Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Abstract

A new procedure for estimating surface diffusivities and tortuosities within realistic models of complex porous structures is reported. Our approach uses Monte-Carlo tracer methods to monitor mean-square displacements for molecules restricted to wander on pore walls within model random mesoporous solids typical of those used as adsorbents, heterogeneous catalysts, and porous membranes. We consider model porous solids formed from initial packings of spheres with unimodal, Gaussian, or bimodal distributions of size; changes in pellet porosity are achieved by increasing microsphere radii and by randomly removing spheres from highly densified packings in order to simulate densification and coarsening, respectively. Geometric tortuosities for the surface phase reached large values at void fractions near 0.04 and 0.42 for densified solids; the surface tortuosity gave a minimum value of 1.9 at a void fraction of ∼0.26. These high tortuosities correspond to percolation thresholds for the void and solid phases, which in turn reflect packing densities at which each phase becomes discontinuous. Surface tortuosities for coarsened solids at low void fractions were similar to those in densified solids; however, at void fractions above ∼0.3, surface tortuosities of coarsened solids increased only gradually with void fraction, because coarsening retains significant overlap among spheres at void fractions above those giving disconnected solids in densified structures. Simulations of bulk diffusion within voids were used to compare the transport properties and connectivity of the void space with those of surfaces that define this void space. Surface and void tortuosities were similar, except for void fractions near the solid percolation threshold, because unconnected solid particles interrupt surface connectivity but not gas phase diffusion paths. Surface and void tortuosities were also similar for channels within linear chains of overlapping hollow spheres as both tortuosities increased with decreasing extent of sphere overlap. These simulations provide a basis for estimates of surface and void tortuosities, which are essential in the interpretation and extrapolation of diffusion rates in complex porous media. Surface and void diffusivity estimates differed significantly from those obtained from lattice and capillary models of complex porous structures. © 2003 Elsevier Ltd. All rights reserved.