Temporal evolution of an ion pair with a perfectly reflecting recombination sphere

Abstract We have examined the temporal evolution of an ion pair with fully suppressed geminate recombination. For this purpose, the Smoluchowski–Debye equation for a pure Coulomb potential with a reflecting boundary condition on the recombination sphere has been solved numerically and analytically (in the last case, only approximately). It has been shown that the probability of the pair non-dissociation decreases in time roughly as a power law. We also discussed the applicability of the conductivity method for studying the non-Langevin recombination in low mobility solids. An example of such an analysis is given for one technical polymer. The relation of these results to the concept of the coulombic traps has also been discussed.