Statistical processes of aggregation and polymerization

Abstract

We study processes in which units (particles) associate into clusters, which are then also capable of dissociation. Such processes are discussed generally in section 2, where a stochastic kinetic equation (10) is proposed which bridges the gap between the conventional kinetic equations (8) and the statistical equilibrium concept of the Gibbs distribution.In section 4 we consider the equilibrium behaviour of a process for which the association rate of two units which are already bound tojandkother units respectively has the form (21). This is very much more general than the equi-reactive bond model usually discussed. The principal results are given in Theorem 1; from a single pair of equations (28) and (29) based on theH_jof (21) one can determine critical points, expected number of bonds, the distribution and moments of cluster size, and most other quantities of interest. This is without reference to any other consideration, such as kinetic or stoichiometric relations.Some particular cases are worked through in section 5. The classic Flory-Stockmayer results for units withfequi-reactive sites are obtained systematically and economically, with all parameters in terms of physically given quantities. Another type of example seems to indicate the existence of a second critical point.Corresponding results for the case of several types of unit are stated and illustrated in section 6.