EFFECTS OF LONG-RANGE ELECTRON-TRANSFER ON CHARGE-TRANSPORT IN STATIC ASSEMBLIES OF REDOX CENTERS

Simulations employing random walks of electrons on distributions of redox molecules in square and simple cubic lattices have been performed to evaluate the influence of long-range electron hopping on the dynamics of charge transport in static assemblies of redox centers. For electron exchange solely between molecules in contact, classical percolation behavior is observed. Electron hopping across distances larger than the contact distance leads to nonzero rates of charge propagation, as measured by an apparent diffusion coefficient, D(ap), at all concentrations of electroactive centers, including concentrations below the percolation threshold. In the limit where the rate of electron hopping becomes relatively insensitive to the distance separating the reactants, D(ap) is found to be directly proportional to the total concentration of redox centers. The results of simulations performed by using parameters appropriate for real systems indicate that at redox concentrations above the percolation threshold D(ap) differs only slightly from that expected for simple percolation behavior; below the critical concentration, charge transport over macroscopic distances still occurs but D(ap) diminishes rapidly toward zero as the concentration of redox centers decreases.