Some Key Ideas of Nonlinear Chemical Dynamics

The phenomena that we will be interested in have the common feature that they occur far from equilibrium. A useful way of thinking about this issue, suggested by Yamaguchi [4], is to distinguish between self-assembled structures and dissipative structures, which arise via self-organization. The former, crystals for example, arise under equilibrium or near-equihbrium conditions. The latter, the subject of our inquiry, are found far from equilibrium [5]. Table 2.1 summarizes the differences. 

One feature that often characterizes systems of interest in nonlinear chemical dynamics is feedback, the influence of a species on the rate of its own production. 

The most commonly occurring form of feedback in these systems is autocatalysis, where the rate of production of species A increases with its concentration. In the simplest case, the rate is proportional to the concentration to some power  

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. 

We list below some of the most interesting and most thoroughly studied phenomena that arise in nonlinear chemical dynamics. 

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