Deconvolution of Permeance in Supported Nanoporous Membranes Michael S. Strano and Henry C. Foley Dept. of Chemical Engineering, University of Delaware, Colburn Laboratory, Newark, DE 19716 Nanoporous membranes porous membranes generally having a porosity below 1 nm have attracted the attention of many researchers because of their potential for technologi- cal advances in gas separations and shape selective catalysis Ž . Saracco et al., 1994 . Permeation experiments often consti- tute a significant contribution to the characterization of these membranes. As the dimensions of a pore approach that of the molecule, transport generally becomes extremely sensi- tive to the molecular dimensions of the probe gas and very high separation factors have been reported for ceramic Ž . Ž . Vercauteren et al., 1998 , zeolite Bai et al., 1995 , and Ž nanoporous carbon membranes Rao and Sircar, 1993, . Acharya et al., 1997 of this type. Ž Several researchers Acharya et al., 1997; Bai et al., 1997; . Hayashi et al., 1997 have examined the dri®ing force normal - ized flux or permeance  of various molecular probes through these membrane systems J ss  s 1 Ž.  p in an attempt to ascertain the effect of molecular dimensions on the overalltransport observed through the membrane and thereby obtain information regarding the selective porosity. This parameter is convenient to measure and use since it is often difficult to define the actual thickness of the active membrane layer in these systems. This is especially true for supported nanoporous membranes where a portion of the membrane material resides within the macroporosity of the support and the interface is typically dominated by surface Ž irregularities and cracks Acharya et al., 1997; Hayashi et al., . 1997; Kusakabe et al., 1998 . The parameter is also used to describe diffusion over a range of linear transport regimes through these materials from the Knudsen mechanism to coupled adsorption and transport. Unfortunately, the permeance is an extrinsic parameter that generally contains a convolution of the effects of Correspondence concerning this article should be addressed to H. C. Foley. membrane porosity, active layer thickness, adsorption, and geometric influences. These effects must be isolated and con- trolled if any meaningful comparison with the observed gas separation factors is to be made as a function of membrane synthesis and permeation conditions. For example, Hayashi Ž . and co-workers 1997 attempted to correlate the observed permeance of gases through a series of carbonized polyimide membranes with the kinetic diameter of the molecular probe for different oxidation temperatures. However, in the ab- sence of knowledge concerning membrane thicknesses, ad- sorption, or variations in the porosityall of which may be strong functions of synthesis temperature a meaningful comparison of membranes in this way is impossible. Conceptually, it has been thought that the permeances of molecular probes through molecular sieving media arise from the transport of an adsorbed phase which migrates along the Ž surface in the direction of the overall driving force Ruthven . and Karger, 1992 . This surface transport has been described using the adsorbed phase concentration gradient as the driv- ing force and by defining a surface diffusion coefficient. Bar- Ž . rer and co-workers 1950 asserted that this surface flow oc- curs in parallel with Knudsen transport. The total flow through the medium was deconvoluted by first measuring the flow of a ‘‘nonadsorbing’’reference gas. The Knudsen contri- bution made by any other nonadsorbing gas was calculated using this flux and the known scaling of the Knudsen diffusiv- ity with molecular weight. The difference between the total flow and the so-called gas-phase flow was attributed to the surface flux. It is now generally recognized that this ‘‘calibra- tion gas’’method is flawed when applied to microporous me- dia. For example, using this method, researchers have ob- served that the surface flow contribution can apparently be negative and that the Knudsen or gas-phase component can appear to be activated with an Arrhenius-like temperature Ž . scaling Nicholson and Petropoulos, 1973; Shindo et al., 1983 . The current consensus is that transport through micro- porous, or, more appropriately, nanoporous systems, is char- acterized by surface diffusion almost exclusively in the low-temperature limit and an ‘‘activated gas-phase’’diffusion Ž at higher temperatures Nicholson and Petropoulos, 1973, . 1979, 1981; Shelekin et al., 1995 . The apparent activation March 2000 Vol. 46, No. 3 AIChE Journal 651