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

Abstract

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 D eff 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 D eff with increasing tracer size. Comparison with theoretical models of hindered diffusion in a single uniform, cylindrical pore reveals that these models significantly overestimate D eff 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.

Molecular Dynamics Simulation of Water Confinement in Disordered Aluminosilicate Subnanopores

“…Therefore, the water properties in simplified ordered pores are not applicable to understanding the confinement effects in such systems. Confined water in disordered silicate-water systems has only been discussed in a few MD simulations 23 – 25 . Water in disordered calcium silicate hydrated gels shows slower diffusion than water in ordered pores 23 .…”

Transport properties and size exclusion effects in wide-pore superficially porous particles

“…(5) and (9) so that it should hold in the present work is unsurprising. However, the same correlation is evident in a separate work using a different geometry, a silica monolith, and different methods for calculating effective diffusion and accessible porosity (Hlushkou et al, 2017). This coincidence recalls Renkin (1954), who defined the dimensionless accessible area, A/A 0 , and studied its correlation with experimentally measured diffusion.…”

“…D eff is the effective diffusion coefficient in a silica monolith from Hlushkou et al (2017). D SPP is intraparticle effective diffusion in the present work.…”

“…The effect of molecule size in restricted diffusion is well-known from theoretical studies of pore diffusion (Brenner and Gaydos, 1977; Dechadilok and Deen, 2006; Carta and Jungbauer, 2010). In a recent study of size exclusion in silica monolithic media, Brownian Dynamics (BD) was used to evaluate effective diffusion in reconstructed media for a wide range of λ , and the results were compared with standard filtration theory (Hlushkou et al, 2017). The agreement was good for small values of λ but, like Wernert et al (2010), they found a straightforward application of theory tended to overpredict effective diffusion for larger values of λ .…”

Analysis of Tortuosity in Compacts of Ternary Mixtures of Spherical Particles

“…It is defined as the ratio of the shortest path between two endpoints through the porous compact to its Euclidean length here with . The tortuosity can be obtained experimentally via direct measurements of diffusion fluxes throughout a porous membrane using diffusion cells, i.e., the Graham and Wicke-Kallenbach cells [ 31 ], and through numerical algorithms such as fast marching method [ 32 ], Lattice-Boltzmann method (LBM) [ 33 ], random walk method [ 33 , 34 , 35 , 36 ], pore centroid method [ 14 , 30 , 37 ] and recently path searching algorithms [ 38 ] and A-star algorithm [ 39 ]. Another option is to directly model the transport processes through the reconstructed microstructure applying methods of computational fluid dynamics [ 30 , 40 , 41 ].…”