DIFFUSION IN A RANDOM MEDIUM - A MONTE-CARLO STUDY

We use lattices with randomly distributed site-barrier energies to study diffusion properties as a function of disorder and temperature. We study the case of ''dynamic'' disorder whereby the random environment is renewed at each successive jump of the hopping particle, and also the case of ''static'' disorder with frozen randomly distributed barriers. The transition characteristics are governed by Boltzmann statistics. We employ standard Monte Carlo techniques to monitor properties such as the mean-square displacement. The trends of the motion are shown to include local trapping at early times, allowing for the search of a crossover time to the conventional diffusive regime, [R2] is similar to, as a function of temperature. We find that the crossover time versus temperature dependence is of the Arrhenius type determined by an effective activation energy barrier for percolation in the case of static disorder. For a uniform distribution of the barriers, this activation barrier is shown to coincide with the threshold concentration for bond percolation, as simple arguments suggest. We also demonstrate that an increase in the degree of dynamic disorder leads to an increase in the particle mobility. Some relationships of the present model to several experimental systems are discussed.