Abstract
AbstractRecently we have carried out a molecular dynamics simulation of a model of diffusion‐controlled reactions in which the solvent is treated on an equal footing with reactants [8]. It is found that the rate of reactive encounter is larger at short times than that given by the Smoluchowski theory. In the present note it will be shown that the enhanced rate is due to a non‐Markovian effect. The theoretical approach for taking into account the non‐Markovian effect is a generalized diffusion equation, neglecting the mean force, with a time‐dependent diffusion coefficient which is related to the memory function of the velocity auto‐correlation function. By using the relaxation‐time approximation for the memory function, it can be shown that the motion of the mutual approach of the reactants is faster at short times than predicted by the classic Fick's law. It is this enhanced transport which is the physical origin of the enhanced reaction rate. Subjected to the absorbing boundary condition for reactivity, the generalized diffusion equation can still be solved analytically. The results have mathematical expressions as simple as those of the classic Smoluchowski theory.
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