Continuous-time-random-walk in three dimensions as a model for electron scavenging and ion recombination in liquids

Time-dependent rates of electron scavenging reactions were calculated using the model of continuous-time-random-walk (CTRW) of Montroll and Weiss for the hopping time distribution functions of an exponential form and a few nonexponential forms. The result was applied to the charge neutralization reaction using the Laplace transform technique. It was found that the rate constant in the CTRW model is smaller than the Smoluchowski transient rate, but is larger than the time-independent (asymptotic) value at the time scale which is comparable or shorter than the average jump time. The differences in the decay pattern and the survival fraction of electrons between the CTRW model and the Smoluchowski treatment are much less than those in the rate constants themselves