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We give the exact solution of the geminate recombination probability of a pair of oppositely charged particles, corresponding to the boundary condition of a partly absorbing sphere of finite radius at the origin. In the limit of an infinite recombination velocity (κ→∞) and a vanishing radius (a→0) we recover the well-known result of Onsager. We use the solution in the formulation of a model of photogeneration and fluorescence quenching in organic solids, with thermalization lengths which are comparable to the lattice spacing. As an illustration we analyze fluorescence quenching and quantum efficiency data for x-metal-free phthalocyanine, assuming the extreme case of complete internal conversion and no thermalization length. We discuss the form of the slope-to-intercept ratio for small applied fields determined from the solution for the generalized escape probability.
Noolandi et al. (Sun,) studied this question.