Radical pair recombination kinetics in one, two and three dimensions

Abstract

When radical pairs are generated in a solid matrix in a low concentration, the initial stage of the radical recombination reaction represents an ensemble of diffusion-controlled reactions proceeding independently in each pair. This paper examines theoretically the “intrapair” reaction kinetics when the radical diffusion has one-, two- and three-dimensional character. In all cases the “intrapair” reaction rate decreases with time. But in the cases of one and two dimensions, unlike that of three dimensions, the reaction results in total annihilation of the radicals. In the one dimensional case, therewith, the number of radicals which survive during a time interval t decreases at long t as t − 1 2 , and in the two dimensional case as (1n Dt/ R 2) −1, where D is a mutual diffusion constant of the radicals and R is the distance at which the radicals recombine. These results are in qualitative agreement with a number of experiments.