Accessibility of a Catalyst’s Fractal Surface to Diffusing and Reacting Molecules

Abstract

Many porous catalysts have a fractal internal surface on molecular scales. Similar to a natural coastline, the fractal roughness of the surface creates a cascade of fjords along the pores. In a heterogeneously catalyzed reaction, molecules diffuse through the pores and react on the surface. Because of the fractal cascades of fjords along the pores, some points on the catalyst’s internal surface are more easily reached than other points. This influences the diffusion of molecules through the pore space and leads to a nonuniform reaction probability distribution over the surface. Gas diffusion within a cascade of fjords is mainly Knudsen diffusion, so that the results are fundamentally different when compared to the often studied molecular diffusion or analogous phenomena, like conduction. The obtained results are useful in the investigation of whether important diffusion limitations within the fjord cascades along a fractal catalyst surface exist, and, if so, on which subset of the surface the active phase may be concentrated without altering the effective reaction rate.