Application of microimaging to diffusion studies in nanoporous materials
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Application of microimaging to diffusion studies in nanoporous materials Christian Chmelik1 · Roger Gläser2 · Jürgen Haase1 · Seungtaik Hwang1 · Jörg Kärger1 Received: 17 June 2020 / Revised: 2 October 2020 / Accepted: 10 October 2020 © The Author(s) 2020
Abstract Microimaging on the basis of, respectively, interference microscopy and IR microscopy permit the observation of the distribution of guest molecules in nanoporous solids and their variation with time. Thus attainable knowledge of both concentration gradients and diffusion fluxes provides direct access to the underlying diffusion phenomena. This includes, in particular, the measurement of transport diffusion under transient, i. e. under non-equilibrium conditions, and of self- or tracer diffusion on considering the rate of tracer exchange. Correlating the difference in guest concentration close to the external surface to its equilibrium value with the influx into the nanoporous solid, microimaging does as well allow the direct determination of surface resistances. Examples illustrating the variety of information thus attainable include the comparison of mass transfer under equilibrium and non-equilibrium conditions, single- and multicomponent diffusion and chemical reactions. They, finally, introduce into the potentials of microimaging for an in-depth study of mass transfer in mixed-matrix membranes. This tutorial review may serve as first introduction into the topic. Further references are linked for the interested reader. Keywords Molecular diffusion · Nanoporous material · Interference microscopy (IFM) · Infrared microscopy (IRM) · Microimaging Abbreviations Symbols A Surface area of a particle (m2) c Concentration of guest molecules (mol m−3) ceq. Concentration in equilibrium with the external gas phase (mol m−3) cprod Concentration of product molecules under stationary conditions (mol m−3) creact Concentration of reactant molecules under stationary conditions (mol m−3) creact, equ. Maximum reactant concentration in equilibrium with the surrounding atmosphere (mol m−3) The paper is dedicated to the memory of Jens Weitkamp, commemorating his stimulations and support in applying microimaging for the in-situ investigation of conversion in nanoporous catalysts. * Christian Chmelik [email protected]‑leipzig.de 1
Faculty of Physics and Earth Sciences, Leipzig University, Leipzig, Germany
Faculty of Chemistry and Mineralogy, Leipzig University, Leipzig, Germany
2
csurf. Actual concentration close to the surface of a crystal (mol m−3) c* Concentration of labelled molecules (mol m−3) c̄ reac. Mean reactant concentration under stationary conditions (mol m−3) D Self- or tracer diffusivity (m2s−1) D0 Corrected diffusivity (m2s−1) Ðii Self-exchange diffusivity (m2s−1) Dij Element of the diffusion matrix, quantitating the effect of the concentration gradient of component j on the flux of component i DT Fickian or transport diffusivity (m2s−1) f Friction coefficient reflecting the interaction of the diffusing molecules
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