Diffusion coefficients in nanoporous solids derived from membrane permeation measurements
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Diffusion coefficients in nanoporous solids derived from membrane permeation measurements Juergen Caro1,2,3 Received: 13 July 2020 / Revised: 26 August 2020 / Accepted: 2 September 2020 © The Author(s) 2020
Abstract Based on the molecular understanding of the interplay of diffusion and adsorption, new membrane materials can be developed and the operational conditions of gas separation membranes can be optimized. Therefore, numerous diffusion and adsorption studies are conducted to optimize membrane materials. However, in an opposite way, transport or Fickian diffusion coefficients DT can be derived from membrane permeation studies with surprising accuracy. From measuring the gas transport through nanoporous supported thin-layer membranes or through mixed matrix membranes with nanoporous fillers in a polymer matrix, the transport diffusion coefficients DT of gases in novel nanoporous materials such as zeolites, MOFs, COFs… can be estimated. Keywords Transport diffusion coefficient · Permeation through nanoporous membrane · Mixed matrix membrane · Supported molecular sieve membrane Symbols C1 Constant concentration of the starting side of the plate in a time lag experiment [mol m−3] D Self-diffusion coefficient (self-diffusivity) [m2 s−1] DT Transport or Fickian diffusion coefficient (diffusivity) [m2 s−1] Di Diffusion coefficient of gas i in a material [m2 s−1] D0 Corrected diffusivity after Darken [m2 s−1] Hi Adsorption (Henry) constant [mol or cm3 gas (STP) m−3 bar−1] MMM Mixed matrix membrane as a composite of a polymer and an porous filler Pc Permeability of the pure continuous polymer of an MMM [mol m−1 s−1 bar−1] Pd Permeability of the pure dispersed nanoporous material in an MMM [mol m−1 s−1 bar−1] * Juergen Caro [email protected]‑hannover.de 1
Saxon Academy of Sciences and Humanities, 04107 Leipzig, Germany
2
School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, China
3
Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, 30167 Hannover, Germany
Pi Permeability of a membrane (see Table 1) [mol m−1 s−1 bar−1] Qt Amount of gas which has passed a membrane after time t in time lag experiment [mol] Si Solubility of gas i in the polymer [cm3 gas (STP) m−3 bar−1] ji Flux (density) through a membrane (see Table 1) [mol m−2 s−1] l Thickness of a plate in a time lag experiment [m] pi Pressure or partial pressure of gas i [Pa or bar] Greek symbols Π Permeance (see Table 1) [mol m−2 s−1 bar−1] Δpi (Partial) pressure difference of gas i over the membrane [Pa or bar] αsol(A,B) Solubility-selectivity of a membrane for binary mixture A/B αdiff(A,B) Diffusion-selectivity of a membrane for binary mixture A/B αA,B Membrane selectivity (see Table 1) φd Volume fraction of the dispersed filler in an MMM δ Thickness of a membrane [m] 𝜕c Concentration gradient in x-direction [mol m−4] 𝜕x
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Vol.:(0123456789)
Adsorption
1 Gas permeation through membranes and the role of diffusion
(Kärger and Ruthven
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