MANY-PARTICLE EFFECTS ON THE RELAXATION KINETICS OF FAST REVERSIBLE-REACTIONS OF THE TYPE A-REVERSIBLE-ARROW-C(B)

Effects of pair correlations between bound and unbound molecules on th e relaxation kinetics of fast reversible reactions of the type A+B rev ersible arrow C are investigated for one-, two-, and three-dimensional reaction systems in a unified manner. Starting from the many-body Smo luchowski equations for reactant molecule distribution functions, whic h an coupled in a hierarchical manner, we derive a set of reaction kin etic equations by using the dynamic superposition approximation. While most of previous theories are applicable only to the pseudo-first ord er case, the present theory is applicable to the second-order case as well. In the pseudo-first order case with B molecules present in exces s of A molecules, we can consider two limiting situations where either A or B molecules are static. The present theory can deal with both li miting cases within a single theoretical framework. Previously, the tw o cases have been approached by using quite different theoretical form alisms. Simple analytic solutions are obtained that are applicable irr espective of the dimensionality of reaction system, and are shown to a gree 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) powe r-law decay phase, in agreement with the computer simulation results o btained by Edelstein and Agmon for the one-dimensional case. (C) 1997 American Institute of Physics.