# Difference between the terms “autocatalysis” and “(branching) chain reaction”

Is there a technical difference between the terms "autocatalysis" and "branching chain reaction"? They both seem to refer to something very similar, namely sequences of reactions in which one of the intermediates is also one of the products, leading to the possibility of exponential growth. Is one of the terms more specific than the other, or are they generally understood to mean the same thing?

There do seem to be some differences in how the terms are used. I've never seen the formose cycle, for example, referred to as a chain reaction, which does seem to imply that the term "chain reaction" means something more specific. If this is the case, what is the defining difference between the two terms?

Here is a diagram of the formose cycle (from the German Wikipedia entry, because it has a much better diagram than the English one) - is there a specific reason why it would not be referred to as a chain reaction?

An autocatalytic reaction is a reaction where the product catalyzes the reaction. An autocatalytic reaction takes the following form (or more complex variations of it).

$\ce{A + B -> 2B}$

An autocatalytic reaction must produce the exact species $\ce{B}$ that cataylzes the reaction. More about autocatalytic reactions, including examples, can be found at this question and this answer.

A chain reaction is one where every step of the mechanism produces another activated intermediate of some kind that can continue to react under the same conditions. Chain reactions continue until they terminate by means specific to the type of chain reaction. Chain reactions may appear to be autocatalytic, but there is a net consumption of both reagents, and the end product does not tend to cataylze the reaction:

$$\ce{A + B}* \ce{ -> C}$$ $$\ce{C + B -> D + B}*$$ Net: $$\ce{ A + B -> D}$$

In the generic example above, the second step produces more $\ce{B}*$, which can reenter the first step. Overall, however, the reaction is not autocatalytic, since no more $\ce{B}$ is being produced and the concentration of $\ce{B}*$ is likely unchanging (steady state). All chain reactions have this feature. While the reactive species may appear on both the reactant side and the product side, there is no net change in the number of reactive species present in the reaction.

A classic introductory chain reaction is the radical halogenation of an alkane like methane. This reaction's mechanism is divided into three regimes: 1) Initiation (generation of radicals where there were none previously), 2) propagation (the chain part), and 3) termination (in which there is a net reduction in radicals, usually by recombination).

Initiation: $$\ce{Cl2 ->[hv] 2Cl*}$$

Propagation: $$1) \ \ \ \ \ \ce{Cl* + CH4 -> HCl + CH3*}$$ $$2) \ \ \ \ \ \ce{CH3* + Cl2 -> CH3Cl + Cl*}$$

Termination: $$\ce{CH3* + Cl* -> CH3Cl}$$ $$\ce{2CH3* -> CH3CH3}$$

The above example is a cyclic chain reaction. Chain reactions can be linear, for example chain-growth polymerization. In this kind of chain reaction, two species, where one is the activated end of a polymer chain $\ce{P}*$ and the other is a new monomer $\ce{M}$, react to form a new activated chain end $\ce{P}'*$ that is one monomer unit longer. $\ce{P}'*$ can then reenter the reaction and react with another $\ce{M}$. Again, this reaction is not autocatalytic. The number of activated chain ends is not increasing (or decreasing).

$$\ce{P}* +\ce{M -> P'}*$$ $$\ce{P'}* +\ce{M -> P''}*$$

The activated chain ends, $\ce{P}*$, can be radicals, anions, cations, the products of ring-opening, or organometallic complexes.

• Many thanks for the answer - I will read it carefully later. But just a quick comment for now: I guess I should have been more specific in my question and said branching chain reaction. – Nathaniel Apr 5 '13 at 11:20
• You mean like nuclear fission of uranium? I suspect in that case then you have a chain reaction that is also autocatalytic. – Ben Norris Apr 5 '13 at 11:47
• Nuclear fission, combustion, PCR, ... – Nathaniel Apr 5 '13 at 13:35
• sorry for the brief responses yesterday, I was pressed for time. A branching step in a chain reaction is defined as one that increases the number of activated intermediates, as opposed to a propagating step, which keeps the number the same. I guess my question is really about what counts as an "active" intermediate - is it just anything that can continue the reaction (in which case autocatalysis and branching chain reactions are probably the same thing), or does it mean something more specific? – Nathaniel Apr 6 '13 at 12:59
• Would it be correct to describe the Formose cycle as a chain reaction? I've edited a diagram into my post. In this case the "initiating" and "terminating" steps are not shown, but would it be correct to describe it as a chain reaction in which all the reactions shown are propagating steps, except for the decomposition of the aldotetrose into two glycoaldehydes, which is a branching step? – Nathaniel Apr 6 '13 at 13:01