General phenomenological treatment of activation, diffusion, and pseudodiffusion control of bimolecular reactions in solution

Abstract

A simple but rigorous and general phenomenological treatment of the bimolecular association A + B ⇌ C in solution gives the fundamental relationship k=k_Dk_A/(k_D+bk_A), where k, k_D, k_A are the observable, diffusion control, and activation control rate constants, respectively, for the forward reaction, and b is the ratio of the geminate recombination probability ā to the non-geminate combination probablity a. The probabilities ā and a can differ. The criterion for diffusion control is a→ 1, while the criterion for activation control is (1 –ā)→ 1. Thus, the criteria for diffusion and activation control involve different parameters. The parameter b can be greater than unity. When b is greater than unity and k_A is large, k reaches a limiting value of k_D/b, corresponding to pseudodiffusion control, rate constant k_ψD. When b is viscosity-and temperature-independent k_ψD and k_D vary in parallel with viscosity and temperature. To estimate the extent of pseudodiffusion control by simulation would require simulations of both ā and a, as well as values of k_D and k_A.