Kinetic theory of bimolecular reactions in liquid. I. Steady-state fluorescence quenching kinetics

Abstract

A microscopic kinetic theory for steady-state fluorescence quenching reaction in liquid is formulated. Based on a linear reaction-Liouville equation for the distribution function in phase space, we derived a memory equation for the relaxation of singlet density function of reactants by use of Mori’s projection operator technique. The expression of the memory kernel is analyzed by the fully renormalized kinetic theory developed by Mazenko. The memory kernel includes the many-body information via a hierarchical structure of a propagator in that. This hierarchy is truncated by a disconnected approximation for the propagator governing the dynamics of an orthogonalized doublet field creating their initial correlation via a bimolecular interaction. This approximation is different from the dynamic superposition approximation for reduced distribution functions made in usual hierarchical approaches. As a result, the detailed description of reactant dynamics becomes available and the memory kernel consists of a geometric series describing the repeated ring collision (reaction) events. We obtain a self-consistent algebraic equation at the diffusion level, which is easily solved by a few iteration, for the response of concentration of reactants to a constant external perturbation. The effects of intensity of external constant perturbation are explicitly considered. The present theory yields the same result with that of the mean-field diffusion theory although the approximations and the assumptions are quite different from each other.