Knudsen diffusion

Abstract: We report gas and water flow measurements through microfabricated membranes in which aligned carbon nanotubes with diameters of less than 2 nanometers serve as pores. The measured gas flow exceeds predictions of the Knudsen diffusion model by more than an order of magnitude. The measured water flow exceeds values calculated from continuum hydrodynamics models by more than three orders of magnitude and is comparable to flow rates extrapolated from molecular dynamics simulations. The gas and water permeabilities of these nanotube-based membranes are several orders of magnitude higher than those of commercial polycarbonate membranes, despite having pore sizes an order of magnitude smaller. These membranes enable fundamental studies of mass transport in confined environments, as well as more energy-efficient nanoscale filtration.

Abstract: Gas-producing mudrock systems are playing an important role in the volatile energy industry in North America and will soon play an equally important role in Europe. Mudrocks are composed of very fine grained particles, and their pores are very small, at the scale of nanometers. Gas production from these strata is much greater than what is anticipated given their very low Darcy permeability. In this paper, images of nanopores obtained by Atomic Force Microscopy (AFM) are presented for the first time. Gas flow in nanopores cannot be described simply by the Darcy equation. Processes such as Knudsen diffusion and slip flow at the solid matrix separate gas flow behaviour from Darcy-type flow. We present a formulation for gas flow in the nanopores of mudrocks based on Knudsen diffusion and slip flow. By comparing this new gas flow formulation and Darcy flow for compressible gas, we introduce an apparent permeability term that includes the complexity of flow in nanopores, and it takes the form of the Darcy equation so that it can easily be implemented in reservoir simulators. Results show that the ratio of apparent permeability to Darcy permeability increases sharply as pore sizes reduce to smaller than 100 nm. Also, Knudsen diffusion's contributions to flow increase as pores become smaller. Unlike Darcy permeability, which is a characteristic of the rock only, permeation of gas in nanopores of mudrocks depends on rock, gas type and operating conditions.

Abstract: An array of aligned carbon nanotubes (CNTs) was incorporated across a polymer film to form a well-ordered nanoporous membrane structure This membrane structure was confirmed by electron microscopy, anisotropic electrical conductivity, gas flow, and ionic transport studies The measured nitrogen permeance was consistent with the flux calculated by Knudsen diffusion through nanometer-scale tubes of the observed microstructure Data on Ru(NH3)6(3+) transport across the membrane in aqueous solution also indicated transport through aligned CNT cores of the observed microstructure The lengths of the nanotubes within the polymer film were reduced by selective electrochemical oxidation, allowing for tunable pore lengths Oxidative trimming processes resulted in carboxylate end groups that were readily functionalized at the entrance to each CNT inner core Membranes with CNT tips that were functionalized with biotin showed a reduction in Ru(NH3)6(3+) flux by a factor of 15 when bound with streptavidin, thereby demonstrating the ability to gate molecular transport through CNT cores for potential applications in chemical separations and sensing

Abstract: Microporous membranes with pore apertures below the nanolevel can exhibit size selectivity by serving as a molecular sieve, which is promising for overcoming Robeson s “upperbound” limits in membrane-based gas separation. Zeolites, polymers of intrinsic microporosity (PIMs), metal oxides, and active carbon are the typical materials used for this purpose. Metal–organic frameworks (MOFs) have attracted much research interest in recent years, and are emerging as a new family of molecular sieves. MOFs are novel porous crystalline materials consisting of metal ions or clusters interconnected by a variety of organic linkers. In addition to promising applications in adsorptive gas separation and storage or in catalysis, their unique properties, such as their highly diversified structures, large range in pore sizes, very high surface areas, and specific adsorption affinities, make MOFs excellent candidates for use in the construction of molecular sieve membranes with superior performance. The preparation of MOF membranes for gas separation is rapidly becoming a research focus. A number of attempts have been made to prepare supported-MOF membranes; however, progress is very limited and so far there are only very few reports of continuous MOF films on porous supports being used as separating membranes. Recently, Guo et al. reported a copper-net-supported HKUST-1 (Cu3(BTC)2; BTC= benzene-1,3,5-tricarboxylate) membrane exhibiting a H2/N2 selectivity of 7 [13] (separation factor of H2 over N2 is calculated as the permeate-to-retentate composition ratio of H2, divided by the same ratio for N2 as proposed by IUPAC) ; this is the first MOF membrane to show gasseparation performance beyond Knudsen diffusion behavior. Very recently, Ranjan and Tsapatsis prepared a microporous metal–organic framework [MMOF, Cu(hfipbb)(H2hfipbb)0.5; hfipbb= 4,4’-(hexafluoroisopropylidene)bis(benzoic acid)] membrane by seeded growth on an alumina support. The ideal selectivity for H2/N2, based on single permeation tests, was 23 at 190 8C. This higher selectivity, compared to the report from Guo et al., might be a result of the smaller effective pore size (ca. 0.32 nm of MMOF versus 0.9 nm of HKUTS-1), which results in a relatively low H2 permeance of this MMOF membrane (10 9 molm 2 s Pa 1 at 190 8C). The authors attributed this finding to the blockage of the onedimensional (1D) straight-pore channels in the membrane. Therefore, with regard to H2 separation, small-pore MOFs having three-dimensional (3D) channel structures are considered to be ideal membrane materials. Zeolitic imidazolate frameworks (ZIFs), a subfamily of MOFs, consist of transition metals (Zn, Co) and imidazolate linkers which form 3D tetrahedral frameworks and frequently resemble zeolite topologies. A number of ZIFs exhibit exceptional thermal and chemical stability. Another important feature of ZIFs is their hydrophobic surfaces, which give ZIF membranes certain advantages over zeolite membranes and sol–gel-derived silica membranes in the separation of H2 in the presence of steam. Very recently we reported the first result from permeation measurements on a ZIF-8 membrane. The ZIF-8 membrane showed a H2/CH4 separation factor greater than 10. Whereas the ZIF-8 pores (0.34 nm) are slightly larger than the kinetic diameter of CO2 (0.33 nm), and are very flexible, the H2/CO2 separation on this ZIF-8 membrane showed Knudsen selectivity. In the current work, we therefore chose ZIF-7 as a promising candidate for the development of a H2-selective membrane to satisfy the above requirements. ZIF-7 (Zn(bim)2) is formed by bridging benzimidazolate (bim) anions and zinc cations with soladite (SOD) topology. The pore size of ZIF-7 (the hexagonal window size in the SOD cage) estimated from crystallographic data is about 0.3 nm, which is just in between the size of H2 (0.29 nm) and CO2 (0.33 nm). We could therefore expect a ZIF-7 membrane to achieve a high selectivity of H2 over CO2 and other gases through a molecular sieving effect. In many cases, it was reported that the heterogeneous nucleation density of MOF crystals on ceramic supports is very low, 14] which makes it extremely difficult to prepare supported-MOF membranes by an in situ synthesis route. Chemical modifications of substrate surfaces have been proposed to direct the nucleation and orientation of the deposited MOF layers. Based on our knowledge in the development of zeolite membranes, we adopted a seeded secondary growth method for the ZIF-7 membrane prepara[*] Prof. Dr. Y.-S. Li, F.-Y. Liang, H. Bux, A. Feldhoff, Prof. Dr. J. Caro Institute of Physical Chemistry and Electrochemistry and the Laboratory for Nano and Quantum Engineering (LNQE) in cooperation with the Center for Solid State Research and New Materials, Leibniz Universit t Hannover Callinstrasse 3A, 30167 Hannover (Germany) Fax: (+49)511-762-19121 E-mail: yanshuo.li@pci.uni-hannover.de juergen.caro@pci.uni-hannover.de