Review on Mechanisms of Gas Permeation through Inorganic Membranes

Abstract

The major mechanisms of gas permeation through solid membranes are described and the applicable equations describing the permeance are presented. The mechanisms depend on the relative size of the permeating molecules and the diameter of the pores. As pore size decreases the operable mechanisms are Hagen-Pouiselle flow, Knudsen diffusion, surface diffusion, gas-translation, and finally solid-state diffusion. The Hagen-Pouiselle mechanism involves flow through large pores, while the Knudsen mechanism involves collision of molecules with the walls of pores of intermediate size. Surface diffusion deals with movement of molecules trapped in the potential field of the walls of pores of relatively small size, while gas-translation involves molecules that can escape the field, but are constrained by the small pores. Finally, solid-state transport comprises dissolution and transport by diffusion within the solid. These mechanisms are illustrated for hydrogen permeance with the use of two membranes, an alumina membrane with intermediate sized pores and a silica on alumina membrane of dense structure. KeywordsPermeation mechanism, Inorganic membrane, Silica membrane, Solid-state diffusion, Glassy membranes mechanism, Hydrogen However, oftentimes the actual selectivity can deviate strongly from that defined above because of interactions between the species with each other or with the walls of the membranes. For example, the preferred adsorption or absorption of one species in the pores of a membrane can block the passage of other species. Thus, single-gas selectivities should be taken as a limiting case approximation.A fundamental expression for transport in membranes is derived from Fick's First Law, which relates the flux of species i to the concentration gradient. The gradient in turn can be related to the concentration in the inlet, cio and outlet, ciL, of a membrane of thickness L:The diffusivity in Fick's first law is the ordinary molecular diffusivity, Di(c) [m 2 ・s-1 ], which may have a concentration dependence. In the case of membranes an effective diffusivity, De,i is used, where the porosity ε and tortuosity τ of the membrane are included. The tortuosity is a factor that accounts for the increased length of a pore by the presence of twists and turns. For example, if a single straight pore is replaced by one having a single 90° turn, the tortuosity would be 2 or 1.4. In an early treatment the relative diameters of the diffusing molecules, dm, and pores, dP, was taken into account through a restrictive factor KrFor many membranes dm/dp is small, so Kr is unity. There have been many proposed mechanisms with a variety of materials based on various interaction and diffusion processes. These mechanisms are in broad terms distinguished by the ratio of pore diameter dp to kinetic diameter dm of the gas molecule. As the pore diameter becomes smaller, that is with increasing value of dm/dp, the interactions between the molecule and the surface become larger in proportion to the ratio of the area of the surface potential fi...

Mechanism of Gas Separation through Amorphous Silicon Oxycarbide Membranes

“…The calculated fitting curve and experimental data match quite well for all species except for H 2 at 200 C. A comparison between the values of the parameters obtained in this work and in the existing literatures is done in the following. The calculated N s value for He was found to be higher than the corresponding 1.0x10 value obtained for SiO 2 (1), [49] but lower than that of another SiO 2 (2), [54] see Table 1. SiO 2 (1) and SiO 2 (2) nomenclature are given here for our convenience.…”

“…Levenberg-Marquardt method was applied for model fitting using Origin 8.0 software. Jump distance, d ¼ 0.8 nm [49] was used for model fitting.…”

“…[20,49,53] Surface diffusion generally occurs at low temperature, when the interaction between the gas molecules and the pore-wall surface becomes stronger compared to the kinetic energy of gas molecules and therefore they cannot escape from the surface potential fields of the pore-wall. Diffusion of gases through microporous materials is described by gas-translational diffusion mechanism, which is a combination of the Knudsen diffusion and surface diffusion, also called as activated Knudsen diffusion mechanism.…”

“…In this mechanism, the permeating molecules are assumed to reside in the solubility sites as well as in equilibrium with the surrounding gas molecules. [49] Gas molecules, vibrating at solubility sites with a characteristics frequency, jump to an adjacent solubility site by surmounting a potential barrier. As shown above, the permeance order of He and H 2 does not show a direct dependence on the size and mass of molecules as well as temperature ( Figure 6).…”

“…3) is indicated in Equation 4. [49,54] The calculated parameters after fitting the permeance data are summarized in Table 2.…”