Relaxation kinetics of diffusion-influenced reactions of the type A+B⇄C perturbed by flash photolysis

Abstract

When the equilibrium of a reversible association–dissociation reaction, A+B⇄C, is perturbed by photolyzing C molecules, its relaxation kinetics cannot be described by conventional theories. Not only are the concentrations of reactant species displaced from equilibrium, but also the recombination dynamics of A and B molecules becomes quite different from the equilibrium bimolecular reaction. In particular, geminate pairs of A and B molecules photolytically produced in a viscous solution would give an almost singular contribution to the recombination dynamics at short times. Their dynamics needs to be treated distinctively from the recombination dynamics of thermally dissociated molecules. In the present paper, we develop a relaxation kinetic theory that takes account of these features of the reaction system in a unified manner. While most of previous theories are applicable only to the system of an isolated pair of geminate A and B molecules or to the pseudo-first-order case, the present theory is applicable to the second-order case as well. Simple analytic solutions are obtained in the Laplace domain, which are applicable irrespective of the dimensionality d of the reaction system. The present theory reveals an interesting feature of a photolytically perturbed reaction system as noted recently by Yang et al.; that is, relaxation of the concentration deviation to equilibrium follows the t−(d+2)/2 power law at long times instead of the t−d/2 power-law relaxation known for the thermally perturbed reaction system.