Kinetics of reversible diffusion influenced reactions: The self-consistent relaxation time approximation

Abstract

The simplest general theory of the kinetics of reversible diffusion-influenced reactions that is exact both at short and long times for A+B⇌C and A+B⇌C+D is presented. The formalism is based on an approximate set of reaction-diffusion equations for the pair distribution functions which incorporate the influence of the chemical reaction by using effective rate constants that are determined self-consistently. For small deviations from equilibrium and contact reactivity, the relaxation function is given explicitly in the Laplace domain in terms of the Smoluchowski rate coefficient that describes the corresponding diffusion controlled irreversible reaction. Consequently, the kinetics can be easily obtained for arbitrary diffusion coefficients and equilibrium concentrations.