Analytical solution of the problem on dipole-dipole relaxation of radical pairs within a modified microreactor model

An exact solution of the problem on dipole-dipole relaxation of micellized radical pairs is derived within a modified microreactor model which allows for the possibility of radical attraction to the micelle wall. If radicals are attracted only weakly, the results closely agree with Steiner's data gained by numerical modeling of motion of two radicals by the Monte Carlo method. As revealed by analysis of the general solution, an attracting wall may cause an apparent increase in the micelle radius. It is suggested that the exact solution be approximated by a sum of two weighted terms, the solution for a micelle with an inert wall and the solution for a radical diffusing solely on the surface. The two-term approximation provides a good fit to the exact solution, whenever the diffusion coefficients on the surface and in the bulk assume close values.