Breakdown of the Debye theory of bulk ion recombination

We have investigated how the rate of diffusion-controlled bulk recombination between electrons and positive ions is influenced by the mean free path of electrons. By use of the Monte Carlo method previously developed we have calculated the rate constant as a function of the mean free path. For mean free paths negligibly short compared with the Onsager length, the rate constant increases linearly with increasing mean free path, in agreement with the Debye theory of bulk ion recombination. However, as the mean free path further increases, the rate constant goes through a maximum and then decreases. The present result quantitatively explains recent experimental data on electron–ion recombination rate constants in liquid methane in which the mean free path of electrons is comparable with the Onsager length.