Pore roughness effects on self- and transport diffusion in nanoporous materials

There are important qualitative and quantitative differences between the parametric dependence of self- and transport diffusion in nanoporous materials. This is well recognized for microporous zeolites, where adsorption effects lead to a different concentration dependence of diffusion in the presence (transport diffusion) or the absence (self- or tracer diffusion) of a concentration gradient. In amorphous mesoporous materials, such differences are much less appreciated, but may become significant when the pore surface is rough down to molecular scales, as is the case, e.g. for many common sol–gel materials. By means of analytical calculations and three-dimensional dynamic Monte-Carlo simulations of Knudsen diffusion in model pores with random fractal surface roughness, it is shown how self-diffusion is strongly influenced by surface roughness, while transport diffusion is roughness independent. Agreement between analytical results and Monte-Carlo simulations is excellent. As many heterogeneous catalytic processes are diffusion limited, the molecular size dependence of Knudsen self-diffusion may significantly affect the selectivity of these processes. The results also have important consequences for the interpretation of experimental diffusion measurements in nanoporous materials.