Permeation of gases through microporous silica hollow-fiber membranes: Application of the transition-site model

In a previous paper [P. Molyneux, “Transition-site” model for the permeation of gases and vapors through compact films of polymers, J. Appl. Polym. Sci. 79 (2001) 981–1024] a transition-site model (TSM) for the activated permeation of gases through compact amorphous solids was developed and applied to organic polymers; the present paper examines the applicability of the TSM to permeation through microporous silica. The basis of the TSM theory for amorphous solids in general is outlined; the present extension to inorganic glasses has revealed that the transition sites (TS) of this theory, which are the three-dimensional saddle-points critical in the molecular sieving action, equate to the doorways long recognized in permeation through amorphous silica and other inorganic glasses. The TSM, which views permeation as a primary process, is contrasted with the conventional sorption–diffusion model (SDM) for permeation. It is pointed out that in the SDM, the widely accepted analysis into two apparently distinct factors – sorption (equilibrium) and diffusion (kinetic) – has the fundamental flaw that these factors are not independent, since both involve the sorbed state. By contrast, the TSM focuses on the permeant molecule in only two states: as the free gas, and as inserted in a doorway D; hence the characteristics of these doorways – (unperturbed) diameter σ_D, spacing λ, and the thermodynamic parameters θ (force constant) and ν (entropy increment) for the insertion process – can be evaluated. The theory is applied to literature data [J.D. Way, D.L. Roberts, Hollow fiber inorganic membranes for gas separations, Sep. Sci. Technol. 27 (1992) 29–41; J.D. Way, A mechanistic study of molecular sieving inorganic membranes for gas separations, Final Report submitted to U.S. Department of Energy under contract DE-FG06-92-ER14290, Colorado School of Mines, Golden, CO, 1993, www.osti.gov/bridge/servlets/purl/10118702-ZAx4Au/native/1011872.pdf; M.H. Hassan, J.D. Way, P.M. Thoen, A.C. Dillon, Single component and mixed gas transport in silica hollow fiber membrane, J. Membr. Sci. 104 (1995) 27–42] on the permeation through microporous silica hollow-fiber membranes (developed by PPG Industries Inc.) of the nine gases: Ar, He, H₂, N₂, O₂, CO, CO₂, CH₄ and C₂H₄, over the temperature range 25–200 °C. The derived Arrhenius parameters for the permeation of these gases (excepting He) lead to estimates of the four doorway-parameters: σ_D, 125 pm; λ, ca. 30 nm; θ, 0.43 nN; ν, 1.7 pN K⁻¹; these values lie within the ranges of those obtained with the glassy organic polymers. Some “secondary effects”, shown particularly by CO and CO₂, are interpreted as host–guest interactions at the doorway. The behavior of He is anomalous, the permeation rising linearly with temperature. This study confirms that the TSM may be applied to gas permeation by activated molecular sieving for this type of inorganic membrane.