Theory of hydrogen permeability in nonporous silica membranes

Abstract The promising properties of silica-based H2-selective membranes have resulted in extensive experimental studies, but these investigations have provided limited information about the mechanism of gas permeation through these membranes. In this work we present a theory of permeation that describes the transport and physical properties of silica-based membranes of the Nanosil type. Nanosil membranes are obtained from the chemical vapor deposition of a thin silica layer on a porous support. The theory is adapted from an existing classical statistical mechanics treatment for vitreous silica glasses. It is found that in the Nanosil membranes the permeation of CO, CO2 and CH4 is inhibited relatively to that of smaller sized species such as hydrogen and the lighter noble gases. Moreover, the latter show an unusual order of gas permeation, He > H2 > D2 > Ne, which does not depend on the size or mass of the diffusing species. The theoretical description is based on jumps of the permeating species between solubility sites in a solid matrix, and assumes equilibrium sorption in the sites, random motion, and a transition state with two degrees of vibrational freedom and one degree of translational freedom. The adapted form of the theoretical equation has a term to account for the loss of rotational degrees of freedom for polyatomic species and is applicable to molecules such as H2 or D2. Agreement between theoretical values and experimentally determined points indicate that the model equations are effective in describing the unusual behavior of hydrogen and the light noble gases. The higher permeation rate of He over H2 or D2 can be accounted for by the larger number of solubility sites that can accommodate the smaller sized He atoms. The lower permeation rate of Ne is due to its lower jump frequency when compared with the vibrational frequency of the other species. The density of solubility sites and the jump distance are important parameters in this analysis. The amorphous structure of silica is formed of 5-, 6-, 7- and 8-membered Si–O bonded rings and gives rise to solubility sites whose size is approximately 0.3 nm. The jump distance should have an inverse relationship with the number of solubility sites per unit volume, but so far this has not been calculated explicitly. In this work, we apply the Perkus–Yevick treatment to a collection of randomly-distributed, non-interacting sites embedded in a solid to clarify this relationship. Our analysis shows that the jump distances used in previous descriptions of vitreous glasses are smaller than the predictions from an array of points of zero volume, which is not possible. On the other hand, the jump distances in our membranes were calculated to be around 0.8 nm, which are physically realistic. The number of solubility sites (Ns ∼ 1026 m−3) was found to be smaller by about one order of magnitude than in vitreous glasses, while the vibrational frequencies, stayed relatively unchanged. The activation energies for permeation through the silica membrane were also smaller than the ones through glass and indicate the presence of a totally different structure. The Nanosil membrane is probably formed of larger Si–O rings which give rise to more open and less dense structures.