Geminate recombination in proton-transfer reactions. III. Kinetics and equilibrium inside a finite sphere

The kinetics of reversible dissociation of a single ion pair inside a finite sphere is described by the transient solution of the Debye-Smoluchowski diffusion equation, with backreaction boundary conditions at contact, and a reflective boundary condition at the sphere's radius. At long times the solution tends to an equilibrium state. A simple analytic expression for the equilibrium coefficient is derived. For an infinitely large sphere ("infinite dilution") it reduces to an expression similar to that of Fuoss, while its dependence on the sphere's radius is qualitatively similar to the concentration dependence of activity coefficients.