Diffusion and magnetic relaxation in model porous media

Diffusion and magnetic relaxation are studied in computer-generated model two-dimensional porous media whose three-dimensional analogs resemble commercially prepared Vycors and aerogels. When diffusion rates are compared for two different samples, one with average pore diameter much shorter than the other but with the same porosity, a crossover is observed where the asymptotic long-time diffusion rate D(t) for the smaller pore becomes larger than the bigger one. However, this crossover disappears for relatively larger pores of fixed porosity. Physically, this crossover is a characteristic of change surface morphology where for a fixed porosity, pore diameters could be made bigger but at the cost of separating the pores from each other by thin but more ordered walls, linked to each other with very narrow necks. This results in a net decrease in the long-time diffusion constant. We have also been able to relate this crossover to the absence of dynamical scaling for the structures. Adding a surface relaxation term at the pore walls increases the effective diffusion rate at early times. We compare our simulation results for the model systems, wherever possible, with some of the general results for porous media obtained analytically.