Isothermal and thermo-osmotic transport of sorbable gases in microporous carbon membranes

Abstract

With the use of helium and a series of gases adsorbed to give dilute films, measurements have been made of thermo-osmotic steady-state pressure ratios established across microporous carbon membranes through which linear temperature gradients were maintained. Two contrasting adsorbents were employed: Carbolac I, a carbon black having an energetically heterogeneous high area surface and Graphon, a graphitized carbon black of one-tenth the surface area of Carbolac but energetically homogeneous. Complementary studies of isothermal transport of the gases through the membranes and determination of equilibrium adsorption isotherms at all temperatures employed for the flow experiments were required in order to analyse the non-isothermal experimental results. Part I is concerned with the equilibrium properties of the adsorbed films. Henry’s law constants, k, energies of adsorption, A E'and isosteric heats of adsorption, for the Gibbs excess adsorption were derived from the experimental isotherms. Taking the thickness of the adsorbed layer as one molecular diameter, the corresponding energies, A E,and heats qBt for absolute adsorption have been calculated. For the very dilute films the ratios AE'jAE and q'BtlqBt can differ appreciably from unity. Also in the Henry law range, values of the thermodynamic equilibrium constants and standard energies, AE&, and entropies, A for absolute adsorption have been evaluated. A linear relation between AS& and AE&, was observed. — A was considerably larger on Carbolac than on Graphon surfaces. This has been interpreted in terms of greater mobility of the adsorbed molecules on the more homogeneous Graphon surface. Good correlations have been found between K or A Eand properties, such as polarizability, a, related to the condensability of the sorbates. Part II is concerned with isothermal transport of the gases through the membranes. For the majority of systems studied the permeability, K and time-lag, L, were independent of pressure. For helium in both membranes the ratio K/^T was independent of temperature and pressure, indicating transport only in the gas phase and the absence of a viscous flow component. For an adsorbed gas the extra flux generated by the mobile adsorbed films per unit area of surface, JJA, were considerably greater for the more homogeneous Graphon membrane. Diffusion coefficients associated with the extra fluxes also indicated greater mobility of adsorbed molecules on the more homogeneous surface. Good correlations between K{MT)^ and ke have been demonstrated and, at constant temperature, a linear relation was observed between KM$ and the product, aTb, of polarizability and boiling-point TB. Gas-phase structure factors obtained by the procedure of Barrer & Gabor (1959) were considerably less than unity, indicating a dominant influence in each membrane of tortuosity and bottlenecks. For each membrane a linear relation has been demonstrated between the products KL and kB from which parameters associated with blind pore character have been obtained. Part III is concerned with the thermo-osmotic transport of the gases in the membranes. The nonisothermal flow is formulated in terms of the thermodynamics of irreversible processes and relations derived between the straight phenomenological coefficients of this treatment and the permeabilities and diffusion coefficients of part II. Equations are also presented relating the overall heat of transport, Q0, at temperature T0 to component heats of transport for the gas-phase flow (Qg, Q*) and extra flow (QB, Q*). In none of the systems studied did Q0 = — %RT0, the ideal value expected for a gas transported by molecular streaming (Knudsen flow). For He, H 2 and Ne in the Carbolac membranes, — ifiRT0 where /?, for a particular gas, is a constant < 1. With increasing sorbability of the flowing gas the temperature dependence of Q0 was progressively modified until, in the presence of substantial extra flow, — Q0 decreased strongly with increasing T0. Calculations of Qs and Q* are presented for the two limiting cases Q e— and Qg = 0. It is shown that Qs must always be negative and positive. A procedure for calculating isobaric permeabilities, utilizing a combination of thermo-osmotic steady-state and isothermal steady-state measurements, has been developed. For various pairs of gases, the ratios of isobaric permeabilities differed greatly from the corresponding ratios of isothermal permeabilities. Enhanced separations of sorbable mixtures by isobaric flow appear to be possible especially for the Graphon membrane.