Abstract
An approximation is introduced that enables one to describe nonhomogeneous reaction–diffusion kinetics via a one-dimensional backward equation for the survival probability of a pair of particles interacting with each other through the effective potential associated with the equilibrium distance distribution in the absence of reaction. Employing the effective potential and mean reaction time approximations, the kinetics of diffusion-controlled reactions in a finite volume are analyzed, a spherical micelle being taken as a typical example of the system. A general relationship between the pseudo-first-order rate constant and the spatial arrangement of reactants is obtained. Several spatial distributions of practical importance are considered and the corresponding rate constants are calculated and compared against the existing exact analytical solutions and the results of numerical random-walk simulations.
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