Theoretical Analysis of the Role of Diffusion in Chemical Reactions, Fluorescence Quenching, and Nonradiative Energy Transfer

Abstract

The kinetics of diffusion-controlled chemical reactions in solution are analyzed by a statistical treatment. To start with, the probability of interaction of two molecules A and B, separated by a given distance at zero time and undergoing Brownian motion subsequently, is determined. The probability of interaction of an A molecule with one of many surrounding B molecules is then deduced. Finally, the course of reaction between A and B molecules distributed at random at zero time in a system containing a large number of molecules of both species, is calculated. The treatment outlined is readily extended to systems in which factors other than random diffusion are operative, as well as to systems in which the distribution of A and B molecules is not random at zero time. A few examples are discussed in detail. The theoretical treatment presented is applied to the kinetics of quenching of electronically excited molecules by collision with quencher molecules in solution, and to the calculation of the extent of nonradiative transfer of electronic excitation energy between molecules which are free to undergo Brownian motion.