Reaction mechanism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Reaction_mechanism

In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs.

A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of an overall chemical reaction. The detailed steps of a reaction are not observable in most cases. The conjectured mechanism is chosen because it is thermodynamically feasible and has experimental support in isolated intermediates (see next section) or other quantitative and qualitative characteristics of the reaction. It also describes each reactive intermediate, activated complex, and transition state, which bonds are broken (and in what order), and which bonds are formed (and in what order). A complete mechanism must also explain the reason for the reactants and catalyst used, the stereochemistry observed in reactants and products, all products formed and the amount of each.

S_N2 reaction mechanism. Note the negatively charged transition state in brackets in which the central carbon atom in question shows five bonds, an unstable condition .

The electron or arrow pushing method is often used in illustrating a reaction mechanism; for example, see the illustration of the mechanism for benzoin condensation in the following examples section.

A reaction mechanism shows how acetone reacts with methanol in acidic environment using curved arrow (electron or arrow pushing method)

Mechanisms also are of interest in inorganic chemistry. A often quoted mechanistic experiment involved the reaction of the labile hexaaquo chromous reductant with the exchange inert pentammine cobalt(III) chloride.

Henry Taube's experiment establishing the role of a bridging ligand in inner sphere electron transfer.

Reaction intermediates

Reaction intermediates are chemical species, often unstable and short-lived. They can, however, sometimes be isolated. They are neither reactants nor products of the overall chemical reaction, but temporary products and/or reactants in the mechanism's reaction steps. Reaction intermediates are often confused with the transition state. The transition states are, in contrast, fleeting, high-energy species that cannot be isolated. The kinetics (relative rates of the reaction steps and the rate equation for the overall reaction) are discussed in terms of the energy required for the conversion of the reactants to the proposed transition states (molecular states that correspond to maxima on the reaction coordinates, and to saddle points on the potential energy surface for the reaction).

Chemical kinetics

Information about the mechanism of a reaction is often provided by analyzing chemical kinetics to determine the reaction order in each reactant.

Illustrative is the oxidation of carbon monoxide by nitrogen dioxide:

CO + NO₂ → CO₂ + NO

The rate law for this reaction is: ${\displaystyle r=k[N{O}_2{]}^2}$ This form shows that the rate-determining step does not involve CO. Instead, the slow step involves two molecules of NO₂. A possible mechanism for the overall reaction that explains the rate law is:

2 NO₂ → NO₃ + NO (slow)

NO₃ + CO → NO₂ + CO₂ (fast)

Each step is called an elementary step, and each has its own rate law and molecularity. The sum of the elementary steps gives the net reaction.

When determining the overall rate law for a reaction, the slowest step is the step that determines the reaction rate. Because the first step (in the above reaction) is the slowest step, it is the rate-determining step. Because it involves the collision of two NO₂ molecules, it is a bimolecular reaction with a rate ${\displaystyle r}$ which obeys the rate law ${\displaystyle r=k[N{O}_2(t){]}^2}$.

Other reactions may have mechanisms of several consecutive steps. In organic chemistry, the reaction mechanism for the benzoin condensation, put forward in 1903 by A. J. Lapworth, was one of the first proposed reaction mechanisms.

Benzoin condensation reaction mechanism. Cyanide ion (CN⁻) acts as a catalyst here, entering at the first step and leaving in the last step. Proton (H⁺) transfers occur at (i) and (ii). The arrow pushing method is used in some of the steps to show where electron pairs go.

A chain reaction is an example of a complex mechanism, in which the propagation steps form a closed cycle. In a chain reaction, the intermediate produced in one step generates an intermediate in another step. Intermediates are called chain carriers. Sometimes, the chain carriers are radicals, they can be ions as well. In nuclear fission they are neutrons.

Chain reactions have several steps, which may include:

1. Chain initiation: this can be by thermolysis (heating the molecules) or photolysis (absorption of light) leading to the breakage of a bond.
2. Propagation: a chain carrier makes another carrier.
3. Branching: one carrier makes more than one carrier.
4. Retardation: a chain carrier may react with a product reducing the rate of formation of the product. It makes another chain carrier, but the product concentration is reduced.
5. Chain termination: radicals combine and the chain carriers are lost.
6. Inhibition: chain carriers are removed by processes other than termination, such as by forming radicals.

Even though all these steps can appear in one chain reaction, the minimum necessary ones are Initiation, propagation, and termination.

An example of a simple chain reaction is the thermal decomposition of acetaldehyde (CH₃CHO) to methane (CH₄) and carbon monoxide (CO). The experimental reaction order is 3/2, which can be explained by a Rice-Herzfeld mechanism.

This reaction mechanism for acetaldehyde has 4 steps with rate equations for each step :

1. Initiation : CH₃CHO → •CH₃ + •CHO (Rate=k₁ [CH₃CHO])
2. Propagation: CH₃CHO + •CH₃ → CH₄ + CH₃CO• (Rate=k₂ [CH₃CHO][•CH₃])
3. Propagation: CH₃CO• → •CH₃ + CO (Rate=k₃ [CH₃CO•])
4. Termination: •CH₃ + •CH₃ → CH₃CH₃ (Rate=k₄ [•CH₃]²)

For the overall reaction, the rates of change of the concentration of the intermediates •CH₃ and CH₃CO• are zero, according to the steady-state approximation, which is used to account for the rate laws of chain reactions.

d[•CH₃]/dt = k₁[CH₃CHO] – k₂[•CH₃][CH₃CHO] + k₃[CH₃CO•] - 2k₄[•CH₃]² = 0

and d[CH₃CO•]/dt = k₂[•CH₃][CH₃CHO] – k₃[CH₃CO•] = 0

The sum of these two equations is k₁[CH₃CHO] – 2 k₄[•CH₃]² = 0. This may be solved to find the steady-state concentration of •CH₃ radicals as [•CH₃] = (k₁ / 2k₄)^1/2 [CH₃CHO]^1/2.

It follows that the rate of formation of CH₄ is d[CH₄]/dt = k₂[•CH₃][CH₃CHO] = k₂ (k₁ / 2k₄)^1/2 [CH₃CHO]^3/2

Thus the mechanism explains the observed rate expression, for the principal products CH₄ and CO. The exact rate law may be even more complicated, there are also minor products such as acetone (CH₃COCH₃) and propanal (CH₃CH₂CHO).

Other experimental methods to determine mechanism

Many experiments that suggest the possible sequence of steps in a reaction mechanism have been designed, including:

• measurement of the effect of temperature (Arrhenius equation) to determine the activation energy
• spectroscopic observation of reaction intermediates
• determination of the stereochemistry of products, for example in nucleophilic substitution reactions
• measurement of the effect of isotopic substitution on the reaction rate
• for reactions in solution, measurement of the effect of pressure on the reaction rate to determine the volume change on formation of the activated complex
• for reactions of ions in solution, measurement of the effect of ionic strength on the reaction rate
• direct observation of the activated complex by pump-probe spectroscopy
• infrared chemiluminescence to detect vibrational excitation in the products
• electrospray ionization mass spectrometry.
• crossover experiments.

Theoretical modeling

A correct reaction mechanism is an important part of accurate predictive modeling. For many combustion and plasma systems, detailed mechanisms are not available or require development.

Even when information is available, identifying and assembling the relevant data from a variety of sources, reconciling discrepant values and extrapolating to different conditions can be a difficult process without expert help. Rate constants or thermochemical data are often not available in the literature, so computational chemistry techniques or group additivity methods must be used to obtain the required parameters.

Computational chemistry methods can also be used to calculate potential energy surfaces for reactions and determine probable mechanisms.

Molecularity

Main article: molecularity

Molecularity in chemistry is the number of colliding molecular entities that are involved in a single reaction step.

• A reaction step involving one molecular entity is called unimolecular.
• A reaction step involving two molecular entities is called bimolecular.
• A reaction step involving three molecular entities is called trimolecular or termolecular.

In general, reaction steps involving more than three molecular entities do not occur, because is statistically improbable in terms of Maxwell distribution to find such a transition state.

Black holes in fiction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Black_holes_in_fiction 

Simulated view of a black hole in front of the Large Magellanic Cloud, with gravitational lensing visible

Black holes, objects whose gravity is so strong that nothing—including light—can escape them, have been depicted in fiction since at least the pulp era of science fiction, before the term black hole was coined. A common portrayal at the time was of black holes as hazards to spacefarers, a motif that has also recurred in later works.

The concept of black holes became popular in science and fiction alike in the 1960s. Authors quickly seized upon the relativistic effect of gravitational time dilation, whereby time passes more slowly closer to a black hole due to its immense gravitational field. Black holes also became a popular means of space travel in science fiction, especially when the notion of wormholes emerged as a relatively plausible way to achieve faster-than-light travel. In this concept, a black hole is connected to its theoretical opposite, a so-called white hole, and as such acts as a gateway to another point in space which might be very distant from the point of entry. More exotically, the point of emergence is occasionally portrayed as another point in time—thus enabling time travel—or even an entirely different universe.

More fanciful depictions of black holes that do not correspond to their known or predicted properties also appear. As nothing inside the event horizon—the distance away from the black hole where the escape velocity exceeds the speed of light—can be observed from the outside, authors have been free to employ artistic license when depicting the interiors of black holes. A small number of works also portray black holes as being sentient.

Besides stellar-mass black holes, supermassive and especially micro black holes also make occasional appearances. Supermassive black holes are a common feature of modern space opera. Recurring themes in stories depicting micro black holes include spaceship propulsion, threatening or causing the destruction of the Earth, and serving as a source of gravity in outer-space settlements.

Early depictions

[V]irtually the whole of gravitational physics can be understood using Newtonian theory. As far as real-world astrophysics goes, the most important exception to this is the existence of black holes. It's probably no coincidence that black holes also happen to be by far the most popular astrophysical phenomena found in science fiction.

Andrew May, How Space Physics Really Works: Lessons from Well-Constructed Science Fiction

The general concept of black holes, objects whose gravity is so strong that nothing—including light—can escape them, was first proposed by John Michell in 1783 and developed further in the framework of Albert Einstein's theory of general relativity by Karl Schwarzschild in 1916. Serious scientific attention remained relatively limited until the 1960s, the same decade the term black hole was coined, though objects with the overall characteristics of black holes had made appearances in fiction decades earlier during the pulp era of science fiction. Examples of this include E. E. Smith's 1928 novel The Skylark of Space with its "black sun", Frank K. Kelly [Wikidata]'s 1935 short story "Starship Invincible" with its "Hole in Space", and Nat Schachner's 1938 short story "Negative Space"—all of which portray the black holes avant la lettre as hazards to spacefarers. Later works that still predate the adoption of the current terminology include Fred Saberhagen's 1965 short story "Masque of the Red Shift" with its "hypermass" and the 1967 Star Trek episode "Tomorrow Is Yesterday" with its "black star".

Time dilation

Once black holes gained mainstream popularity, many of the early works featuring black holes focused on the concept of gravitational time dilation, whereby time passes more slowly closer to a black hole due to the effects of general relativity. One consequence of this is that the process of crossing the event horizon—the distance away from the black hole where the escape velocity exceeds the speed of light—appears to an outside observer to take an infinite amount of time. In Poul Anderson's 1968 short story "Kyrie", a telepathic scream from a being falling into a black hole thus becomes drawn out for eternity. Similarly, a spaceship appears forever immovable at the event horizon in Brian Aldiss's 1976 short story "The Dark Soul of the Night". In Frederik Pohl's 1977 novel Gateway, an astronaut is wracked with survivor's guilt over the deaths of his companions during an encounter with a black hole, compounded by the process appearing to still be ongoing. Later sequels in Pohl's Heechee Saga, from the 1980 novel Beyond the Blue Event Horizon onward, portray time dilation being exploited by aliens who reside near a black hole to experience the passage of time more slowly than the rest of the universe; other aliens do likewise in David Brin's 1984 short story "The Crystal Spheres" while waiting for the universe to be more filled with life. In Alastair Reynolds's 2000 novel Revelation Space, aliens use the relativistic effect to hide. In Bill Johnson's 1982 short story "Meet Me at Apogee", travel to various levels of time dilation is commercialized and used by people with incurable diseases, among others. In the 2014 film Interstellar, a planet orbits a black hole so closely that it experiences extreme time dilation, with time passing approximately 60,000 times slower than on Earth.

Space travel

See also: Space travel in science fiction and Wormholes in fiction

Black holes have also been portrayed as ways to travel through space. In particular, they often serve as a means to achieve faster-than-light travel. The proposed mechanism involves travelling through the singularity at the center of a black hole and emerging at some other, perhaps very distant, place in the universe. More exotically, the point of emergence is occasionally portrayed as another point in time—thus enabling time travel—or even an entirely different universe. To explain why the immense gravitational field of the black hole does not crush the travellers and their vessels, the special theorized properties of rotating black holes are sometimes invoked by authors; astrophysicists Steven D. Bloom and Andrew May argue that the strong tidal forces would nevertheless invariably be fatal, May pointing specifically to spaghettification. According to The Encyclopedia of Science Fiction, early stories employing black holes for this purpose tended to use alternative terminology to obfuscate the underlying issues. Thus, Joe Haldeman's 1974 fix-up novel The Forever War, where a network of black holes is used for interstellar warfare, calls them "collapsars", while George R. R. Martin's 1972 short story "The Second Kind of Loneliness" has a "nullspace vortex".

Speculation that black holes might be connected to their hypothetical opposites, white holes, followed in the 1970s—the resulting arrangement being known as a wormhole. Wormholes were appealing to writers due to their relative theoretical plausibility as a means of faster-than-light travel, and they were further popularized by speculative works of non-fiction such as Adrian Berry's 1977 book The Iron Sun: Crossing the Universe Through Black Holes. Black holes and associated wormholes thus quickly became commonplace in fiction; according to science fiction scholar Brian Stableford, writing in the 2006 work Science Fact and Science Fiction: An Encyclopedia, "wormholes became the most fashionable mode of interstellar travel in the last decades of the twentieth century". Ian Wallace's 1979 novel Heller's Leap is a murder mystery involving a journey through a black hole. Joan D. Vinge's 1980 novel The Snow Queen is set on a circumbinary planet where a black hole between the binary stars serves as the gateway between the system and the outside world, while Paul Preuss's 1980 novel The Gates of Heaven and its 1981 follow-up Re-Entry feature black holes that are used for travel through both space and time. In the 1989 anime film Garaga, human colonization of the cosmos is enabled by interstellar gateways associated with black holes. The entire Earth is transported through a wormhole in Roger MacBride Allen's 1990 novel The Ring of Charon. Travel between universes is depicted in Pohl and Jack Williamson's 1991 novel The Singers of Time, the concept having earlier made a more fanciful appearance in the 1975 film The Giant Spider Invasion, where the spiders of the title arrive at Earth through a black hole. In the 2009 film Star Trek, a black hole created to neutralize a supernova threat has the side-effect of transporting two nearby spaceships into the past, where they end up altering the course of history. In Bolivian science fiction writer Giovanna Rivero's 2012 novel Helena 2022: La vera crónica de un naufragio en el tiempo, a spaceship ends up in 1630s Italy as a result of an accidental encounter with a black hole.

Small and large

Black holes need not necessarily be stellar-mass; the decisive factor is whether sufficient mass is contained within a small enough space—the Schwarzschild radius. The principal mechanism of black hole formation is the gravitational collapse of a massive star, but other origins have been hypothesized, including so-called primordial black holes forming shortly after the Big Bang. Primordial black holes could theoretically be of virtually any conceivable size, though the smallest ones would by now have evaporated into nothing due to the quantum mechanical effect known as Hawking radiation.

The concept of micro black holes was first theorized scientifically in the 1970s, and quickly became popular in science fiction. In Larry Niven's 1974 short story "The Hole Man", a microscopic black hole is used as a murder weapon by exploiting the tidal effects at short range, and in Niven's 1975 short story "The Borderland of Sol", one is used by space pirates to capture spaceships. Small black holes are used to power spaceship propulsion in Arthur C. Clarke's 1975 novel Imperial Earth, Charles Sheffield's 1978 short story "Killing Vector", and the 1997 film Event Horizon. Artificial black holes that are created unintentionally at nuclear facilities appear in Michael McCollum's 1979 short story "Scoop" and Martin Caidin's 1980 novel Star Bright In David Langford's 1982 novel The Space Eater, a small black hole is used as a weapon against a rebellious planet. Earth is endangered by miniature black holes in Gregory Benford's 1985 novel Artifact, Thomas Thurston Thomas's 1986 novel The Doomsday Effect, and Brin's 1990 novel Earth, and the planet's destruction in this way forms part of the backstory in Dan Simmons's 1989 novel Hyperion, while the Moon's destruction by a small black hole is depicted in Paul J. McAuley's 1990 short story "How We Lost the Moon" and is suspected to have occurred in Neal Stephenson's 2015 novel Seveneves. Small black holes are used as a way to provide an artificial gravity of sorts by placing them inside inhabited structures or settled asteroids in Sheffield's 1989 novel Proteus Unbound, Reynolds's 2008 novel House of Suns, and Iain M. Banks's 2010 novel Surface Detail. The titular material in Wil McCarthy's 2000 novel The Collapsium is made up of a lattice of micro black holes and makes teleportation possible.

At the opposite end of the spectrum, black holes can have masses comparable to that of an entire galaxy. Supermassive black holes, with masses that can be in excess of billions of times the mass of the Sun, are thought to exist in the center of most galaxies. Sufficiently large and massive black holes would have a low average density and could theoretically contain intact stars and planets within their event horizons. An enormous low-density black hole of this kind appears in Barry N. Malzberg's 1975 novel Galaxies. In Benford's Galactic Center Saga, starting with the 1977 novel In the Ocean of Night, the vicinity of the supermassive black hole at the Galactic Center of the Milky Way makes an attractive destination for spacefaring civilizations due to the high concentration of stars that can serve as sources of energy in the region; a similar use is found for a regular-sized black hole in Benford's 1986 short story "As Big as the Ritz", where its accretion disk provides ample solar energy for a space habitat. McAuley's 1991 novel Eternal Light involves a journey to the central supermassive black hole to investigate a hypervelocity star on a trajectory towards the Solar System. According to The Encyclopedia of Science Fiction, "the immense black hole at the galactic core has become almost a cliché of contemporary space opera" such as Greg Egan's 2008 novel Incandescence.

Hazards to spacefarers

The pulp-era motif of black holes posing danger to spacefarers resurfaced decades later, following the popularization of black holes in fiction. In the 1975 Space: 1999 episode "Black Sun", one threatens to destroy the Moon as it travels through space; the episode was one of those included in Edwin Charles Tubb's 1975 novelization Breakaway. In Isaac Asimov's 1976 short story "Old-fashioned", astronauts surmise that an unseen object keeping them in orbit must be a modestly-sized black hole, having wreaked havoc with their spaceship through tidal forces. In Edward Bryant's 1976 novel Cinnabar, a computer self-destructs by intentionally entering a black hole. In Mildred Downey Broxon's 1978 short story "Singularity", scientists study a civilization on a planet that will shortly be destroyed by an approaching black hole. John Varley's 1978 short story "The Black Hole Passes" depicts an outpost in the Oort cloud being imperiled by a small black hole. In Stephen Baxter's 1993 short story "Pilot", a spaceship extracts energy from a rotating black hole's ergosphere to widen its event horizon and cause a pursuer to fall into it. Black holes also appear as obstacles in the 2007 video game Super Mario Galaxy.

Interior

Because what lies beyond the event horizon is unknown and by definition unobservable from outside, authors have been free to employ artistic license when depicting the interiors of black holes. The 1979 film The Black Hole, noted for its inaccurate portrayal of the known properties of black holes, depicts the inside as an otherworldly place bearing the hallmarks of Christian conceptions of the afterlife. In Benford's 1990 novel Beyond the Fall of Night, a sequel to Clarke's 1948 novel Against the Fall of Night, the inside of a black hole is used as a prison, a role it also serves in Alan Moore and Dave Gibbons's 1985 Superman comic book story "For the Man Who Has Everything". Alien lifeforms inhabit the interior of a black hole in McCarthy's 1995 novel Flies from the Amber. Expeditions into black holes to explore the interior are depicted in Geoffrey A. Landis's 1998 short story "Approaching Perimelasma" and Egan's 1998 short story "The Planck Dive".

Sentient

See also: Stars in fiction § Sentient, Sun in fiction § Sentient, and Extrasolar planets in fiction § Living

In much the same way as stars—and, to a lesser extent, planets—have been anthropomorphized as living and thinking beings, so have black holes. An intelligent, talking black hole appears in Varley's 1977 short story "Lollipop and the Tar Baby". In Sheffield's Proteus Unbound, microscopic black holes are determined to contain intelligence through signals emanating from them. In Benford's 2000 novel Eater, a black hole that is sentient as a result of electromagnetic interactions in its accretion disk seeks to devour the Solar System.

Chain-growth polymerization

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Chain-growth_polymerization 

 

Chain-growth polymerization (AE) or chain-growth polymerisation (BE) is a polymerization technique where monomer molecules add onto the active site on a growing polymer chain one at a time. There are a limited number of these active sites at any moment during the polymerization which gives this method its key characteristics.

Chain-growth polymerization involves 3 types of reactions :

1. Initiation: An active species I* is formed by some decomposition of an initiator molecule I
2. Propagation: The initiator fragment reacts with a monomer M to begin the conversion to the polymer; the center of activity is retained in the adduct. Monomers continue to add in the same way until polymers P_i* are formed with the degree of polymerization i
3. Termination: By some reaction generally involving two polymers containing active centers, the growth center is deactivated, resulting in dead polymer

Introduction

IUPAC definition

chain polymerization: A chain reaction in which the growth of a polymer chain proceeds exclusively by reaction(s) between monomer and reactive site(s) on the polymer chain with regeneration of the reactive site(s) at the end of each growth step. (See Gold Book entry for note.)

An example of chain-growth polymerization by ring opening to polycaprolactone

In 1953, Paul Flory first classified polymerization as "step-growth polymerization" and "chain-growth polymerization". IUPAC recommends to further simplify "chain-growth polymerization" to "chain polymerization". It is a kind of polymerization where an active center (free radical or ion) is formed, and a plurality of monomers can be polymerized together in a short period of time to form a macromolecule having a large molecular weight. In addition to the regenerated active sites of each monomer unit, polymer growth will only occur at one (or possibly more) endpoint.

Many common polymers can be obtained by chain polymerization such as polyethylene (PE), polypropylene (PP), polyvinyl chloride (PVC), poly(methyl methacrylate) (PMMA), polyacrylonitrile (PAN), polyvinyl acetate (PVA).

Typically, chain-growth polymerization can be understood with the chemical equation:

${\displaystyle P_x^{\ast }+M\to P_{x+1}^{\ast }+L(x=1,2,\mathrm{3...})}$

In this equation, P is the polymer while x represents degree of polymerization, * means active center of chain-growth polymerization, M is the monomer which will react with active center, and L may be a low-molar-mass by-product obtained during chain propagation. For most chain-growth polymerizations, there is no by-product L formed. However there are some exceptions, such as the polymerization of amino acid N-carboxyanhydrides to oxazolidine-2,5-diones.

This type of polymerization is described as "chain" or "chain-growth" because the reaction mechanism is a chemical chain reaction with an initiation step in which an active center is formed, followed by a rapid sequence of chain propagation steps in which the polymer molecule grows by addition of one monomer molecule to the active center in each step. The word "chain" here does not refer to the fact that polymer molecules form long chains. Some polymers are formed instead by a second type of mechanism known as step-growth polymerization without rapid chain propagation steps.

Reaction steps

All chain-growth polymerization reactions must include chain initiation and chain propagation. Chain transfer and chain termination steps also occur in many but not all chain-growth polymerizations.

Chain initiation

Chain initiation is the initial generation of a chain carrier, which is an intermediate such as a radical or an ion which can continue the reaction by chain propagation. Initiation steps are classified according to the way that energy is provided: thermal initiation, high energy initiation, and chemical initiation, etc. Thermal initiation uses molecular thermal motion to dissociate a molecule and form active centers. High energy initiation refers to the generation of chain carriers by radiation. Chemical initiation is due to a chemical initiator.

For the case of radical polymerization as an example, chain initiation involves the dissociation of a radical initiator molecule (I) which is easily dissociated by heat or light into two free radicals (2 R°). Each radical R° then adds a first monomer molecule (M) to start a chain which terminates with a monomer activated by the presence of an unpaired electron (RM₁°).

• I → 2 R°
• R° + M → RM₁°

Chain propagation

IUPAC defines chain propagation as a reaction of an active center on the growing polymer molecule, which adds one monomer molecule to form a new polymer molecule (RM₁°) one repeat unit longer.

For radical polymerization, the active center remains an atom with an unpaired electron. The addition of the second monomer and a typical later addition step are

• RM₁° + M → RM₂°
• ...............
• RM_n° + M → RM_n+1°

For some polymers, chains of over 1000 monomer units can be formed in milliseconds.

Chain termination

In a chain termination step, the active center disappears, resulting in the termination of chain propagation. This is different from chain transfer in which the active center only shifts to another molecule but does not disappear.

For radical polymerization, termination involves a reaction of two growing polymer chains to eliminate the unpaired electrons of both chains. There are two possibilities.

1. Recombination is the reaction of the unpaired electrons of two chains to form a covalent bond between them. The product is a single polymer molecule with the combined length of the two reactant chains:

• RM_n° + RM_m° → P_n+m

2. Disproportionation is the transfer of a hydrogen atom from one chain to the other, so that the two product chain molecules are unchanged in length but are no longer free radicals:

• RM_n° + RM_m° → P_n + P_m

Initiation, propagation and termination steps also occur in chain reactions of smaller molecules. This is not true of the chain transfer and branching steps considered next.

Chain transfer

An example of chain transfer in styrene polymerization. Here X = Cl and Y = CCl₃.

In some chain-growth polymerizations there is also a chain transfer step, in which the growing polymer chain RM_n° takes an atom X from an inactive molecule XY, terminating the growth of the polymer chain: RM_n° + XY → RM_nX + Y°. The Y fragment ls a new active center which adds more monomer M to form a new growing chain YM_n°. This can happen in free radical polymerization for chains RM_n°, in ionic polymerization for chains RM_n⁺ or RM_n^–, or in coordination polymerization. In most cases chain transfer will generate a by-product and decrease the molar mass of the final polymer.

Chain transfer to polymer: Branching

Another possibility is chain transfer to a second polymer molecule, result in the formation of a product macromolecule with a branched structure. In this case the growing chain takes an atom X from a second polymer chain whose growth had been completed. The growth of the first polymer chain is completed by the transfer of atom X. However the second molecule loses an atom X from the interior of its polymer chain to form a reactive radical (or ion) which can add more monomer molecules. This results in the addition of a branch or side chain and the formation of a product macromolecule with a branched structure.

Classes of chain-growth polymerization

The International Union of Pure and Applied Chemistry (IUPAC) recommends definitions for several classes of chain-growth polymerization.

Radical polymerization

Based on the IUPAC definition, radical polymerization is a chain polymerization in which the kinetic-chain carriers are radicals. Usually, the growing chain end bears an unpaired electron. Free radicals can be initiated by many methods such as heating, redox reactions, ultraviolet radiation, high energy irradiation, electrolysis, sonication, and plasma. Free radical polymerization is very important in polymer chemistry. It is one of the most developed methods in chain-growth polymerization. Currently, most polymers in our daily life are synthesized by free radical polymerization, including polyethylene, polystyrene, polyvinyl chloride, polymethyl methacrylate, polyacrylonitrile, polyvinyl acetate, styrene butadiene rubber, nitrile rubber, neoprene, etc.

Ionic polymerization

Ionic polymerization is a chain polymerization in which the kinetic-chain carriers are ions or ion pairs. It can be further divided into anionic polymerization and cationic polymerization. Ionic polymerization generates many polymers used in daily life, such as butyl rubber, polyisobutylene, polyphenylene, polyoxymethylene, polysiloxane, polyethylene oxide, high density polyethylene, isotactic polypropylene, butadiene rubber, etc. Living anionic polymerization was developed in the 1950s. The chain will remain active indefinitely unless the reaction is transferred or terminated deliberately, which allows the control of molar weight and dispersity (or polydispersity index, PDI).

Coordination polymerization

Coordination polymerization is a chain polymerization that involves the preliminary coordination of a monomer molecule with a chain carrier. The monomer is first coordinated with the transition metal active center, and then the activated monomer is inserted into the transition metal-carbon bond for chain growth. In some cases, coordination polymerization is also called insertion polymerization or complexing polymerization. Advanced coordination polymerizations can control the tacticity, molecular weight and PDI of the polymer effectively. In addition, the racemic mixture of the chiral metallocene can be separated into its enantiomers. The oligomerization reaction produces an optically active branched olefin using an optically active catalyst.

Living polymerization

Living polymerization was first described by Michael Szwarc in 1956. It is defined as a chain polymerization from which chain transfer and chain termination are absent. In the absence of chain-transfer and chain termination, the monomer in the system is consumed and the polymerization stops but the polymer chain remains active. If new monomer is added, the polymerization can proceed.

Due to the low PDI and predictable molecular weight, living polymerization is at the forefront of polymer research. It can be further divided into living free radical polymerization, living ionic polymerization and living ring-opening metathesis polymerization, etc.

Ring-opening polymerization

Ring-opening polymerization is defined as a polymerization in which a cyclic monomer yields a monomeric unit which is acyclic or contains fewer cycles than the monomer. Generally, the ring-opening polymerization is carried out under mild conditions, and the by-product is less than in the polycondensation reaction. A high molecular weight polymer is easily obtained. Common ring-opening polymerization products includes polypropylene oxide, polytetrahydrofuran, polyepichlorohydrin, polyoxymethylene, polycaprolactam and polysiloxane.

Reversible-deactivation polymerization

Reversible-deactivation polymerization is defined as a chain polymerization propagated by chain carriers that are deactivated reversibly, bringing them into one or more active-dormant equilibria. An example of a reversible-deactivation polymerization is group-transfer polymerization.

Comparison with step-growth polymerization

Polymers were first classified according to polymerization method by Wallace Carothers in 1929, who introduced the terms addition polymer and condensation polymer to describe polymers made by addition reactions and condensation reactions respectively. However this classification is inadequate to describe a polymer which can be made by either type of reaction, for example nylon 6 which can be made either by addition of a cyclic monomer or by condensation of a linear monomer.

Flory revised the classification to chain-growth polymerization and step-growth polymerization, based on polymerization mechanisms rather than polymer structures. IUPAC now recommends that the names of step-growth polymerization and chain-growth polymerization be further simplified to polycondensation (or polyaddition if no low-molar-mass by-product is formed when a monomer is added) and chain polymerization.

Most polymerizations are either chain-growth or step-growth reactions. Chain-growth includes both initiation and propagation steps (at least), and the propagation of chain-growth polymers proceeds by the addition of monomers to a growing polymer with an active centre. In contrast step-growth polymerization involves only one type of step, and macromolecules can grow by reaction steps between any two molecular species: two monomers, a monomer and a growing chain, or two growing chains. In step growth, the monomers will initially form dimers, trimers, etc. which later react to form long chain polymers.

In chain-growth polymerization, a growing macromolecule increases in size rapidly once its growth is initiated. When a macromolecule stops growing it generally will add no more monomers. In step-growth polymerization on the other hand, a single polymer molecule can grow over the course of the whole reaction.

In chain-growth polymerization, long macromolecules with high molecular weight are formed when only a small fraction of monomer has reacted. Monomers are consumed steadily over the course of the whole reaction, but the degree of polymerization can increase very quickly after chain initiation. However in step-growth polymerization the monomer is consumed very quickly to dimer, trimer and oligomer. The degree of polymerization increases steadily during the whole polymerization process.

The type of polymerization of a given monomer usually depends on the functional groups present, and sometimes also on whether the monomer is linear or cyclic. Chain-growth polymers are usually addition polymers by Carothers' definition. They are typically formed by addition reactions of C=C bonds in the monomer backbone, which contains only carbon-carbon bonds. Another possibility is ring-opening polymerization, as for the chain-growth polymerization of tetrahydrofuran or of polycaprolactone (see Introduction above).

Step-growth polymers are typically condensation polymers in which an elimination product as such as H₂O are formed. Examples are polyamides, polycarbonates, polyesters, polyimides, polysiloxanes and polysulfones. If no elimination product is formed, then the polymer is an addition polymer, such as a polyurethane or a poly(phenylene oxide).^[18] Chain-growth polymerization with a low-molar-mass by-product during chain growth is described by IUPAC as "condensative chain polymerization".

Compared to step-growth polymerization, living chain-growth polymerization shows low molar mass dispersity (or PDI), predictable molar mass distribution and controllable conformation. Generally, polycondensation proceeds in a step-growth polymerization mode.

Application

Chain polymerization products are widely used in many aspects of life, including electronic devices, food packaging, catalyst carriers, medical materials, etc. At present, the world's highest yielding polymers such as polyethylene (PE), polyvinyl chloride (PVC), polypropylene (PP), etc. can be obtained by chain polymerization. In addition, some carbon nanotube polymer is used for electronical devices. Controlled living chain-growth conjugated polymerization will also enable the synthesis of well-defined advanced structures, including block copolymers. Their industrial applications extend to water purification, biomedical devices and sensors.

Synchrotron radiation

From Wikipedia, the free encyclopedia

Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (a ⊥ v). It is produced artificially in some types of particle accelerators or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization, and the frequencies generated can range over a large portion of the electromagnetic spectrum.

Pictorial representation of the radiation emission process by a source moving around a Schwarzschild black hole in a de Sitter universe.

Electromagnetic field observed far from the source (in arbitrary unit) of a positive accelerated point charge. When the velocity increase, the radiation concentrates along the trajectory. This field can be calculated using Liénard–Wiechert potential.

Synchrotron radiation is similar to bremsstrahlung radiation, which is emitted by a charged particle when the acceleration is parallel to the direction of motion. The general term for radiation emitted by particles in a magnetic field is gyromagnetic radiation, for which synchrotron radiation is the ultra-relativistic special case. Radiation emitted by charged particles moving non-relativistically in a magnetic field is called cyclotron emission. For particles in the mildly relativistic range (≈85% of the speed of light), the emission is termed gyro-synchrotron radiation.

In astrophysics, synchrotron emission occurs, for instance, due to ultra-relativistic motion of a charged particle around a black hole. When the source follows a circular geodesic around the black hole, the synchrotron radiation occurs for orbits close to the photosphere where the motion is in the ultra-relativistic regime.

Synchrotron radiation from a bending magnet

Synchrotron radiation from an undulator

Synchrotron radiation from an astronomical source

History

Synchrotron radiation was first observed by technician Floyd Haber, on April 24, 1947, at the 70 MeV electron synchrotron of the General Electric research laboratory in Schenectady, New York. While this was not the first synchrotron built, it was the first with a transparent vacuum tube, allowing the radiation to be directly observed.

As recounted by Herbert Pollock:

On April 24, Langmuir and I were running the machine and as usual were trying to push the electron gun and its associated pulse transformer to the limit. Some intermittent sparking had occurred and we asked the technician to observe with a mirror around the protective concrete wall. He immediately signaled to turn off the synchrotron as "he saw an arc in the tube". The vacuum was still excellent, so Langmuir and I came to the end of the wall and observed. At first we thought it might be due to Cherenkov radiation, but it soon became clearer that we were seeing Ivanenko and Pomeranchuk radiation.

Description

A direct consequence of Maxwell's equations is that accelerated charged particles always emit electromagnetic radiation. Synchrotron radiation is the special case of charged particles moving at relativistic speed undergoing acceleration perpendicular to their direction of motion, typically in a magnetic field. In such a field, the force due to the field is always perpendicular to both the direction of motion and to the direction of field, as shown by the Lorentz force law.

The power carried by the radiation is found (in SI units) by the relativistic Larmor formula:

$${\displaystyle P_{\gamma }=\frac{q^2}{6\pi {\epsilon }_0{c}^3}{a}^2{\gamma }^4=\frac{q^{2}c}{6\pi {\epsilon }_0}\frac{{\beta }^4{\gamma }^4}{{\rho }^2},}$$ where

• ${\displaystyle {\epsilon }_0}$ is the vacuum permittivity,
• ${\displaystyle q}$ is the particle charge,
• ${\displaystyle a}$ is the magnitude of the acceleration,
• ${\displaystyle c}$ is the speed of light,
• ${\displaystyle \gamma }$ is the Lorentz factor,
• ${\displaystyle \beta =v/c}$,
• ${\displaystyle \rho }$ is the radius of curvature of the particle trajectory.

The force on the emitting electron is given by the Abraham–Lorentz–Dirac force.

When the radiation is emitted by a particle moving in a plane, the radiation is linearly polarized when observed in that plane, and circularly polarized when observed at a small angle. However, in quantum mechanics, this radiation is emitted in discrete packets of photons, which introduces quantum fluctuations in the emitted radiation and the particle's trajectory. For a given acceleration, the average energy of emitted photons is proportional to ${\displaystyle {\gamma }^3}$ and the emission rate to ${\displaystyle \gamma }$.

From accelerators

Main article: Synchrotron light source

Circular accelerators will always produce gyromagnetic radiation as the particles are deflected in the magnetic field. However, the quantity and properties of the radiation are highly dependent on the nature of the acceleration taking place. For example, due to the difference in mass, the factor of ${\displaystyle {\gamma }^4}$ in the formula for the emitted power means that electrons radiate energy at approximately 10¹³ times the rate of protons.

Energy loss from synchrotron radiation in circular accelerators was originally considered a nuisance, as additional energy must be supplied to the beam in order to offset the losses. However, beginning in the 1980s, circular electron accelerators known as light sources have been constructed to deliberately produce intense beams of synchrotron radiation for research.

In astronomy

Messier 87's astrophysical jet, HST image. The blue light from the jet emerging from the bright AGN core, towards the lower right, is due to synchrotron radiation.

Synchrotron radiation is also generated by astronomical objects, typically where relativistic electrons spiral (and hence change velocity) through magnetic fields. Two of its characteristics include power-law energy spectra and polarization. It is considered to be one of the most powerful tools in the study of extra-solar magnetic fields wherever relativistic charged particles are present. Most known cosmic radio sources emit synchrotron radiation. It is often used to estimate the strength of large cosmic magnetic fields as well as analyze the contents of the interstellar and intergalactic media.

History of detection

This type of radiation was first detected in the Crab Nebula in 1956 by Jan Hendrik Oort and Theodore Walraven, and a few months later in a jet emitted by Messier 87 by Geoffrey R. Burbidge. It was confirmation of a prediction by Iosif S. Shklovsky in 1953. However, it had been predicted earlier (1950) by Hannes Alfvén and Nicolai Herlofson. Solar flares accelerate particles that emit in this way, as suggested by R. Giovanelli in 1948 and described by J.H. Piddington in 1952.

T. K. Breus noted that questions of priority on the history of astrophysical synchrotron radiation are complicated, writing:

In particular, the Russian physicist V.L. Ginzburg broke his relationships with I.S. Shklovsky and did not speak with him for 18 years. In the West, Thomas Gold and Sir Fred Hoyle were in dispute with H. Alfven and N. Herlofson, while K.O. Kiepenheuer and G. Hutchinson were ignored by them.

The bluish glow from the central region of the Crab Nebula is due to synchrotron radiation.

From supermassive black holes

It has been suggested that supermassive black holes produce synchrotron radiation in "jets", generated by the gravitational acceleration of ions in their polar magnetic fields. The nearest such observed jet is from the core of the galaxy Messier 87. This jet is interesting for producing the illusion of superluminal motion as observed from the frame of Earth. This phenomenon is caused because the jets are traveling very near the speed of light and at a very small angle towards the observer. Because at every point of their path the high-velocity jets are emitting light, the light they emit does not approach the observer much more quickly than the jet itself. Light emitted over hundreds of years of travel thus arrives at the observer over a much smaller time period, giving the illusion of faster than light travel, despite the fact that there is actually no violation of special relativity.

Pulsar wind nebulae

A class of astronomical sources where synchrotron emission is important is pulsar wind nebulae, also known as plerions, of which the Crab nebula and its associated pulsar are archetypal. Pulsed emission gamma-ray radiation from the Crab has recently been observed up to ≥25 GeV, probably due to synchrotron emission by electrons trapped in the strong magnetic field around the pulsar. Polarization in the Crab nebula at energies from 0.1 to 1.0 MeV, illustrates this typical property of synchrotron radiation.

Interstellar and intergalactic media

Much of what is known about the magnetic environment of the interstellar medium and intergalactic medium is derived from observations of synchrotron radiation. Cosmic ray electrons moving through the medium interact with relativistic plasma and emit synchrotron radiation which is detected on Earth. The properties of the radiation allow astronomers to make inferences about the magnetic field strength and orientation in these regions. However, accurate calculations of field strength cannot be made without knowing the relativistic electron density.

In supernovae

When a star explodes in a supernova, the fastest ejecta move at semi-relativistic speeds approximately 10% the speed of light. This blast wave gyrates electrons in ambient magnetic fields and generates synchrotron emission, revealing the radius of the blast wave at the location of the emission. Synchrotron emission can also reveal the strength of the magnetic field at the front of the shock wave, as well as the circumstellar density it encounters, but strongly depends on the choice of energy partition between the magnetic field, proton kinetic energy, and electron kinetic energy. Radio synchrotron emission has allowed astronomers to shed light on mass loss and stellar winds that occur just prior to stellar death.