Photoinduced electron transfer and geminate recombination on a micelle surface: Analytical theory and Monte Carlo simulations

A detailed theoretical analysis of photoinduced electron transfer and geminate recombination on the surface of a spherical micelle is presented. An exact point-particle analytical theory is first developed for one donor and N competing acceptors in random fixed positions on the micelle surface. The method is applicable to any restricted geometry system. Starting with a neutral donor and acceptors, the time dependent probability of having an excited neutral donor and the time dependent probability of having ions are calculated for various numbers of acceptors and various forward and back electron-transfer parameters. The theoretical results are compared to Monte Carlo simulations of the problem, and the exact agreement obtained demonstrates that the ensemble averages are properly performed. Comparison is also made to a previously reported approximate analytical theory. The analytical theory and the Monte Carlo simulations are then extended to include the effects of donor–acceptor and acceptor–acceptor excluded volume. Although donor–acceptor excluded volume may be included exactly, inclusion of acceptor–acceptor excluded volume renders the problem intractable. An approximate method of handling acceptor–acceptor excluded volume by utilizing the pair correlation function for the system is presented and compared to Monte Carlo simulations of the full problem. An approximate technique is suggested for generating the pair correlation function for curved disks on the surface of a sphere.