Modified Smoluchowski equation and a unified theory of the diffusion-controlled recombination

A unified theory of the diffusion-controlled recombination based on the modified Smoluchowski equation is developed which takes into account simultaneously the diffusion transport, the chemical reaction, and the physical interaction between reactants. The stationary solution of this equation suggests a method for calculating the physical quantities characterizing the reactivity of active particles in the homogeneous and geminate processes with no need of any information about the solution of the corresponding time-dependent boundary value problem. A correlation between escape probability and apparent rate constant is established. Some results of the general theory are used for the theoretical description of ion pair neutralization and reaction between free ions. The validity of the physical model used in the present paper is briefly discussed.