The probability of the jump-diffusion-controlled reaction of a species pair

Abstract

The kinetic theory of bimolecular reactions A+b→P (products) proposed earlier is applied to the case where the reactive species make random walks about the sites of some spatial lattice. The corresponding kinetic equations are derived. In the framework of the discrete model of random walks, definitions are given to the survival and reaction probabilities for a species pair A … B and to the rate constant. The relation between these quantities is found, and a method for calculating them is proposed. Obtained are formulae for the survival and reaction probabilities and the rate constant, corresponding to some simple types of interaction between the species localized in a homogeneous and isotropic matrix. Described is a procedure by which one can make the transition to the continuous model based on a diffusion equation for which the boundary conditions are derived.