Many-particle effects on the relaxation kinetics of fast reversible reactions of the type A+B⇄C

Abstract

Effects of pair correlations between bound and unbound molecules on the relaxation kinetics of fast reversible reactions of the type A+B⇄C are investigated for one-, two-, and three-dimensional reaction systems in a unified manner. Starting from the many-body Smoluchowski equations for reactant molecule distribution functions, which are coupled in a hierarchical manner, we derive a set of reaction kinetic equations by using the dynamic superposition approximation. While most of previous theories are applicable only to the pseudo-first order case, the present theory is applicable to the second-order case as well. In the pseudo-first order case with B molecules present in excess of A molecules, we can consider two limiting situations where either A or B molecules are static. The present theory can deal with both limiting cases within a single theoretical framework. Previously, the two cases have been approached by using quite different theoretical formalisms. Simple analytic solutions are obtained that are applicable irrespective of the dimensionality of reaction system, and are shown to agree well with the full numerical solutions. The present theory shows that in the time dependence of the reactant concentration a transient rapid relaxation period precedes the well known long-time t−d/2 power-law decay phase, in agreement with the computer simulation results obtained by Edelstein and Agmon for the one-dimensional case.