Diffusion-controlled ion recombination in multipair clusters in low-permittivity solvents

A master equation formalism is presented which describes the evolution of the number of reactive particles in a multipair spur. This technique is particularly appropriate for modeling ion combination in low-permittivity solvents. For the simple case where all the cation-anion distances are identically distributed, the equations can be solved analytically in terms of the geminate survival probability. An analytic solution for the free-ion yield from an ensemble of isolated clusters also follows. Solutions are compared with simulation results and with other models of the same process.