Pair-correlation kinetics and the reversible diffusion-controlled reaction

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Abstract
It has long been known that the time course of a bimolecular reaction occurring in a condensed host depends on the behavior of the nonequilibrium pair-correlation function for reactant pairs. The classical analysis of such reactions has led to a kind of standard rule: The association rate constant for a diffusion-controlled reaction is 4πDR and this rate constant produces the fastest possible kinetics. This result is only (approximately) true for the case of an irreversible reaction, however. Here, we reexamine this old problem, looking closely at the reversible case. We report a result that challenges the standard wisdom: When the reaction is highly reversible the relaxation of the related kinetics to equilibrium can be much faster than the model in which 4πDR is the association rate constant. We suggest that our work provides a natural resolution to a well-known, long-standing controversy in the study of electrically active impurities in silicon grown by the Czochralski method.