CLUSTER APPROACH TO SIMULATING HOPPING IN RANDOM MEDIA

A simple cluster method for simulating hopping transport in dilute three-dimensional random systems has been developed to examine dispersive charge transport in glasses and energy transfer in isotopically mixed crystals. To determine the concentration and time dependence of the diffusion, we compare our results to the well-known problem of heat conduction in a sphere with the surface held at zero degrees. Our results indicate that dispersive transport can occur in dilute random systems because some of the hopping particles may not be able to avoid paths which include hard hops. For the parameters used in these simulations, at least 20% of the diffusing particles are responsible for the long dispersive tail. We have applied our cluster method to the problem of triplet migration in benzene-deuterate-benzene crystals. From these simulations we obtain very good agreement with the experimental results on threshold and shape of the concentration dependence of the energy-transfer efficiency. © 1979 The American Physical Society.