Kinetics of diffusion-influenced bimolecular reactions in solution. I. General formalism and relaxation kinetics of fast reversible reactions

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Abstract
A general theoretical framework for treating the kinetics of diffusion-influenced bimolecular reactions in solution is presented. It is based on a hierachy of phenomenological kinetic equations for the reduced distribution functions of reactant molecules. With this formalism, a perturbation series expression for the rate coefficient for irreversible reactions involving a long-ranged sink function is derived. For a delta-function sink, it reduces to that obtained previously by Northrup and Hynes [Chem. Phys. Lett. 54, 244 (1978)]. It is demonstrated that the correctness of the Smoluchowski’s expression for the rate coefficient in the low concentration limit results from a cancellation of errors. For diffusion-influenced reversible reactions involving a delta-function sink, explicit expressions for the time-dependent forward and reverse rate coefficients are derived. Experimental data on the relaxation kinetics of the triiodide ion formation reaction are reinterpreted, and consideration of diffusion effects is found to be essential. It is shown that the rate coefficient for the diffusive encounter of reactant molecules is not the upper bound to the bimolecular rate coefficient for reversible reactions.