Sorption kinetics: measurement of surface resistance
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Sorption kinetics: measurement of surface resistance Douglas M. Ruthven1 · Jörg Kärger2 · Stefano Brandani3 · Enzo Mangano3 Received: 10 June 2020 / Revised: 14 August 2020 / Accepted: 18 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The problem of measuring sorption kinetics in microporous adsorbents and distinguishing experimentally between surface resistance and internal diffusion is discussed and reviewed with reference to several commonly used experimental techniques; direct uptake rate measurements, zero length column (ZLC), frequency response, PFG NMR and interference microscopy. Keywords Intra-crystalline diffusion · Surface resistance · Frequency response · PFG NMR · ZLC · Interference microscopy · Uptake rates Abbreviations c External gas phase concentration of adsorbing component D Intra-crystalline diffusivity F Flow rate f Fraction of open pore mouths g Magnetic field gradient K Dimensionless adsorption equilibrium constant k Surface permeance (ratio of flux/concentration difference over surface layer) L Dimensionless parameter defined in Eq. 11 L´ Defined by Eq. 12 ℓ Half thickness of adsorbent crystal m Measure of intensity of field gradient pulses (= δg) mt/m∞ Fractional approach to equilibrium (= γ in Eq. 15) q Adsorbed phase (intra-crystalline) concentration of adsorbing component − q Average value of q within crystal R Crystal radius (or equivalent radius) t Time VF Volume of fluid phase within the ZLC cell
Vs Volume of (solid) adsorbent in ZLC cell δ Thickness of surface layer; field gradient pulse width (PFG NMR)—see Eq. 15. η See Eq. 14 λ kℓ/D (Dimensionless parameter) τ Time constant—see Eq. 10 ψ PFG NMR signal intensity—see Eq. 15 ω Angular frequency
* Douglas M. Ruthven [email protected]
The most obvious approach to the study of adsorption kinetics is to measure the transient uptake/release curve for a small sample of adsorbent in response to a step change in the pressure (or partial pressure) of the sorbate. The response curve is then matched to an appropriate kinetic model to determine the relevant parameters. For an isothermal
1
Department of Chemical Engineering, University of Maine, Orono, ME 04469, USA
2
Faculty of Physics and Geosciences, University of Leipzig, 04103 Leipzig, Germany
3
School of Engineering, University of Edinburgh, Edinburgh EH9 3JL, UK
In early studies of microporous adsorbents it was commonly assumed that the sorption kinetics were controlled by intraparticle diffusion. For slow systems this assumption is often correct but the possibility of significant surface resistance should not be excluded a priori since surface resistance is in fact quite common, especially when diffusion is rapid. The purpose of this paper is to summarize and review the approaches that can be used to confirm the rate controlling mechanism and to determine surface rate coefficients from some of the more common experimental techniques for studying sorption kinetics and micropore diffusion.
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