Tracer-Size-Dependent Pore Space Accessibility and Long-Time Diffusion Coefficient in Amorphous, Mesoporous Silica

Heterogeneous porous materials are widely used as fixed beds in adsorption, separation, and catalysis. An important aspect of mass transport in these materials is the hindrance to diffusion of molecules with dimensions approaching the pore size. We numerically study hindered diffusion of finite-size, passive (i.e., nonadsorbing, nonreacting) tracer particles in physically reconstructed amorphous, mesoporous silica from a hierarchical, macroporous–mesoporous silica monolith. The long-time, effective diffusion coefficient Deff is determined as a function of λ, the ratio of the tracer diameter to the average size of the mesopores. Results demonstrate a strong reduction of Deff with increasing tracer size. Comparison with theoretical models of hindered diffusion in a single uniform, cylindrical pore reveals that these models significantly overestimate Deff for λ > 0.2. Morphological analysis of the mesopore pore space accessible for finite-size tracers shows that its effective geometrical and topological properties are a function of λ. The nonuniform distribution of mesopore size results in an increased fraction of pores that become impermeable for larger tracers. As a consequence, not only is the accessible mesopore space (porosity) reduced for larger values of λ but also the connectivity of the accessible pore network decreases. Thus, in contrast to a single uniform pore, an increase of tracer size leads to two complementary effects in a heterogeneous porous medium: a constriction of the accessible pore space in individual pores and a reduction of the number of available diffusion paths in the pore network.