Theory of diffusion-controlled reactions on spherical surfaces and its application to reactions on micellar surfaces

Abstract

Diffusion-controlled reactions of a pair of particles on a spherical surface are studied. An analytical expression for the pair survival probability is derived in the case of a pair of freely diffusing particles. The decay of the pair survival probability is found to be well approximated by a single exponential. A simple approximate method for calculating the decay time which characterizes the exponential is presented. The decay time of a pair of particles interacting with each other by an arbitrary force is derived by use of this method. The results are applied to analyze available experimental data on reactions occurring on micellar surfaces, including the dismutation reaction of Br2− on the surface of cationic micelles and that of Ag2+ on the surface of anionic micelles, and the diffusion coefficients of these species on the micellar surfaces are estimated.