Surface barriers and symmetry of adsorption and desorption processes
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Surface barriers and symmetry of adsorption and desorption processes German Sastre1 · Jörg Kärger2 · Douglas M. Ruthven3 Received: 8 May 2020 / Revised: 25 August 2020 / Accepted: 27 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Adsorption and desorption of hydrocarbons in a realistic model (2496 atoms) of ZSM-5 zeolite (MFI), including an external surface and a reservoir for molecules, have been studied using classical molecular dynamics, with special focus on surface barriers. Different degrees of surface blocking have been modeled according to experimental observations. Using previous molecular dynamics results, from the analysis of adsorption and desorption path lengths, we demonstrate that surface barriers are symmetric, i.e. with equal paths for desorption and adsorption, in agreement with the principle of microscopic reversibility and in contradiction with a model proposed recently. A new thermodynamic analysis confirms the symmetry of adsorption/desorption paths. Keywords Zeolites · Silicalite · MFI · Surface barriers · Diffusion · Molecular dynamics · Adsorption · Microporous materials Abbreviations D (Transport or Fickian) diffusivity (cm2s−1) K Surface permeance (cm·s−1), defined by Flux = k·Δc (‘c’ is concentracion) ka and kd Adsorption and desorption rate constants K Equilibrium constant µz,g,ads,des µ+ Chemical potential (z = surface, g = gas, + = transition state, ads/ des = adsorption, desorption) F Helmholtz free energy
1 Introduction Adsorption/desorption rates in micro-porous crystals may be controlled by many different rate processes including both extra-crystalline and intra-crystalline mass and heat transfer as well as surface resistance. For an individual spherical crystal (radius R) surrounded by fluid (gas or liquid) one may usually assume isothermal behavior with rapid equilibration at the external surface. In this situation the mass transfer rate is controlled by the combined effects of intracrystalline diffusion and surface resistance. To a first approximation the time constant for mass transfer is given by the sum of the time constants for these processes:
𝜏 = 𝜏surf + 𝜏diff = R2 ∕15D + R∕3k * German Sastre [email protected] * Douglas M. Ruthven [email protected] 1
Instituto de Tecnologia Quimica U.P.V.-C.S.I.C. Universidad Politecnica de Valencia. Avenida Los Naranjos S/N, Valencia 46022, Spain
2
Faculty of Physics and Earth Sciences, University of Leipzig, Linnéstraße 5, Leipzig 04103, Germany
3
Department of Chemical and Biological Engineering, University of Maine, Orono, ME, USA
(1)
with D denoting the diffusivity (= coefficient of transport diffusion in uptake and release measurement) or the tracer (self-) diffusivity in tracer exchange experiments. k stands for the permeance (in the given context synonymously used with the term permeability) of the crystal surface, defined as the ratio between the flux through the surface and the difference between the boundary concentration and the concentration in
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