Chain reaction

Chain reaction

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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
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...

 leads to a self-amplifying chain of events
Chain of events
A chain of events is a number of actions and their effects that are contiguous and linked together.-Chain reaction:A chain reaction is a chain of events where one or more events in the chain causes additional reaction in an earlier stage of the chain...

.

Chain reactions are one way in which systems which are in thermodynamic non-equilibrium 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 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 macrosopic metaphor for chain reactions is thus a snowball causing larger snowfall until finally an avalanche results ("snowball effect"). This is a result of stored gravitaional potential energy 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 an prompt critical
Prompt critical
In nuclear engineering, an assembly is prompt critical if for each nuclear fission event, one or more of the immediate or prompt neutrons released causes an additional fission event. This causes a rapid, exponential increase in the number of fission events...

 event, which may be finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion. However, this reaction cannot be reversed.

Chemical chain reactions


In 1913 the German chemist Max Bodenstein
Max Bodenstein
Max Ernst August Bodenstein was a German physical chemist known for his work in chemical kinetics...

 first put forth the idea of chemical chain reactions. If two molecules react, not only molecules of the final reaction products are formed, but also some unstable molecules, having the property of being able to 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 1923, Danish and Dutch scientists Christian Christiansen
Christian Christiansen
Christian Christiansen was a Danish physicist.Christiansen first taught at the local polytechnical school. In 1886 he was appointed to a chair for physics at the University of Copenhagen....

 and Hendrik Anthony Kramers
Hendrik Anthony Kramers
Hendrik Anthony "Hans" Kramers was a Dutch physicist.-Background and education:...

, in an analysis of 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 in the traditional way classically previously proposed for initiation of chemical reactions, by
van' t Hoff
Jacobus Henricus van 't Hoff
Jacobus Henricus van 't Hoff, Jr. was a Dutch physical and organic chemist and the first winner of the Nobel Prize in chemistry. He is best known for his discoveries in chemical kinetics, chemical equilibrium, osmotic pressure, and stereochemistry...

.

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 by Soviet physicist Nikolay Semyonov
Nikolay Semyonov
Nikolay Nikolayevich Semyonov was a Russian/Soviet physicist and chemist. Semyonov was awarded the 1956 Nobel Prize in Chemistry for his work on the mechanism of chemical transformation.-Life:...

 in 1934. Semyanov shared the Nobel Prize in 1956 with Sir Cyril Norman Hinshelwood
Cyril Norman Hinshelwood
Sir Cyril Norman Hinshelwood OM PRS was an English physical chemist.Born in London, his parents were Norman Macmillan Hinshelwood, a chartered accountant, and Ethe Frances née Smith. He was educated first in Canada, returning in 1905 on the death of his father to a small flat in Chelsea where he...

, who independently developed many of the same quantitative concepts.

The main steps of chain reaction are the following.
  • Initiation (at this step an active particle, often a free radical, is produced);
  • propagation (may comprise several elementary steps, as, for instance, reaction elementary acts, where the active particle through reaction forms another active particle which continues the reaction chain by entering the next elementary step); particular cases are:
* chain branching (the case of propagation step when more new active particles form in the step than enter it);
* chain transfer (the case in which one active particle enters an elementary reaction with the inactive particle which as a result becomes another active particle along with forming of another inactive particle from the initial active one);
  • termination (elementary step in which active particle loses its activity without transferring the chain; e. g. recombination
    Recombination
    Recombination may refer to:* Recombination , the process by which genetic material is broken and joined to other genetic material* Recombination , in semiconductors, the elimination of mobile charge carriers...

     of the free radicals).

Nuclear chain reactions



A nuclear chain reaction was proposed by Leó Szilárd
Leó Szilárd
Leó Szilárd was an Austro-Hungarian physicist and inventor who conceived the nuclear chain reaction in 1933, patented the idea of a nuclear reactor with Enrico Fermi, and in late 1939 wrote the letter for Albert Einstein's signature that resulted in the Manhattan Project that built the atomic bomb...

 in 1933, shortly after the neutron was discovered, but more than five years before nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

 was discovered. Szilárd knew of chemical chain reactions, and he had been reading about an energy-producing nuclear reaction
Nuclear reaction
In nuclear physics and nuclear chemistry, a nuclear reaction is semantically considered to be the process in which two nuclei, or else a nucleus of an atom and a subatomic particle from outside the atom, collide to produce products different from the initial particles...

 involving high-energy protons bombarding lithium, demonstrated by John Cockcroft
John Cockcroft
Sir John Douglas Cockcroft OM KCB CBE FRS was a British physicist. He shared the Nobel Prize in Physics for splitting the atomic nucleus with Ernest Walton, and was instrumental in the development of nuclear power....

 and Ernest Walton
Ernest Walton
Ernest Thomas Sinton Walton was an Irish physicist and Nobel laureate for his work with John Cockcroft with "atom-smashing" experiments done at Cambridge University in the early 1930s, and so became the first person in history to artificially split the atom, thus ushering the nuclear age...

, in 1932. Now, Szilárd proposed to use neutrons theoretically-produced from certain nuclear reactions in lighter isotopes, to induce further reactions in light isotopes that produced more neutrons. This would in theory produce a chain reaction at the level of the nucleus. He did not envision nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

 as one of these neutron-producing reactions, since this reaction was not known at the time. Experiments he proposed using beryllium
Beryllium
Beryllium is the chemical element with the symbol Be and atomic number 4. It is a divalent element which occurs naturally only in combination with other elements in minerals. Notable gemstones which contain beryllium include beryl and chrysoberyl...

 and indium
Indium
Indium is a chemical element with the symbol In and atomic number 49. This rare, very soft, malleable and easily fusible post-transition metal is chemically similar to gallium and thallium, and shows the intermediate properties between these two...

 failed.

Later, after nuclear fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

 was discovered in 1938, Szilárd immediately realized the possibility of using neutron-induced fission as the particular nuclear reaction needed for a chain-reaction, so long as fission also produced neutrons. In 1939, with Enrico Fermi, Szilárd proved this neutron-multiplying reaction in uranium. In this reaction, a neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

 plus a fission
Nuclear fission
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts , often producing free neutrons and photons , and releasing a tremendous amount of energy...

able atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

 causes a fission resulting in a larger number of neutrons than the single one that was consumed in the initial reaction. Thus was born the practical nuclear chain reaction
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...

 by the mechanism of neutron-induced nuclear fission.

Specifically, if one or more of the produced neutrons themselves interact with other fissionable nuclei, and these also undergo fission, then there is a possibility that the macroscopic overall fission reaction will not stop, but continue throughout the reaction material. This is then a self-propagating and thus self-sustaining chain reaction. This is the principle for nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...

s and atomic bombs.

[The above description is somewhat simplified. The crucial issue is whether enough of those secondary neutrons themselves produce a further fission. The nuclear chain reaction is described in significantly more detail in the article on Stan Ulam, who "discovered" or realized the details of the amplification concept, when fission by prompt fission neutrons were the mechanism].

Demonstration of a self-sustaining nuclear chain reaction was accomplished by Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...

 and others, in the successful operation of Chicago Pile-1
Chicago Pile-1
Chicago Pile-1 was the world's first man-made nuclear reactor. CP-1 was built on a rackets court, under the abandoned west stands of the original Alonzo Stagg Field stadium, at the University of Chicago. The first self-sustaining nuclear chain reaction was initiated in CP-1 on December 2, 1942...

, the first artificial nuclear reactor, in late 1942.

Electron avalanche in gases


An electron avalanche
Electron avalanche
An electron avalanche is a process in which a number of free electrons in a medium are subjected to strong acceleration by an electric field, ionizing the medium's atoms by collision , thereby forming "new" electrons to undergo the same process in successive cycles...

 happens between two unconnected electrodes in a gas when an electric field exceeds a certain theshold. Random thermal collisions of gas atoms may result in a a few free electrons and positively-charged gas ions, in a process called impact ionizaton. Acceleration of these free electrons in a strong electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

 causes them to gain energy, and when they impact other atoms, the energy causes release of new free electrons and ions (ionization), which fuels the same process. If this process happens faster than it is naturally quenched by ions recombining, the new ions multiply in successive cycles until the gas breaks down into a plasma and current flows freely in a discharge.

Electron avalanches are essential to the dielectric breakdown process within gases. The process can culminate in corona discharge
Corona discharge
In electricity, a corona discharge is an electrical discharge brought on by the ionization of a fluid surrounding a conductor that is electrically energized...

s, streamer
Streamer
Streamer or streamers may refer to:* Pennon, a small pointed flag* Campaign streamer, flag used by military units* Paper streamer* Positive streamer, lightning bolt* Streamer moth, the geometer moth Anticlea derivata...

s, leader
Leader (spark)
A leader is a hot, highly conductive channel of plasma that plays a critical part during dielectric breakdown within in a long electric spark.-Mechanism:...

s, or in a spark
Electric spark
An electric spark is a type of electrostatic discharge that occurs when an electric field creates an ionized electrically conductive channel in air producing a brief emission of light and sound. A spark is formed when the electric field strength exceeds the dielectric field strength of air...

 or continuous electric arc
Electric arc
An electric arc is an electrical breakdown of a gas which produces an ongoing plasma discharge, resulting from a current flowing through normally nonconductive media such as air. A synonym is arc discharge. An arc discharge is characterized by a lower voltage than a glow discharge, and relies on...

 that completely bridges the gap. The process may extends to huge sparks — streamers in lightning
Lightning
Lightning is an atmospheric electrostatic discharge accompanied by thunder, which typically occurs during thunderstorms, and sometimes during volcanic eruptions or dust storms...

 discharges propagate by formation of electron avalanches created in the high potential gradient ahead of the streamers' advancing tips. Once begun, avalanches are often intensified by the creation of photoelectrons as a result of ultraviolet radiation emitted by the excited medium's atoms in the aft-tip region.

The process can also be used to detect radiation that initiates the process, as the passage of a single particles can amplified to large discharges. This is the mechanism of a Geiger counter
Geiger counter
A Geiger counter, also called a Geiger–Müller counter, is a type of particle detector that measures ionizing radiation. They detect the emission of nuclear radiation: alpha particles, beta particles or gamma rays. A Geiger counter detects radiation by ionization produced in a low-pressure gas in a...

 and also the visualization possible with a spark chamber and other wire chamber
Wire chamber
A multi-wire chamber is a detector for particles of ionizing radiation which is an advancement of the concept of the Geiger counter and the proportional counter....

s.

Avalanche breakdown in semiconductors


An avalanche breakdown
Avalanche breakdown
Avalanche breakdown is a phenomenon that can occur in both insulating and semiconducting materials. It is a form of electric current multiplication that can allow very large currents within materials which are otherwise good insulators. It is a type of electron avalanche...

 process can happen in semiconductors, which in some ways conduct electricity analogously to a mildy-ionized gas. Semiconductors rely on free electrons knocked out of the crystal by thermal vibration for conduction. Thus, unlike metals, semiconductors become better conductors the higher the temperature. This sets up conditions for the same type of positive feedback-- heat from current flow causes temperature to rise, which inceases charge carriers, lowering resistance, and causing more current to flow. This can continue to the point of complete breakdown of normal resistance at a semiconductor junction, and failure of the device (this may be temporary or permanent depending on whether there is physical damage to the crystal). Certain devices, such as avalanche diode
Avalanche diode
In electronics, an avalanche diode is a diode that is designed to go through avalanche breakdown at a specified reverse bias voltage. The junction of an avalanche diode is designed to prevent current concentration at hot spots, so that the diode is undamaged by the breakdown...

s, deliberately make use of the effect.

Chain Reactions in Economics


In 1963 Friedman and Schwartz proposed a positive feedback loop as a mechanism for catastrophic failures in economics: “It happens that a liquidity crisis in a unit fractional reserve banking system is precisely the kind of event that trigger- and often has triggered- a chain reaction. And economic collapse often has the character of a cumulative process. Let it go beyond a certain point, and it will tend for a time to gain strength from its own development as its effects spread and return to intensify the process of collapse”.

Further examples

  • For example in a chemical reaction
    Chemical reaction
    A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...

     every step of H2
    Hydrogen
    Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

     + Cl2
    Chlorine
    Chlorine is the chemical element with atomic number 17 and symbol Cl. It is the second lightest halogen, found in the periodic table in group 17. The element forms diatomic molecules under standard conditions, called dichlorine...

     chain reaction consumes one molecule
    Molecule
    A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

     of H2 or Cl2, one free radical H· or Cl· producing one HCl
    Hydrochloric acid
    Hydrochloric acid is a solution of hydrogen chloride in water, that is a highly corrosive, strong mineral acid with many industrial uses. It is found naturally in gastric acid....

     molecule and another free radical.
  • A cascading failure
    Cascading failure
    A cascading failure is a failure in a system of interconnected parts in which the failure of a part can trigger the failure of successive parts.- Cascading failure in power transmission :...

    , a failure in a system of interconnected parts, for example a power transmission grid, where the service provided depends on the operation of a preceding part, and the failure of a preceding part can trigger the failure of successive parts.
  • Polymerase chain reaction
    Polymerase chain reaction
    The polymerase chain reaction is a scientific technique in molecular biology to amplify a single or a few copies of a piece of DNA across several orders of magnitude, generating thousands to millions of copies of a particular DNA sequence....

    , a technique used in molecular biology
    Molecular biology
    Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...

     to amplify (make many copies of) a piece of DNA
    DNA
    Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...

     by in vitro
    In vitro
    In vitro refers to studies in experimental biology that are conducted using components of an organism that have been isolated from their usual biological context in order to permit a more detailed or more convenient analysis than can be done with whole organisms. Colloquially, these experiments...

    enzymatic
    Enzyme
    Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

     replication
    DNA replication
    DNA replication is a biological process that occurs in all living organisms and copies their DNA; it is the basis for biological inheritance. The process starts with one double-stranded DNA molecule and produces two identical copies of the molecule...

     using a DNA polymerase
    DNA polymerase
    A DNA polymerase is an enzyme that helps catalyze in the polymerization of deoxyribonucleotides into a DNA strand. DNA polymerases are best known for their feedback role in DNA replication, in which the polymerase "reads" an intact DNA strand as a template and uses it to synthesize the new strand....

    .

See also


IUPAC Gold Book - Chain reaction