Knudsen Self- and Fickian Diffusion in Rough Nanoporous Media

The effect of pore surface roughness on Knudsen diffusion in nanoporous media is investigated by dynamic Monte-Carlo simulations and analytical calculations. A conceptual difference is found between the roughness dependence of the macroscopic, transport diffusivity and the microscopic, selfdiffusivity, which is reminiscent of diffusion in zeolites, where a similar difference arises due to adsorption effects and intermolecular interactions. Because of the dependence of the self-diffusivity on molecular residence times, self-diffusion may be roughness dependent, while transport diffusion is not. Detailed proofs are given. The differences become significant when the pore surface is rough down to molecular scales, as is the case, e.g., for many common sol-gel materials. Simulations are in good agreement with analytical calculations for several tested rough, fractal pore structures. These results are important for the interpretation of experimental diffusion measurements and for the study of diffusionreaction processes in nanoporous catalysts with a rough internal surface.