Modeling of Aqueous Transport in Rigid Porous Matrices near the Percolation Threshold

Abstract

To demonstrate control of passive diffusion of small molecules through rigid ceramic matrices via manipulation of matrix porosity near the percolation threshold, and to model such control using percolation scaling relationships on both infinite and finite lattices. Rigid alumina disks of controlled porosity were prepared using standard ceramic casting and sintering techniques. Structural void space distributions in sintered disks were measured by dimensional and volume displacement (pycnometry) methods. The impact of void space on transport was determined by tracking the diffusion of ionized benzoic acid across sintered disks mounted in Stokes diffusion cells. Critical percolation thresholds were estimated by fitting structural and transport-dependent results to percolation scaling relationships. Finite-size scaling studies were performed by adding polymer microspheres of known diameter to the disks to generate artificially large pores. Nonlinear least squares techniques were used to fit both structural and transport-dependent properties of rigid alumina disks to total disk porosity using percolation scaling relationships. The critical percolation threshold determined from structural properties (0.129) was lower than that determined from benzoic acid transport (0.169). The transport-derived percolation threshold exactly matched that expected for a tetrakaidecahedral (14 sided) lattice. Finite-size scaling was demonstrated through a nonzero effective volume fraction for transport at the percolation threshold. Manipulation of total disk porosity near the percolation threshold was shown to be a suitable means of controlling the transport rate of a model small molecule, while deliberate enlargement of individual pores was demonstrated to decrease this threshold without increasing total porosity. The lower-than-expected percolation threshold obtained from the structural model was ascribed to limitations of the measurement technique. The threshold determined from the aqueous transport model was concluded to represent the true threshold for this system.