EFFECTIVE POTENTIAL APPROXIMATION TO REACTION-DIFFUSION KINETICS IN NONHOMOGENEOUS MEDIA - MICELLAR SYSTEMS

An approximation is introduced that enables one to describe nonhomogen eous reaction-diffusion kinetics via a one-dimensional backward equati on for the survival probability of a pair of particles interacting wit h each other through the effective potential associated with the equil ibrium distance distribution in the absence of reaction. Employing the effective potential and mean reaction time approximations, the kineti cs 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 dist ributions 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 simulat ions.