On the validity of the one-particle diffusion model of geminate recombination in micelles

Abstract

Diffusion and recombination of a pair of geminate particles in a micelle is usually modeled by letting one particle act as a fixed sink in the center of the micelle while the other is diffusing with the relative diffusion coefficient. In order to test whether this simplified model is realistic we have performed a series of Monte Carlo calculations for situations where either both particles are moving or one is fixed at the micellar boundary. We find that the short time evolution, which is essentially a free diffusion, is well described by the center model. The long time behavior during the quasi-equilibrium depends on the model but can be made to agree by a rescaling of the reaction constant. This is explained as a geometrical model dependence of the reencounter probability. Essential differences exist in the transition period between the two time scales. The center model predicts that the rate of recombination has a very sharp and well defined transition from the algebraic time dependence, characteristic of free diffusion, to the exponential dependence found in the quasi-equilibrium. This behavior is not found in the other models.