Statistical mechanical models of chemical reactions: Analytic solution of models of A+B⇌AB in the Percus-Yevick approximation

Abstract

We introduce models for the association of spherically symmetric atoms into diatomic molecules. In the Percus-Yevick approximation, we solve analytically for the equilibrium properties of a one-parameter family of such models corresponding to A + B ⇌ AB association. We focus in detail on the behaviour of the association constant, comparing alternative definitions of that quantity. We find that our results are insensitive to the details of the repulsive core of the AB potential as long as it is several times larger than k B T (k B = Boltzmann's constant, T = temperature). As a result, we conclude that a limiting-case model in which the repulsive core of the AB potential is a hard core is of particular interest and utility. The mathematics of the Percus-Yevick approximation simplifies considerably in this limiting-case analysis.