Population Explosion—Autocatalysis

In Section 5.6 we noted that, for a branching-chain reaction, the population of chain carriers may grow without limit. As a consequence reaction velocity accelerates independent of chemical heating. At low reactant concentrations the rate law for carrier formation is, from (5.35), 

Here n chain carriers are formed in the initiation step for which the rate per carrier is Vi. In the branching step (or steps) a carriers are formed for each one that is consumed the rate is a — l)r [R]. The termination rate is r7r[R].(4) 

To illustrate the general considerations consider the hydrogen-oxygen system for which the important elementary steps at low pressure appear to be the following, where S is used for surface and the values in parentheses represent Zl/f (kJ mol )  

Chain initiation occurs by surface reaction, as in this example, or homogeneously, as in the CO + Og chain.Since heterogeneous processes are very significant in the kinetics of branching chains great care in surface preparation is required to achieve reproducible results. The propagation 

Semenov, Some Problems in Chemical Kinetics and Reactivity, translation by M. Boudart (Princeton, N.J. Princeton University Press, 1958), Vol. 2, Chapter 9 for a general discussion of ignition in branching-chain systems. 

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Autocatalysis, with n = 1, characterizes biological population growth, for example, since the number of offspring born is proportional to the number of individuals in the population. It leads to the Malthusian population explosion. In chemical systems, where autocatalysis is less common, it can also result in explosion, since the solution to Eq. (2.1) is an exponentially growing concentration. Of relevance to polymer systems is the fact that any exothermic reaction is inherently autocatalytic, since an increase in the product concentration corresponds to production of heat, which leads to an increase in the rate constant of the reaction via the Arrhenius factor. If the reaction in question is lengthening a polymer chain by addition of the monomer, the rate should increase as the chain grows if the heat produced is not rapidly removed from the system. 

Situations of this type are grouped under the term autocatalysis, which means that the system produces its catalyst as it goes along. As in the growth of populations, the acceleration can become so intense that the word explosion properly describes the catastrophic event. The explosion may fizzle if reactants are exhausted before the situation has gone out of hand — the rate... 

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