Theory of diffusion-assisted reactions on micelle surfaces: Photoinduced electron transfer followed by back transfer

A general theory of diffusion-assisted irreversible reactions on micelle surfaces is presented. An exact solution for the experimental observables is given in a matrix form in terms of the eigenmodes of the diffusion operator in the same geometry but without interaction potential and reaction. Photoinduced electron transfer followed by back transfer is considered in detail as a practically important example of reaction. Excellent agreement of the matrix solution with the numerical solution of the corresponding partial differential equations via a standard discretization procedure is observed for typical sets of parameter values.