Hindrance Factor Expression for Diffusion in Random Mesoporous Adsorbents Obtained from Pore-Scale Simulations in Physical Reconstructions

Hindered diffusion of solutes is the rate-limiting step in many processes for which random porous media play a central role as providers of adsorbing or reactive interfaces. The key to an optimized layout of these processes is the knowledge of the overall diffusive hindrance factor H(λ) = D_eff,H(λ)/D_m, which quantifies the degree to which diffusion through a material (represented by the effective diffusion coefficient D_eff,H) is hindered compared with diffusion in the bulk liquid (represented by D_m) in dependence of λ, the ratio of solute size to mean pore size. To arrive at an adequate hindrance factor expression for random mesoporous silica, we use electron tomography to physically reconstruct the mesopore space of three macro-mesoporous silica monoliths. The samples share the same general mesopore shape and topology at varied mean feature size, as established by morphological analysis, and serve as realistic models in pore-scale simulations of hindered diffusion. From a large set of D_eff,H(λ) values for 0 ≤ λ ≤ 0.9, we derive a quantitative expression for H(λ) that captures the morphological evolution (in dependence of λ) and allows a prediction of the extent of hindered diffusion from material properties. We propose the expression for structures of similar morphology as the investigated samples, which potentially encompasses all mesoporous silica materials obtained through sol–gel processing.