Theoretical approaches to reversible diffusion-influenced reactions: Monomer–excimer kinetics

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Abstract
Three formalisms that describe the influence of diffusion on the kinetics of the reversible reaction, A+B⇌AB, are discussed and compared. The simplest involves a modification of the irreversible rate equations of Smoluchowski theory; the second is based on a generalization of physically appealing convolution relations that hold rigorously for reversible reactions between isolated pairs, and the third can be obtained by using a superposition approximation to truncate the hierarchy of equations satisfied by the reactive reduced distribution functions. The various formalisms are developed to the point that their implementation requires knowledge only of the time-dependent irreversible association rate coefficient and the microscopic dissociation rate constant. All these approaches give the correct equilibrium concentrations at infinite time, have the same short-time behavior, reduce correctly when the dissociation rate is zero, and become equivalent in the reaction-controlled limit. However, none of them provides an exact treatment of the underlying many-particle diffusive model of the reaction. Some illustrative calculations are presented and the relative merits of these approaches are discussed. All three approaches predict that the relaxation of a small initial deviation of the concentrations from their equilibrium values is nonexponential, except, of course, in the reaction-controlled limit. With a view towards treating monomer–excimer kinetics, the formalisms are generalized to incorporate unimolecular decay pathways.