A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction,
positive feedback
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...
leads to a self-amplifying
chain of events
A chain of events is a number of actions and their effects that are contiguous and linked together that results in a particular outcome. In the physical sciences, chain reactions are a primary example.
Determinism
''Determinism'' is the philo ...
.
Chain reactions are one way that systems which are not in
thermodynamic equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
can release energy or increase entropy in order to reach a state of higher entropy. For example, a system may not be able to reach a lower energy state by releasing energy into the environment, because it is hindered or prevented in some way from taking the path that will result in the energy release. If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.
A macroscopic metaphor for chain reactions is thus a snowball causing a larger snowball until finally an avalanche results ("
snowball effect
A snowball effect is a process that starts from an initial state of small significance and builds upon itself, becoming larger (graver, more serious), and also perhaps potentially dangerous or disastrous (a vicious circle), though it might be be ...
"). This is a result of stored
gravitational potential energy
Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conver ...
seeking a path of release over friction. Chemically, the equivalent to a snow avalanche is a spark causing a forest fire. In nuclear physics, a single stray neutron can result in a
prompt critical
In nuclear engineering, prompt criticality describes a nuclear fission event in which criticality (the threshold for an exponentially growing nuclear fission chain reaction) is achieved with prompt neutrons alone (neutrons that are released immed ...
event, which may finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion.
Numerous chain reactions can be represented by a
mathematical model based on
Markov chains.
Chemical chain reactions
History
In 1913, the German chemist
Max Bodenstein
Max Ernst August Bodenstein (July 15, 1871 – September 3, 1942) was a German physical chemist known for his work in chemical kinetics. He was first to postulate a chain reaction mechanism and that explosions are branched chain reactions, lat ...
first put forth the idea of
chemical
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., w ...
chain reactions. If two molecules react, not only molecules of the final reaction products are formed, but also some unstable molecules which can further react with the parent molecules with a far larger probability than the initial reactants. (In the new reaction, further unstable molecules are formed besides the stable products, and so on.)
In 1918,
Walther Nernst proposed that the
photochemical
Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible light (400–7 ...
reaction between
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
and
chlorine
Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
is a chain reaction in order to explain what is known as the ''
quantum yield The quantum yield (Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system.
Applications
Fluorescence spectroscopy
The fluorescence quantum yield is defined as the ratio of the numb ...
'' phenomena. This means that one
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
of light is responsible for the formation of as many as 10
6 molecules of the product
HCl. Nernst suggested that the photon dissociates a Cl
2 molecule into two Cl atoms which each initiate a long chain of reaction steps forming HCl.
[Laidler K.J., ''Chemical Kinetics'' (3rd ed., Harper & Row 1987) p.288-290 ]
In 1923, Danish and Dutch scientists
Christian Christiansen and
Hendrik Anthony Kramers
Hendrik Anthony "Hans" Kramers (17 December 1894 – 24 April 1952) was a Dutch physicist who worked with Niels Bohr to understand how electromagnetic waves interact with matter and made important contributions to quantum mechanics and statistical ...
, in an analysis of the formation of polymers, pointed out that such a chain reaction need not start with a molecule excited by light, but could also start with two molecules colliding violently due to thermal energy as previously proposed for initiation of chemical reactions by
van' t Hoff.
[
Christiansen and Kramers also noted that if, in one link of the reaction chain, two or more unstable molecules are produced, the reaction chain would branch and grow. The result is in fact an exponential growth, thus giving rise to explosive increases in reaction rates, and indeed to chemical explosions themselves. This was the first proposal for the mechanism of chemical explosions.
A quantitative chain chemical reaction theory was created later on by Soviet physicist ]Nikolay Semyonov
Nikolay Nikolayevich Semyonov (or Semënov), (russian: Никола́й Никола́евич Семёнов; – 25 September 1986) (often referred to in English as Semenoff, Semenov, Semionov, or Semyonova) was a Soviet physicist and chem ...
in 1934. Semyonov shared the Nobel Prize in 1956 with Sir Cyril Norman Hinshelwood
Sir Cyril Norman Hinshelwood (19 June 1897 – 9 October 1967) was a British physical chemist and expert in chemical kinetics. His work in reaction mechanisms earned the 1956 Nobel Prize in chemistry.
Education
Born in London, his parents we ...
, who independently developed many of the same quantitative concepts.[http://nobelprize.org/nobel_prizes/chemistry/laureates/1956/press.html History of the chemical chain reaction from 1913 to the Nobel work recognized in 1956]
Typical steps
The main types of steps in chain reaction are of the following types.[
* Initiation (formation of active particles or chain carriers, often ]free radical
A daughter category of ''Ageing'', this category deals only with the biological aspects of ageing.
Ageing
Ailments of unknown cause
Biogerontology
Biological processes
Causes of death
Cellular processes
Gerontology
Life extension
Metabo ...
s, in either a thermal or a photochemical step)
* Propagation
Propagation can refer to:
* Chain propagation in a chemical reaction mechanism
*Crack propagation, the growth of a crack during the fracture of materials
* Propaganda, non-objective information used to further an agenda
* Reproduction, and other fo ...
(may comprise several elementary steps in a cycle, where the active particle through reaction forms another active particle which continues the reaction chain by entering the next elementary step). In effect the active particle serves as a catalyst for the overall reaction of the propagation cycle. Particular cases are:
:: * chain branching (a propagation step where one active particle enters the step and two or more are formed);
:: * chain transfer
Chain transfer is a polymerization reaction by which the activity of a growing polymer chain is transferred to another molecule.
:P• + XR' → PX + R'•
Chain transfer reactions reduce the average molecular weight of the final polymer. Ch ...
(a propagation step in which the active particle is a growing polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
chain which reacts to form an inactive polymer whose growth is terminated and an active small particle (such as a radical), which may then react to form a new polymer chain).
* Termination (elementary step in which the active particle loses its activity; e. g. by recombination of two free radicals).
The ''chain length'' is defined as the average number of times the propagation cycle is repeated, and equals the overall reaction rate divided by the initiation rate.[
Some chain reactions have complex ]rate equation
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reac ...
s with fractional order or mixed order kinetics.
Detailed example: the hydrogen-bromine reaction
The reaction H2 + Br2 → 2 HBr proceeds by the following mechanism:[ Laidler K.J., ''Chemical Kinetics'' (3rd ed., Harper & Row 1987) p.291-4 ][P. Atkins and J. de Paula ''Physical Chemistry'' (8th ed., W.H. Freeman 2006), p.830-1 ]
* Initiation
: Br2 → 2 Br• (thermal) or Br2 + hν → 2 Br• (photochemical)
: each Br atom is a free radical, indicated by the symbol « • » representing an unpaired electron.
* Propagation (here a cycle of two steps)
: Br• + H2 → HBr + H•
: H• + Br2 → HBr + Br•
: the sum of these two steps corresponds to the overall reaction H2 + Br2 → 2 HBr, with catalysis
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
by Br• which participates in the first step and is regenerated in the second step.
* Retardation (inhibition)
: H• + HBr → H2 + Br•
: this step is specific to this example, and corresponds to the first propagation step in reverse.
* Termination 2 Br• → Br2
: recombination of two radicals, corresponding in this example to initiation in reverse.
As can be explained using the steady-state approximation, the thermal reaction has an initial rate of fractional order (3/2), and a complete rate equation with a two-term denominator ( mixed-order kinetics).[
]
Further chemical examples
* The reaction 2 H2 + O2 → 2 H2O provides an example of chain branching. The propagation is a sequence of two steps whose net effect is to replace an H atom by another H atom plus two OH radicals. This leads to an explosion under certain conditions of temperature and pressure.
** H• + O2 → •OH + •O•
** •O• + H2 → •OH + H•
* In chain-growth polymerization, the propagation step corresponds to the elongation of the growing polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
chain. Chain transfer corresponds to transfer of the activity from this growing chain, whose growth is terminated, to another molecule which may be a second growing polymer chain. For polymerization, the kinetic chain length In polymer chemistry the kinetic chain length of a polymer, ''ν'', is the average number of units called monomers added to a growing chain during chain-growth polymerization. During this process, a polymer chain is formed when monomers are bonded t ...
defined above may differ from the degree of polymerization
The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule.
For a homopolymer, there is only one type of monomeric unit and the ''number-average'' degree of polymerization is given b ...
of the product macromolecule.
* Polymerase chain reaction
The polymerase chain reaction (PCR) is a method widely used to rapidly make millions to billions of copies (complete or partial) of a specific DNA sample, allowing scientists to take a very small sample of DNA and amplify it (or a part of it) ...
, a technique used in molecular biology
Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physi ...
to amplify (make many copies of) a piece of DNA by ''in vitro
''In vitro'' (meaning in glass, or ''in the glass'') studies are performed with microorganisms, cells, or biological molecules outside their normal biological context. Colloquially called " test-tube experiments", these studies in biology ...
'' enzymatic
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. ...
replication using a DNA polymerase
A DNA polymerase is a member of a family of enzymes that catalyze the synthesis of DNA molecules from nucleoside triphosphates, the molecular precursors of DNA. These enzymes are essential for DNA replication and usually work in groups to create ...
.
Acetaldehyde pyrolysis and rate equation
The pyrolysis
The pyrolysis (or devolatilization) process is the thermal decomposition of materials at elevated temperatures, often in an inert atmosphere. It involves a change of chemical composition. The word is coined from the Greek-derived elements ''py ...
(thermal decomposition) of acetaldehyde, CH3CHO (g) → CH4 (g) + CO (g), proceeds via the Rice-Herzfeld mechanism:
*Initiation (formation of free radicals):
: CH3CHO (g) → •CH3 (g) + •CHO (g) k1
The methyl and CHO groups are free radicals.
*Propagation (two steps):
: •CH3 (g) + CH3CHO (g) → CH4 (g) + •CH3CO (g) k2
This reaction step provides methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Ea ...
, which is one of the two main products.
: •CH3CO (g) → CO (g) + •CH3 (g) k3
The product •CH3CO (g) of the previous step gives rise to carbon monoxide
Carbon monoxide (chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simple ...
(CO), which is the second main product.
The sum of the two propagation steps corresponds to the overall reaction CH3CHO (g) → CH4 (g) + CO (g), catalyzed
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
by a methyl radical •CH3.
*Termination:
: •CH3 (g) + •CH3 (g) → C2H6 (g) k4
This reaction is the only source of ethane
Ethane ( , ) is an organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is isolated on an industrial scale from natural gas and as a petroc ...
(minor product) and it is concluded to be the main chain ending step.
Although this mechanism explains the principal products, there are others that are formed in a minor degree, such as acetone
Acetone (2-propanone or dimethyl ketone), is an organic compound with the formula . It is the simplest and smallest ketone (). It is a colorless, highly volatile and flammable liquid with a characteristic pungent odour.
Acetone is miscib ...
(CH3COCH3) and propanal (CH3CH2CHO).
Applying the Steady State Approximation
In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, ...
for the intermediate species CH3(g) and CH3CO(g), the rate law for the formation of methane and the order of reaction are found:[
The rate of formation of the product methane is
]