Hindrance of solute diffusion within membranes as measured with microporous membranes of known pore geometry

Abstract

1. 1. Mica sheets were made into membranes by a process of bombardment with fission fragments from a U 235 source and subsequent etching with hydrofluoric acid. Pores formed by this process were essentially straight through the membrane, extremely uniform in size and elliptical in cross-section. On eight of these membranes, with pore radii ranging from 45 to 300 Å, air flow, water flow, and diffusion rates for a graded series of 7 solutes were measured. From measurements of the diffusion rate of mostly non-electrolytes, with radii between 2.5 and 22.5 Å, the true hindrance effect on diffusion within pores was determined. 2. 2. Restriction of diffusion for even relatively small solutes is a very significant effect and can be adequately described by the Renkin equation D m/ D 0 = (1−R s/R p 2×(1−2.104 R s/R p + 2.09 (R s/R p−0.95 (R s/R p) 5) for membranes which have well-defined, straight through pores, where D m/ D 0 is the ratio of solute diffusivity in the membrane to that in free solution, and R s / R p is the ratio of solute radius to pore radius. An approximation to the Renkin equation, D m/ D 0 = (1−R s/R p) 4 , which is much simpler to use, correlates as well with the data in the range 0 < R s / R p < 0.2. 3. 3. Water flow under small pressure drops is well described by the assumption of Poiseuille flow for this range of pore diameters, and therefore no effects due to “anomalous” water were apparent. 4. 4. In most membrane operations there is a considerable resistance to diffusion due to the presence of a liquid film boundary layer along the surface of the membrane. This boundary layer resistance was not inversely proportional to the solute diffusivity as has often been assumed in the “unstirred layer” theory, but instead was found under these experimental conditions to be proportional to the −0.6 power of the solute diffusivity. 5. 5. Boundary layer diffusion resistances were obtained by two independent methods: an electrochemical polarographic method and a membrane substitution method using membranes of known permeability to calibrate the diffusion cell. 6. 6. Heteroporous membranes do not differ from isoporous membranes very much in regard to the relative hindrance of solute molecules, as long as the ratio of solute radius to mean pore radius is less than 0.2. For larger solute molecules, heteroporous membranes become increasingly less effective in hindering diffusion rates through the membrane.