Transport under confinement: Hindrance factors for diffusion in core-shell and fully porous particles with different mesopore space morphologies

Abstract We quantify confinement effects on hindered transport in mesoporous silica particles through using physical reconstructions of their mesopore space morphology obtained by electron tomography as geometric models in direct diffusion simulations for passive, finite-size tracers. Studied are fully porous particles with mean mesopore sizes of d meso  = 16.0 and 23.9 nm, prepared by classical sol–gel processing, and solid core–porous shell particles ( d meso  = 9.4 and 16.8 nm) originating from a layer-by-layer assembly of sol particles around a solid, impermeable core followed by thermal consolidation of the porous shell. Because shell thickness and core size are independently adjustable, core–shell particles allow to decouple the intraparticle diffusion distance in a fixed-bed reactor or chromatographic column from the external surface area of the particles and the hydraulic permeability of the bed, impossible with fully porous particles. Effective diffusivity, accessible porosity, and pore network connectivity recorded in the four reconstructions as a function of λ, the ratio of tracer to mean mesopore size, demonstrate an unfavorable shell morphology for the core–shell particles that opposes their design advantage over fully porous particles. The reconstructions reveal that core–shell particles contain an increased number of narrow and constricted as well as closed pores. These structural features reflect compacted and sintered packings and are most likely formed during shell consolidation. The presented expressions for hindered diffusion and accessible porosity can be used to optimize mesopore space morphologies in sensitive applications, e.g., catalysis under confinement and controlled drug release.