 ] This yields a wide variety of applications for MIPs from efficient extraction to pharmaceutical/medical uses. [ 32 ] [ 34 ] MIPs offer many advantages over protein binding sites. Proteins are difficult and expensive to purify, denature (pH, heat, proteolysis), and are difficult to immobilize for reuse. Synthetic polymers are cheap, easy to synthesize, and allow for elaborate, synthetic side chains to be incorporated. Unique side chains allow for higher affinity, selectivity, and specificity.
Molecularly imprinted assays Molecularly imprinted polymers arguably demonstrate their greatest potential as alternative affinity reagents for use in diagnostic applications, due to their comparable (and in some regards superior) performance to antibodies. Many studies have therefore focused on the development of molecularly imprinted assays (MIAs) since the seminal work by Vlatakis et al. in 1993, where the term “molecularly imprinted [sorbet] assay” was first introduced. Initial work on ligand binding assays utilising MIPs in place of antibodies consisted of radio-labelled MIAs, however the field has now evolved to include numerous assay formats such as fluorescence MIAs, enzyme-linked MIAs, and molecularly imprinted nanoparticle assay (MINA). [ 39 ]
Molecularly imprinted polymers have also been used to enrich low abundant phosphopeptides from a cell lysate, [ 40 ] outperforming titanium dioxide (TiO 2 ) enrichment- a gold standard to enrich phosphopeptides.
In a paper published in 1931, [ 41 ] Polyakov reported the effects of presence of different solvents (benzene, toluene and xylene) on the silica pore structure during drying a newly prepared silica. When H 2 SO 4 was used as the polymerization initiator (acidifying agent), a positive correlation was found between surface areas, e.g. load capacities, and the molecular weights of the respective solvents. Later on, in 1949 Dickey reported the polymerization of sodium silicate in the presence of four different dyes (namely methyl, ethyl, n-propyl and n-butyl orange). The dyes were subsequently removed, and in rebinding experiments it was found that silica prepared in the presence of any of these "pattern molecules" would bind the pattern molecule in preference to the other three dyes. Shortly after this work had appeared, several research groups pursued the preparation of specific adsorbents using Dickey's method. Some commercial interest was also shown by the fact that Merck patented a nicotine filter, [ 42 ] consisting of nicotine imprinted silica, able to adsorb 10.7% more nicotine than non-imprinted silica. The material was intended for use in cigarettes, cigars and pipes filters. Shortly after this work appeared, molecular imprinting attracted wide interest from the scientific community as reflected in the 4000 original papers published in the field during for the period 1931–2009 (from Scifinder). However, although interest in the technique is new, commonly the molecularly imprinted technique has been shown to be effective when targeting small molecules of molecular weight <1000. [ 43 ] Therefore, in following subsection molecularly imprinted polymers are reviewed into two categories, for small and big templates.
Production of novel MIPs has implicit challenges unique to this field. These challenges arise chiefly from the fact that all substrates are different and thus require different monomer and cross-linker combinations to adequately form imprinted polymers for that substrate. The first, and lesser, challenge arises from choosing those monomers which will yield adequate binding sites complementary to the functional groups of the substrate molecule. For example, it would be unwise to choose completely hydrophobic monomers to be imprinted with a highly hydrophilic substrate. These considerations need to be taken into account before any new MIP is created. Molecular modelling can be used to predict favourable interactions between templates and monomers, allowing intelligent monomer selection.
Secondly, and more troublesome, the yield of properly created MIPs is limited by the capacity to effectively wash the substrate from the MIP once the polymer has been formed around it. [ 44 ] In creating new MIPs, a compromise must be created between full removal of the original template and damaging of the substrate binding cavity. Such damage is generally caused by strong removal methods and includes collapsing of the cavity, distorting the binding points, incomplete removal of the template and rupture of the cavity.
Most of the developments in MIP production during the last decade have come in the form of new polymerization techniques in an attempt to control the arrangement of monomers and therefore the polymers structure. However, there have been very few advances in the efficient removal of the template from the MIP once it has been polymerized. Due to this neglect, the process of template removal is now the least cost efficient and most time-consuming process in MIP production. [ 45 ] Furthermore, in order of MIPs to reach their full potential in analytical and biotechnological applications, an efficient removal process must be demonstrated.
There are several different methods of extraction which are currently being used for template removal. These have been grouped into 3 main categories: Solvent extraction, physically assisted extraction, and subcritical or supercritical solvent extraction. | https://en.wikipedia.org/wiki/Molecularly_imprinted_polymer |
A notable molecule editor is a computer program for creating and modifying representations of chemical structures .
Molecule editors can manipulate chemical structure representations in either a simulated two-dimensional space or three-dimensional space , via 2D computer graphics or 3D computer graphics , respectively. Two-dimensional output is used as illustrations or to query chemical databases . Three-dimensional output is used to build molecular models, usually as part of molecular modelling software packages.
Database molecular editors such as Leatherface, [ 1 ] RECAP, [ 2 ] and Molecule Slicer [ 3 ] allow large numbers of molecules to be modified automatically according to rules such as 'deprotonate carboxylic acids' or 'break exocyclic bonds' that can be specified by a user.
Molecule editors typically support reading and writing at least one file format or line notation . Examples of each include Molfile and simplified molecular input line entry specification (SMILES), respectively.
Files generated by molecule editors can be displayed by molecular graphics tools. | https://en.wikipedia.org/wiki/Molecule_editor |
Molecule mining is the process of data mining , or extracting and discovering patterns, as applied to molecules . Since molecules may be represented by molecular graphs , this is strongly related to graph mining and structured data mining . The main problem is how to represent molecules while discriminating the data instances. One way to do this is chemical similarity metrics , which has a long tradition in the field of cheminformatics .
Typical approaches to calculate chemical similarities use chemical fingerprints, but this loses the underlying information about the molecule topology . Mining the molecular graphs directly
avoids this problem. So does the inverse QSAR problem which is preferable for vectorial mappings. | https://en.wikipedia.org/wiki/Molecule_mining |
Stellar molecules are molecules that exist or form in stars . Such formations can take place when the temperature is low enough for molecules to form – typically around 6,000 K (5,730 °C; 10,340 °F) or cooler. [ 1 ] Otherwise the stellar matter is restricted to atoms and ions in the forms of gas or – at very high temperatures – plasma .
Matter is made up by atoms (formed by protons and other subatomic particles ). When the environment is right, atoms can join together and form molecules , which give rise to most materials studied in materials science . But certain environments, such as high temperatures, don't allow atoms to form molecules, as the environmental energy exceeds that of the dissociation energy of the bonds within the molecule. Stars have very high temperatures, primarily in their interior, and therefore there are few molecules formed in stars. [ 2 ]
By the mid-18th century, scientists surmised that the source of the Sun's light was incandescence , rather than combustion . [ 3 ]
Although the Sun is a star, its photosphere has a low enough temperature of 6,000 K (5,730 °C; 10,340 °F), and therefore molecules can form. Water has been found on the Sun, and there is evidence of H 2 in white dwarf stellar atmospheres. [ 2 ] [ 4 ]
Cooler stars include absorption band spectra that are characteristic of molecules. Similar absorption bands can be found through observation of solar sun spots , which are cool enough to allow persistence of stellar molecules. Molecules found in the Sun include MgH , CaH , FeH , CrH , NaH , OH , SiH , VO , and TiO . Others include CN , CH , MgF , NH , C 2 , SrF , ZrO , YO , ScO , and BH . [ 5 ]
Stars of most types can contain molecules, even the Ap category of A-type stars . Only the hottest O-, B-, and A-type stars have no detectable molecules. Carbon-rich white dwarfs, even though very hot, have spectral lines of C 2 and CH . [ 6 ]
Measurements of simple molecules that may be found in stars are performed in laboratories to determine the wavelengths of the spectra lines. Also, it is important to measure the dissociation energy and oscillator strengths (how strongly the molecule interacts with electromagnetic radiation). These measurements are inserted into formula that can calculate the spectrum under different conditions of pressure and temperature. However, man-made conditions are often different from those in stars, because it is hard to achieve the temperatures, and also local thermal equilibrium , as found in stars, is unlikely. Accuracy of oscillator strengths and actual measurement of dissociation energy is usually only approximate. [ 6 ]
A numerical model of a star's atmosphere will calculate pressures and temperatures at different depths, and can predict the spectrum for different elemental concentrations.
The molecules in stars can be used to determine some characteristics of the star. The isotopic composition can be determined if the lines in the molecular spectrum are observed. The different masses of different isotopes cause vibration and rotation frequencies to significantly vary. Secondly the temperature can be determined, as the temperature will change the numbers of molecules in the different vibrational and rotational states. Some molecules are sensitive to the ratio of elements, and so indicate elemental composition of the star. [ 6 ] Different molecules are characteristic of different kinds of stars, and are used to classify them. [ 5 ] Because there can be numerous spectral lines of different strength, conditions at different depths in the star can be determined. These conditions include temperature and speed towards or away from the observer. [ 6 ]
The spectrum of molecules has advantages over atomic spectral lines, as atomic lines are often very strong, and therefore only come from high in the atmosphere. Also the profile of the atomic spectral line can be distorted due to isotopes or overlaying of other spectral lines. [ 6 ] The molecular spectrum is much more sensitive to temperature than atomic lines. [ 6 ]
The following molecules have been detected in the atmospheres of stars: | https://en.wikipedia.org/wiki/Molecules_in_stars |
Molekel is a free software multiplatform molecular visualization program. [ 1 ] It was originally developed at the University of Geneva by Peter F. Flükiger in the 1990s for Silicon Graphics Computers. In 1998, Stefan Portmann took over responsibility and released Version 3.0. Version 4.0 was a nearly platform independent version. Further developments lead to version 4.3, before Stefan Portmann moved on and ceased to develop the codes. In 2006, the Swiss National Supercomputing Centre (CSCS) restarted the project and version 5.0 was released on 21 December 2006. [ 2 ]
Molekel uses VTK and Qwt and therefore as well Qt .
This article about molecular modelling software is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molekel |
MoleMax was the first digital epiluminescence microscopy ( dermatoscopy ) system developed in cooperation with medical faculty Department of Dermatology [ 1 ] of the Medical University of Vienna . It is currently owned and distributed by DermaMedicalSystems. [ 2 ]
In 1997, MoleMax was presented to international experts at the Melanoma World Congress and the following Dermatology World Congress in Sydney and generated great public interest. Since then, over 2000 MoleMax systems are in use in over 50 countries.
Today, MoleMax is worldwide accepted clinical standard in digital epiluminescence microscopy .
Thanks to the worldwide patented [ 3 ] light polarisation technique for cameras with skin contact, these camera systems do not require any immersion fluid for the epiluminescence microscopic analysis.
The MoleMax system was part of multiple scientific works such as measurements of the growth rate of pigmented skin lesions [ 4 ] [ 5 ] and verification of follow-up imaging. [ 6 ] Images made by this system also ended up in large public image databases such as HAM10000. [ 7 ] | https://en.wikipedia.org/wiki/Molemax |
Molisch's test is a sensitive chemical test , named after Austrian botanist Hans Molisch , for the presence of carbohydrates , based on the dehydration of the carbohydrate by sulfuric acid or hydrochloric acid to produce an aldehyde, which condenses with two molecules of a phenol (usually α-naphthol , though other phenols such as resorcinol and thymol also give colored products), resulting in a violet ring. [ 1 ] [ 2 ] [ 3 ]
The test solution is combined with a small amount of Molisch's reagent ( α-naphthol dissolved in ethanol) in a test tube . After mixing, a small amount of concentrated sulfuric acid is slowly added down the sides of the sloping test-tube, without mixing, to form a layer. A positive reaction is indicated by appearance of a purple red ring at the interface between the acid and test layers. [ 4 ]
All carbohydrates – monosaccharides , disaccharides , and polysaccharides (except trioses and tetroses )– should give a positive reaction, and nucleic acids and glycoproteins also give a positive reaction, as all these compounds are eventually hydrolyzed to monosaccharides by strong mineral acids. Pentoses are then dehydrated to furfural , while hexoses are dehydrated to 5- hydroxymethylfurfural . Either of these aldehydes, if present, will condense with two molecules of α-naphthol to form a purple-colored product, as illustrated below by the example of glucose : [ 5 ] | https://en.wikipedia.org/wiki/Molisch's_test |
A molluscivore is a carnivorous animal that specialises in feeding on molluscs such as gastropods , bivalves , brachiopods and cephalopods . Known molluscivores include numerous predatory (and often cannibalistic) molluscs, (e.g. octopuses , murexes , decollate snails and oyster drills ), arthropods such as crabs and firefly larvae , and vertebrates such as fish , birds and mammals . [ 1 ] Molluscivory is performed in a variety of ways with some animals highly adapted to this method of feeding. A similar behaviour, durophagy , describes the feeding of animals that consume hard-shelled or exoskeleton bearing organisms, such as corals , shelled molluscs, or crabs. [ 2 ]
Molluscivory can be performed in several ways:
Whales : Sperm whales , pilot whales , Cuvier's beaked whale , Risso's dolphin and species in the genera Mesoplodon , and Hyperoodon and the superfamily Physeteroidea are classified as molluscivores, eating mainly squid. [ 3 ]
Pinnipeds : Elephant seals , Ross seals and South American fur seals are classed as molluscivores. [ 3 ] The walrus eats benthic bivalve molluscs, especially clams , for which it forages by grazing along the sea bottom, searching and identifying prey with its sensitive vibrissae . [ 4 ] The walrus sucks the meat out by sealing its powerful lips to the organism and withdrawing its piston-like tongue rapidly into its mouth, creating a vacuum. The walrus palate is uniquely vaulted, enabling effective suction.
Several species of pufferfish and loaches are molluscivores. As many molluscs are protected by a shell , the feeding techniques applied amongst molluscivore fish are highly specialized and usually divided into two groups: "crushers" and "slurpers." Pufferfish tend to be crushers and will use their beak -like teeth to break the shell in order to gain access to the meat inside. Loaches are specialized slurpers, and will make use of their characteristically shaped snout in order to grab hold of, then suck out the animal living inside the shell.
The black carp ( Mylopharyngodon piceus ) commonly feeds by crushing large molluscs with pharyngeal teeth , extracting soft tissue, and spitting out shell fragments. Four-year-old juveniles are capable of consuming approximately 1–2 kg of molluscs per day. This bottom-dwelling molluscivore was purposely imported into the United States in the early 1970s for use as a food fish and also as a biological control agent for snails—an intermediate host for a trematode parasite in fish reared on fish farms. [ 5 ] Two snail-eating cichlids , Trematocranus placodon and Maravichromis anaphyrmis , have been tried as biological control agents of schistosomes in fish ponds in Africa. [ 6 ] Redear sunfish ( Lepomis micropholus ) and bluegill ( Lepomis macrochirus ) have been used to control quagga mussels ( Dreissena bugensis ) in the lower Colorado River in the US. [ 7 ]
The common name of some fish reflects their molluscivorous feeding, for example, the "snail-crusher hap" ( Trematocranus placodon ), ""red rock sheller" ( Haplochromis sp. ), "Rusinga oral sheller" ( Haplochromis sp. ) and "rainbow sheller" ( Haplochromis sp. ). The redear sunfish is also known as the "shellcracker".
Gray's monitor (or "butaan") is well known for its diet, which consists primarily of ripe fruit; however, several prey items are also consumed, including snails. [ 8 ] Monitors are generally carnivorous animals, which makes the Gray's monitor somewhat of an exception amongst the varanid family.
The prehistoric placodont reptiles is an extinct taxon of marine animals that superficially resembled lizards and turtles, most of whose dentition of peg-like incisors and enormous, molar-like teeth allowed them to prey on molluscs and brachiopods by plucking their prey off of the substrate, and crushing the shells. [ 9 ] [ 10 ]
Among birds , the eponymous shorebirds known as oystercatchers are renowned for feeding upon bivalves. At least one bird of prey is also primarily a molluscivore—the snail kite , Rostrhamus sociabilis . The limpkin is a small rail-like bird that feeds almost entirely on apple snails. Other birds that will eat molluscs occasionally include mergansers , ducks , coots , dippers and spoonbills . [ 11 ]
Cone snails : Some cone snails hunt and eat other kinds of snails, such as cowries, olive shells, turbo snails, and conch snails, while others will eat other cone snails. Conus marmoreus and Conus omaria are able to kill and swallow prey that are larger than themselves; some Conus species can swallow prey that weigh up to half of their own weight. Snails' bodies are attached to their shell by a columellar muscle that holds onto the columella , the axis of the snail. This muscle also allows the snail to retract back into its shell. If this muscle is broken, the snail will lose its shell and die. It is hard to detach this muscle in a live snail, or even in a dead snail. It is thought that the conotoxins in the venom of cone snails are able to completely relax this muscle so that the body can be pulled out from its shell. The cone snail uses its foot to hold the shell of its prey. Using a strong, steady pulling motion, the body of the snail can be forced out and then swallowed whole. Complete digestion of a snail can take many hours, even days. [ 12 ]
Starfish : Primitive starfish, such as Astropecten and Luidia , swallow their prey whole and start to digest it in their cardiac stomachs. Shell valves and other inedible materials are ejected through their mouths. The semi-digested fluid is passed into their pyloric stomachs and caeca where digestion continues and absorption occurs. [ 13 ] The margined sea star ( Astropecten articulatus ) is a well known molluscivore. It catches prey with its arms which it then takes to the mouth. The prey is then trapped by the long, moving prickles around the mouth cavity and swallowed food.
In more advanced species of starfish, the cardiac stomach can be everted from the organism's body to engulf and digest food. When the prey is a clam, the starfish pulls with its tube feet to separate the two valves slightly, and inserts a small section of its stomach, which releases enzymes to digest the prey. The stomach and the partially digested prey are later retracted into the disc. Here the food is passed on to the pyloric stomach, which always remains inside the disc. [ 14 ] Because of this ability to digest food outside the body, starfish can hunt prey much larger than their mouths.
Crabs : The freshwater crabs Syntripsa matannensis and Syntripsa flavichela are classed as molluscivores. [ 15 ] Using their massive and powerful claws, adult Florida stone crabs ( Menippe mercenaria ) feed on acorn barnacles , hard-shelled clams, scallops , and conch . [ 16 ] | https://en.wikipedia.org/wiki/Molluscivore |
In trigonometry , Mollweide's formula is a pair of relationships between sides and angles in a triangle. [ 1 ] [ 2 ]
A variant in more geometrical style was first published by Isaac Newton in 1707 and then by Friedrich Wilhelm von Oppel [ de ] in 1746. Thomas Simpson published the now-standard expression in 1748. Karl Mollweide republished the same result in 1808 without citing those predecessors. [ 3 ]
It can be used to check the consistency of solutions of triangles . [ 4 ]
Let a , {\displaystyle a,} b , {\displaystyle b,} and c {\displaystyle c} be the lengths of the three sides of a triangle.
Let α , {\displaystyle \alpha ,} β , {\displaystyle \beta ,} and γ {\displaystyle \gamma } be the measures of the angles opposite those three sides respectively. Mollweide's formulas are
Because in a planar triangle 1 2 γ = 1 2 π − 1 2 ( α + β ) , {\displaystyle {\tfrac {1}{2}}\gamma ={\tfrac {1}{2}}\pi -{\tfrac {1}{2}}(\alpha +\beta ),} these identities can alternately be written in a form in which they are more clearly a limiting case of Napier's analogies for spherical triangles (this was the form used by Von Oppel),
Dividing one by the other to eliminate c {\displaystyle c} results in the law of tangents ,
In terms of half-angle tangents alone, Mollweide's formula can be written as
or equivalently
Multiplying the respective sides of these identities gives one half-angle tangent in terms of the three sides,
which becomes the law of cotangents after taking the square root,
where s = 1 2 ( a + b + c ) {\textstyle s={\tfrac {1}{2}}(a+b+c)} is the semiperimeter .
The identities can also be proven equivalent to the law of sines and law of cosines .
In spherical trigonometry , the law of cosines and derived identities such as Napier's analogies have precise duals swapping central angles measuring the sides and dihedral angles at the vertices. In the infinitesimal limit, the law of cosines for sides reduces to the planar law of cosines and two of Napier's analogies reduce to Mollweide's formulas above. But the law of cosines for angles degenerates to 0 = 0. {\displaystyle 0=0.} By dividing squared side length by the spherical excess E , {\displaystyle E,} we obtain a non-vanishing ratio, the spherical trigonometry relation:
In the infinitesimal limit, as the half-angle tangents of spherical sides reduce to lengths of planar sides, the half-angle tangent of spherical excess reduces to twice the area A {\displaystyle A} of a planar triangle, so on the plane this is:
and likewise for a {\displaystyle a} and b . {\displaystyle b.}
As corollaries (multiplying or dividing the above formula in terms of a {\displaystyle a} and b {\displaystyle b} ) we obtain two dual statements to Mollweide's formulas. The first expresses the area in terms of two sides and the included angle, and the other is the law of sines:
We can alternately express the second formula in a form closer to one of Mollweide's formulas (again the law of tangents):
A generalization of Mollweide's formula holds for a cyclic quadrilateral ◻ A B C D . {\displaystyle \square ABCD.} Denote the lengths of sides | A B | = a , {\displaystyle |AB|=a,} | B C | = b , {\displaystyle |BC|=b,} | C D | = c , {\displaystyle |CD|=c,} and | D A | = d {\displaystyle |DA|=d} and angle measures ∠ D A B = α , {\displaystyle \angle {DAB}=\alpha ,} ∠ A B C = β , {\displaystyle \angle {ABC}=\beta ,} ∠ B C D = γ , {\displaystyle \angle {BCD}=\gamma ,} and ∠ C D A = δ . {\displaystyle \angle {CDA}=\delta .} If E {\displaystyle E} is the point of intersection of the diagonals, denote ∠ C E D = θ . {\displaystyle \angle {CED}=\theta .} Then: [ 5 ]
Several variant formulas can be constructed by substituting based on the cyclic quadrilateral identities,
As rational relationships in terms of half-angle tangents of two adjacent angles, these formulas can be written:
A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d {\displaystyle d} approaches zero, a cyclic quadrilateral converges into a triangle △ A ′ B ′ C ′ , {\displaystyle \triangle A'B'C',} and the formulas above simplify to the analogous triangle formulas. Relabeling to match the convention for triangles, in the limit a ′ = b , {\displaystyle a'=b,} b ′ = c , {\displaystyle b'=c,} c ′ = a , {\displaystyle c'=a,} α ′ = α + δ − π = π − θ , {\displaystyle \alpha '=\alpha +\delta -\pi =\pi -\theta ,} β ′ = β , {\displaystyle \beta '=\beta ,} and γ ′ = γ . {\displaystyle \gamma '=\gamma .} | https://en.wikipedia.org/wiki/Mollweide's_formula |
A notable molecule editor is a computer program for creating and modifying representations of chemical structures .
Molecule editors can manipulate chemical structure representations in either a simulated two-dimensional space or three-dimensional space , via 2D computer graphics or 3D computer graphics , respectively. Two-dimensional output is used as illustrations or to query chemical databases . Three-dimensional output is used to build molecular models, usually as part of molecular modelling software packages.
Database molecular editors such as Leatherface, [ 1 ] RECAP, [ 2 ] and Molecule Slicer [ 3 ] allow large numbers of molecules to be modified automatically according to rules such as 'deprotonate carboxylic acids' or 'break exocyclic bonds' that can be specified by a user.
Molecule editors typically support reading and writing at least one file format or line notation . Examples of each include Molfile and simplified molecular input line entry specification (SMILES), respectively.
Files generated by molecule editors can be displayed by molecular graphics tools. | https://en.wikipedia.org/wiki/Molsketch |
Molten salt is salt which is solid at standard temperature and pressure but liquified due to elevated temperature. A salt that is liquid even at standard temperature and pressure is usually called a room-temperature ionic liquid , and molten salts are technically a class of ionic liquids.
As a reference, molten sodium chloride , table salt has a melting point (m.p.) of 801 °C (1,474 °F). A variety of eutectic mixtures have been developed with lower melting points:
Alkali metal nitrates are relatively low melting and thermally stable. The least stable, LiNO 3 (m.p. 255 °C (491 °F)) decomposes only at 474 °C (885 °F). At the other extreme, cesium nitrate melts at 414 °C (777 °F) and decomposes at 584 °C. [ 2 ]
Molten salts have a variety of uses.
One industrial application is the production of magnesium, which begins with production of magnesium chloride by chlorination of magnesium oxide :
Electrolysis of the resulting molten magnesium chloride is conducted at 700 °C (1,292 °F): [ 6 ]
Aluminium metal is produced from aluminium oxides by electrolysis of a molten mixture of sodium hexafluoroaluminate and alumina at 950 °C (1,740 °F). This conversion is called the Hall-Haroult process . [ 7 ]
Molten salts (fluoride, chloride, and nitrate ) can be used as heat transfer fluids as well as for thermal storage . This thermal storage is used in concentrated solar power plants. [ 8 ] [ 9 ]
Molten-salt reactors are a type of nuclear reactor that uses molten salt(s) as a coolant or as a solvent in which the fissile material is dissolved. Experimental salts using lithium can be formed that have a melting point of 116 °C while still having a heat capacity of 1.54 J/(g·K). [ 4 ]
Molten chloride salt mixtures are commonly used as quenching baths for various alloy heat treatments , such as annealing and martempering of steel . Cyanide and chloride salt mixtures are used for surface modification of alloys such as carburizing and nitrocarburizing of steel.
Cryolite (a fluoride salt) is used as a solvent for aluminium oxide in the production of aluminium in the Hall-Héroult process .
Fluoride, chloride, and hydroxide salts can be used as solvents in pyroprocessing of nuclear fuel .
Ambient-temperature molten salts (also known as ionic liquids ) are present in the liquid phase at standard conditions for temperature and pressure . Examples of such salts include N -ethylpyridinium bromide and aluminium chloride mix, discovered in 1951, [ 10 ] and ethylammonium nitrate discovered by Paul Walden . Other ionic liquids take advantage of asymmetrical quaternary ammonium cations like alkylated imidazolium ions, and large, branched anions like the bistriflimide ion. | https://en.wikipedia.org/wiki/Molten_salt |
Molybdenite is a mineral of molybdenum disulfide , Mo S 2 . Similar in appearance and feel to graphite , molybdenite has a lubricating effect that is a consequence of its layered structure. The atomic structure consists of a sheet of molybdenum atoms sandwiched between sheets of sulfur atoms. The Mo-S bonds are strong, but the interaction between the sulfur atoms at the top and bottom of separate sandwich-like tri-layers is weak, resulting in easy slippage as well as cleavage planes .
Molybdenite crystallizes in the hexagonal crystal system as the common polytype 2H and also in the trigonal system as the 3R polytype. [ 3 ] [ 4 ] [ 7 ]
Molybdenite occurs in high temperature hydrothermal ore deposits.
Its associated minerals include pyrite , chalcopyrite , quartz , anhydrite , fluorite , and scheelite . Important deposits include the disseminated porphyry molybdenum deposits at Questa, New Mexico and the Henderson and Climax mines in Colorado . Molybdenite also occurs in porphyry copper deposits of Arizona , Utah , and Mexico .
The element rhenium is always present in molybdenite as a substitute for molybdenum, usually in the parts per million (ppm ) range, but often up to 1–2%. High rhenium content results in a structural variety detectable by X-ray diffraction techniques. Molybdenite ores are essentially the only source for rhenium. The presence of the radioactive isotope rhenium-187 and its daughter isotope osmium -187 provides a useful geochronologic dating technique.
Molybdenite is extremely soft with a metallic luster, and is superficially almost identical to graphite, to the point where it is not possible to positively distinguish between the two minerals without scientific equipment. It marks paper in much the same way as graphite. Its distinguishing feature from graphite is its higher specific gravity, as well as its tendency to occur in a matrix .
Molybdenite is an important ore of molybdenum, and is the most common source of the metal. [ 4 ] While molybdenum is rare in the Earth's crust, molybdenite is relatively common and easy to process, and accounts for much of the metal's economic viability. Molybdenite is purified by froth flotation , and then oxidized to form soluble molybdate . Reduction of ammonium molybdate yields pure molybdenum metal, which is used for fertilizer, as a catalyst, and in battery electrodes. By far the most common use of molybdenum is as an alloy with iron. Ferromolybdenum is an important component of high strength and corrosion-resistant steel.
Multilayer molybdenite flakes are semiconductors with an indirect bandgap . In contrast, monolayer flakes have a direct gap. [ 8 ] In the early years of the 20th century, molybdenite was used in some of the first crude semiconductor diodes , called cat's whisker detectors , which served as a demodulator in early crystal radios . Monolayer molybdenite shows good charge carrier mobility and can be used to create small or low-voltage transistors . [ 9 ] The transistors can detect and emit light and may have future use in optoelectronics . [ 10 ]
Media related to Molybdenite at Wikimedia Commons | https://en.wikipedia.org/wiki/Molybdenite |
Molybdenum(V) chloride is the inorganic compound with the empirical formula MoCl 5 . This dark volatile solid is used in research to prepare other molybdenum compounds. It is moisture-sensitive and soluble in chlorinated solvents.
Usually called molybdenum pentachloride, it is in fact partly a dimer with the molecular formula Mo 2 Cl 10 . [ 1 ] In the dimer, each molybdenum has local octahedral symmetry and two chlorides bridge between the molybdenum centers. [ 2 ] A similar structure is also found for the pentachlorides of W, Nb and Ta. [ 3 ] In the gas phase and partly in solution, the dimers partially dissociate to give a monomeric MoCl 5 . [ 4 ] The monomer is paramagnetic, with one unpaired electron per Mo center, reflecting the fact that the formal oxidation state is +5, leaving one valence electron on the metal center.
MoCl 5 is prepared by chlorination of Mo metal but also chlorination of MoO 3 . The unstable hexachloride MoCl 6 is not produced in this way. [ 5 ]
MoCl 5 is reduced by acetonitrile to afford an orange acetonitrile complex , MoCl 4 (CH 3 CN) 2 . This complex in turn reacts with THF to give MoCl 4 (THF) 2 , a precursor to other molybdenum-containing complexes. [ 6 ]
Molybdenum(IV) bromide is prepared by treatment of MoCl 5 with hydrogen bromide :
The reaction proceeds via the unstable molybdenum(V) bromide, which releases bromine at room temperature. [ 7 ]
MoCl 5 is a good Lewis acid toward non-oxidizable ligands. It forms an adduct with chloride to form [MoCl 6 ] − . In organic synthesis , the compound finds occasional use in chlorinations , deoxygenation , and oxidative coupling reactions. [ 8 ]
MoCl 5 is reduced by acetonitrile : [ 9 ]
Although it polymerizes tetrahydrofuran , MoCl 5 is stable in diethyl ether . Reduction of such solutions with tin gives MoCl 4 ((CH 3 CH 2 ) 2 O) 2 and MoCl 3 ((CH 3 CH 2 ) 2 O) 3 , depending on conditions. [ 10 ]
MoCl 5 is an aggressive oxidant and readily hydrolyzes to release HCl. | https://en.wikipedia.org/wiki/Molybdenum(V)_chloride |
Molybdenum blue is a term applied to:
The "heteropoly-molybdenum blues", are used extensively in analytical chemistry and as catalysts. The formation of "isopoly-molybdenum blues" which are intense blue has been used as a sensitive test for reducing reagents. They have recently been shown to contain very large anionic species based on the so-called "big wheel" containing 154 Mo atoms, with a formula [Mo 154 O 462 H 14 (H 2 O) 70 ] 14− . [ 2 ]
The molybdenum blue pigment is historically documented [ 3 ] but may not be in use today.
The first heteropoly molybdate and first heteropolymetallate, yellow ammonium phosphomolybdate , (NH 4 ) 3 PMo 12 O 40 was discovered by Berzelius in 1826. [ 4 ] The phosphorus atom in the anion is termed the heteroatom , other heteroatoms are silicon and arsenic. The heteropoly-molybdenum blues have structures based on the Keggin structure . The blue colour arises because the near-colourless anion, such as the phosphomolybdate anion, PMo 12 O 3− 40 , can accept more electrons (i.e. be reduced) to form an intensely coloured mixed-valence complex. This can occur in one electron or two electron steps. [ 4 ] The reduction process is reversible and the structure of the anion is essentially unchanged. [ 4 ]
The structure of the anion, PMo V 4 Mo VI 8 O 7− 40 , has been determined in the solid state and is a β-isomer (i.e. with one of the four groups of edge-shared octahedra on the α-Keggin ion rotated through 60°). [ 5 ] Similar structures have been found with silicon, germanium or arsenic heteroatoms. [ 4 ]
The intense blue colour of the reduced anion is the basis for the use of heteropoly-molybdenum blues in quantitative and qualitative analytical techniques.
This property is exploited as follows:
The determination of phosphorus, arsenic, silicon and germanium are examples of the use of heteropoly-molybdenum blue in analytical chemistry. The following example describes the determination of phosphorus. A sample containing the phosphate is mixed with an acid solution of Mo VI , for example ammonium molybdate , to produce PMo 12 O 3− 40 , which has an α- Keggin structure . This anion is then reduced by, for example, ascorbic acid or SnCl 2 , to form the blue coloured β-keggin ion, PMo 12 O 7− 40 . [ 5 ] The amount of the blue coloured ion produced is proportional to the amount of phosphate present and the absorption can be measured using a colorimeter to determine the amount of phosphorus. Examples of procedures are:
The comparison of the measured absorption against readings taken for analyses of standard solutions means that a detailed understanding of the structure of the blue complex was unnecessary.
This colorimetric method is ineffective when comparable amounts of arsenate are present in solution with phosphate. This is due to the strong chemical likeness of arsenate and phosphate. The resultant molybdenum blue for arsenate, using the same procedure, does produce a slightly different spectral signature, however. [ 11 ]
Recently, paper-based devices have become very attractive to use colorimetric determination for making inexpensive, disposable and convenient analytical devices for the determination of reactive phosphate in the field. By using an inexpensive and portable infrared Lightbox system, one can create uniform and repeatable lighting environments to take advantage of the peak absorbance of the molybdenum blue reaction in order to improve limit of detection of paper-based devices. This system may act as a substitute for expensive, lab-equipment spectrometers. [ 12 ]
The Folin–Wu and the Somogyi–Nelson methods are both based on the same principles. In the first step, glucose (or a reducing sugar) is oxidised using a solution of Cu(II) ion, which is reduced to Cu(I) by the process. In the second step, the Cu(I) ions are then oxidised back to Cu(II) using a colourless hetero-polymolybdate complex, which is, in the process, reduced to give the characteristic blue colour. Finally the absorption of the hetero-poly molybdenum blue is measured using a colorimeter and compared to standards prepared from reacting sugar solutions of known concentration, to determine the amount of reducing-sugar present. The Folin–Wu method [ 13 ] uses a reagent that contains sodium tungstate . The exact nature of the blue complex in this procedure is not known. The Somogyi-Nelson method uses an arsenomolybdate complex formed by the reaction of ammonium molybdate , (NH 4 ) 6 Mo 7 O 24 , with sodium arsenate, Na 2 HAsO 7 . [ 14 ] [ 15 ] [ 16 ]
Some drugs that contain a catechol group react with phosphomolybdic acid (H 3 PMo 12 O 40 ) to give the heteropoly-molybdenum blue colour. [ 17 ] Micro quantities of the drugs can be determined.
Examples of simple tests [ 18 ] are shown below that rely on the production of the molybdenum blue colour either due to reduction:
or by detection of the heteroatom
Dittmer's spray reagent for phospholipids is used in thin layer chromatography to detect phospholipids. The spray reagent is prepared as follows:
When applied to the TLC plate, compounds containing phosphate ester show up immediately as blue spots. [ 19 ]
The isopoly-molybdenum blues have been known for many years. They are the cause of the "blue waters" found near Idaho Springs, known to Native Americans. They were first documented by Scheele and Berzelius. [ 2 ] The compounds responsible for the blue colour were not known until 1995. [ 20 ] Before then it was well known that there were polymolybdates of Mo(VI). Molybdenum(VI)oxide, MoO 3 , when dissolved in aqueous alkali forms the tetrahedral molybdate anion, MoO 2− 4 . Dissolving molybdate salts in strong acid produces "molybdic acid", MoO 3 ·2H 2 O. In between these extremes of pH, polymeric ions are produced which are mostly built from MoO 6 octahedral units sharing corners and edges. Examples include Mo 7 O 6− 24 , Mo 8 O 4− 26 and Mo 36 O 112 (H 2 O) 8− 16 , which contain the {(Mo)Mo 5 }-type unit comprising a central MoO 7 pentagonal bipyramid sharing edges with five MoO 6 octahedra. The later unit occurs also in the giant mixed-valence molybdenum blue species [H x Mo 368 O 1032 (H 2 O) 240 (SO 4 ) 48 ] 48− ( x ≈ 16) [ 21 ] as well as in the cluster described in the next section. The molybdenum blue species are obtained by reduction of acidified molybdate(VI) solutions.
The first publication of the structure of wheel shaped cluster anion, first determined for the nitrosyl derivative by Achim Müller et al. [ 20 ] was announced in New Scientist as "Big Wheel rolls back the molecular frontier". [ 22 ] Further work by the same group then refined the initial findings and determined the structure of the wheel produced in molybdate solutions as [Mo 154 O 462 H 14 (H 2 O) 70 ] 14− . [ 20 ] The Mo 154 -type cluster was then shown to be the basic structural type of molybdenum blue compounds obtained under slightly different conditions. [ 2 ]
The structure of the big wheel is constructed from units containing 11 Mo atoms ({Mo 11 }-type units), 14 of which are linked together to form the {Mo 154 }-type cluster that has an external diameter of 3.4 nm. (12 {Mo 11 }-type units are also involved in the construction of higher symmetrical spherical systems called Keplerates [ 2 ] ) These units consist of a central MoO 7 bipyramid sharing edges with 5 MoO 6 octahedra (an illustration of this is on page 155 of the review [ 23 ] ). With 5 more linking MoO 6 octahedra the repeating {Mo 11 }-type unit is built up.
Along with other aggregates, a hollow, spherical structure self-assembles from approximately 1,165 Mo 154 wheels. This was termed a vesicle by analogy with lipid vesicles. Unlike lipid vesicles that are stabilised by hydrophobic interactions it is believed that the vesicle is stabilised by an interplay of van der Waals attraction, long-range electrostatic repulsion with further stabilization arising from hydrogen bonding involving water molecules encapsulated between the wheel-shaped clusters and in the vesicles' interior. The radius of the vesicle is 45 nm. [ 24 ]
A pigment termed molybdenum blue is recorded in 1844 as a mixture of molybdenum with " oxyde of tin or phosphate of lime ". [ 3 ] An alternative formulation involves "digesting" molybdenum sulfide with nitric acid to form molybdic acid, which is then mixed with tin filings and a little muriatic acid (HCl) . [ 3 ] This is evaporated and heated with alumina. A 1955 paper states that molybdenum blue is unstable and is not used commercially as a pigment. [ 25 ] The chemistry of these pigments has not been investigated. | https://en.wikipedia.org/wiki/Molybdenum_blue |
In chemistry , molybdenum bronze is a generic name for certain mixed oxides of molybdenum with the generic formula A x Mo y O z where A may be hydrogen , an alkali metal cation (such as Li + , Na + , K + ), and Tl + . These compounds form deeply coloured plate-like crystals with a metallic sheen, hence their name. These bronzes derive their metallic character from partially occupied 4d bands. [ 1 ] The oxidation states in K 0.28 MoO 3 are K +1 , O 2− , and Mo +5.72 . MoO 3 is an insulator, with an unfilled 4d band.
These compounds have been much studied since the 1980s due to their markedly anisotropic electrical properties, reflecting their layered structure. The electrical resistivity can vary considerably depending on the direction, in some cases by 200:1 or more. They are generally non-stoichiometric compounds . Some are metals and some are semiconductors.
The first report of a "molybdenum bronze" was by Alfred Stavenhagen and E. Engels in 1895. They reported that electrolysis of molten Na 2 MoO 4 and MoO 3 gave indigo-blue needles with metallic sheen, which they analysed by weight as Na 2 Mo 5 O 7 . [ 2 ] The first unambiguous synthesis of alkali molybdenum bronzes was reported only in 1964, by Wold and others. [ 3 ] They obtained two potassium bronzes, "red" K 0.26 MoO 3 and "blue" K 0.28 MoO 3 , by electrolysis of molten K 2 MoO 4 + MoO 3 at 550 °C and 560 °C, respectively. Sodium bronzes were also obtained by the same method. It was observed that at a slightly higher temperature (about 575 °C and above) only MoO 2 is obtained. [ 3 ] [ 4 ]
Another preparation technique involves crystallization from the melt in a temperature gradient. This report also called attention to the marked anisotropic resistivity of the purple lithium bronze Li 0.9 Mo 6 O 17 and its metal-to-insulator transition at about 24 K . [ 5 ]
Hydrogen bronzes H x MoO 3 were obtained in 1950 by Glemser and Lutz, by ambient-temperature reactions. [ 6 ] [ Note 1 ] The hydrogen in these compounds can be replaced by alkali metals by treatment with solutions of the corresponding halides. Reactions are conducted in an autoclave at about 160 °C. [ 7 ]
Molybdenum bronzes are classified in three major families: [ 4 ] [ 7 ]
The hydrogen molybdenum bronzes have similar appearances but different compositions:
Other molybdenum bronzes with anomalous electrical properties have been reported, which do not fit in these families. These include | https://en.wikipedia.org/wiki/Molybdenum_bronze |
Molybdenum disilicide ( MoSi 2 , or molybdenum silicide ), an intermetallic compound , a silicide of molybdenum , is a refractory ceramic with primary use in heating elements . It has moderate density , melting point 2030 °C, and is electrically conductive . At high temperatures it forms a passivation layer of silicon dioxide , protecting it from further oxidation. The thermal stability of MoSi 2 alongside its high emissivity make this material, alongside WSi 2 attractive for applications as a high emissivity coatings in heat shields for atmospheric entry . [ 3 ] MoSi 2 is a gray metallic-looking material with tetragonal crystal structure (alpha-modification); its beta-modification is hexagonal and unstable. [ 4 ] It is insoluble in most acids but soluble in nitric acid and hydrofluoric acid .
While MoSi 2 has excellent resistance to oxidation and high Young's modulus at temperatures above 1000 °C, it is brittle in lower temperatures. Also, at above 1200 °C it loses creep resistance. These properties limits its use as a structural material , but may be offset by using it together with another material as a composite material .
Molybdenum disilicide and MoSi 2 -based materials are usually made by sintering . Plasma spraying can be used for producing its dense monolithic and composite forms; material produced this way may contain a proportion of β-MoSi 2 due to its rapid cooling.
Molybdenum disilicide heating elements can be used for temperatures up to 1800 °C, in electric furnaces used in laboratory and production environment in production of glass , steel , electronics , ceramics , and in heat treatment of materials. While the elements are brittle, they can operate at high power without aging, and their electrical resistivity does not increase with operation time. Their maximum operating temperature has to be lowered in atmospheres with low oxygen content due to breakdown of the passivation layer. [ 5 ]
Molybdenum disilicide is used in microelectronics as a contact material. It is often used as a shunt over polysilicon lines to increase their conductivity and increase signal speed. | https://en.wikipedia.org/wiki/Molybdenum_disilicide |
hR9 , R3m , No 160 (3R) [ 5 ]
Molybdenum disulfide (or moly) is an inorganic compound composed of molybdenum and sulfur . Its chemical formula is MoS 2 .
The compound is classified as a transition metal dichalcogenide . It is a silvery black solid that occurs as the mineral molybdenite , the principal ore for molybdenum. [ 6 ] MoS 2 is relatively unreactive. It is unaffected by dilute acids and oxygen . In appearance and feel, molybdenum disulfide is similar to graphite . It is widely used as a dry lubricant because of its low friction and robustness. Bulk MoS 2 is a diamagnetic , indirect bandgap semiconductor similar to silicon , with a bandgap of 1.23 eV. [ 2 ]
MoS 2 is naturally found as either molybdenite , a crystalline mineral, or jordisite, a rare low temperature form of molybdenite. [ 7 ] Molybdenite ore is processed by flotation to give relatively pure MoS 2 . The main contaminant is carbon. MoS 2 also arises by thermal treatment of virtually all molybdenum compounds with hydrogen sulfide or elemental sulfur and can be produced by metathesis reactions from molybdenum pentachloride . [ 8 ]
All forms of MoS 2 have a layered structure, in which a plane of molybdenum atoms is sandwiched by planes of sulfide ions. These three strata form a monolayer of MoS 2 . Bulk MoS 2 consists of stacked monolayers, which are held together by weak van der Waals interactions .
Crystalline MoS 2 exists in one of two phases, 2H- MoS 2 and 3R- MoS 2 , where the "H" and the "R" indicate hexagonal and rhombohedral symmetry, respectively. In both of these structures, each molybdenum atom exists at the center of a trigonal prismatic coordination sphere and is covalently bonded to six sulfide ions. Each sulfur atom has pyramidal coordination and is bonded to three molybdenum atoms. Both the 2H- and 3R-phases are semiconducting. [ 10 ]
A third, metastable crystalline phase known as 1T- MoS 2 was discovered by intercalating 2H- MoS 2 with alkali metals . [ 11 ] This phase has trigonal symmetry and is metallic. The 1T-phase can be stabilized through doping with electron donors such as rhenium , [ 12 ] or converted back to the 2H-phase by microwave radiation. [ 13 ] The 2H/1T-phase transition can be controlled via the incorporation of sulfur (S) vacancies . [ 14 ]
Nanotube -like and buckyball -like molecules composed of MoS 2 are known. [ 15 ]
While bulk MoS 2 in the 2H-phase is known to be an indirect-band gap semiconductor, monolayer MoS 2 has a direct band gap. The layer-dependent optoelectronic properties of MoS 2 have promoted much research in 2-dimensional MoS 2 -based devices. 2D MoS 2 can be produced by exfoliating bulk crystals to produce single-layer to few-layer flakes either through a dry, micromechanical process or through solution processing.
Micromechanical exfoliation, also pragmatically called " Scotch-tape exfoliation ", involves using an adhesive material to repeatedly peel apart a layered crystal by overcoming the van der Waals forces. The crystal flakes can then be transferred from the adhesive film to a substrate. This facile method was first used by Konstantin Novoselov and Andre Geim to obtain graphene from graphite crystals. However, it can not be employed for a uniform 1-D layers because of weaker adhesion of MoS 2 to the substrate (either silicon, glass or quartz); the aforementioned scheme is good for graphene only. [ 16 ] While Scotch tape is generally used as the adhesive tape, PDMS stamps can also satisfactorily cleave MoS 2 if it is important to avoid contaminating the flakes with residual adhesive. [ 17 ]
Liquid-phase exfoliation can also be used to produce monolayer to multi-layer MoS 2 in solution. A few methods include lithium intercalation [ 18 ] to delaminate the layers and sonication in a high-surface tension solvent. [ 19 ] [ 20 ]
MoS 2 excels as a lubricating material (see below) due to its layered structure and low coefficient of friction . Interlayer sliding dissipates energy when a shear stress is applied to the material. Extensive work has been performed to characterize the coefficient of friction and shear strength of MoS 2 in various atmospheres. [ 21 ] The shear strength of MoS 2 increases as the coefficient of friction increases. This property is called superlubricity . At ambient conditions, the coefficient of friction for MoS 2 was determined to be 0.150, with a corresponding estimated shear strength of 56.0 MPa. [ 21 ] Direct methods of measuring the shear strength indicate that the value is closer to 25.3 MPa. [ 22 ]
The wear resistance of MoS 2 in lubricating applications can be increased by doping MoS 2 with Cr . Microindentation experiments on nanopillars of Cr-doped MoS 2 found that the yield strength increased from an average of 821 MPa for pure MoS 2 (at 0% Cr) to 1017 MPa at 50% Cr. [ 23 ] The increase in yield strength is accompanied by a change in the failure mode of the material. While the pure MoS 2 nanopillar fails through a plastic bending mechanism, brittle fracture modes become apparent as the material is loaded with increasing amounts of dopant. [ 23 ]
The widely used method of micromechanical exfoliation has been carefully studied in MoS 2 to understand the mechanism of delamination in few-layer to multi-layer flakes. The exact mechanism of cleavage was found to be layer dependent. Flakes thinner than 5 layers undergo homogenous bending and rippling, while flakes around 10 layers thick delaminated through interlayer sliding. Flakes with more than 20 layers exhibited a kinking mechanism during micromechanical cleavage. The cleavage of these flakes was also determined to be reversible due to the nature of van der Waals bonding. [ 24 ]
In recent years, MoS 2 has been utilized in flexible electronic applications, promoting more investigation into the elastic properties of this material. Nanoscopic bending tests using AFM cantilever tips were performed on micromechanically exfoliated MoS 2 flakes that were deposited on a holey substrate. [ 17 ] [ 25 ] The Young's modulus of monolayer flakes was 270 GPa, [ 25 ] while the thicker flakes were stiffer, with a Young's modulus of 330 GPa. [ 17 ] Molecular dynamic simulations found the in-plane Young's modulus of MoS 2 to be 229 GPa, which matches the experimental results within error. [ 26 ]
Bertolazzi and coworkers also characterized the failure modes of the suspended monolayer flakes. The strain at failure ranges from 6 to 11%. The average yield strength of monolayer MoS 2 is 23 GPa, which is close to the theoretical fracture strength for defect-free MoS 2 . [ 25 ]
The band structure of MoS 2 is sensitive to strain. [ 27 ] [ 28 ] [ 29 ]
Molybdenum disulfide is stable in air and attacked only by aggressive reagents . It reacts with oxygen upon heating forming molybdenum trioxide :
Chlorine attacks molybdenum disulfide at elevated temperatures to form molybdenum pentachloride :
Molybdenum disulfide is a host for formation of intercalation compounds . This behavior is relevant to its use as a cathode material in batteries. [ 30 ] [ 31 ] One example is a lithiated material, Li x MoS 2 . [ 32 ] With butyl lithium , the product is LiMoS 2 . [ 6 ]
Due to weak van der Waals interactions between the sheets of sulfide atoms, MoS 2 has a low coefficient of friction . MoS 2 in particle sizes in the range of 1–100 μm is a common dry lubricant . [ 34 ] Few alternatives exist that confer high lubricity and stability at up to 350 °C in oxidizing environments. Sliding friction tests of MoS 2 using a pin on disc tester at low loads (0.1–2 N) give friction coefficient values of <0.1. [ 35 ] [ 36 ]
MoS 2 is often a component of blends and composites that require low friction. For example, it is added to graphite to improve sticking. [ 33 ] A variety of oils and greases are used, because they retain their lubricity even in cases of almost complete oil loss, thus finding a use in critical applications such as aircraft engines . When added to plastics , MoS 2 forms a composite with improved strength as well as reduced friction. Polymers that may be filled with MoS 2 include nylon ( trade name Nylatron ), Teflon and Vespel . Self-lubricating composite coatings for high-temperature applications consist of molybdenum disulfide and titanium nitride , using chemical vapor deposition .
Examples of applications of MoS 2 -based lubricants include two-stroke engines (such as motorcycle engines), bicycle coaster brakes , automotive CV and universal joints , ski waxes [ 37 ] and bullets . [ 38 ]
Other layered inorganic materials that exhibit lubricating properties (collectively known as solid lubricants (or dry lubricants)) includes graphite, which requires volatile additives and hexagonal boron nitride . [ 39 ]
MoS 2 is employed as a cocatalyst for desulfurization in petrochemistry , for example, hydrodesulfurization . The effectiveness of the MoS 2 catalysts is enhanced by doping with small amounts of cobalt or nickel . The intimate mixture of these sulfides is supported on alumina . Such catalysts are generated in situ by treating molybdate/cobalt or nickel-impregnated alumina with H 2 S or an equivalent reagent. Catalysis does not occur at the regular sheet-like regions of the crystallites, but instead at the edge of these planes. [ 40 ]
MoS 2 finds use as a hydrogenation catalyst for organic synthesis . [ 41 ] As it is derived from a common transition metal , rather than a group 10 metal, MoS 2 is chosen when price or resistance to sulfur poisoning are of primary concern. MoS 2 is effective for the hydrogenation of nitro compounds to amines and can be used to produce secondary amines via reductive amination . [ 42 ] The catalyst can also effect hydrogenolysis of organosulfur compounds , aldehydes , ketones , phenols and carboxylic acids to their respective alkanes . [ 41 ] However, it suffers from low activity, often requiring hydrogen pressures above 96 MPa and temperatures above 185 °C.
MoS 2 plays an important role in condensed matter physics research. [ 43 ]
MoS 2 and related molybdenum sulfides are efficient catalysts for hydrogen evolution , including the electrolysis of water ; [ 44 ] [ 45 ] thus, are possibly useful to produce hydrogen for use in fuel cells . [ 46 ]
MoS 2 @Fe- N -C core/shell [ 47 ] nanosphere with atomic Fe-doped surface and interface ( MoS 2 /Fe- N -C) can be used as a used an electrocatalyst for oxygen reduction and evolution reactions (ORR and OER) bifunctionally because of reduced energy barrier due to Fe-N 4 dopants and unique nature of MoS 2 /Fe- N -C interface.
As in graphene , the layered structures of MoS 2 and other transition metal dichalcogenides exhibit electronic and optical properties [ 48 ] that can differ from those in bulk. [ 49 ] Bulk MoS 2 has an indirect band gap of 1.2 eV, [ 50 ] [ 51 ] while MoS 2 monolayers have a direct 1.8 eV electronic bandgap , [ 52 ] supporting switchable transistors [ 53 ] and photodetectors . [ 54 ] [ 49 ] [ 55 ]
MoS 2 nanoflakes can be used for solution-processed fabrication of layered memristive and memcapacitive devices through engineering a MoO x / MoS 2 heterostructure sandwiched between silver electrodes. [ 56 ] MoS 2 -based memristors are mechanically flexible, optically transparent and can be produced at low cost.
The sensitivity of a graphene field-effect transistor (FET) biosensor is fundamentally restricted by the zero band gap of graphene, which results in increased leakage and reduced sensitivity. In digital electronics, transistors control current flow throughout an integrated circuit and allow for amplification and switching. In biosensing, the physical gate is removed and the binding between embedded receptor molecules and the charged target biomolecules to which they are exposed modulates the current. [ 57 ]
MoS 2 has been investigated as a component of flexible circuits. [ 58 ] [ 59 ]
In 2017, a 115-transistor, 1-bit microprocessor implementation was fabricated using two-dimensional MoS 2 . [ 60 ]
MoS 2 has been used to create 2D 2-terminal memristors and 3-terminal memtransistors . [ 61 ]
Due to the lack of spatial inversion symmetry, odd-layer MoS2 is a promising material for valleytronics because both the CBM and VBM have two energy-degenerate valleys at the corners of the first Brillouin zone, providing an exciting opportunity to store the information of 0s and 1s at different discrete values of the crystal momentum. The Berry curvature is even under spatial inversion (P) and odd under time reversal (T), the valley Hall effect cannot survive when both P and T symmetries are present. To excite valley Hall effect in specific valleys, circularly polarized lights were used for breaking the T symmetry in atomically thin transition-metal dichalcogenides. [ 62 ] In monolayer MoS 2 , the T and mirror symmetries lock the spin and valley indices of the sub-bands split by the spin-orbit couplings, both of which are flipped under T; the spin conservation suppresses the inter-valley scattering. Therefore, monolayer MoS2 have been deemed an ideal platform for realizing intrinsic valley Hall effect without extrinsic symmetry breaking. [ 63 ]
MoS 2 also possesses mechanical strength, electrical conductivity, and can emit light, opening possible applications such as photodetectors. [ 64 ] MoS 2 has been investigated as a component of photoelectrochemical (e.g. for photocatalytic hydrogen production) applications and for microelectronics applications. [ 53 ]
Under an electric field MoS 2 monolayers have been found to superconduct at temperatures below 9.4 K. [ 65 ] | https://en.wikipedia.org/wiki/Molybdenum_disulfide |
Molybdenum is an essential element in most organisms. [ 1 ] It is most notably present in nitrogenase [ 2 ] which is an essential part of nitrogen fixation . [ 3 ] [ 4 ]
Molybdenum is an essential element in most organisms; a 2008 research paper speculated that a scarcity of molybdenum in the Earth's early oceans may have strongly influenced the evolution of eukaryotic life (which includes all plants and animals). [ 1 ]
At least 50 molybdenum-containing enzymes have been identified, mostly in bacteria. [ 5 ] [ 6 ] Those enzymes include aldehyde oxidase , sulfite oxidase and xanthine oxidase . [ 7 ] With one exception, Mo in proteins is bound by molybdopterin to give the molybdenum cofactor. The only known exception is nitrogenase , which uses the FeMoco cofactor, which has the formula Fe 7 MoS 9 C. [ 8 ]
In terms of function, molybdoenzymes catalyze the oxidation and sometimes reduction of certain small molecules in the process of regulating nitrogen , sulfur , and carbon . [ 9 ] In some animals, and in humans, the oxidation of xanthine to uric acid , a process of purine catabolism , is catalyzed by xanthine oxidase , a molybdenum-containing enzyme. The activity of xanthine oxidase is directly proportional to the amount of molybdenum in the body. An extremely high concentration of molybdenum reverses the trend and can inhibit purine catabolism and other processes. Molybdenum concentration also affects protein synthesis , metabolism , and growth. [ 10 ]
Mo is a component in most nitrogenases . Among molybdoenzymes, nitrogenases are unique in lacking the molybdopterin. [ 11 ] [ 12 ] Nitrogenases catalyze the production of ammonia from atmospheric nitrogen:
The biosynthesis of the FeMoco active site is highly complex. [ 13 ]
Molybdate is transported in the body as MoO 2− 4 . [ 10 ]
Molybdenum is an essential trace dietary element . [ 14 ] Four mammalian Mo-dependent enzymes are known, all of them harboring a pterin -based molybdenum cofactor (Moco) in their active site: sulfite oxidase , xanthine oxidoreductase , aldehyde oxidase , and mitochondrial amidoxime reductase . [ 15 ] People severely deficient in molybdenum have poorly functioning sulfite oxidase and are prone to toxic reactions to sulfites in foods. [ 16 ] [ 17 ] The human body contains about 0.07 mg of molybdenum per kilogram of body weight, [ 18 ] with higher concentrations in the liver and kidneys and lower in the vertebrae. [ 19 ] Molybdenum is also present within human tooth enamel and may help prevent its decay. [ 20 ]
Acute toxicity has not been seen in humans, and the toxicity depends strongly on the chemical state. Studies on rats show a median lethal dose (LD 50 ) as low as 180 mg/kg for some Mo compounds. [ 21 ] Although human toxicity data is unavailable, animal studies have shown that chronic ingestion of more than 10 mg/day of molybdenum can cause diarrhea, growth retardation, infertility , low birth weight, and gout ; it can also affect the lungs, kidneys, and liver. [ 22 ] [ 23 ] Sodium tungstate is a competitive inhibitor of molybdenum. Dietary tungsten reduces the concentration of molybdenum in tissues. [ 19 ]
Low soil concentration of molybdenum in a geographical band from northern China to Iran results in a general dietary molybdenum deficiency , and is associated with increased rates of esophageal cancer . [ 24 ] [ 25 ] [ 26 ] Compared to the United States, which has a greater supply of molybdenum in the soil, people living in those areas have about 16 times greater risk for esophageal squamous cell carcinoma . [ 27 ]
Molybdenum deficiency has also been reported as a consequence of non-molybdenum supplemented total parenteral nutrition (complete intravenous feeding) for long periods of time. It results in high blood levels of sulfite and urate , in much the same way as molybdenum cofactor deficiency . Since pure molybdenum deficiency from this cause occurs primarily in adults, the neurological consequences are not as marked as in cases of congenital cofactor deficiency. [ 28 ]
A congenital molybdenum cofactor deficiency disease, seen in infants, is an inability to synthesize molybdenum cofactor , the heterocyclic molecule discussed above that binds molybdenum at the active site in all known human enzymes that use molybdenum. The resulting deficiency results in high levels of sulfite and urate , and neurological damage. [ 29 ] [ 30 ]
Most molybdenum is excreted from the human body as molybdate in the urine. Furthermore, urinary excretion of molybdenum increases as dietary molybdenum intake increases. Small amounts of molybdenum are excreted from the body in the feces by way of the bile; small amounts also can be lost in sweat and in hair. [ 31 ] [ 32 ]
High levels of molybdenum can interfere with the body's uptake of copper , producing copper deficiency . Molybdenum prevents plasma proteins from binding to copper, and it also increases the amount of copper that is excreted in urine . Ruminants that consume high levels of molybdenum suffer from diarrhea , stunted growth, anemia , and achromotrichia (loss of fur pigment). These symptoms can be alleviated by copper supplements, either dietary or injection. [ 33 ] The effective copper deficiency can be aggravated by excess sulfur . [ 19 ] [ 34 ]
Copper reduction or deficiency can also be deliberately induced for therapeutic purposes by the compound ammonium tetrathiomolybdate , in which the bright red anion tetrathiomolybdate is the copper-chelating agent. Tetrathiomolybdate was first used therapeutically in the treatment of copper toxicosis in animals. It was then introduced as a treatment in Wilson's disease , a hereditary copper metabolism disorder in humans; it acts both by competing with copper absorption in the bowel and by increasing excretion. It has also been found to have an inhibitory effect on angiogenesis , potentially by inhibiting the membrane translocation process that is dependent on copper ions. [ 35 ] This is a promising avenue for investigation of treatments for cancer , age-related macular degeneration , and other diseases that involve a pathologic proliferation of blood vessels. [ 36 ] [ 37 ]
In some grazing livestock, most strongly in cattle, molybdenum excess in the soil of pasturage can produce scours ( diarrhea ) if the pH of the soil is neutral to alkaline; see teartness . | https://en.wikipedia.org/wiki/Molybdenum_in_biology |
The molybdovanadate reagent is a solution containing both the molybdate and vanadate ions. It is commonly used in the determination of phosphate ion content. [ 1 ] [ 2 ] The reagent used contains ammonium molybdovanadate with the addition of a strong acid such as perchloric acid , sulfuric acid , or nitric acid. [ 3 ] It is used for purposes such as the analysis of wine , canned fruits and other fruit-based products such as jams and syrups . [ 4 ] [ 5 ]
The reagent appears as a clear, yellow liquid without odour. It is harmful if inhaled, a recognised carcinogen and can cause eye burns.
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Molybdovanadate_reagent |
Moment-resisting frame is a rectilinear assemblage of beams and columns, with the beams rigidly connected to the columns.
Resistance to lateral forces is provided primarily by rigid frame action – that is, by the development of bending moment and shear force in the frame members and joints. By virtue of the rigid beam–column connections, a moment frame cannot displace laterally without bending the beams or columns depending on the geometry of the connection. The bending rigidity and strength of the frame members is therefore the primary source of lateral stiffness and strength for the entire frame. [ 1 ]
The 1994 Northridge earthquake revealed a common flaw in steel-frame construction — poorly welded moment connections — and building codes were revised to strengthen them. [ 2 ]
Steel moment-resisting frames have been in use for more than one hundred years, dating to the earliest use of structural steel in building construction. Steel building construction with the frame carrying the vertical loads initiated with the Home Insurance Building in Chicago, a 10-story structure constructed in 1884 with a height of 138 ft, often credited with being the first skyscraper. This and other tall buildings in Chicago spawned an entire generation of tall buildings, constructed with load bearing steel frames supporting concrete floors and non-load bearing, unreinforced masonry infill walls at their perimeters. Framing in these early structures typically utilized "H" shapes built up from plates, and "L" and "Z" sections. [ 3 ] | https://en.wikipedia.org/wiki/Moment-resisting_frame |
A moment is a mathematical expression involving the product of a distance and a physical quantity such as a force or electric charge . Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. For example, the moment of force, often called torque , is the product of a force on an object and the distance from the reference point to the object. In principle, any physical quantity can be multiplied by a distance to produce a moment. Commonly used quantities include forces, masses , and electric charge distributions; a list of examples is provided later.
In its most basic form, a moment is the product of the distance to a point, raised to a power, and a physical quantity
(such as force or electrical charge) at that point:
where Q {\displaystyle Q} is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity is not concentrated solely at a single point, the moment is the integral of that quantity's density over space:
where ρ {\displaystyle \rho } is the distribution of the density of charge, mass, or whatever quantity is being considered.
More complex forms take into account the angular relationships between the distance and the physical quantity, but the above equations capture the essential feature of a moment, namely the existence of an underlying r n ρ ( r ) {\displaystyle r^{n}\rho (r)} or equivalent term. This implies that there are multiple moments (one for each value of n ) and that the moment generally depends on the reference point from which the distance r {\displaystyle r} is measured, although for certain moments (technically, the lowest non-zero moment) this dependence vanishes and the moment becomes independent of the reference point.
Each value of n corresponds to a different moment: the 1st moment corresponds to n = 1; the 2nd moment to n = 2, etc. The 0th moment ( n = 0) is sometimes called the monopole moment ; the 1st moment ( n = 1) is sometimes called the dipole moment , and the 2nd moment ( n = 2) is sometimes called the quadrupole moment , especially in the context of electric charge distributions.
Moments of mass:
Assuming a density function that is finite and localized to a particular region, outside that region a 1/ r potential may be expressed as a series of spherical harmonics :
The coefficients q ℓ m {\displaystyle q_{\ell m}} are known as multipole moments , and take the form:
where r ′ {\displaystyle \mathbf {r} '} expressed in spherical coordinates ( r ′ , φ ′ , θ ′ ) {\displaystyle \left(r',\varphi ',\theta '\right)} is a variable of integration. A more complete treatment may be found in pages describing multipole expansion or spherical multipole moments . (The convention in the above equations was taken from Jackson [ 1 ] – the conventions used in the referenced pages may be slightly different.)
When ρ {\displaystyle \rho } represents an electric charge density, the q l m {\displaystyle q_{lm}} are, in a sense, projections of the moments of electric charge: q 00 {\displaystyle q_{00}} is the monopole moment; the q 1 m {\displaystyle q_{1m}} are projections of the dipole moment, the q 2 m {\displaystyle q_{2m}} are projections of the quadrupole moment, etc.
The multipole expansion applies to 1/ r scalar potentials, examples of which include the electric potential and the gravitational potential . For these potentials, the expression can be used to approximate the strength of a field produced by a localized distribution of charges (or mass) by calculating the first few moments. For sufficiently large r , a reasonable approximation can be obtained from just the monopole and dipole moments. Higher fidelity can be achieved by calculating higher order moments. Extensions of the technique can be used to calculate interaction energies and intermolecular forces.
The technique can also be used to determine the properties of an unknown distribution ρ {\displaystyle \rho } . Measurements pertaining to multipole moments may be taken and used to infer properties of the underlying distribution. This technique applies to small objects such as molecules, [ 2 ] [ 3 ] but has also been applied to the universe itself, [ 4 ] being for example the technique employed by the WMAP and Planck experiments to analyze the cosmic microwave background radiation.
In works believed to stem from Ancient Greece , the concept of a moment is alluded to by the word ῥοπή ( rhopḗ , lit. "inclination") and composites like ἰσόρροπα ( isorropa , lit. "of equal inclinations"). [ 5 ] [ 6 ] [ 7 ] The context of these works is mechanics and geometry involving the lever . [ 8 ] In particular, in extant works attributed to Archimedes , the moment is pointed out in phrasings like:
Moreover, in extant texts such as The Method of Mechanical Theorems , moments are used to infer the center of gravity , area, and volume of geometric figures.
In 1269, William of Moerbeke translates various works of Archimedes and Eutocious into Latin . The term ῥοπή is transliterated into ropen . [ 6 ]
Around 1450, Jacobus Cremonensis translates ῥοπή in similar texts into the Latin term momentum ( lit. "movement" [ 10 ] ). [ 11 ] [ 6 ] : 331 The same term is kept in a 1501 translation by Giorgio Valla , and subsequently by Francesco Maurolico , Federico Commandino , Guidobaldo del Monte , Adriaan van Roomen , Florence Rivault , Francesco Buonamici , Marin Mersenne [ 5 ] , and Galileo Galilei . That said, why was the word momentum chosen for the translation? One clue, according to Treccani , is that momento in medieval Italy, the place the early translators lived, in a transferred sense meant both a "moment of time" and a "moment of weight" (a small amount of weight that turns the scale ). [ b ]
In 1554, Francesco Maurolico clarifies the Latin term momentum in the work Prologi sive sermones . Here is a Latin to English translation as given by Marshall Clagett : [ 6 ]
"[...] equal weights at unequal distances do not weigh equally, but unequal weights [at these unequal distances may] weigh equally. For a weight suspended at a greater distance is heavier, as is obvious in a balance . Therefore, there exists a certain third kind of power or third difference of magnitude—one that differs from both body and weight—and this they call moment . [ c ] Therefore, a body acquires weight from both quantity [i.e., size] and quality [i.e., material], but a weight receives its moment from the distance at which it is suspended. Therefore, when distances are reciprocally proportional to weights, the moments [of the weights] are equal, as Archimedes demonstrated in The Book on Equal Moments . [ d ] Therefore, weights or [rather] moments like other continuous quantities, are joined at some common terminus, that is, at something common to both of them like the center of weight, or at a point of equilibrium. Now the center of gravity in any weight is that point which, no matter how often or whenever the body is suspended, always inclines perpendicularly toward the universal center.
In addition to body, weight, and moment, there is a certain fourth power, which can be called impetus or force. [ e ] Aristotle investigates it in On Mechanical Questions , and it is completely different from [the] three aforesaid [powers or magnitudes]. [...]"
in 1586, Simon Stevin uses the Dutch term staltwicht ("parked weight") for momentum in De Beghinselen Der Weeghconst .
In 1632, Galileo Galilei publishes Dialogue Concerning the Two Chief World Systems and uses the Italian momento with many meanings, including the one of his predecessors. [ 12 ]
In 1643, Thomas Salusbury translates some of Galilei's works into English . Salusbury translates Latin momentum and Italian momento into the English term moment . [ f ]
In 1765, the Latin term momentum inertiae ( English : moment of inertia ) is used by Leonhard Euler to refer to one of Christiaan Huygens 's quantities in Horologium Oscillatorium . [ 13 ] Huygens 1673 work involving finding the center of oscillation had been stimulated by Marin Mersenne , who suggested it to him in 1646. [ 14 ] [ 15 ]
In 1811, the French term moment d'une force ( English : moment of a force ) with respect to a point and plane is used by Siméon Denis Poisson in Traité de mécanique . [ 16 ] An English translation appears in 1842.
In 1884, the term torque is suggested by James Thomson in the context of measuring rotational forces of machines (with propellers and rotors ). [ 17 ] [ 18 ] Today, a dynamometer is used to measure the torque of machines.
In 1893, Karl Pearson uses the term n-th moment and μ n {\displaystyle \mu _{n}} in the context of curve-fitting scientific measurements. [ 19 ] Pearson wrote in response to John Venn , who, some years earlier, observed a peculiar pattern involving meteorological data and asked for an explanation of its cause. [ 20 ] In Pearson's response, this analogy is used: the mechanical "center of gravity" is the mean and the "distance" is the deviation from the mean. This later evolved into moments in mathematics . The analogy between the mechanical concept of a moment and the statistical function involving the sum of the n th powers of deviations was noticed by several earlier, including Laplace , Kramp , Gauss , Encke , Czuber , Quetelet , and De Forest . [ 21 ] | https://en.wikipedia.org/wiki/Moment_(physics) |
The moment distance index (MDI) is a shape-based metric or shape index that can be used to analyze spectral reflectance curves and waveform lidar , proposed by Dr. Eric Ariel L. Salas and Dr. Geoffrey M. Henebry (Salas and Henebry, 2014). [ 1 ] In the case of spectral data, the shape of the reflectance curve should unmask fine points of the spectra usually not considered by existing band-specific indices. It has been used to identify spectral regions for chlorophyll and carotenoids, [ 2 ] detect greenhouses using WorldView-2 , Landsat , and Sentinel-2 satellite data, [ 3 ] [ 4 ] [ 5 ] identify greenhouse crops, [ 6 ] compute canopy heights, [ 7 ] estimate green vegetation fraction, [ 8 ] and optimize Fourier-transform infrared (FTIR) scans for soil spectroscopy. [ 9 ]
Various approaches have been devised to analyze medium and fine spectral resolution data and maximize their use to extract specific information for vegetation biophysical and biochemical properties. Combinations of spectral bands, called indices, have been used to diminish the effects of soil background and/or atmospheric conditions while highlighting specific spectral features associated with plant or canopy properties. Vegetation Indices (VIs) use the concept of band ratio and differences or weighted linear combinations to take advantage of the visible and NIR bands, two important spectral bands for vegetation studies, in measuring the photosynthetic activity of the plant and explore vegetation dynamics. There is an extensive list of such indices, including the normalized difference vegetation index , ratio-based indices such as the modified simplerRatio , soil-distance-based indices such as the modified soil adjusted vegetation index , and many others. Whereas most indices incorporate two-band or three-band relations – slope-based, distance-based on soil line or optimized (slope-based and distance-based concepts combined) – no approach deals with the raw shape of the spectral curve. MDI, however, investigates the shape of the reflectance curve using multiple spectral bands not considered by other indices, which could carry additional spectral information useful for vegetation monitoring.
A full-waveform lidar system has the ability to record many returns per emitted pulse, as a function of time, to reveal the vertical structure of the illuminated object, showing position of the individual targets, and finer details of the signature of intercepted surfaces or the proportion of the canopy complexity. Information associated with the illuminated object can be decoded from the generated backscattered waveform, as key features of the waveform such as the shape, area, and power are directly related to the geometry of the illuminated object. The richness of the lidar waveform holds a promise to address the challenge of characterizing in detail the geometric and reflection characteristics of vegetation structure, e.g., the vertical canopy volume distribution. MDI utilizes the raw waveform and place importance on its shape and its return power. MDI departs from the usual Gaussian modeling in detecting peaks (canopy and ground) for example in canopy height estimation and focus more on the full geometry (raw shape) and radiometry (raw power) of the lidar waveform to retain richness of the data.
The moment distance is a matrix of distances computed from two reference locations (pivots) to each spectral or waveform point within the specified range.
Assume that a curve (reflectance or absorption curve or backscattered waveform) is displayed in Cartesian coordinates with the abscissa displaying the wavelength λ or time lapse t and the ordinate displaying the reflectance ρ or the backscattered power p . Let the subscript LP denote the left pivot (located in a shorter wavelength for the spectral curve and earlier temporal reference point for the waveform) and subscript RP denote the right pivot (located in a longer wavelength for the spectral curve and later temporal reference point for the waveform). Let λ LP and λ RP be the wavelength locations observed at the left and right pivots for a reflectance data, respectively, where left (right) indicates a shorter (longer) wavelength. Let t LP and t RP be the time value observed at the left and right pivots for a waveform data, respectively, where left (right) indicates an earlier (later) time. The proposed MD approach can be described in a set of equations.
For spectral data, the index is given as:
M D I = M D R P − M D L P {\displaystyle MDI=MD_{RP}-MD_{LP}}
M D R P = ∑ i = λ R P λ L P ( ρ i 2 + ( λ R P − i ) 2 ) 0.5 {\displaystyle MD_{RP}=\textstyle \sum _{i=\lambda _{RP}}^{\lambda _{LP}}\displaystyle (\rho _{i}^{2}+({\lambda _{RP}}-i)^{2})^{0.5}}
M D L P = ∑ i = λ L P λ R P ( ρ i 2 + ( i − λ L P ) 2 ) 0.5 {\displaystyle MD_{LP}=\textstyle \sum _{i=\lambda _{LP}}^{\lambda _{RP}}\displaystyle (\rho _{i}^{2}+(i-{\lambda _{LP}})^{2})^{0.5}}
where M D I R P {\displaystyle MDI_{RP}} is the moment distance from the right pivot, M D I L P {\displaystyle MDI_{LP}} is the moment distance from the left pivot, λ L P {\displaystyle {\lambda _{LP}}} is the wavelength location at left pivot, λ R P {\displaystyle {\lambda _{RP}}} is the wavelength location at right pivot, ρ i {\displaystyle \rho _{i}} is the spectral reflectance at a given wavelength, and i {\displaystyle i} is successive wavelength location.
For waveform lidar data, the index is given as:
M D I = M D L P − M D R P {\displaystyle MDI=MD_{LP}-MD_{RP}}
M D R P = ∑ i = t R P t L P ( ρ i 2 + ( t R P − i ) 2 ) 0.5 {\displaystyle MD_{RP}=\textstyle \sum _{i=t_{RP}}^{t_{LP}}\displaystyle (\rho _{i}^{2}+({t_{RP}}-i)^{2})^{0.5}}
M D L P = ∑ i = t L P t R P ( ρ i 2 + ( i − t L P ) 2 ) 0.5 {\displaystyle MD_{LP}=\textstyle \sum _{i=t_{LP}}^{t_{RP}}\displaystyle (\rho _{i}^{2}+(i-{t_{LP}})^{2})^{0.5}}
where the moment distance from the left pivot (MD LP ) is the sum of the hypotenuses constructed from the left pivot to the power at successively later times (index i {\displaystyle i} from t LP to t RP ): one base of each triangle is difference from the left pivot ( i {\displaystyle i} − t LP ) along the abscissa and the other base is simply the backscattered power at i {\displaystyle i} . Similarly, the moment distance from the right pivot (MD RP ) is the sum of the hypotenuses constructed from the right pivot to the power at successively earlier times (index i {\displaystyle i} from t RP to t LP ): one base of each triangle is the difference from the right pivot ( t RP − i {\displaystyle i} ) along the abscissa and the other base is simply the backscattered power at i {\displaystyle i} .
MDI is an unbounded metric. It increases or decreases as a nontrivial function of the number of spectral bands or bins considered and the shape of the spectrum or waveform that spans those contiguous bands or bins. The number of bands or bins is a function of the spectral resolution of the imaging spectrometer or the temporal resolution of the lidar (digitization rate) and the length of the reference range (i.e., full extent or subsets of the curve) being analyzed. | https://en.wikipedia.org/wiki/Moment_distance_index |
In planetary sciences , the moment of inertia factor or normalized polar moment of inertia is a dimensionless quantity that characterizes the radial distribution of mass inside a planet or satellite . Since a moment of inertia has dimensions of mass times length squared, the moment of inertia factor is the coefficient that multiplies these.
For a planetary body with principal moments of inertia A < B < C {\displaystyle A<B<C} , the moment of inertia factor is defined as
where C is the first principal moment of inertia of the body, M is the mass of the body, and R is the mean radius of the body. [ 1 ] [ 2 ] For a sphere with uniform density , C / M R 2 = 2 / 5 {\displaystyle C/MR^{2}=2/5} . [ note 1 ] [ note 2 ] For a differentiated planet or satellite, where there is an increase of density with depth, C / M R 2 < 2 / 5 {\displaystyle C/MR^{2}<2/5} . The quantity is a useful indicator of the presence and extent of a planetary core , because a greater departure from the uniform-density value of 2/5 conveys a greater degree of concentration of dense materials towards the center.
The Sun has by far the lowest moment of inertia factor value among Solar System bodies; it has by far the highest central density ( 162 g/cm 3 , [ 3 ] [ note 3 ] compared to ~13 for Earth [ 4 ] [ 5 ] ) and a relatively low average density (1.41 g/cm 3 versus 5.5 for Earth). Saturn has the lowest value among the gas giants in part because it has the lowest bulk density ( 0.687 g/cm 3 ). [ 6 ] Ganymede has the lowest moment of inertia factor among solid bodies in the Solar System because of its fully differentiated interior, [ 7 ] [ 8 ] a result in part of tidal heating due to the Laplace resonance , [ 9 ] as well as its substantial component of low density water ice . Callisto is similar in size and bulk composition to Ganymede, but is not part of the orbital resonance and is less differentiated. [ 7 ] [ 8 ] The Moon is thought to have a small core, but its interior is otherwise relatively homogenous. [ 10 ] [ 11 ]
The polar moment of inertia is traditionally determined by combining measurements of spin quantities ( spin precession rate and/or obliquity ) with gravity quantities (coefficients of a spherical harmonic representation of the gravity field). These geodetic data usually require an orbiting spacecraft to collect.
For bodies in hydrostatic equilibrium , the Darwin–Radau relation can provide estimates of the moment of inertia factor on the basis of shape, spin, and gravity quantities. [ 26 ]
The moment of inertia factor provides an important constraint for models representing the interior structure of a planet or satellite. At a minimum, acceptable models of the density profile must match the volumetric mass density and moment of inertia factor of the body. | https://en.wikipedia.org/wiki/Moment_of_inertia_factor |
In mathematics , a moment problem arises as the result of trying to invert the mapping that takes a measure μ {\displaystyle \mu } to the sequence of moments
More generally, one may consider
for an arbitrary sequence of functions M n {\displaystyle M_{n}} .
In the classical setting, μ {\displaystyle \mu } is a measure on the real line , and M {\displaystyle M} is the sequence { x n : n = 1 , 2 , … } {\displaystyle \{x^{n}:n=1,2,\dotsc \}} . In this form the question appears in probability theory , asking whether there is a probability measure having specified mean , variance and so on, and whether it is unique.
There are three named classical moment problems: the Hamburger moment problem in which the support of μ {\displaystyle \mu } is allowed to be the whole real line; the Stieltjes moment problem , for [ 0 , ∞ ) {\displaystyle [0,\infty )} ; and the Hausdorff moment problem for a bounded interval, which without loss of generality may be taken as [ 0 , 1 ] {\displaystyle [0,1]} .
The moment problem also extends to complex analysis as the trigonometric moment problem in which the Hankel matrices are replaced by Toeplitz matrices and the support of μ is the complex unit circle instead of the real line. [ 1 ]
A sequence of numbers m n {\displaystyle m_{n}} is the sequence of moments of a measure μ {\displaystyle \mu } if and only if a certain positivity condition is fulfilled; namely, the Hankel matrices H n {\displaystyle H_{n}} ,
should be positive semi-definite . This is because a positive-semidefinite Hankel matrix corresponds to a linear functional Λ {\displaystyle \Lambda } such that Λ ( x n ) = m n {\displaystyle \Lambda (x^{n})=m_{n}} and Λ ( f 2 ) ≥ 0 {\displaystyle \Lambda (f^{2})\geq 0} (non-negative for sum of squares of polynomials). Assume Λ {\displaystyle \Lambda } can be extended to R [ x ] ∗ {\displaystyle \mathbb {R} [x]^{*}} . In the univariate case, a non-negative polynomial can always be written as a sum of squares. So the linear functional Λ {\displaystyle \Lambda } is positive for all the non-negative polynomials in the univariate case. By Haviland's theorem, the linear functional has a measure form, that is Λ ( x n ) = ∫ − ∞ ∞ x n d μ {\displaystyle \Lambda (x^{n})=\int _{-\infty }^{\infty }x^{n}d\mu } . A condition of similar form is necessary and sufficient for the existence of a measure μ {\displaystyle \mu } supported on a given interval [ a , b ] {\displaystyle [a,b]} .
One way to prove these results is to consider the linear functional φ {\displaystyle \varphi } that sends a polynomial
to
If m k {\displaystyle m_{k}} are the moments of some measure μ {\displaystyle \mu } supported on [ a , b ] {\displaystyle [a,b]} , then evidently
Vice versa, if ( 1 ) holds, one can apply the M. Riesz extension theorem and extend φ {\displaystyle \varphi } to a functional on the space of continuous functions with compact support C c ( [ a , b ] ) {\displaystyle C_{c}([a,b])} ), so that
By the Riesz representation theorem , ( 2 ) holds iff there exists a measure μ {\displaystyle \mu } supported on [ a , b ] {\displaystyle [a,b]} , such that
for every f ∈ C c ( [ a , b ] ) {\displaystyle f\in C_{c}([a,b])} .
Thus the existence of the measure μ {\displaystyle \mu } is equivalent to ( 1 ). Using a representation theorem for positive polynomials on [ a , b ] {\displaystyle [a,b]} , one can reformulate ( 1 ) as a condition on Hankel matrices. [ 2 ] [ 3 ]
The uniqueness of μ {\displaystyle \mu } in the Hausdorff moment problem follows from the Weierstrass approximation theorem , which states that polynomials are dense under the uniform norm in the space of continuous functions on [ 0 , 1 ] {\displaystyle [0,1]} . For the problem on an infinite interval, uniqueness is a more delicate question. [ 4 ] There are distributions, such as log-normal distributions , which have finite moments for all the positive integers but where other distributions have the same moments.
When the solution exists, it can be formally written using derivatives of the Dirac delta function as
The expression can be derived by taking the inverse Fourier transform of its characteristic function .
An important variation is the truncated moment problem , which studies the properties of measures with fixed first k moments (for a finite k ). Results on the truncated moment problem have numerous applications to extremal problems , optimisation and limit theorems in probability theory . [ 3 ]
The moment problem has applications to probability theory. The following is commonly used: [ 5 ]
Theorem (Fréchet-Shohat) — If μ {\textstyle \mu } is a determinate measure (i.e. its moments determine it uniquely), and the measures μ n {\textstyle \mu _{n}} are such that ∀ k ≥ 0 lim n → ∞ m k [ μ n ] = m k [ μ ] , {\displaystyle \forall k\geq 0\quad \lim _{n\rightarrow \infty }m_{k}\left[\mu _{n}\right]=m_{k}[\mu ],} then μ n → μ {\textstyle \mu _{n}\rightarrow \mu } in distribution.
By checking Carleman's condition , we know that the standard normal distribution is a determinate measure, thus we have the following form of the central limit theorem :
Corollary — If a sequence of probability distributions ν n {\textstyle \nu _{n}} satisfy m 2 k [ ν n ] → ( 2 k ) ! 2 k k ! ; m 2 k + 1 [ ν n ] → 0 {\displaystyle m_{2k}[\nu _{n}]\to {\frac {(2k)!}{2^{k}k!}};\quad m_{2k+1}[\nu _{n}]\to 0} then ν n {\textstyle \nu _{n}} converges to N ( 0 , 1 ) {\textstyle N(0,1)} in distribution. | https://en.wikipedia.org/wiki/Moment_problem |
Moment redistribution refers to the behavior of statically indeterminate structures that are not completely elastic , but have some reserve plastic capacity. When one location first yields , further application of load to the structure causes the bending moment to redistribute differently from what a purely elastic analysis would suggest.
When the load is applied to a beam, the beam resists the load first elastically, then elasto-plastically until the full plastic moment is reached at some point. When the maximum moment is reached, a plastic hinge has formed, which for further load increments behaves as a pin joint. Further increment in load does not increase the moment at the points where the plastic hinges are formed. The increased load increases the moment in the less stressed sections of the beam; hence due to this, further plastic hinges are formed. This process of shift of application of moment in the beam is termed as moment redistribution in a beam. [ 1 ]
This engineering-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Moment_redistribution |
Discovered by British engineer Christopher Cockerell , the momentum curtain is a unique and efficient way to reduce friction between a vehicle and its surface of travel, be it water or land, by levitating the vehicle above this surface via a cushion of air. It is this principle of levitation upon which a hovercraft is based, and Christopher Cockerell set about applying his momentum curtain theory to hovercraft to increase their abilities in overcoming friction in travel. [ 1 ] [ 2 ]
Levitating a vehicle above the ground/water to reduce its drag was not a new concept. John Thornycroft , in 1877, discovered that trapping air beneath a ship's hull, or pumping air beneath it with bellows , decreased the effects of friction upon the hull thereby increasing the ship's top attainable speeds. [ 3 ] However, technology at the time was insufficient for Thornycroft's ideas to be developed further.
Cockerell used the idea of pumped air under a hull (this then becoming a plenum , i.e. the opposite of a vacuum ) and improved upon it further. Simply pumping air between a hull and the ground wasted a lot of energy in terms of leakage of air around the edges of the hull. Cockerell discovered that by means of generating a wall (curtain) of high-speed downward-directed air around the edges of a hull, that less air leaked out from the sides (due to the momentum of the high-speed air molecules), and thus a greater pressure could be attained beneath the hull. So, with the same input power, a greater amount of lift could be developed, and the hull could be lifted higher above the surface, reducing friction and increasing clearance. This theory was tried, tested and developed throughout the 1950s and 1960s until it was finally realised in full-scale in the SR-N1 hovercraft. | https://en.wikipedia.org/wiki/Momentum_curtain |
Momentum diffusion most commonly refers to the diffusion , or spread of momentum between particles ( atoms or molecules ) of matter , often in the fluid state.
This transport of momentum can occur in any direction of the fluid flow. Momentum diffusion can be attributed to either external pressure or shear stress or both.
When pressure is applied on an incompressible fluid the velocity of the fluid will change. The fluid accelerates or decelerates depending on the relative direction of pressure with respect to the flow direction. This is because applying pressure on the fluid has caused momentum diffusion in that direction. Understanding the exact nature of diffusion is a key aspect toward understanding momentum diffusion due to pressure. [ 1 ]
A fluid flowing along a flat plate will stick to it at the point of contact and this is known as the no-slip condition . This is an outcome of the adhesive forces between the flat plate and the fluid. The presence of the wall has an effect up to a certain distance
in the fluid (in the direction perpendicular to the wall area and flow ) and this is known as the boundary layer .
Any layer of fluid that is not in contact with the wall will be flowing with a certain velocity and will be sandwiched between two layers of fluid. Now the layer just above it (flowing with a greater velocity) will try to drag it in the direction of flow, whereas the layer just below it (flowing with a lesser velocity) will try to slow it down. The attraction between the layers of the fluid is the result of cohesive forces, and viscosity is the property that explains the nature and strength of cohesive forces within a fluid.
It is common to experience the fact that the flowing fluid will exert a certain amount of force on the plate, trying to pull it in its flow direction. The flat plate exerts an equal amount of force on the fluid. ( Newton's third law )
Experiments on the fluid flow parallel to a flat plate reveal that the force, known as shear stress can be expressed mathematically as
τ = − μ d u / d y {\displaystyle \tau =-\mu du/dy}
Note this is valid only for one dimensional fluid flow in rectangular coordinates. The τ {\displaystyle \tau } is the shear stress at any layer of the fluid where d u / d y {\displaystyle du/dy} (i.e. the gradient of velocity in a direction perpendicular to the flow and the area of the flat plate), is the local gradient and μ {\displaystyle \mu } is the viscosity.
The units of shear stress are Force/Unit Area. This is N / m 2 {\displaystyle N/m^{2}} in M.K.S system. This can also be interpreted as k g / m ⋅ s 2 {\displaystyle kg/m{\cdot }s^{2}} . However, these are also the units of momentum flux. This is the precise reason why shear stress in a fluid can also be interpreted as the flux of momentum. The diffusion of momentum is in the direction of decreasing velocity. This means that momentum is being transferred from the fluid in the upper layers (which has greater momentum) toward the fluid that is close to the wall (which has lesser momentum due to its lower velocity).
The phrase "momentum diffusion" can also refer to the diffusion of the probability for a single particle to have a particular momentum. [ 2 ] In this case, it is the probability distribution function that diffuses in momentum space, rather than the (conserved) quantity of momentum that diffuses among many particles. | https://en.wikipedia.org/wiki/Momentum_diffusion |
Momentum mapping format is a key technique in the Material Point Method (MPM) for transferring physical quantities such as momentum , mass , and stress between a material point and a background grid. [ 1 ]
The Material Point Method (MPM) is a numerical technique using a mixed Eulerian-Lagrangian description. It discretises the computational domain with material points and employs a background grid to solve the momentum equations. Proposed by Sulsky et al. in 1994. [ 1 ]
MPM has since been expanded to various fields such as computational solid dynamics. Currently, MPM features several momentum mapping schemes, with the four main ones being PIC ( Particle-in-cell ), FLIP (Fluid-Implicit Particle), hybrid format, and APIC (Affine Particle-in-Cell). Understanding these schemes in-depth is crucial for the further development of MPM. [ 1 ]
MPM represents materials as collections of material points (or particles). Unlike other particle methods such as SPH [ 2 ] ( Smoothed-particle hydrodynamics ) and DEM [ 3 ] ( Discrete element method ), MPM also uses a background grid to solve the momentum equations arising from particle interactions. MPM can be categorized as a mixed particle/ grid method or a mixed Lagrangian-Eulerian method. By combining the strengths of both frameworks, MPM aims to be the most effective numerical solver for large deformation problems. [ 4 ] It has been further developed and applied to various challenging problems such as high-speed impact (Huang et al., 2011 [ 5 ] ), landslides (Fern et al., 2019 [ 6 ] ), saturated porous media (He et al., 2024 [ 7 ] ), and fluid-structure interaction (Li et al., 2022). [ 8 ]
The Material Point Method (MPM) community has developed several momentum mapping schemes, among which PIC, FLIP, the hybrid scheme, and APIC are the most common. The FLIP scheme is widely used for dynamic problems due to its energy conservation properties, although it can introduce numerical noise and instability (Bardenhagen, 2002 [ 9 ] ), potentially leading to computational failure. Conversely, the PIC scheme is known for numerical stability and is advantageous for static problems, but it suffers from significant numerical dissipation (Brackbill et al., 1988 [ 10 ] ), which is unacceptable for strongly dynamic responses. Nairn et al. combined FLIP and PIC linearly (Nairn, 2015 [ 11 ] ) to create a hybrid scheme, adjusting the proportion of each component based on empirical rather than theoretical analysis. Hammerquist and Nairn (2017 [ 12 ] ) introduced an improved scheme called XPIC-m (for eXtended Particle-In-Cell of order m), which addresses the excessive filtering and numerical diffusion of PIC while suppressing the noise caused by the nonlinear space in FLIP used in MPM. XPIC-1 (eXtended Particle-In-Cell of order 1) is equivalent to the standard PIC method. Jiang et al. (2017, [ 13 ] 2015 [ 14 ] ) introduced the Affine Particle In Cell (APIC) method, where particle velocities are represented locally affine, preserving linear and angular momentum during the transfer process. This significantly reduces numerical dissipation and avoids the velocity noise and instability seen in FLIP. Fu et al. (2017 [ 15 ] ) introduced generalized local functions into the APIC method, proposing the Polynomial Particle In Cell (PolyPIC) method. PolyPIC views G2P (Grid-to-Particle) transfer as a projection of the particle's local grid velocity, preserving linear and angular momentum , thereby improving energy and vorticity retention compared to the original APIC. Additionally, PolyPIC retains the filtering properties of APIC and PIC, providing robustness against noise. [ 15 ]
In the PIC scheme, particle velocities during the Grid-to-Particle (G2P) substep are directly overwritten by extrapolating the nodal velocities to the particles themselves: [ 13 ] [ 14 ]
V p n + 1 = ∑ I S I p n V I n + 1 {\displaystyle \mathbf {V} _{p}^{n+1}=\sum _{I}^{}S_{Ip}^{n}\mathbf {V} _{I}^{n+1}}
In the FLIP scheme, the material point velocities are updated by interpolating the velocity increments of the grid nodes over the current time step: [ 14 ]
a I n = f I i n t , n + f I e x t , n m I n {\displaystyle \mathbf {a} _{I}^{n}={\frac {f_{I}^{int,n}+f_{I}^{ext,n}}{m_{I}^{n}}}}
V p n + 1 = V p n + ∑ I S I p n a I n Δ t {\displaystyle \mathbf {V} _{p}^{n+1}=\mathbf {V} _{p}^{n}+\sum _{I}^{}S_{Ip}^{n}\mathbf {a} _{I}^{n}\Delta t}
The hybrid scheme's momentum mapping can be mathematically represented as: [ 13 ]
V p n + 1 = ( 1 − α F L I P ) V p P I C , n + 1 + α F L I P ) V p F L I P , n + 1 {\displaystyle \mathbf {V} _{p}^{n+1}=(1-\alpha _{FLIP}^{})\mathbf {V} _{p}^{PIC,n+1}+\alpha _{FLIP}^{})\mathbf {V} _{p}^{FLIP,n+1}}
where the parameters are defined as shown here below
Based on the idea of "providing the local velocity field around the material point to the background grid by transferring the material point's velocity gradient," Jiang et al. (2015 [ 14 ] ) proposed the APIC method. In this method, the particle velocity is locally affine , mathematically expressed as: [ 14 ]
V p a f f i n e = V p + C p ( x − x p ) {\displaystyle \mathbf {V} _{p}^{affine}=\mathbf {V} _{p}^{}+\mathbf {C} _{p}(\mathbf {x} _{}^{}-\mathbf {x} _{p}^{})}
where the parameters are defined as shown here below:
PIC ( Particle-In-Cell ), FLIP (Fluid-Implicit Particle), hybrid (hybrid solution) and APIC ( Affine [ 13 ] ) The different numerical methods used in Particle-In-Cell fluid simulation greatly show how they map momentum and time integrals between material points and grids, and how they differ from each other. The typical time integration schemes for PIC, FLIP, hybrid, and APIC [ 14 ] schemes have their own unique characteristics. The evolution of momentum on the grid under each scheme is identical. Despite the differences among these four-momentum mapping formats, their common points are still dominant. In the P2G process, the momentum mapping in PIC, FLIP, and hybrid schemes is the same. The material point positions are updated in the same manner across all four schemes. During the G2P stage, PIC transfers the updated momentum on grid nodes directly back to the material points, FLIP uses incremental mapping, and the hybrid scheme linearly combines FLIP and PIC using a coefficient. APIC mapping maintains an additional affine matrix on top of the PIC mapping. [ 14 ]
Numerical tests on ring collision highlight the performance of different momentum mapping schemes in dynamic problems. The mean stress distribution and total energy evolution curve at typical time are the key contents of researchers' attention. Due to the PIC mapping scheme canceling out velocities in opposite directions, significant energy loss occurs, preventing effective conversion of kinetic energy into strain energy. [ 14 ] GIMP_FLIP (Generalized Interpolation Material Point - Fluid Implicit Particle ) shows notable numerical noise and instability, with severe oscillations in mean stress, leading to numerical fracture. GIMP_FLPI0.99 exhibits improved stability but still carries the risk of numerical fracture. Tests indicate that increasing the PIC component enhances numerical stability, with stress distribution becoming more uniform and regular, and the probability of numerical fracture decreasing. However, energy loss also becomes more pronounced. GIMP_APIC (Generalized Interpolation Material Point - Affine Particle-In-Cell) demonstrates the best performance, providing a stable and smooth stress distribution while maintaining excellent energy conservation characteristics. [ 13 ] [ 14 ]
Recently, Qu et al. proposed PowerPIC (Qu et al., 2022), a more stable and accurate mapping scheme based on optimization, which also maintains volume and uniform particle distribution characteristics. [ 16 ] | https://en.wikipedia.org/wiki/Momentum_mapping_format |
In fluid dynamics , momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor , by W.J.M. Rankine (1865), [ 1 ] Alfred George Greenhill (1888) and Robert Edmund Froude (1889). [ 2 ]
The rotor is modeled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of a helicopter is hovering . This disc creates a flow around the rotor. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the rotor, torque and induced velocity. Friction is not included.
For a stationary open rotor with no outer duct, such as a helicopter in hover, the power required to produce a given thrust is:
where:
A device which converts the translational energy of the fluid into rotational energy of the axis or vice versa is called a Rankine disk actuator . The real life implementations of such devices include marine and aviation propellers , windmills , helicopter rotors , centrifugal pumps , wind turbines , turbochargers and chemical agitators . | https://en.wikipedia.org/wiki/Momentum_theory |
Momentus Inc , sometimes styled Momentus space , is an American spaceflight company founded by Mikhail Kokorich which plans to offer space infrastructure services in the form of on-orbit services. [ 1 ] [ 2 ] [ 3 ] The company advertises three orbital tug services which are based around spacecraft electric propulsion and vary in payload mass and Delta-v . As of late 2022 the company has launched one demonstration mission, which produced mixed results. [ 4 ]
Momentus space was a 2018 graduate of the Y Combinator program.
Momentus space received 8.3 million US dollars of seed funding in November 2018. [ 3 ] The investors were Prime Movers Lab, Liquid 2 Ventures , One Way Ventures, Mountain Nazca, Y Combinator, and others.
In 2019, Momentus claimed that its Microwave Electrothermal Thruster (MET) was successfully tested in space, though the U.S. Securities and Exchange Commission accused it of misleading investors via this claim. [ 5 ]
In 2020, Momentus was merged with a SPAC which valued it at 1.2 Billion US dollars [ 6 ] though its valuation quickly dropped to half of this value when it began public trading. [ 2 ]
Momentus space had its first demonstration launch of a vehicle in 2022, which achieved mixed results: multiple anomalies were reported and two of the seven payloads were not deployed.
Momentus space lists plans to offer "space infrastructure" services, including space transportation, on-orbit refueling, and on-orbit services of satellites. Space transportation in the form of space tugs is particularly emphasized. The website lists three models of tug with successively larger payload masses and Delta-v capabilities, in ascending order, name Vigoride , Ardoride, and Fervoride. A still larger tug, called Valoride, has since been removed from their website. [ 3 ] These tugs are propelled by the company's Microwave Electrothermal Thruster (MET), a form of spacecraft electric propulsion in which water is ionized by microwaves and accelerated out of the spacecraft. The specific impulse of these propulsion systems is targeted to be "two or three times" that of chemical propulsion systems, putting them at the low end of existing electric propulsion systems (this conversely puts them at the high end of the specific thrust, or thrust per unit input power). [ 3 ]
On May 26, 2022, Momentus space launched its first demonstration mission on a SpaceX Falcon 9 launch vehicle as part of the Transporter-5 multi-payload ride-share launch. [ 7 ] The Momentus Vigoride -3 space tug was one of several private space tugs launched by that mission. The Vigoride tug carried several payloads for two customers, FOSSA Systems and Orbit NTNU . The Vigoride spacecraft experienced multiple anomalies: at least one due to folding solar panels not deploying, and at least one which caused an off-nominal communication mode. [ 4 ] [ 8 ] [ 9 ] The spacecraft deployed two FOSSA satellites on May 28, 3 days after its launch, and four more between June and August inclusive. Between August and September inclusive, the spacecraft deployed its Orbit NTNU payload, called SelfieSat. As of September 2022, two remaining FOSSA payloads remained un-deployed on the Vigoride spacecraft. [ 10 ]
Another Vigoride demonstration mission, using the Vigoride-5 spacecraft, launched on the SpaceX Transporter-6 launch on 3 January 2023. [ 11 ] Another Vigoride mission, using the Vigoride-6 spacecraft, launched on SpaceX Transporter-7. [ 12 ]
On October 10, 2023, Momentus integrated customers's payloads onto a SpaceX Falcon 9 launch vehicle as part of the Transporter-9 mission. [ 13 ] For this mission, Momentus acted in the capacity of integrator rather than providing orbital services using a Vigoride spacecraft. [ 14 ] The launch vehicle launched successfully on November 11. However, three of the five payloads failed to deploy. [ 15 ] | https://en.wikipedia.org/wiki/Momentus_space |
Momo ( Chinese : 陌陌; pinyin: mò mò) is a free social search and instant messaging mobile app . The app allows users to chat with nearby friends and strangers. Momo provides users with free instant messaging services through Wifi , 3G and 4G . The client software is available for Android , [ 1 ] iOS , [ 2 ] [ 3 ] and Windows Phone . [ 4 ]
Momo officially began operations in July 2011, and a month later, launched the first version of the app for iOS . [ 5 ] Momo filed for a NASDAQ IPO on November 7, 2014 and was listed in December 2014. [ 6 ]
Tang Yan, Zhang Sichuan, Lei Xiaoliang, Yong Li, and Li Zhiwei co-founded Beijing Momo Technology Co., Ltd. in July 2011. [ 5 ] Prior to founding the company, Tang Yan worked as editor and then editor-in-chief at NetEase . In October 2014, Tang was named by Fortune Magazine as one of its "40 Under 40," a list of the most powerful business elites under the age of 40. [ 5 ] The other co-founders all have prior experience with major Chinese Internet companies.
In order to facilitate foreign investments , Momo’s co-founders incorporated a holding company called Momo Technology Company Limited in the British Virgin Islands in November 2011. In July 2014, Momo Technology Company Limited was renamed to Momo Inc. and re-domiciled to the Cayman Islands. [ 5 ] In December 2011, Momo established Momo Technology HK Company Limited (Momo HK) as a wholly owned subsidiary in Hong Kong . In March 2012, Momo HK established Beijing Momo Information Technology Co., Ltd.(Beijing Momo IT), a wholly owned People’s Republic of China subsidiary . In May 2013, Beijing Momo established Chengdu Momo Technology Co., Ltd.(Chengdu Momo), as a wholly owned subsidiary. [ 5 ]
In December 2011, Momo announced reaching half a million users. [ 7 ] Three months later, the number of Momo users reached 2 million. [ 8 ] Momo reached 10 million users on its first anniversary in August 2012. [ 9 ] In October 2012, Momo surpassed 15 million users.
In 2014, App Annie reported that Momo was the number 2 non-game app of 2013 in terms of revenue. [ 10 ] In February 2014, TechNode reported that Momo had announced reaching 100 million registered users. Momo executives also claimed they had reached 40 million monthly active users (MAU). [ 11 ] According to Momo, in June 2014, total registered users and MAU reached 148 million and 52.4 million respectively. [ 12 ] China Internet Watch reported more conservative estimates. In the months of August and September 2014, Momo had 51.279 and 52.101 million MAU. While Momo’s MAU grew, Wechat and QQ both lost MAU within the same time frame. [ 13 ] Momo's prospectus reported 60.2 million MAU in September 2014. [ 5 ]
Momo reportedly raised USD 2.5 million in Series A financing. Angel investor, PurpleSky Capital (ZiHui ChuangTou), and Matrix Hong Kong led this round of financing. [ 14 ] However, Momo's Form F-1 filed with the SEC reports that USD 5 million was raised in this round of financing. [ 5 ] Momo Inc. completed its Series B financing in October 2012. This round of financing was led by two institution investors and received $100 million valuation. China Renaissance Partners acted as the exclusive financial advisor. [ 15 ] There was much speculation as to whether or not Chinese e-commerce giant, Alibaba Group , was involved in this round of financing. [ 16 ] Momo’s registration statement verifies this claim. [ 5 ] In total, Momo raised approximately USD 40 million. [ 16 ] In October 2013, raised USD 45 million in Series C financing. Matrix Hong Kong, Gothic Partners, L.P., PJF Acorn I Trust, Gansett Partners, L.L.C., PH momo investment Ltd., Tenzing Holding 2011 Ltd., Alibaba Investment Limited, and DST Team Fund Limited were all issued and sold Series C preferred shares. [ 5 ]
Momo’s mobile application is available on Android , iOS , and Windows platforms. It enables users to establish and expand their social relationships based on similar locations and interests. [ 17 ] Some features of the application include subsections like: Nearby Users, Groups, Message Board, Topics, and Nearby Events. Users can send multimedia instant messages as well as play single and multiplayer games within the app’s platform. [ 5 ] Users also make a Facebook -like profile and are encouraged to include as much information as possible. Momo execs claim that this allows their software to create more accurate matches with nearby strangers. Momo is claimed to "sift through the clutter of mobile Internet users to find personalized matches for its users". [ 18 ] Momo offers users paid membership subscriptions. [ 19 ] A membership will cost around USD 2 a month, or less if a user commits to a longer term of use. Benefits of a paid membership include: VIP logos, advanced search options, discounts in the emoticon store, higher limits on maximum users in a group, and the ability to see a list of recent visitors to a user’s profile page. [ 5 ] As of September 30, 2014, there was 2.3 million paid subscriptions. [ 5 ] Like many other instant messaging services, Momo has integrated mobile games into their platform to monetize off their large user base. Third parties develop games, and revenues from in-game purchases are shared between Momo and the developers.
In August 2014, Momo launched Dao Dian Tong, a marketing tool for local merchants. Through Dao Dian Tong, local businesses and merchants can construct profile pages that allow Momo users to find them with the Momo’s LBS. Members can see the businesses just as they would see other Momo users. [ 5 ] Momo plans to further monetize user traffic by referring users from the Momo platform to e-commerce companies. Alibaba was specifically mentioned in Momo’s Form F-1. [ 5 ]
In December 2012, Momo made an official announcement to accuse Sina Corp of copycatting straight from all the features of Momo Group. However, Sina Corp did not give its formal response. [ citation needed ]
On December 10, 2014, NetEase released a statement accusing that Tang Yan has professional ethic issues, business ethics issues, and has been detained due to personal affairs by the local police in 2007. [ 20 ]
On April 27, 2012, Mike Sui , a mixed-race comedian and performer in China, first posted his "12 Beijingers" [ 21 ] viral video which attracted nearly 5.17 million hits. In this video, one character mentions Momo, for the first time calling it a magical tool to get laid (Chinese: 约炮神器; pinyin: yuē pào shén qì ). [ 22 ] Momo has spent millions of dollars to reverse the image of Momo as a one-night stand app. [ 5 ] Momo, through its Weibo account, continues to engage the online community through various campaigns. Momo’s latest online campaign focused on supporting the homeless cats and dogs of China. [ 23 ]
Although Momo is widely considered as a social media application, there are claims that meetings on Momo resulted in marriage. [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Momo_(software) |
Momordicilin or 24-[1′-hydroxy,1′-methyl-2′-pentenyloxyl]-ursan-3-one is a chemical compound, a triterpenoid with formula C 36 H 60 O 3 , found in the fresh fruit of the bitter melon ( Momordica charantia ). [ 1 ]
The compound is soluble in ethyl acetate and chloroform but not in petrol . It crystallizes as needles that melt at 170−171 °C. It was isolated in 1997 by S. Begum and others. [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Momordicilin |
Mon ( 紋 ) , also called monshō ( 紋章 ) , mondokoro ( 紋所 ) , and kamon ( 家紋 ) , are Japanese emblems used to decorate and identify an individual, a family, or (more recently) an institution, municipality or business entity. While mon is an encompassing term that may refer to any such device, kamon and mondokoro refer specifically to emblems that are used to identify a family. An authoritative mon reference compiles Japan's 241 general categories of mon based on structural resemblance (a single mon may belong to multiple categories), with 5,116 distinct individual mon . However, it is well acknowledged that there are a number of lost or obscure mon . [ 1 ] [ 2 ] Among mon , the mon officially used by the family is called jōmon ( 定紋 ) . Over time, new mon have been created, such as kaemon ( 替紋 ) , which is unofficially created by an individual, and onnamon ( 女紋 ) , which is created by a woman after marriage by modifying part of her original family's mon , so that by 2023 there will be a total of 20,000 to 25,000 mon . [ 3 ]
The devices are similar to the badges and coats of arms in European heraldic tradition, which likewise are used to identify individuals and families. Mon are often referred to as crests in Western literature, the crest being a European heraldic device similar to the mon in function. Japanese mon influenced Louis Vuitton 's monogram designs through Japonisme in Europe in the late 1800s. [ 4 ] [ 5 ] [ 6 ]
Mon originated in the mid- Heian period ( c. 900–1000 ) as a way to identify individuals and families among the nobility. They had a pecking order, and when gissha ( 牛車 , bullock cart ) passed each other on the road, the one with the lower status had to give way, and the mon was painted on the gissha . The Heiji Monogatari Emaki , an emakimono ( 絵巻物 , picture scroll) depicting the Heiji rebellion , shows mon painted on gissha . Gradually, the nobility began to use mon on their own costumes, and the samurai class that emerged in the late Heian period and came to power in the Kamakura period (1185–1333) also began to use mon . [ 3 ] [ 7 ] By the 12th century, sources give a clear indication that heraldry had been implemented as a distinguishing feature, especially for use in battle. It is seen on flags, tents, and equipment. On the battlefield, mon served as army standards , even though this usage was not universal and uniquely designed army standards were just as common as mon -based standards (cf. sashimono , uma-jirushi ).
Gradually, mon spread to the lower classes, and in the Muromachi period (1336–1573), merchants painted emblems on their shop signs, which became mon . In the Edo period (1603–1867), kabuki actors used mon , and the general public was allowed to choose and use their favorite mon . By the Genroku period (1680–1709) in the early Edo period, the use of mon was fully established among the general public. However, the use of the chrysanthemum mon used by the imperial family and the hollyhock mon used by the Tokugawa clan ( Tokugawa shogunate ) was prohibited. [ 3 ] [ 7 ] Mon were also adapted by various organizations, such as merchant and artisan guilds , temples and shrines, theater troupes and even criminal gangs. In an illiterate society, they served as useful symbols for recognition.
Japanese traditional formal attire generally displays the mon of the wearer. Commoners without mon often used those of their patron or the organization they belonged to. In cases when none of those were available, they sometimes used one of the few mon which were seen as "vulgar", or invented or adapted whatever mon they wished, passing it on to their descendants. It was not uncommon for shops, and therefore shop-owners, to develop mon to identify themselves.
Occasionally, patron clans granted the use of their mon to their retainers as a reward. Similar to the granting of the patron's surnames, this was considered a very high honor. Alternatively, the patron clan may have added elements of its mon to that of its retainer, or chosen an entirely different mon for them.
Mon motifs can be broadly classified into five categories: animals, plants, nature, buildings and vehicles, and tools and patterns, each with its own meaning. The most common animal motifs are the crane and the turtle , which, according to tradition, were symbols of longevity and were used to wish the family a long and prosperous life. Plant mon were symbols of wealth and elegance, so they were often used to wish for the improvement of the family's social status and economic power, and motifs such as wisteria and paulownia were often used. Mon depicting buildings, vehicles, or tools often indicated occupation or status. For example, a mon with a torii gate indicated a family associated with Shinto , a mon with a gissha wheel indicated nobility, and a mon with a crowbar indicated a family associated with construction. The mon of nature was a symbol of respect for nature and prayers for a good harvest, and motifs such as the moon, mountains, and thunder were used. [ 3 ] [ 7 ]
The most commonly used mon motifs are wisteria , paulownia , hawk feathers, flowering quince , and creeping woodsorrel , which are called the godaimon ( 五大紋 , five major mon ) . However, according to a dictionary of mon published by Shogakukan , oak is listed instead of paulownia. [ 3 ] There are more than 150 types of wisteria mon , and their use by the Fujiwara clan led to their popularization. [ 8 ]
Similar to the blazon in European heraldry, mon are also named by the content of the design, even though there is no set rule for such names. Unlike in European heraldry, however, this "blazon" is not prescriptive—the depiction of a mon does not follow the name—instead the names only serve to describe the mon . The pictorial depictions of the mon are not formalized and small variations of what is supposed to be the same mon can sometimes be seen, but the designs are for the most part standardized through time and tradition.
The degree of variation tolerated differ from mon to mon as well. For example, the paulownia crest with 5-7-5 leaves is reserved for the prime minister, whereas paulownia with fewer leaves could be used by anyone. The imperial chrysanthemum also specifies 16 petals, whereas chrysanthemum with fewer petals are used by other lesser imperial family members.
Japanese heraldry does not have a cadency or quartering system, but it is not uncommon for cadet branches of a family to choose a slightly different mon from the senior branch. Each princely family ( shinnōke ), for example, uses a modified chrysanthemum crest as their mon . Mon holders may also combine their mon with that of their patron, benefactor or spouse, sometimes creating increasingly complicated designs.
Mon are essentially monochrome; the color does not constitute part of the design and they may be drawn in any color.
Virtually all modern Japanese families have a mon , but unlike before the Meiji Restoration when rigid social divisions existed, mon play a more specialized role in everyday life. On occasions when the use of a mon is required, one can try to look up their families in the temple registries of their ancestral hometown or consult one of the many genealogical publications available. Many websites also offer mon lookup services. Professional wedding planners , undertakers and other "ritual masters" may also offer guidance on finding the proper mon .
Mon are seen widely on stores and shops engaged in traditional crafts and specialties. They are favored by sushi restaurants, which often incorporate a mon into their logos. Mon designs can even be seen on the ceramic roof tiles of older houses. Mon designs frequently decorate senbei , sake , tofu and other packaging for food products to lend them an air of elegance, refinement and tradition. The paulownia mon appears on the obverse side of the 500 yen coin .
Items symbolizing family crafts, arts or professions were often chosen as a mon ; likewise, mon were, and still are, also passed down a lineage of artists. Geisha typically wear the mon of their okiya (geisha house) on their clothing when working; individual geisha districts, known as hanamachi , also have their own distinctive mon , such as the plover crest ( chidori ) of Ponto-chō in Kyoto .
A woman may still wear her maiden mon if she wishes and pass it on to her daughters; she does not have to adopt her husband's or father's mon . Flowers, trees, plants and birds are also common elements of mon designs. [ 9 ]
Mon also add formality to a kimono . A kimono may have one, three or five mon . The mon themselves can be either formal or informal, depending on the formality of the kimono, with formality ranging from the most formal 'full sun' ( hinata ) crests to the least formal 'shadow' ( kage ) crests. Very formal kimono display more mon , frequently in a manner that makes them more conspicuous; the most formal kimono display mon on both sides of the chest, on the back of each sleeve, and in the middle of the back. On the armor of a warrior, it might be found on the kabuto (helmet), on the do (breast plate), and on flags and various other places. Mon also adorned coffers, tents, fans and other items of importance.
As in the past, modern mon are not regulated by law, with the exception of the Imperial Chrysanthemum , which doubles as the national emblem, and the paulownia, which is the mon of the office of prime minister and also serves as the emblem of the cabinet and government (see national seals of Japan for further information). Some local governments and associations may use a mon as their logo or trademark , thus enjoying its traditional protection, but otherwise mon are not recognized by law. One of the best known examples of a mon serving as a corporate logo is that of Mitsubishi , a name meaning 'three lozenges' (occasionally translated as 'three buffalo nuts '), which are represented as rhombuses. [ 10 ] Another example of corporate use is the logo for the famous soy sauce maker Kikkoman , which uses the family mon of the founder, [ 11 ] and finally, the logo of music instrument/equipment and motorcycle builder Yamaha , which shows three tuning forks interlocked into the shape of a capital 'Y' in reference to both their name and the origin of the company. [ 12 ]
Japanese mon are sometimes used as charges or crests in Western heraldry . They are blazoned in traditional heraldic style rather than in the Japanese style. Examples include the swastika with arrows used by Japanese ambassador Hasekura Tsunenaga , the Canadian-granted arms of the Japanese-Canadian politician David Tsubouchi , [ 13 ] and Akihito 's arms as a Knight of the Garter . [ 14 ] | https://en.wikipedia.org/wiki/Mon_(emblem) |
In homological algebra , a monad is a 3-term complex
of objects in some abelian category whose middle term B is projective , whose first map A → B is injective , and whose second map B → C is surjective . Equivalently, a monad is a projective object together with a 3-step filtration B ⊃ ker( B → C ) ⊃ im( A → B ). In practice A , B , and C are often vector bundles over some space, and there are several minor extra conditions that some authors add to the definition. Monads were introduced by Horrocks ( 1964 , p.698).
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monad_(homological_algebra) |
In mathematical logic , monadic second-order logic ( MSO ) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. [ 1 ] It is particularly important in the logic of graphs , because of Courcelle's theorem , which provides algorithms for evaluating monadic second-order formulas over graphs of bounded treewidth . It is also of fundamental importance in automata theory , where the Büchi–Elgot–Trakhtenbrot theorem gives a logical characterization of the regular languages .
Second-order logic allows quantification over predicates . However, MSO is the fragment in which second-order quantification is limited to monadic predicates (predicates having a single argument). This is often described as quantification over "sets" because monadic predicates are equivalent in expressive power to sets (the set of elements for which the predicate is true).
Monadic second-order logic comes in two variants. In the variant considered over structures such as graphs and in Courcelle's theorem, the formula may involve non-monadic predicates (in this case the binary edge predicate E ( x , y ) {\displaystyle E(x,y)} ), but quantification is restricted to be over monadic predicates only. In the variant considered in automata theory and the Büchi–Elgot–Trakhtenbrot theorem, all predicates, including those in the formula itself, must be monadic, with the exceptions of equality ( = {\displaystyle =} ) and ordering ( < {\displaystyle <} ) relations.
Existential monadic second-order logic (EMSO) is the fragment of MSO in which all quantifiers over sets must be existential quantifiers , outside of any other part of the formula. The first-order quantifiers are not restricted. By analogy to Fagin's theorem , according to which existential (non-monadic) second-order logic captures precisely the descriptive complexity of the complexity class NP , the class of problems that may be expressed in existential monadic second-order logic has been called monadic NP. The restriction to monadic logic makes it possible to prove separations in this logic that remain unproven for non-monadic second-order logic. For instance, in the logic of graphs , testing whether a graph is disconnected belongs to monadic NP, as the test can be represented by a formula that describes the existence of a proper subset of vertices with no edges connecting them to the rest of the graph; however, the complementary problem, testing whether a graph is connected, does not belong to monadic NP. [ 2 ] [ 3 ] The existence of an analogous pair of complementary problems, only one of which has an existential second-order formula (without the restriction to monadic formulas) is equivalent to the inequality of NP and coNP , an open question in computational complexity.
By contrast, when we wish to check whether a Boolean MSO formula is satisfied by an input finite tree , this problem can be solved in linear time in the tree, by translating the Boolean MSO formula to a tree automaton [ 4 ] and evaluating the automaton on the tree. In terms of the query, however, the complexity of this process is generally nonelementary . [ 5 ] Thanks to Courcelle's theorem , we can also evaluate a Boolean MSO formula in linear time on an input graph if the treewidth of the graph is bounded by a constant.
For MSO formulas that have free variables , when the input data is a tree or has bounded treewidth, there are efficient enumeration algorithms to produce the set of all solutions, [ 6 ] ensuring that the input data is preprocessed in linear time and that each solution is then produced in a delay linear in the size of each solution, i.e., constant-delay in the common case where all free variables of the query are first-order variables (i.e., they do not represent sets). There are also efficient algorithms for counting the number of solutions of the MSO formula in that case. [ 7 ]
The satisfiability problem for monadic second-order logic is undecidable in general because this logic subsumes first-order logic .
The monadic second-order theory of the infinite complete binary tree , called S2S , is decidable . [ 8 ] As a consequence of this result, the following theories are decidable:
For each of these theories (S2S, S1S, WS2S, WS1S), the complexity of the decision problem is nonelementary . [ 5 ] [ 9 ]
Monadic second-order logic of trees has applications in formal verification . Decision procedures for MSO satisfiability [ 10 ] [ 11 ] [ 12 ] have been used to prove properties of programs manipulating linked data structures , [ 13 ] as a form of shape analysis , and for symbolic reasoning in hardware verification . [ 14 ] | https://en.wikipedia.org/wiki/Monadic_second-order_logic |
Monarch Watch is a volunteer-based citizen science organization that tracks the fall migration of the monarch butterfly . [ 1 ] It is self-described as "a nonprofit education, conservation, and research program based at the University of Kansas that focuses on the monarch butterfly, its habitat, and its spectacular fall migration ." [ 2 ]
The informal organization is largely supported by teachers and students participating in "classroom projects, collaborative research" among other opportunities. [ 3 ] Its founder and director is Orley R. "Chip" Taylor, a "world-renowned expert on butterflies and their migration patterns." [ 2 ] [ 4 ] The organization creates and distributes tags to place on monarch butterflies in order to track their migration path from Canada and the United States to south-central Mexico . [ 5 ] The tagging method used is derived from the one that was developed by Canadian scientist, Fred Urquhart . [ 3 ] The tagging process was adapted by Orley Taylor to minimize the damage to the butterflies. Color-coded tags are glued to a monarch butterfly's wing. [ 3 ] Volunteers have tagged over 1.5 million monarchs in the last 26 years from Colorado to Canada. [ 6 ]
The monarch butterfly is also known as the milkweed butterfly due to its subsistence on the milkweed plant for its habitat. [ 3 ] Largely due to commercial farming practices, the habitats of monarch butterflies have declined. [ 7 ] In an effort to mitigate the destruction of the monarch butterflies natural habitat, Monarch Watch has called for volunteers to plant milkweed wherever possible. Milkweed is essential to the life-cycle of the monarch butterfly as they lay their eggs on the underside of the plant's leaves. [ 8 ] It is possible to register and certify a site that is designated as a "Monarch Waystation." [ 9 ] These sites can also be added to an interactive map that is monitored by Monarch Watch. The program also offers free milkweed plugs to people that engage in the creation of habitats for monarchs and pollinators. [ 10 ] Primary consideration is given to non-profits and schools. There is an application process to receive the milkweed from Monarch Watch. [ 11 ]
Monarch Watch is not only focused on tracking the fall migration of monarchs, but also on the conservation of the monarch butterfly through the preservation and restoration of monarch habitats. [ 12 ] The destruction of habitats has negatively affected the monarch butterfly population as well as that of other pollinators . [ 12 ] Habitat shrinkage has resulted in the extinction of several species of pollinators over the last 50 years. [ 5 ] The monarch butterfly is also affected by parasites and the "declining winter habitat in Mexico." [ 8 ] Monarch Watch's efforts in this arena are specifically referred to at the "Bring Back the Monarchs Campaign." [ 12 ] The Bring Back the Monarchs Campaign is an offshoot of the Monarch Waystation Program.
Beyond offering free milkweed plugs, Monarch Watch also offers a shop by which an individual can purchase milkweed for the purpose of creating monarch habitats. The milkweed species offered to the buyer is contingent on the buyer's zip code, in an effort to ensure that only native milkweed is planted in the appropriate regional areas. [ 13 ] | https://en.wikipedia.org/wiki/Monarch_Watch |
Mond gas is a cheap coal gas that was used for industrial heating purposes. [ 1 ] Coal gases are made by decomposing coal through heating it to a high temperature. Coal gases were the primary source of gas fuel during the 1940s and 1950s until the adoption of natural gas . They were used for lighting, heating, and cooking, typically being supplied to households through pipe distribution systems. The gas was named after its discoverer, Ludwig Mond . [ 2 ] : 10
In 1889, Ludwig Mond discovered that the combustion of coal with air and steam produced ammonia along with an extra gas, which was named the Mond gas. He discovered this while looking for a process to form ammonium sulfate , which was useful in agriculture. [ 1 ] The process involved reacting low-quality coal with superheated steam, which produced the Mond gas. The gas was then passed through dilute sulfuric acid spray, which ultimately removed the ammonia , forming ammonium sulfate. [ 3 ]
Mond modified the gasification process by restricting the air supply and filling the air with steam, providing a low working temperature. This temperature was below ammonia's point of dissociation , maximizing the amount of ammonia that could be produced from the nitrogen, a product from superheating coal. [ 4 ]
The Mond gas process was designed to convert cheap coal into flammable gas, which was made up of mainly hydrogen, while recovering ammonium sulfate. The gas produced was rich in hydrogen and poor in carbon monoxide. Although it could be used for some industrial purposes and power generation, the gas was limited for heating or lighting. [ 4 ]
In 1897, the first Mond gas plant began at the Brunner Mond & Company in Northwich, Cheshire. Mond plants which recovered ammonia needed to be large in order to be profitable, using at least 182 tons of coal per week. [ 2 ] : 61 [ 4 ]
Predominant reaction in Mond Gas Process: C + 2H 2 O = CO 2 + 2H 2 [ 4 ]
The Mond gas was composed of roughly:
Mond gas could be produced and used more efficiently than other gases in the late 19th and early 20th century. The gas was used as fuel for street lighting and basic residential uses that required gas such as ovens, kilns, furnaces, and boilers. [ 5 ]
The Mond gas could be produced very cheaply since it required only a low-quality coal, offering large savings for many processes. [ 3 ] The production of Mond gas did not require much labor. [ 2 ] : 15
The Mond gas became popularized during the industrial power generation in the beginning of the 20th century, since industries were very interested in a source of low-cost energy. The Mond gas provided a boost to the gas engine industry in particular. For example, a large gas engine that used Mond gas was 5–6 times more efficient than a standard steam engine. This is primarily because Mond gas was produced from the lowest cost coal rather than steam coal , resulting in cheaper electricity at about 1/20 of the normal price. [ 3 ]
The Mond gas was used primarily during the early 20th century, and its process was further developed by the Power Gas Corporation as the Lymn system; however, the gas has been widely forgotten. [ 3 ] [ 4 ]
The use of coal gases has become far less popular due to the adoption of natural gas in the 1960s. [ citation needed ] Natural gases were better for the environment because they burned more cleanly than other fuels such as coal and oil and could also be transported more safely and efficiently over sea. [ citation needed ] | https://en.wikipedia.org/wiki/Mond_gas |
The Mond process , sometimes known as the carbonyl process , is a technique created by Ludwig Mond in 1890, [ 1 ] to extract and purify nickel . The process was used commercially before the end of the 19th century, [ 2 ] and particularly by the International Nickel Company in the Sudbury Basin . [ 3 ] This process converts nickel oxides into nickel metal with very high purity being attainable in just a single step.
This process involves the fact that carbon monoxide combines with nickel readily and reversibly to give nickel carbonyl . No other element forms a carbonyl compound under the mild conditions used in the process. [ 2 ]
This process has three steps:
1. Nickel oxide reacts with syngas at 200 °C to give nickel, together with impurities including iron and cobalt .
2. The impure nickel reacts with carbon monoxide at 50–60 °C to form the gas nickel carbonyl , leaving the impurities as solids.
3. The mixture of nickel carbonyl and syngas is heated to 220–250 °C, resulting in decomposition back to nickel and carbon monoxide:
Steps 2 and 3 illustrate a chemical transport reaction , exploiting the properties that (1) carbon monoxide and nickel readily combine to give a volatile complex and (2) this complex degrades back to nickel and carbon monoxide at higher temperatures. The decomposition may be engineered to produce powder, but more commonly an existing substrate is coated with nickel. For example, nickel pellets are made by dropping small, hot pellets through the carbonyl gas; this deposits a layer of nickel onto the pellets.
This process has also been used for plating nickel onto other metals, where a complex shape or sharp corners have made precise results difficult to achieve by electroplating. Although the results are good, the toxicity makes it impractical as an industrial process. Such parts are now plated by electroless nickel plating instead. | https://en.wikipedia.org/wiki/Mond_process |
Mondex was a smart card electronic cash system, implemented as a stored-value card and owned by Mastercard .
Pioneered by two bankers from NatWest in 1990, it was spun-off to a separate consortium later on, then sold to Mastercard.
Mondex allowed users to use its electronic card as they would with cash, enabling peer-to-peer offline transfers between cards, which did not need any authorization, via Mondex ATMs, computer card readers, personal 'wallets' and specialized telephones. This offline nature of the system and other unique features made Mondex stand out from leading competitors at the time, such as Visa Cash , which was a closed system and was much closer in concept to a traditional payment cards' transactional operation. [ 1 ]
Mondex also allowed for a full-card locking mechanism, usage with multiple currencies within a single card, and a certain degree of user anonymity. Mondex cards were at some point common place in many universities at a certain point as they were mostly trialed there, and were also issued as multi-application cards - like combo credit cards, ID cards, and loyalty membership cards. [ 2 ]
The system was introduced around the world in more than a dozen nations, with various differing implementations. Despite continuous investment from Mastercard, the Mondex scheme did not seem to catch on worldwide and the last place where it operated, Taiwan, had its cards disabled in 31 May 2008, being succeeded by a similar but more technologically advanced system, named Mastercard Cash, which utilized contactless operation, culminating in the TaiwanMoney Card .
The Mondex scheme was a forerunner in the cashless society that is common today via mobile payment , digital wallets , and contactless payment , and was far ahead of its time. [ 3 ]
The Mondex scheme was invented in 1990 by Tim Jones and Graham Higgins of NatWest in the United Kingdom . In March 1992 internal tests of the system, known at the time as 'Byte', started running at one of NatWest's major computer centres, Goodman's Fields in London . [ 4 ]
Development continued in secret until December 1993, when the system was publicly unveiled with an announcement that the Midland Bank (which had recently been acquired by HSBC ) had joined the scheme as a 50/50 investment partner.
Initial public trials of the payment system were carried out from July 1995 in Swindon , Wiltshire . The public phase had required the development and manufacture of numerous merchant devices and smart cards, with BT , NatWest and the Midland Bank sponsoring and installing retail terminals at the car parks, payphones, buses and at merchants in the town, and issuing Mondex cards to residents. Within the first five weeks of the trial, 1,900 terminals had reportedly been installed at 620 retailers, and 6,000 cardholders had signed up, with a target of 40,000 cardholders and 1,000 vendors being pursued during the course of the one year trial. By September 1995, all buses, car parks and payphones were meant to accept Mondex, and 20 cashpoints and 300 payphones were meant to support funds transfers using the system. [ 5 ]
In July 1996, NatWest and Midland Bank sold the intellectual property rights to develop the Mondex concept, technology, and brand to a new group called Mondex International, with 17 major banks joining the group as shareholders. [ 6 ] From that point on, Mondex International managed the Mondex brand, oversaw its franchisees and signed contracts with new ones around the globe. It also managed the Mondex technology and developed its software.
In November that same year, Mastercard acquired 51% ownership of Mondex International and fully endorsed the Mondex scheme, promptly abandoning its own electronic cash system which had been in development up until then. [ 7 ] [ 8 ] Mastercard then acquired full ownership of the company in June 2001. [ 9 ]
In 1996 Visa and Mastercard agreed to what was known as the Upper West Side trial. Visa deployed Visa Cash, their own electronic cash scheme, and Mastercard deployed Mondex to see if the people on Manhattan Island would embrace the concept and the technology as a means of replacing cash.
Mondex launched in a number of markets during the 1990s, expanding from the original trial in Swindon to Hong Kong , New York and Guelph , Canada . [ 10 ] It was also trialled on several British university campuses from the late 1990s, including the University of Edinburgh , University of Exeter (between 1997 and 2001), University of York , University of Nottingham , Aston University and Sheffield Hallam University .
Throughout the late 90s and early 2000s trials continued to be executed throughout the world, with varying degrees of customer adoption and popularity. At the end, even the more successful of these trials failed their purpose, as most of the countries which had Mondex pilots never saw a national implementation of the system - in many locations the scheme stayed in an experimental phase until the local Mondex franchisee shut its doors.
As a stored-value system, Mondex cards were designed as an electronic replacement for cash - they always held a certain value, allowing offline transactions to be possible without needing a line of credit or communication with the credit company, like with a traditional credit card. This way they were able to be offered to a sector that wasn't catered by traditional forms of electronic payment. [ 11 ]
All value circulated between Mondex cards was issued by an 'originator' - in order to create Mondex value the originator (a part of the local Mondex franchise) would exchange cash with the Mondex partnering banks and provide them with an equal amount of Mondex electronic value, which could be later withdrawn by cardholders using the bank accounts associated to their cards. [ 12 ]
Mondex is an open-loop implementation of the electronic cash scheme - instead of transactions occurring only in one way, money can be transferred between any Mondex user.
A transfer of funds using the Mondex card (dubbed an 'electronic purse') operated through a Mondex-enabled device, and in principle occurred between 2 cards - whether it was 2 customers or a customer and a seller. [ 11 ]
Both would insert their cards into a device which would facilitate the transfer of funds and record the transaction onto the card.
The card's memory consisted of the last 10 transactions. [ 11 ]
In order to top-up their cards, users could use an ATM, go to a bank branch, or visit several stores and businesses with compatible hardware.
Mondex cards that were issued by banks allowed cardholders to transfer funds to and from their personal bank account, which was linked directly to their card. [ 11 ]
Mondex cards could be used in any store or machine that supported it and had the necessary equipment. Depending on the country where the system was implemented, Mondex cards were accepted at a variety of businesses - supermarkets, department stores, public transport, taxis, car parks, vending machines, restaurants, cafés and many more. Some countries even allowed usage of the cards in lottery games. [ 13 ]
Mondex cards carried five 'electronic pockets', separate from one another, each containing money denominated in a different currency. This allowed transactions to be made using one of the 5 currencies loaded on the card. The currencies in the 'pockets' could be unloaded and replaced at any time. [ 14 ]
Mondex cards included a locking mechanism - a PIN would be chosen and inserted to lock the card, and before operating the card again (to view the latest transactions or transfer funds) the cardholder had to insert his PIN and unlock it.
The Z notation was used to prove security properties about Mondex, allowing it to achieve ITSEC level E6, ITSEC's highest granted security-level classification. [ 15 ] [ 16 ]
In many countries the electronic purse was issued on a multi-application card, implementing two or more uses within a single card.
In some instances, the Mondex card was issued alongside a regular credit card, allowing transactions to be made either with money stored in the Mondex wallet or via the traditional credit card. [ 17 ]
Other multi-application uses included a user card in a private health service - holding personal health records and other details in cases of emergency; [ 18 ] and a club membership card, containing special discounts and benefits. Mondex was also used in numerous locations as an Employee/Student ID, [ 19 ] and as a mass-transit electronic ticket scheme (to be used for buying a ticket or storing a ticket bought in advance). [ 20 ]
A number of devices allowed operation of Mondex cards (transferring value, viewing card balance, locking/unlocking cards, et cetera), to be used for either personal or commercial use: [ 21 ]
Notes: The community trial launch date denominates a public trial of the Mondex scheme in that country, not the internal company trials that began prior. The commercial and trial shutdown dates indicate the point where fund withdrawals from the cards were disabled.
Sherbrooke trial:
August 1999 [ 33 ]
Sherbrooke trial:
October 2001 [ 35 ]
October 1997
December 1998 [ 42 ]
Governmental schools trial: July 2001 [ 55 ]
Swindon trial: July 1995 | https://en.wikipedia.org/wiki/Mondex |
In economics , money illusion , or price illusion , is a cognitive bias where money is thought of in nominal, rather than real terms. In other words, the face value (nominal value) of money is mistaken for its purchasing power (real value) at a previous point in time. Viewing purchasing power as measured by the nominal value is false, as modern fiat currencies have no intrinsic value and their real value depends purely on the price level . The term was coined by Irving Fisher in Stabilizing the Dollar . It was popularized by John Maynard Keynes in the early twentieth century, and Irving Fisher wrote an important book on the subject, The Money Illusion , in 1928. [ 1 ]
The existence of money illusion is disputed by monetary economists who contend that people act rationally (i.e. think in real prices) with regard to their wealth. [ 2 ] Eldar Shafir , Peter A. Diamond , and Amos Tversky (1997) have provided empirical evidence for the existence of the effect and it has been shown to affect behaviour in a variety of experimental and real-world situations. [ 3 ]
Shafir et al. [ 3 ] also state that money illusion influences economic behaviour in three main ways:
Money illusion can also influence people's perceptions of outcomes. Experiments have shown that people generally perceive an approximate 2% cut in nominal income with no change in monetary value as unfair, but see a 2% rise in nominal income where there is 4% inflation as fair, despite them being almost rational equivalents. This result is consistent with the 'Myopic Loss Aversion theory'. [ 4 ] Furthermore, the money illusion means nominal changes in price can influence demand even if real prices have remained constant. [ 5 ]
Explanations of money illusion generally describe the phenomenon in terms of heuristics . Nominal prices provide a convenient rule of thumb for determining value and real prices are only calculated if they seem highly salient (e.g. in periods of hyperinflation or in long term contracts).
Some have suggested that money illusion implies that the negative relationship between inflation and unemployment described by the Phillips curve might hold, contrary to more recent macroeconomic theories such as the "expectations-augmented Phillips curve". [ 6 ] If workers use their nominal wage as a reference point when evaluating wage offers, firms can keep real wages relatively lower in a period of high inflation as workers accept the seemingly high nominal wage increase. These lower real wages would allow firms to hire more workers in periods of high inflation.
Money illusion is believed to be instrumental in the Friedmanian version of the Phillips curve . Actually, money illusion is not enough to explain the mechanism underlying this Phillips curve. It requires two additional assumptions. First, prices respond differently to modified demand conditions: an increased aggregate demand exerts its influence on commodity prices sooner than it does on labour market prices. Therefore, the drop in unemployment is, after all, the result of decreasing real wages and an accurate judgement of the situation by employees is the only reason for the return to an initial (natural) rate of unemployment (i.e. the end of the money illusion, when they finally recognize the actual dynamics of prices and wages). The other (arbitrary) assumption refers to a special informational asymmetry: whatever employees are unaware of in connection with the changes in (real and nominal) wages and prices can be clearly observed by employers. The new classical version of the Phillips curve was aimed at removing the puzzling additional presumptions, but its mechanism still requires money illusion. [ 7 ] | https://en.wikipedia.org/wiki/Money_illusion |
In geometry , Monge's theorem , named after Gaspard Monge , states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear .
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane . Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words, if the two external tangents are considered to intersect at the point at infinity , then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent.
The simplest proof employs a three-dimensional analogy. [ 1 ] Let the three circles correspond to three spheres of different radii; the circles correspond to the equators that result from a plane passing through the centers of the spheres. The three spheres can be sandwiched uniquely between two planes. Each pair of spheres defines a cone that is externally tangent to both spheres, and the apex of this cone corresponds to the intersection point of the two external tangents, i.e., the external homothetic center (center of similarity). Since one line of the cone lies in each plane, the apex of each cone must lie in both planes, and hence somewhere on the line of intersection of the two planes. Therefore, the three external homothetic centers are collinear.
This proof is somewhat flawed, however, as it cannot account for cases where the smallest circle is located between the other two, nor any case where one circle is fully contained by another. It can be made fully general by using cones of equal apex angle rather than spheres, creating three similar cones. Any pair of similar three dimensional objects has a center of similarity, about which you could scale either object to coincide with the other; these lines of similarity replace the external tangents of the previous proof. Further, the line connecting any two apex points must also intersect their center of similarity. The three apex points always define a plane in three dimensions, and all three centers of similarity must lie in the plane containing the circular bases. Hence, the three centers must lie on the intersection of the two planes, which must be a line in three dimensions. [ 2 ]
Monge's theorem can also be proved by using Desargues' theorem .
Another easy proof uses Menelaus' theorem , since the ratios can be calculated with the diameters of each circle, which will be eliminated by cyclic forms when using Menelaus' theorem.
Desargues' theorem also asserts that 3 points lie on a line, and has a similar proof using the same idea of considering it in 3 rather than 2 dimensions and writing the line as an intersection of 2 planes. | https://en.wikipedia.org/wiki/Monge's_theorem |
The Mongol cosmological system is mainly based on the positions, relationships and movements of the Sun, the Moon, the five major planets in the Solar System and the various constellations in the sky. This system of belief is centered around local wild fauna and oral transmission, with few written sources. Mongol cosmology was largely influenced by Chinese civilisation and Buddhism . [ 1 ]
Generally, stars represent animals turning around the Polar Star which is symbolized by the Altan Gadas ( Mongolian : Алтан Гадас , lit. "Golden Spike"). Constellations include Num Sum ( Mongolian : Нум сум , lit. "Bow and Arrow") for the Swan, Doloon Burkhan ( Mongolian : Долоон бурхан , lit. Seven Gods) for the seven stars of the Big Dipper , Gurvan Maral Od ( Mongolian : Гурван марал од , lit. Three Deer Stars) for Orion's Belt, and Hun Tavan Od ( Mongolian : Хүн таван од , lit. Five Man Stars) is Cassiopeia .
Mongolian astrology calculates the positions of each of the planets visible with the naked eye: Mercury, Venus, Mars, Jupiter and Saturn.
The names of the celestial and the days they are associated with are:
The noun van at the end of the name of the final three indicates royal status. Therefore a possible translation of Pluto is "the Earth king"; Uranus as "the sky king", and Neptune as "the ocean king." The names of the remaining celestial bodies excluding the Earth come from Sanskrit and are largely used in Mongolian, but in an unofficial way.
The star located above Mizar in the Big Bear constellation is prominent in Mongolian astrology. It symbolises the recovery and protection star. According to legend, it was placed there by Tengeriin, the god of heaven, to protect Mizar. In the thirteenth century, to become an archer for Genghis Khan one had to be able to identify these two stars with the naked eye.
Mongolian expertise in astrology and astronomy goes back to the fourteenth and fifteenth century astronomer, mathematician and viceroy in Samarkand, Taraghay, known as Ulug Beg, whose empire spread to Central Asia. Turning away from his royal obligations, he examined celestial bodies and astronomical questions. He was the first to precisely measure Saturn's revolution period (Sanchir) with a sextant of 40 meters radius.
Mongolians are particularly attached to the Great Bear. This constellation is limited for them to the seven Dipper stars making the bear's tail and body, but the legend concerning it is probably the most famous in Mongolia .
Once upon a time, there were eight orphan brothers gifted with outstanding capabilities living within a kingdom. The king and the queen lived within it peacefully. One day, a monster came and kidnapped the queen. The king asked the eight brothers to bring her back and said: "If one of you succeeds to rescue my beloved, I will give to him a golden arrow". The orphans went together to assist their queen. They searched the monster during two days and three nights, when in the middle of the third night, they found and killed the monster. They brought back the queen in the castle. The king did not cut out the arrow in eight parts, he decided to threw it in the sky. The first to catch it could keep it. The younger brother succeeded the test and changed immediately into the North Star (Polar Star). The seven others changed into the seven gods, the seven Gods visiting their younger brother every night. The name Doloon burkhan (the Seven Gods) come from this legend to appoint the Great Bear and the Golden Stick, Altan Hadaas, the Polar Star.
One tradition, based on the birth years in the Chinese calendar , concerns the link between Mongolian people and the Great Bear as one star of this constellation is attributed to each of them. Chinese and Mongolian calendars have some similarities (the Mongolian calendar is a lunar calendar). Each year is symbolized by an animal, itself associated to a star of the constellation Great Bear. The first, Dubhe, corresponds to the Rat 's year, the second, Merak, corresponds to the Ox and so on until the end of the Great Bear's tail where Alkaid symbolizes the year of the Horse . Then we come back to the first, the Goat year and we repeat the same way until the twelfth and latest year of the Chinese calendar, that of the Pig . Therefore, the two stars at the end of the tail are assigned one time only.
At the origin of the world, there were vast dry meadows, burned by the seven suns which lit the world. Erkhii Mergen, a very good archer, promise the people that he would shoot all the suns without missing once. If he should fail, he would cut off his thumbs and live in a hole and never drink pure water. He shot six of the seven suns, but at his seventh shot a swallow flew in between and was hit in its tail--this became the swallow. The man kept his promise, cut his thumbs off, and turned into a marmot. [ 2 ]
At that time lived a monster named Raah which frightened the entire world. He devoured all who were in its way. The god Orchiwaani owned a magic spring: whoever drank from it became immortal. One day, Raah stole the spring and drunk. The Moon and the Sun caught the monster in the act and reported to Orchiwaani. Seething with rage to hear about this piece of news he went to fight the monster. He cut its head many times but it grew again immediately because Raah had become immortal. He thought then to cut its tail in order to allow all that it ate to leave again directly. Just as Orchiwaani would seize the monster to finish it off, it escaped and disappeared between the Moon and the Sun. Then Orchiwaani asked the Moon, who recaptured Raah and cut its rump and its tail. In revenge, the monster comes back sometimes to eat the Moon or the Sun which exit immediately, giving rise to moon and solar eclipses. [ citation needed ]
When there is an eclipse, some Mongolians believe it to mean that Raah devours the Moon or the Sun and they make a lot of noise so that the monster liberates the eclipsed star. In the 13th century, Guillaume de Rubruck wrote:
"Some [Mongolian people] have knowledge in astronomy and predict them [to other Mongolian people] the Lunar and Solar eclipses and, when it is about to produce one, everybody stocks up on food because they do not pass the door of their habitation. And while the eclipse happened, they play the drum and instruments and do big noise and clamors. When the eclipse is finished, they devote themselves to beverage and festivity and do big party." [ 3 ]
According to a Mongolian legend, a woman devoting herself to count one hundred stars in the sky will dream about her future husband.
Sometimes, Mongolians honor the Great Bear (Doloon Burkhan) by throwing milk in its direction. Milk, of white color, symbolizes purity in Mongolia. They pray so that something may be fulfilled, but for several persons, not for just one person, because this would bring bad luck. Milk can be replaced by vodka which, even if it is colorless, symbolizes the dark color and the strength for Mongolians. By doing this, it avoids bad luck, quarrels, fear and fends off evil spirits. [ citation needed ] | https://en.wikipedia.org/wiki/Mongolian_cosmogony |
The Mongolian gerbil or Mongolian jird ( Meriones unguiculatus ) is a rodent belonging to the subfamily Gerbillinae . [ 3 ] Their body size is typically 110–135 mm ( 4 + 1 ⁄ 4 – 5 + 1 ⁄ 4 in), with a 95–120 mm ( 3 + 3 ⁄ 4 – 4 + 3 ⁄ 4 in) tail, and body weight 60–130 g (2– 4 + 1 ⁄ 2 oz), with adult males larger than females. [ 4 ] The animal is used in science and research or kept as a small house pet . Their use in science dates back to the latter half of the 19th century, but they only started to be kept as pets in the English-speaking world after 1954, when they were brought to the United States. However, their use in scientific research has fallen out of favor.
The first known mention of gerbils came in 1866, by Father Armand David , who sent "yellow rats" to the French National Museum of Natural History in Paris, from northern China. They were named Gerbillus unguiculatus by the scientist Alphonse Milne-Edwards in 1867. [ 2 ]
There is a popular misconception about the meaning of this scientific name, appearing both in printed works [ 5 ] and in websites, [ 6 ] due to the genus Meriones sharing the name with Greek warrior Meriones in Homer's Iliad ; however, translations like "clawed warrior" are incorrect. The genus was named by Johann Karl Wilhelm Illiger in 1811, [ 7 ] deriving from the Greek word μηρος (femur). Combined with 'unguiculate', meaning to have claws or nails in Latin, the name can be loosely translated as 'clawed femur'. [ 8 ]
Mongolian gerbils inhabit grassland, shrubland and desert, including semidesert and steppes in China, Mongolia , and the Russian Federation . [ 9 ]
Soil on the steppes is sandy and is covered with grasses , herbs, and shrubs. The steppes have cool, dry winters and hot summers. The temperature can get up to 50 °C (122 °F), but the average temperature for most of the year is around 20 °C (68 °F). [ 10 ] [ self-published source? ]
In the wild, these gerbils live in patriarchal groups generally consisting of one parental pair, the most recent litter, and a few older pups; sometimes the dominant female's sister(s) also live with them. Only the dominant females will produce pups, and will mostly mate with the dominant male while in estrus (heat), female gerbils are generally more loyal than male gerbils. [ citation needed ] One group of gerbils generally ranges over 325–1,550 square metres (400–1,900 sq yd). [ 11 ]
A group lives in a central burrow with 10–20 exits. Some deeper burrows with only one to three exits in their territory may exist. These deeper burrows are used to escape from predators when they are too far from the central burrow. A group's burrows often interconnect with other groups. [ citation needed ]
Gerbils have a long history of use in scientific research, although nowadays they are rarely used. For example, in the United Kingdom in 2017, only around 300 Mongolian gerbils were used in experimental procedures, compared to over 2 million mice . [ 12 ]
Most gerbils used in scientific research are derived from the Tumblebrook Farm strain, which has its origins in 20 pairs of wild-caught Mongolian gerbils sent to Japan in 1935. Eleven of these animals were subsequently sent to Dr. V. Schwentker's Tumblebrook Farm in Brant Lake, New York , United States in 1954, [ 13 ] with additional animals later sent to Charles River Ltd in Italy in 1996. [ 14 ] [ 15 ] [ 16 ]
Gerbils have a wide hearing range, from detection of low frequency foot drumming to higher frequency chirps and therefore may be a more suitable model of human hearing loss than mice and rats , which are high-frequency specialists. [ 17 ]
Male gerbils can produce ultrasonic sounds with frequencies ranging from approximately 27 to 35 kHz and amplitudes ranging from approximately 0 to 70 dBa. Their larynx is involved in the production of these ultrasonic sounds. Experimentation revealed five findings of interest, which are that adults only emit ultrasonic sounds when stimulated socially, males signal more frequently than females, dominant males are more active in vocalizations than subordinate males, ultrasounds are triggered by conspecific odors, and that d-amphetamine, a central nervous system stimulant, contributes high levels of ultrasounds while chlorpromazine, an antipsychotic medication, lowers the emission rate. In addition, there's been a relationship between the ultrasonic sounds and their ability to reproduce. [ failed verification ] [ 18 ]
10–20% of gerbils exhibit spontaneous epileptiform seizures, typically in response to a stressor such as handling or cage cleaning. [ 19 ] Epilepsy in gerbils has a genetic basis, and seizure -prone and seizure -resistant lines have been bred. [ 20 ] [ 21 ]
Like other desert rodents such as fat sandrats , Mongolian gerbils are susceptible to diet-induced diabetes , although incidence is low. [ 22 ] A diabetes-prone line has recently been generated, showing that gerbil diabetes has at least some genetic basis. [ 23 ] [ 24 ]
Laboratory gerbils are derived from a small number of founders, and so genetic diversity was generally assumed to be low. Initial genetic studies based on small numbers of genetic markers appeared to support this, [ 25 ] [ 26 ] but more recent genome-wide Genotyping-by-Sequencing (GBS) data has shown that genetic diversity is actually quite high. [ 14 ] It has been suggested that laboratory gerbils should be considered domesticated, and designated " M. unguiculatus forma domestica" to differentiate them from wild animals. [ 27 ] A Mongolian gerbil genome sequence was published in 2018 [ 28 ] and a genetic map comprising 22 linkage groups (one per chromosome) in 2019. [ 29 ]
In the wild, Mongolian gerbils breed in February and October. Males do not become sexually mature for about 70–80 days, while the vaginal opening occurs in females about 33–50 days after birth. [ 30 ] For other gerbils such as the hairy footed gerbil , sexual maturity has a slightly earlier and longer window of 60-90 [ 31 ] days in comparison with a later and shorter window for Mongolian gerbils, 70–84 days. [ 30 ] Females reach sexual maturity shortly after this opening occurs. They experience oestrus cycles every 4–6 days. Mongolian gerbils are regarded as monogamous within science. [ 32 ] Even with this said, many Mongolian gerbils have still been found in laboratory tests regarding their sexual reproduction behavior to have shown signs of promiscuity and mating with other females while their monogamous partner is absent in laboratory setting. [ 32 ]
Gerbils are for the most part selective when it comes to picking a mate for copulation. An average litter size for the Mongolian Gerbil is around 4–8 pups. If the litter only contains around 1–2 young then the mother will neglect them and they will die from starvation. [ 32 ] Mongolian Gerbils are monogamous and mate with their selected partner for life. When their mate dies, many gerbils refrain from seeking other mates to reproduce with. [ 32 ] Males generally find new mates whereas females may not. When older females lose their mate they almost always give up on seeking reproduction. [ 32 ] Their behavior tends to vary when faced with different settings; in the wild, the large population of gerbils means that finding and selecting a mate is not a problem. Within a laboratory setting, though, many gerbils tend to keep to themselves and refrain from copulation. [ 32 ]
Gerbils are social animals, and live in groups in the wild. [ 33 ] They rely on their sense of smell to identify other members of their clan. [ 34 ] Gerbils are known to attack and often kill those carrying an unfamiliar scent. Groups of gerbils often have a "dominant" gerbil which may "bully" the others by humping them. [ 35 ]
A gentle and hardy animal, the Mongolian gerbil has become a popular small house pet . It was first brought from China to Paris in the 19th century, and became a popular house pet there. [ 36 ] It was later brought to the United States in 1954 by Dr. Victor Schwentker for use in research. [ 37 ] Dr. Schwentker soon recognized their potential as pet animals. [ 38 ] Selective breeding for the pet trade has resulted in a wide range of different color and pattern varieties. [ 39 ] Gerbils became popular pets in the US around the late 1950s and were imported to the United Kingdom in 1964, where they became popular pets too. [ 40 ] They are now found in pet shops throughout the UK and the US.
However, due to the threat they pose to indigenous ecosystems and existing agricultural operations, it is illegal to purchase, import, or keep a gerbil as a pet in the U.S. state of California . [ 41 ] It is also illegal to import the animal into New Zealand and Australia. [ 42 ] [ 43 ]
Gerbils are typically not aggressive, and they rarely bite unprovoked or without stress. They are small and easy to handle, since they are sociable creatures that enjoy the company of humans and other gerbils. [ 44 ] [ 45 ] Gerbils also have adapted their kidneys to produce a minimum of waste to conserve body fluids, which makes them very clean with little odor. Gerbils have many different aesthetic coat patterns, such as pied slate, described below.
Misalignment of incisors due to injury or malnutrition may result in overgrowth, which can cause injury to the roof of the mouth. Symptoms include a dropped or loss of appetite, drooling, weight loss, or foul breath. [ 46 ]
Common injuries are caused by gerbils being dropped or falling, often while inside of a hamster ball , which can cause broken limbs or a fractured spine (for which there is no treatment). [ 46 ] [ 47 ]
A common problem for all small rodents is neglect, which can cause the gerbils to not receive adequate food and water, causing serious health concerns, including dehydration, starvation, stomach ulcers, eating of bedding material, and cannibalism. [ 46 ]
Between 20 and 50% of pet gerbils have the seizure disorder epilepsy . [ 48 ] The seizures are thought to be caused by fright, handling, or a new environment. The attacks can be mild to severe, but do not typically appear to have any long-term effects, except for rare cases where death results from very severe seizures. [ 49 ] A way to prevent a gerbil from having a seizure is to refrain from blowing in the animal's face (often used to "train" the pet not to bite). This technique is used in a lab environment to induce seizures for medical research. [ 50 ]
Tumors , both benign and malignant, are fairly common in pet gerbils, and are most common in females over the age of two. Usually, the tumors involve the ovaries, causing an extended abdomen, or the skin, with tumors most often developing around the ears, feet, midabdomen, and base of the tail, appearing as a lump or abscess. [ 49 ]
Gerbils can lose their tails due to improper handling, being attacked by another animal, or getting their tails stuck. The first sign is a loss of fur from the tip of the tail, then, the skinless tail dies off and sloughs, with the stump usually healing without complications. [ 49 ]
The most common infectious disease in gerbils is Tyzzer's disease , a bacterial disease, which stress can make animals more susceptible to. It produces symptoms such as ruffled fur, lethargy, hunched posture, poor appetite, diarrhoea, and often death. It quickly spreads between gerbils in close contact. [ 49 ]
A problem with the inner ear may cause a gerbil to lean noticeably to one side. This may be caused by ear infections. Gerbils with "extreme white spotting" colouring are susceptible to deafness; this is thought to be due to the lack of pigmentation in and around the ear. [ 51 ]
Many color varieties of gerbils are available in pet shops today, generally the result of years of selective breeding .
Over 20 different coat colors occur in the Mongolian gerbil, which has been captive-bred the longest. [ 52 ]
The fat-tailed gerbil or duprasi is also kept as a pet. They are smaller than the common Mongolian gerbils, and have long, soft coats and short, fat tails, appearing more like a hamster . The variation on the normal duprasi coat is more gray in color, which may be a mutation, or it may be the result of hybrids between the Egyptian and Algerian subspecies of duprasi. [ 53 ] [ 54 ]
White spotting has been reported in not only the Mongolian gerbil, but also the pallid gerbil [ 55 ] and possibly Sundervall's Jird. [ 56 ]
A long-haired mutation, a grey agouti or chinchilla mutation, white spotting, and possibly a dilute mutation have also appeared in Shaw's jirds , [ 57 ] and white spotting and a dilute mutation have shown up in bushy-tailed jirds . [ 58 ] | https://en.wikipedia.org/wiki/Mongolian_gerbil |
In algebra , a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. That is to say, a monic polynomial is one that can be written as [ 1 ]
with n ≥ 0. {\displaystyle n\geq 0.}
Monic polynomials are widely used in algebra and number theory , since they produce many simplifications and they avoid divisions and denominators. Here are some examples.
Every polynomial is associated to a unique monic polynomial. In particular, the unique factorization property of polynomials can be stated as: Every polynomial can be uniquely factorized as the product of its leading coefficient and a product of monic irreducible polynomials .
Vieta's formulas are simpler in the case of monic polynomials: The i th elementary symmetric function of the roots of a monic polynomial of degree n equals ( − 1 ) i c n − i , {\displaystyle (-1)^{i}c_{n-i},} where c n − i {\displaystyle c_{n-i}} is the coefficient of the (n−i) th power of the indeterminate .
Euclidean division of a polynomial by a monic polynomial does not introduce divisions of coefficients. Therefore, it is defined for polynomials with coefficients in a commutative ring .
Algebraic integers are defined as the roots of monic polynomials with integer coefficients.
Every nonzero univariate polynomial ( polynomial with a single indeterminate ) can be written
where c n , … , c 0 {\displaystyle c_{n},\ldots ,c_{0}} are the coefficients of the polynomial, and the leading coefficient c n {\displaystyle c_{n}} is not zero. By definition, such a polynomial is monic if c n = 1. {\displaystyle c_{n}=1.}
A product of monic polynomials is monic. A product of polynomials is monic if and only if the product of the leading coefficients of the factors equals 1 .
This implies that, the monic polynomials in a univariate polynomial ring over a commutative ring form a monoid under polynomial multiplication.
Two monic polynomials are associated if and only if they are equal, since the multiplication of a polynomial by a nonzero constant produces a polynomial with this constant as its leading coefficient.
Divisibility induces a partial order on monic polynomials. This results almost immediately from the preceding properties.
Let P ( x ) {\displaystyle P(x)} be a polynomial equation , where P is a univariate polynomial of degree n . If one divides all coefficients of P by its leading coefficient c n , {\displaystyle c_{n},} one obtains a new polynomial equation that has the same solutions and consists to equate to zero a monic polynomial.
For example, the equation
is equivalent to the monic equation
When the coefficients are unspecified, or belong to a field where division does not result into fractions (such as R , C , {\displaystyle \mathbb {R} ,\mathbb {C} ,} or a finite field ), this reduction to monic equations may provide simplification. On the other hand, as shown by the previous example, when the coefficients are explicit integers, the associated monic polynomial is generally more complicated. Therefore, primitive polynomials are often used instead of monic polynomials when dealing with integer coefficients.
Monic polynomial equations are at the basis of the theory of algebraic integers , and, more generally of integral elements .
Let R be a subring of a field F ; this implies that R is an integral domain . An element a of F is integral over R if it is a root of a monic polynomial with coefficients in R .
A complex number that is integral over the integers is called an algebraic integer . This terminology is motivated by the fact that the integers are exactly the rational numbers that are also algebraic integers. This results from the rational root theorem , which asserts that, if the rational number p q {\textstyle {\frac {p}{q}}} is a root of a polynomial with integer coefficients, then q is a divisor of the leading coefficient; so, if the polynomial is monic, then q = ± 1 , {\displaystyle q=\pm 1,} and the number is an integer. Conversely, an integer p is a root of the monic polynomial x − a . {\displaystyle x-a.}
It can be proved that, if two elements of a field F are integral over a subring R of F , then the sum and the product of these elements are also integral over R . It follows that the elements of F that are integral over R form a ring, called the integral closure of R in K . An integral domain that equals its integral closure in its field of fractions is called an integrally closed domain .
These concepts are fundamental in algebraic number theory . For example, many of the numerous wrong proofs of the Fermat's Last Theorem that have been written during more than three centuries were wrong because the authors supposed wrongly that the algebraic integers in an algebraic number field have unique factorization .
Ordinarily, the term monic is not employed for polynomials of several variables. However, a polynomial in several variables may be regarded as a polynomial in one variable with coefficients being polynomials in the other variables. Being monic depends thus on the choice of one "main" variable. For example, the polynomial
is monic, if considered as a polynomial in x with coefficients that are polynomials in y :
but it is not monic when considered as a polynomial in y with coefficients polynomial in x :
In the context of Gröbner bases , a monomial order is generally fixed. In this case, a polynomial may be said to be monic, if it has 1 as its leading coefficient (for the monomial order).
For every definition, a product of monic polynomials is monic, and, if the coefficients belong to a field , every polynomial is associated to exactly one monic polynomial. | https://en.wikipedia.org/wiki/Monic_polynomial |
Monilink Limited (stylized MONILINK ) was the banking service operating in the United Kingdom that gave customers access to their financial information directly from their mobile phones . Created in 2003 Monilink was a joint venture between Monitise and LINK . Promotional material promised consumers that, through the service: “The future of banking is in your hands”.
Latterly, Monilink offered customers the chance to check their bank balance in real-time, view a mini statement detailing the last six transactions and add credit to up to five pay as you go phones. Future services would include options to move money between accounts, pay bills, and purchase travel tickets.
The company became inactive around 2011 and was dissolved in 2015.
By June 2008, HSBC , First Direct , Alliance & Leicester , NatWest , Royal Bank of Scotland , Ulster Bank and Lloyds TSB . Alliance & Leicester withdrew, after being taken over by Santander .
All the mobile phone companies in the UK enable Monilink: Vodafone , O2 , Orange , T-Mobile and 3 . Tesco Mobile and Virgin Mobile are also participating.
MONILINK was recognised by the World Economic Forum in 2006 as a technology pioneer in the area of mobile banking . | https://en.wikipedia.org/wiki/Monilink |
The Obukhov length is used to describe the effects of buoyancy on turbulent flows, particularly in the lower tenth of the atmospheric boundary layer . It was first defined by Alexander Obukhov [ 1 ] in 1946. [ 2 ] [ 3 ] It is also known as the Monin–Obukhov length because of its important role in the similarity theory developed by Monin and Obukhov. [ 4 ] A simple definition of the Monin-Obukhov length is that height at which turbulence is generated more by buoyancy than by wind shear.
The Obukhov length is defined by
where u ∗ {\displaystyle u_{*}} is the frictional velocity , θ ¯ v {\displaystyle {\bar {\theta }}_{v}} is the mean virtual potential temperature , ( w ′ θ v ′ ¯ ) s {\displaystyle ({\overline {w^{'}\theta _{v}^{'}}})_{s}} is the surface virtual potential temperature flux, k is the von Kármán constant . If not known, the virtual potential temperature flux can be apprioximated with: [ 5 ]
where θ {\displaystyle \theta } is potential temperature, and r {\displaystyle r} is mixing ratio.
By this definition, L {\displaystyle L} is usually negative in the daytime since w ′ θ v ′ ¯ {\displaystyle {\overline {w^{'}\theta _{v}^{'}}}} is typically positive during the daytime over land, positive at night when w ′ θ v ′ ¯ {\displaystyle {\overline {w^{'}\theta _{v}^{'}}}} is typically negative, and becomes infinite at dawn and dusk when w ′ θ v ′ ¯ {\displaystyle {\overline {w^{'}\theta _{v}^{'}}}} passes through zero.
A physical interpretation of L {\displaystyle L} is given by the Monin–Obukhov similarity theory . During the day − L {\displaystyle -L} is the height at which the buoyant production of turbulence kinetic energy (TKE) is equal to that produced by the shearing action of the wind (shear production of TKE).
This article about atmospheric science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monin–Obukhov_length |
Monique Glenda Zaahl OMB (born 4 November 1975) is a South African geneticist . She was formerly a professor of genetics at Stellenbosch University , where she conducted influential research into iron overload . She is now the managing director of Gene Diagnostics, a private genetic testing company.
Zaahl completed her undergraduate degree at Stellenbosch University , where she became interested in human genetics as a result of the influence of Professor Louise Warnich. [ 1 ] She obtained her PhD at Stellenboch in 2003; she received the 2001 Commonwealth Split-Site Scholarship to complete part of her doctoral research at Oxford University under the supervision of Kathryn Robson. [ 2 ]
In 2004, she joined the Stellenbosch faculty as a lecturer. [ 2 ] She was promoted to senior lecturer in 2006, associate professor in 2010, and head of the Department of Genetics in 2011; [ 2 ] she was tenured as a full professor shortly afterwards. [ 3 ] Her research at Stellenbosch focused on iron -related causes of disease, particularly via investigation of the genetic mechanisms of iron metabolism and iron overload . [ 2 ]
In 2009, while still at Stellenbosch, [ 2 ] she founded Gene Diagnostics, a private genetic testing company. The Star said it was the first such company owned by a black woman . [ 1 ] She ultimately left academia to run the company full time. It received support from the Cyril Ramaphosa Foundation 's Black Umbrellas business incubation programme, and in 2021 it moved its headquarters from Somerset West to Woodstock, Cape Town . [ 4 ]
At the 2006 National Women in Science Awards, Zaahl was named the Best Emerging Young Scientist. [ 5 ] [ 2 ] In 2009, the National Science and Technology Forum awarded her the National Research Foundation -sponsored T. W. Kambule Award for young black researchers. [ 6 ] In April 2010, President Jacob Zuma admitted her to the Order of Mapungubwe , granting her the award in Bronze "For her outstanding contribution to the field of genetics and research into disorders resulting from iron overload." [ 7 ] | https://en.wikipedia.org/wiki/Monique_Zaahl |
Monitor mode , or RFMON (Radio Frequency MONitor) mode, allows a computer with a wireless network interface controller (WNIC) to monitor all traffic received on a wireless channel. Unlike promiscuous mode , which is also used for packet sniffing , monitor mode allows packets to be captured without having to associate with an access point or ad hoc network first. Monitor mode only applies to wireless networks, while promiscuous mode can be used on both wired and wireless networks. Monitor mode is one of the eight modes that 802.11 wireless adapter can operate in: Master (acting as an access point), Managed (client, also known as station), Ad hoc , Repeater , Mesh , Wi-Fi Direct , TDLS and Monitor mode.
Uses for monitor mode include: geographical packet analysis, observing of widespread traffic and acquiring knowledge of Wi-Fi technology through hands-on experience. It is especially useful for auditing unsecure channels (such as those protected with WEP ). Monitor mode can also be used to help design Wi-Fi networks. For a given area and channel, the number of Wi-Fi devices currently being used can be discovered. This helps to create a better Wi-Fi network that reduces interference with other Wi-Fi devices by choosing the least used Wi-Fi channels.
Software such as KisMAC or Kismet , in combination with packet analyzers that can read pcap files, provide a user interface for passive wireless network monitoring .
Usually the wireless adapter is unable to transmit in monitor mode and is restricted to a single wireless channel, though this is dependent on the wireless adapter's driver, its firmware, and features of its chipset. Also, in monitor mode the adapter does not check to see if the cyclic redundancy check (CRC) values are correct for packets captured, so some captured packets may be corrupted.
The Microsoft Windows Network Driver Interface Specification (NDIS) API has supported extensions for monitor mode since NDIS version 6, first available in Windows Vista . [ 1 ] NDIS 6 supports exposing 802.11 frames to the upper protocol levels, [ 2 ] while previous versions only exposed fake Ethernet frames translated from the 802.11 frames. Monitor mode support in NDIS 6 is an optional feature and may or may not be implemented in the client adapter driver. The implementation details and compliance with the NDIS specifications vary from vendor to vendor. In many cases, monitor mode support is not properly implemented by the vendor. For example, Ralink drivers report incorrect dBm readings and Realtek drivers do not include trailing 4-byte CRC values. [ citation needed ]
For versions of Windows prior to Windows Vista, some packet analyzer applications such as Wildpackets' OmniPeek and TamoSoft's CommView for WiFi provide their own device drivers to support monitor mode.
Linux's interfaces for 802.11 drivers support monitor mode and many drivers offer that support. [ 3 ] STA drivers ( Ralink , Broadcom ) and every other manufacturer’s provided driver doesn’t support monitor mode. [ 4 ] FreeBSD , NetBSD , OpenBSD , and DragonFly BSD also provide an interface for 802.11 drivers that supports monitor mode, and many drivers for those operating systems support monitor mode as well. In Mac OS X 10.4 and later releases, the drivers for AirPort Extreme network adapters allow the adapter to be put into monitor mode. Libpcap 1.0.0 and later provides an API to select monitor mode when capturing on those operating systems. | https://en.wikipedia.org/wiki/Monitor_mode |
The Monitor of Settlement and Open Space Development (IÖR-Monitor) is a specialized information system on land use issues in Germany. Since 2010, it has been providing information on the land use structure and its development as well as on landscape quality in high spatial resolution for the terrestrial territory of the Federal Republic of Germany on the basis of indicators. The IOER monitor thus complements the official land use statistics and the environmental-economic accounts with basic information for assessing land development, especially with regard to its sustainability.
The Monitor of Settlement and Open Space Development is a permanent, scientific service provided free of charge by the Leibniz Institute for Ecological Spatial Development (IÖR) in Dresden and part of its research-based policy and social consulting. It therefore also bears the short name IÖR-Monitor. The monitor is successively supplemented with new time periods and indicators in order to be able to assess the state and development of land throughout Germany. For this purpose, IÖR uses the most accurate geotopographic data in Germany (ATKIS Basis-DLM) for all land use indicators, the Digital Land Cover Model (LBM-DE) for the indicators hemeroby and degree of naturalness, official house perimeters (HU-DE) and house coordinates (HK-DE) for the building indicators, as well as geospatial data (protected areas, legally defined floodplains), population grids (from the 2011 census) and statistical data (population, GDP), which are processed in combination. [ 1 ]
Almost 80 indicators of the categories settlement, open space, traffic, buildings, landscape quality (e.g. "hemeroby index", "ecotone density"), landscape and nature conservation, ecosystem services , population, risk and relief are now offered. [ 2 ] For each indicator, the calculation methodology and meaning is presented in a fact sheet. Recurring, central terms are explained in a glossary.
The following options are available for the output of the indicators:
The IÖR-Monitor provides information on the condition and development of land and soil, which is only available to a limited extent and requires protection. It serves as a basis for evaluations and is of particular importance for land budget policy and spatial and sectoral planning at all levels (federal, state, planning regions, counties and municipalities). The IÖR-Monitor can be used, for example, to display [ 3 ] and compare variables such as land sealing, [ 4 ] population density, transport area per inhabitant and the accessibility of urban green spaces. This information is also of interest to science, business, interested private users and the media and can be accessed on the Internet at any time. In the 3rd Geo Progress Report of the Federal Government, the IOER monitor is cited as an "excellent example of open government". Furthermore, Germany is classified as a European leader in the survey and monitoring of the land use structure based on the analysis results of the monitor. [ 5 ] After being selected by a jury, the IÖR monitor was able to present itself to a broad public as a service for responsible future design at the Week of the Environment (2016). [ 6 ]
By providing information on settlement and transport land development, the IÖR-Monitor contributes to the national sustainability strategy of 2002, in which the German government set the goal of reducing land consumption by settlement and transport uses in Germany to 30 hectares per day by 2020 (30-hectare target). [ 7 ] Accurate and up-to-date land monitoring is needed to evaluate the achievement of this target. | https://en.wikipedia.org/wiki/Monitor_of_Settlement_and_Open_Space_Development |
A water scoop is a simple hydropower machine – that is, a machine used to extract power from the flow of water. Unlike a water wheel it operates intermittently, like a seesaw : A container (a bucket or cup) at the end of a lever is filled with water in the upper position. The container side becomes heavier, and so the lever with the filled container moves downward, which may be used to operate a machine drive. In the lower position the container is emptied, and the lever moves back into the upward position.
Because of their inferior efficiency compared to a water mill, water scoops are less common, and have been used in the past mostly for applications where linear motion is required rather than rotation, for example hammers in smitheries , saws in sawmills , and stamp mills in mining . They are also used for fulling and, nowadays, to operate animated sculptures in fountains .
A monjolo is a type of water scoop used for the processing and grinding of grains and introduced in Brazil by the Portuguese during the colonial period. [ 1 ] It can be used to peel and grind dry beans, resulting in a thicker flour. [ 2 ]
It is formed by a wooden beam suspended so that the part that supports the pestle is larger than the other, which ends with a trough. A spout fills the trough with the water, thus raising the pestle. When the trough is full, it lowers the trough, and when the trough spills the water, the beam falls, causing the pestle to hit the mortar . As such, the monjolo is an important tool for agricultural facilitation. It is common for rural people to seek to live near a river or stream as a source of water. The monjolo is considered one of the most useful machines for planters of multiple crops. [ 3 ]
This article about renewable energy is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monjolo |
In mathematics, Monk's formula , found by Monk (1959) , is an analogue of Pieri's formula that describes the product of a linear Schubert polynomial by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology of a flag manifold .
Write t ij for the transposition (i j) , and s i = t i,i+1 . Then 𝔖 s r = x 1 + ⋯ + x r , and Monk's formula states that for a permutation w ,
S s r S w = ∑ i ≤ r < j ℓ ( w t i j ) = ℓ ( w ) + 1 S w t i j , {\displaystyle {\mathfrak {S}}_{s_{r}}{\mathfrak {S}}_{w}=\sum _{{i\leq r<j} \atop {\ell (wt_{ij})=\ell (w)+1}}{\mathfrak {S}}_{wt_{ij}},}
where ℓ ( w ) {\displaystyle \ell (w)} is the length of w . The pairs ( i , j ) appearing in the sum are exactly those such that i ≤ r < j , w i < w j , and there is no i < k < j with w i < w k < w j ; each wt ij is a cover of w in Bruhat order . | https://en.wikipedia.org/wiki/Monk's_formula |
In mathematics , the monkey saddle is the surface defined by the equation
or in cylindrical coordinates
It belongs to the class of saddle surfaces , and its name derives from the observation that a saddle used by a monkey would require two depressions for its legs and one for its tail. The point ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} on the monkey saddle corresponds to a degenerate critical point of the function z ( x , y ) {\displaystyle z(x,y)} at ( 0 , 0 ) {\displaystyle (0,0)} . The monkey saddle has an isolated umbilical point with zero Gaussian curvature at the origin, while the curvature is strictly negative at all other points.
One can relate the rectangular and cylindrical equations using complex numbers x + i y = r e i φ : {\displaystyle x+iy=re^{i\varphi }:}
By replacing 3 in the cylindrical equation with any integer k ≥ 1 , {\displaystyle k\geq 1,} one can create a saddle with k {\displaystyle k} depressions. [ 1 ]
Another orientation of the monkey saddle is the Smelt petal defined by x + y + z + x y z = 0 , {\displaystyle x+y+z+xyz=0,} so that the z- axis of the monkey saddle corresponds to the direction ( 1 , 1 , 1 ) {\displaystyle (1,1,1)} in the Smelt petal. [ 2 ] [ 3 ]
Another function, which has not three but four areas - in each quadrant of the R 2 {\displaystyle \mathbb {R} ^{2}} , in which the function goes to minus infinity, is given by z = x 4 − 6 x 2 y 2 + y 4 {\displaystyle z=x^{4}-6x^{2}y^{2}+y^{4}} .
The term horse saddle may be used in contrast to monkey saddle, to designate an ordinary saddle surface in which z ( x , y ) has a saddle point , a local minimum or maximum in every direction of the xy -plane. In contrast, the monkey saddle has a stationary point of inflection in every direction. | https://en.wikipedia.org/wiki/Monkey_saddle |
Mono-BOC-cystamine ( mono BOC protected cystamine ) is a tert -butyloxycarbonyl (BOC) derivative of cystamine used as crosslinker in biotechnology and molecular biology applications. [ 1 ] This compound was originally reported by Hansen et al . [ 2 ]
The disulfide chain allows the mono-BOC-cystamine to be easily cleaved, allowing removal of the tagging residue when desired.
Mono-BOC-cystamine is used as a crosslinker for the synthesis of cleavable photo-cross-linking reagent. [ 3 ]
Mono-BOC-cystamine is used as a crosslinker for the synthesis of a biodegradable cystamine spacer in PGA-cystamine-Gd-DO3A, which shows improved MRI contrast for breast carcinoma imaging in mice. [ 4 ] | https://en.wikipedia.org/wiki/Mono-BOC-cystamine |
Monoallelic gene expression (MAE) is the phenomenon of the gene expression , when only one of the two gene copies ( alleles ) is actively expressed ( transcribed ), while the other is silent. [ 1 ] [ 2 ] [ 3 ] Diploid organisms bear two homologous copies of each chromosome (one from each parent), a gene can be expressed from both chromosomes (biallelic expression) or from only one (monoallelic expression). [ 4 ] MAE can be Random monoallelic expression (RME) or Constitutive monoallelic expression (constitutive) . Constitutive monoallelic expression occurs from the same specific allele throughout the whole organism or tissue, as a result of genomic imprinting . [ 5 ] RME is a broader class of monoallelic expression, which is defined by random allelic choice in somatic cells , so that different cells of the multi-cellular organism express different alleles.
X-chromosome inactivation (XCI), is the most striking and well-studied example of RME. XCI leads to the transcriptional silencing of one of the X chromosomes in female cells, which results in expression of the genes that located on the other, remaining active X chromosome . XCI is critical for balanced gene expression in female mammals . The allelic choice of XCI by individual cells takes place randomly in epiblasts of the preimplantation embryo, [ 6 ] which leads to mosaic gene expression of the paternal and maternal X chromosome in female tissues. [ 7 ] [ 8 ] XCI is a chromosome-wide monoallelic expression, that includes expression of all genes that are located on X chromosome, in contrast to autosomal RME (aRME) that relates to single genes that are interspersed over the genome . aRME's can be fixed [ 9 ] or dynamic, depending whether or not the allele-specific expression is conserved in daughter cells after mitotic cell division .
Fixed aRME are established either by silencing of one allele that previously has been biallelically expressed, or by activation of a single allele from previously silent gene. Expression activation of the silent allele is coupled with a feedback mechanism that prevents expression of the second allele. Another scenario is also possible due to limited time-window of low-probability initiation, that could lead to high frequencies of cells with single-allele expression. It is estimated that 2 [ 10 ] [ 11 ] -10 [ 12 ] % of all genes are fixed aRME. Studies
of fixed aRME require either expansion of monoclonal cultures or lineage-traced in vivo or in vitro cells that are mitotically.
Dynamic aRME occurs as a consequence of stochastic allelic expression. Transcription happens in bursts , which results in RNA molecules being synthesized from each allele separately. So over time, both alleles have a probability to initiate transcription. Transcriptional bursts are allelically stochastic, and lead to either maternal or paternal allele being accumulated in the cell. The gene transcription burst frequency and intensity combined with RNA-degradation rate form the shape of RNA distribution at the moment of observation and thus whether the gene is bi- or monoallelic. Studies that distinguish fixed and dynamic aRME require single-cell analyses of clonally related cells. [ 13 ]
Allelic exclusion is a process of gene expression when one allele is expressed and the other one kept silent. Two most studied cases of allelic exclusion are monoallelic expression of immunoglobulins in B and T cells [ 14 ] [ 15 ] [ 16 ] and olfactory receptors in sensory neurons. [ 17 ] Allelic exclusion is cell-type specific (as opposed to organism-wide XCI), which increases intercellular diversity, thus specificity towards certain antigens or odors .
Allele-biased expression is skewed expression level of one allele over the other, but both alleles are still expressed (in contrast to allelic exclusion). This phenomenon is often observed in cells of immune function [ 18 ] [ 19 ]
Methods of MAE detection are based on the difference between alleles, which can be distinguished either by the sequence of expressed mRNA or protein structure. Methods of MAE detection can be divided into single gene or whole genome MAE analysis. Whole genome MAE analysis cannot be performed based on protein structure yet, so these are completely NGS based techniques.
Single-gene analysis
Genome-wide analysis | https://en.wikipedia.org/wiki/Monoallelic_gene_expression |
Monoamine nuclei are clusters of cells that primarily use monoamine neurotransmitters to communicate. The raphe nuclei , ventral tegmental area , and locus coeruleus have been included in texts about monoamine nuclei. [ 1 ] These nuclei receive a variety of inputs including from other monoamines, as well as from glutaminergic , GABAergic , and substance p related pathways. The catacholaminergic pathways mainly project upwards into the cortical and limbic regions, power sparse descending axons have been observed in animals models. Both ascending and descending serotonergic pathways project from the raphe nuclei. Raphe nuclei in the obscurus, pallid us, and magnus descend into the brainstem and spinal cord, while the raphe ponds, raphe dorsals, and nucleus centralism superior projected up into the medial forebrain bundle before branching off. [ 2 ] Monoamine nuclei have been studied in relation to major depressive disorder , with some abnormalities observed, [ 3 ] however MAO-B levels appear to be normal during depression in these regions. [ 4 ] | https://en.wikipedia.org/wiki/Monoamine_nuclei |
Monoamine precursors are precursors of monoamines and monoamine neurotransmitters in the body. [ 1 ] [ 2 ] The amino acids L -tryptophan and L -5-hydroxytryptophan (5-HTP; oxitriptan) are precursors of serotonin and melatonin , while the amino acids L -phenylalanine , L -tyrosine , and L -DOPA (levodopa) are precursors of dopamine , epinephrine (adrenaline), and norepinephrine (noradrenaline). [ 1 ] [ 2 ]
Administration of monoamine precursors can increase the levels of monoamine neurotransmitters in the body and brain. [ 2 ] Monoamine precursors may be used in combination with peripherally selective aromatic L -amino acid decarboxylase inhibitors (AAAD inhibitors; also known as DOPA decarboxylase (DDC) inhibitors) such as carbidopa and benserazide to restrict metabolism and activation in the periphery. [ 3 ] Carbidopa/levodopa and levodopa/benserazide are used to increase brain dopamine levels in the treatment of Parkinson's disease . [ 3 ] Carbidopa/oxitriptan (EVX-101), which increases brain serotonin levels, is under development as an antidepressant for possible use in the treatment of depression . [ 4 ] [ 5 ]
Droxidopa ( L -DOPS) is a synthetic precursor or prodrug of norepinephrine used orally in the treatment of certain types of hypotension and other conditions. [ 6 ] [ 7 ] Dipivefrine is a synthetic precursor or prodrug of epinephrine used as an ophthalmic medication . [ 7 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monoamine_precursor |
Monoaminergic means "working on monoamine neurotransmitters ", which include serotonin , dopamine , norepinephrine , epinephrine , and histamine .
A monoaminergic , or monoaminergic drug , is a chemical, which functions to directly modulate the serotonin, dopamine, norepinephrine, epinephrine, and/or histamine neurotransmitter systems in the brain. Monoaminergics include catecholaminergics (which can be further divided into adrenergics and dopaminergics ), serotonergics , and histaminergics .
Examples of monoaminergic drugs include monoamine precursors , monoamine receptor modulators , monoamine reuptake inhibitors , monoamine releasing agents , and monoamine metabolism modulators such as monoamine oxidase inhibitors .
This drug article relating to the nervous system is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monoaminergic |
Monoaminergic cell groups refers to collections of neurons in the central nervous system that have been demonstrated by histochemical fluorescence to contain one of the neurotransmitters serotonin , dopamine , norepinephrine [ 1 ] or epinephrine . [ 2 ] Thus, it represents the combination of catecholaminergic cell groups and serotonergic cell groups .
This neuroanatomy article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Monoaminergic_cell_groups |
Monobasic may refer to: | https://en.wikipedia.org/wiki/Monobasic |
Monobenzyl phthalate ( MBzP ) also known as 1,2-Benzenedicarboxylic acid, 1-(phenylmethyl) ester is an organic compound with the condensed structural formula C 6 H 5 CH 2 OOCC 6 H 4 COOH. It is the major metabolite of butyl benzyl phthalate (BBP), a common plasticizer. [ 2 ] BBP can also be metabolized into monobutyl phthalate (MBP). [ 3 ] [ 4 ] Like many phthalates , BBP has attracted attention as a potential endocrine disruptor . [ 5 ] [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Monobenzyl_phthalate |
Monoblepharis is a genus of fungi belonging to the family Monoblepharidaceae . [ 1 ]
The genus has almost cosmopolitan distribution . [ 1 ]
Species: [ 1 ] | https://en.wikipedia.org/wiki/Monoblepharis |
Monobutyl phthalate ( MBP ) is an organic compound with the condensed structural formula CH 3 (CH 2 ) 3 OOCC 6 H 4 COOH. It is a white solid that features both an butyl ester group and a carboxylic acid group. It is the major metabolite of dibutyl phthalate . Like many phthalates , MBP has attracted attention as a potential endocrine disruptor . [ 3 ]
MBP is also the secondary metabolite of butyl benzyl phthalate , less than monobenzyl phthalate (MBzP). It hydrolyses to phthalic acid and 1-butanol . [ 4 ] | https://en.wikipedia.org/wiki/Monobutyl_phthalate |
Monocarpic plants are those that flower and set seeds only once, and then die .
The term is derived from Greek ( mono , "single" + karpos , "fruit" or "grain"), and was first used by Alphonse de Candolle . Other terms with the same meaning are hapaxanth and semelparous . The antonym is polycarpic , a plant that flowers and sets seeds many times during its lifetime; the antonym of semelparous is iteroparous . Plants which flower en masse (gregariously) before dying are known as plietesials . The term hapaxanth is most often in conjunction with describing some of the taxa of Arecaceae (palms) and some species of bamboo , but rarely used otherwise; its antonym is pleonanth . This was first used by Alexander Braun .
Monocarpic plants are not necessarily annuals , because some monocarpic plants can live a number of years before they will flower. In some monocarpic plants, flowering signals senescence , while in others the production of fruits and seeds causes changes within the plants which lead to death. These changes are induced by chemicals that act as hormones , redirecting the resources of the plants from the roots and leaves to the production of fruits and or seeds. [ 1 ]
The century plant in the genus Agave , some terrestrial bromeliads of the genus Puya , Tillandsia utriculata , some yuccas , and many bamboos can take 8 to 20 years or in the case of some bamboos even over 100 years to bloom and then die. Hawaiian silverswords and their relatives in the genus Wilkesia may take 10–50 years before flowering.
Monocot plant families that include monocarpic species include Agavaceae , Araceae , Arecaceae , Bromeliaceae , Musaceae , and Poaceae . Dicot plant families that include monocarpic species include Acanthaceae , Apocynaceae , Asteraceae , and Fabaceae . Few dicot shrubs with multiple branching and secondary growth species have been described. Those that have include Strobilanthes species, Cerberiopsis candelabrum , Tachigali versicolor and other Tachigali species. [ 2 ]
Some monocarpic plants can be kept alive if the flowers are removed as soon as they have finished blooming before seed formation begins, or if the flower buds are removed before they begin blooming. [ 3 ] | https://en.wikipedia.org/wiki/Monocarpic_plant |
Monochloramine , often called chloramine , is the chemical compound with the formula NH 2 Cl. Together with dichloramine (NHCl 2 ) and nitrogen trichloride (NCl 3 ), it is one of the three chloramines of ammonia . [ 3 ] It is a colorless liquid at its melting point of −66 °C (−87 °F), but it is usually handled as a dilute aqueous solution , in which form it is sometimes used as a disinfectant . Chloramine is too unstable to have its boiling point measured. [ 4 ]
Chloramine is used as a disinfectant for water. It is less aggressive than chlorine and more stable against light than hypochlorites . [ 5 ]
Chloramine is commonly used in low concentrations as a secondary disinfectant in municipal water distribution systems as an alternative to chlorination . This application is increasing. Chlorine (referred to in water treatment as free chlorine) is being displaced by chloramine—to be specific, monochloramine—which is much less reactive and does not dissipate as rapidly as free chlorine. Chloramine also has a much lower, but still active, tendency than free chlorine to convert organic materials into chlorocarbons such as chloroform and carbon tetrachloride . Such compounds have been identified as carcinogens and in 1979 the United States Environmental Protection Agency (EPA) began regulating their levels in US drinking water . [ 6 ]
Some of the unregulated byproducts may possibly pose greater health risks than the regulated chemicals. [ 7 ] [ clarification needed ]
Due to its acidic nature, adding chloramine to the water supply may increase exposure to lead in drinking water , especially in areas with older housing; this exposure can result in increased lead levels in the bloodstream , which may pose a significant health risk. Fortunately, water treatment plants can add caustic chemicals at the plant which have the dual purpose of reducing the corrosivity of the water, and stabilizing the disinfectant. [ 8 ]
In swimming pools , chloramines are formed by the reaction of free chlorine with amine groups present in organic substances , mainly those biological in origin (e.g., urea in sweat and urine ). Chloramines, compared to free chlorine, are both less effective as a sanitizer and, if not managed correctly, more irritating to the eyes of swimmers. Chloramines are responsible for the distinctive "chlorine" smell of swimming pools, which is often misattributed to elemental chlorine by the public. [ 9 ] [ 10 ] Some pool test kits designed for use by homeowners do not distinguish free chlorine and chloramines, which can be misleading and lead to non-optimal levels of chloramines in the pool water. [ 11 ] There is also evidence that exposure to chloramine can contribute to respiratory problems , including asthma , among swimmers . [ 12 ] Respiratory problems related to chloramine exposure are common and prevalent among competitive swimmers. [ 13 ]
Though chloramine's distinctive smell has been described by some as pleasant and even nostalgic, [ 14 ] its formation in pool water as a result of bodily fluids being exposed to chlorine can be minimised by encouraging showering and other hygiene methods prior to entering the pool, [ 15 ] as well as refraining from swimming while suffering from digestive illnesses and taking breaks to use the bathroom, instead of simply urinating in the pool. [ 16 ] [ 17 ]
US EPA drinking water quality standards limit chloramine concentration for public water systems to 4 parts per million (ppm) based on a running annual average of all samples in the distribution system. In order to meet EPA-regulated limits on halogenated disinfection by-products , many utilities are switching from chlorination to chloramination . While chloramination produces fewer regulated total halogenated disinfection by-products, it can produce greater concentrations of unregulated iodinated disinfection byproducts and N -nitrosodimethylamine . [ 18 ] [ 19 ] Both iodinated disinfection by-products and N -nitrosodimethylamine have been shown to be genotoxic , causing damage to the genetic information within a cell resulting in mutations which may lead to cancer . [ 19 ]
Another newly-identified byproduct of chloramine is chloronitramide anions , whose toxicity has not yet been determined. [ 20 ]
In the year 2000, Washington, DC , switched from chlorine to monochloramine, causing lead to leach from unreplaced pipes. The number of babies with elevated blood lead levels rose about tenfold, and by one estimate fetal deaths rose between 32% and 63%. [ 21 ]
Trenton, Missouri made the same switch, causing about one quarter of tested households to exceed EPA drinking water lead limits in the period from 2017 to 2019. 20 children tested positive for lead poisoning in 2016 alone. [ 21 ] In 2023, Virginia Tech Professor Marc Edwards said lead spikes occur in several water utility system switchovers per year, due to lack of sufficient training and lack of removal of lead pipes. [ 21 ] Lack of utility awareness that lead pipes are still in use is also part of the problem; the EPA has required all water utilities in the United States to prepare a complete lead pipe inventory by October 16, 2024. [ 22 ]
Chloramine is a highly unstable compound in concentrated form. Pure chloramine decomposes violently above −40 °C (−40 °F). [ 23 ] Gaseous chloramine at low pressures and low concentrations of chloramine in aqueous solution are thermally slightly more stable. Chloramine is readily soluble in water and ether , but less soluble in chloroform and carbon tetrachloride . [ 5 ]
In dilute aqueous solution, chloramine is prepared by the reaction of ammonia with sodium hypochlorite : [ 5 ]
This reaction is also the first step of the Olin Raschig process for hydrazine synthesis. The reaction has to be carried out in a slightly alkaline medium ( pH 8.5–11). The acting chlorinating agent in this reaction is hypochlorous acid (HOCl), which has to be generated by protonation of hypochlorite , and then reacts in a nucleophilic substitution of the hydroxyl against the amino group . The reaction occurs quickest at around pH 8. At higher pH values the concentration of hypochlorous acid is lower, at lower pH values ammonia is protonated to form ammonium ions ( NH + 4 ), which do not react further.
The chloramine solution can be concentrated by vacuum distillation and by passing the vapor through potassium carbonate which absorbs the water. Chloramine can be extracted with ether.
Gaseous chloramine can be obtained from the reaction of gaseous ammonia with chlorine gas (diluted with nitrogen gas):
Pure chloramine can be prepared by passing fluoroamine through calcium chloride :
The covalent N−Cl bonds of chloramines are readily hydrolyzed with release of hypochlorous acid : [ 24 ]
The quantitative hydrolysis constant ( K value) is used to express the bactericidal power of chloramines, which depends on their generating hypochlorous acid in water. It is expressed by the equation below, and is generally in the range 10 −4 to 10 −10 ( 2.8 × 10 −10 for monochloramine):
In aqueous solution, chloramine slowly decomposes to dinitrogen and ammonium chloride in a neutral or mildly alkaline (pH ≤ 11) medium:
However, only a few percent of a 0.1 M chloramine solution in water decomposes according to the formula in several weeks. At pH values above 11, the following reaction with hydroxide ions slowly occurs:
In an acidic medium at pH values of around 4, chloramine disproportionates to form dichloramine , which in turn disproportionates again at pH values below 3 to form nitrogen trichloride :
At low pH values, nitrogen trichloride dominates and at pH 3–5 dichloramine dominates. These equilibria are disturbed by the irreversible decomposition of both compounds:
In water, chloramine is pH-neutral. It is an oxidizing agent (acidic solution: E ° = +1.48 V , in basic solution E ° = +0.81 V ): [ 5 ]
Reactions of chloramine include radical , nucleophilic , and electrophilic substitution of chlorine, electrophilic substitution of hydrogen, and oxidative additions .
Chloramine can, like hypochlorous acid, donate positively charged chlorine in reactions with nucleophiles (Nu − ):
Examples of chlorination reactions include transformations to dichloramine and nitrogen trichloride in acidic medium, as described in the decomposition section.
Chloramine may also aminate nucleophiles ( electrophilic amination ):
The amination of ammonia with chloramine to form hydrazine is an example of this mechanism seen in the Olin Raschig process:
Chloramine electrophilically aminates itself in neutral and alkaline media to start its decomposition:
The chlorohydrazine (N 2 H 3 Cl) formed during self-decomposition is unstable and decomposes itself, which leads to the net decomposition reaction:
Monochloramine oxidizes sulfhydryls and disulfides in the same manner as hypochlorous acid, [ 25 ] but only possesses 0.4% of the biocidal effect of HClO. [ 26 ] | https://en.wikipedia.org/wiki/Monochloramine |
A monochord , also known as sonometer [ citation needed ] (see below ), is an ancient musical and scientific laboratory instrument , involving one ( mono- ) string ( chord ). The term monochord is sometimes used as the class-name for any musical stringed instrument having only one string and a stick shaped body, also known as musical bows . According to the Hornbostel–Sachs system, string bows are bar zithers (311.1) while monochords are traditionally board zithers (314). The "harmonical canon", or monochord is, at its least, "merely a string having a board under it of exactly the same length, upon which may be delineated the points at which the string must be stopped to give certain notes," allowing comparison. [ 2 ]
A string is fixed at both ends and stretched over a sound box. One or more movable bridges are then manipulated to demonstrate mathematical relationships among the frequencies produced. "With its single string, movable bridge and graduated rule , the monochord ( kanōn [Greek: law]) straddled the gap between notes and numbers, intervals and ratios , sense-perception and mathematical reason." [ 3 ] However, "music, mathematics, and astronomy were [also] inexorably linked in the monochord." [ 4 ] As a pedagogical tool for demonstrating mathematical relationships between intervals, the monochord remained in use throughout the Middle Ages. [ 5 ]
The monochord can be used to illustrate the mathematical properties of musical pitch and to illustrate Mersenne's laws regarding string length and tension: "essentially a tool for measuring musical intervals". [ 4 ] For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked , it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) Play ⓘ . Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy's Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the tetractys , measured out on a monochord. [ citation needed ] The mathematics involved include the multiplication table , least common multiples , and prime and composite numbers . [ 4 ]
"As the name implies, only one string is needed to do the experiments; but, since ancient times, several strings were used, all tuned in exact unison, each with a moveable bridge, so that various intervals can be compared to each other [consonance and dissonance] ." [ 4 ] A "bichord instrument" is one, "having two strings in unison for each note [a course ]," such as the mandolin . [ 6 ] With two strings one can easily demonstrate how various musical intervals sound. Both open strings are tuned to the same pitch, and then the movable bridge is put in a mathematical position on the second string to demonstrate, for instance, the major third (at 4/5th of the string length) Play ⓘ or the minor third (at 5/6th of the string length) Play ⓘ .
Many contemporary composers focused on microtonality and just intonation such as Harry Partch , Ivor Darreg , Tony Conrad , Glenn Branca , Bart Hopkin , and Yuri Landman constructed multistring variants of sonometers with movable bridges.
Parts of a monochord include a tuning peg , nut , string, moveable bridge, fixed bridge, calibration marks, belly or resonating box , and an end pin . [ 4 ]
Instruments derived from the monochord (or its moveable bridge) include the guqin , dan bau , koto , vina , hurdy-gurdy , and clavichord ("hence all keyboard instruments"). [ 4 ] A monopipe is the wind instrument version of a monochord; a variable open pipe which can produce variable pitches , a sliding cylinder with the numbers of the monochord marked. [ 7 ] End correction must be used with this method, to achieve accuracy.
The monochord is mentioned in Sumerian writings, and, according to some, was reinvented by Pythagoras (sixth century BCE). [ 4 ] Dolge attributes the invention of the moveable bridge to Guido of Arezzo around 1000 CE. [ 8 ]
In 1618, Robert Fludd devised a mundane monochord (also celestial or divine monochord ) that linked the Ptolemaic universe to musical intervals. "Was it [Mersenne's discoveries through use of the monochord (1637)] physical intuition or a Pythagorean confidence in the importance of small whole numbers? ... It was the latter." [ 9 ]
The psalmodicon , a similar instrument but with a chromatic fret board replacing the moveable bridge, was developed in Denmark in the 1820s and became widespread throughout Scandinavia in churches as an alternative to the organ. Scandinavian immigrants also brought it to the United States. It became quite rare by the latter 20th century, but more recently has been revived by folk musicians.
An image of the celestial monochord was used on the 1952 cover of Anthology of American Folk Music by Harry Everett Smith and in the 1977 book The Cosmographical Glass: Renaissance Diagrams of the Universe (p. 133) by S. K. Heninger Jr. , ISBN 978-0-87328-208-6 . A reproduction of the monochordum mundanum ( mundane monochord ) illustration from page 90 of Robert Fludd's "Utriusque Cosmi, Maioris scilicet et Minoris, Metaphysica, Physica, Atque Technica Historia" ("Tomus Primus"), 1617, was used as the cover art for Kepler Quartet's 2011 audio CD, Ben Johnston : String Quartets Nos. 1, 5 & 10 ( New World Records Cat. No. 80693), which is classical music that uses pitch ratios extended to higher partials beyond the standard Pythagorean tuning system.
A modern playing technique used in experimental rock as well as contemporary classical music is 3rd bridge . This technique shares the same mechanism as used on the monochord, by dividing the string into two sections with an additional bridge.
A sonometer is a diagnostic instrument used to measure the tension, frequency or density of vibrations. They are used in medical settings to test both hearing and bone density. A sonometer, or audiometer, is used to determine hearing sensitivity, while a clinical bone sonometer measures bone density to help determine such conditions as the risk of osteoporosis.
In audiology, the device is used to test for hearing loss and other disorders of the ear. The audiometer measures the ability to hear sounds at frequencies normally detectable by the human ear. Several test are usually conducted using the audiometer which will then be used to assess hearing ability. Results typically are recorded on a chart known as an audiogram.
A clinical bone sonometer is a device which tests for the risk of bone fractures associated with osteoporosis. This test, called an ultrasound bone densitometry screening, is not typically used for diagnostic purposes; it is generally used as a risk assessment tool. Testing is often recommended for those whose personal history indicates a possible high risk for osteoporosis. Testing is usually conducted by an orthopedist, rheumatologist or neurologist specializing in the treatment of osteoporosis. The patient simply places his or her heel in the sonometer, and it is then scanned using ultrasound to determine bone density. This is a fast and low-cost procedure generally lasting 30 seconds or less. Results typically are available immediately following the procedure. Two score results are possible: a T-score, which compares a patient's scan against that of a young person of the same gender; and a Z-score, which compares the scan against someone of similar age, weight and gender. The T-scores results are used to assess the risk of osteoporosis. A score above -1 indicates a low risk for osteoporosis; below -1 to -2.5 indicates a risk of developing osteoporosis; and a score below -2.5 indicates more intensive testing should be performed and that osteoporosis is likely present. The Z-score reports how much bone the patient has as compared to others his age. If this number is high or low, further testing may be ordered. | https://en.wikipedia.org/wiki/Monochord |
Monochorionic twins are monozygotic (identical) twins that share the same placenta . If the placenta is shared by more than two twins (see multiple birth ), these are monochorionic multiples . Monochorionic twins occur in 0.3% of all pregnancies. [ 1 ] Seventy-five percent of monozygotic twin pregnancies are monochorionic; the remaining 25% are dichorionic diamniotic . [ 2 ] If the placenta divides, this takes place before the third day after fertilization . [ 2 ]
Monochorionic twins generally have two amniotic sacs (called Monochorionic-Diamniotic "MoDi"), but sometimes, in the case of monoamniotic twins (Monochorionic-Monoamniotic "MoMo"), they also share the same amniotic sac. Monoamniotic twins occur when the split takes place after the ninth day after fertilization. [ 2 ] Monoamniotic twins are always monozygotic (identical twins). [ 3 ] Monochorionic-Diamniotic twins are always monozygotic. [ citation needed ]
By performing an obstetric ultrasound at a gestational age of 10–14 weeks, monochorionic-diamniotic twins are discerned from dichorionic twins. The presence of a "T-sign" at the inter-twin membrane-placental junction is indicative of monochorionic-diamniotic twins (that is, the junction between the inter-twin membrane and the external rim forms a right angle ), whereas dichorionic twins present with a "lambda (λ) sign" (that is, the chorion forms a wedge -shaped protrusion into the inter-twin space, creating a rather curved junction). [ 4 ] The "lambda sign" is also called the "twin peak sign". At ultrasound at a gestational age of 16–20 weeks, the "lambda sign" is indicative of dichorionicity but its absence does not exclude it. [ 5 ]
In contrast, the placentas may be overlapping for dichorionic twins, making it hard to distinguish them, making it difficult to discern mono- or dichorionic twins on solely the appearance of the placentas on ultrasound. [ citation needed ]
In addition to a shared placenta, monochorionic twins also have their circulatory systems intermingled in random and unpredictable circulatory anastomoses . This can cause disproportionate blood supply, resulting in twin-to-twin transfusion syndrome (TTTS) in 20% [ 1 ] of MoDi pregnancies. This is the main complication of monochorionic twins.
The 80% of MoDi pregnancies without TTTS still have high rates of birth weight discordance, fetal growth restriction , prematurity and resultant cesarean section deliveries. [ 1 ] One twin may also fail to develop a proper heart and become dependent on the pumping activity of the other twin's heart, resulting in twin reversed arterial perfusion . [ 2 ] If one twin dies in utero, blood accumulates in that twin's body, causing exsanguination of the remaining twin. [ 2 ]
In the case of monoamniotic twins the risk of complications is substantially higher because of additional potential umbilical cord entanglement and compression . [ 3 ] However, the perinatal mortality of monochorionic twins is fairly low. [ 1 ] | https://en.wikipedia.org/wiki/Monochorionic_twins |
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