A new approach to diffusion-limited reaction rate theory

Abstract

A new approach to the diffusion-limited reaction rate theory is developed on the base of a similar approach to consideration of Brownian coagulation, recently proposed by the author. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only to the special case of reactions with a large reaction radius, $\bar r_A \ll R_{AB} \ll \bar r_B$ (where $\bar r_A$, $\bar r_B$ are the mean interparticle distances), and becomes inappropriate to calculation of the reaction rate in the case of a relatively small reaction radius, $R_{AB} \ll \bar r_A$, $\bar r_B$. In the latter, most general case particles collisions occurmainly in the kinetic regime (rather than in the diffusion one) characterized by a homogeneous (at random) spatial distribution of particles. Homogenization of particles distribution occurs owing to particles diffusion mixing on the length scale of the mean interparticle distance with the characteristic diffusion time being small in comparison with the characteristic reaction time. The calculated reaction rate for a small reaction radius in 3D formally (and casually) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, however, notably deviates at large times from the traditional result in the plane (2D) geometry.