Critical Evaluation of Macroscopic Theories for Multi-Component Diffusion in Ideal Langmuir Sorbents
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AA8.12.1
Critical Evaluation of Macroscopic Theories for Multi-Component Diffusion in Ideal Langmuir Sorbents Nieck E. Benes1 and Henk Verweij Department of Materials Science & Engineering, Ohio State University, 2041 College Road, Columbus OH 43210-1178, USA Internet: www.mse.eng.ohio-state.edu/fac_staff/faculty/verweij/ Department of Chemical Engineering & MESA+ Research Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Internet: http://ims.ct.utwente.nl/personen/docenten/benes.html Abstract Materials research involves many areas for which a proper understanding of multicomponent mass transport is essential. Examples include sintering and transport-limited reaction in syntheses. In addition, materials may be principally designed for direct manipulation of mass transport, as in membrane materials. Macroscopic descriptions for mass transport are available, but physical interpretation of related transport parameters is generally not straightforward and often relies on microscopic considerations. We will show that, even for diffusion in a simple ideal Langmuir type lattice, macroscopic theories should be used with caution. Differences in mobilities of dissimilar species can set off percolation behavior, causing the flux of the more mobile species to vanish. Such behavior is, for instance, observed for zeolite membranes and cannot be predicted by commonly accepted macroscopic transport theories. Correlations between successive movements of molecules cause a decrease in the self-diffusion coefficient, DS. For nonequilibrium transport it can be shown that correlation effects in most cases disappear in which case non-equilibrium transport becomes related to the component diffusion coefficient D, instead of the smaller DS. Introduction Mass transport in micro-porous media plays an import role in many chemical processes, such as catalyzed reactions in zeolites and size selective molecular separations utilizing micro-porous membranes. Discussions on transport in such media are generally given in terms of fluxes, diffusion coefficients and driving forces. In literature various definitions are used for different diffusion coefficients, which may lead to confusion. By means of Monte Carlo simulations, we shall examine the relationships between tracer-, component, self and chemical diffusion coefficients. In the calculations, the micro-porous medium is assumed to consist of a cubic lattice of independent fixed sites, each of which can be occupied by a single mobile molecule. It is assumed that the mobile molecules, hopping from one site to another on a simple cubic lattice, have no mutual interactions other than ‘hard core’ (self-blocking) interactions. Movement is only allowed when the nearest neighboring site is vacant. Theory Even in thermodynamic equilibrium, i.e., where is no net transport of molecules, Brownian motions of molecules in micro-porous will occur. Displacement due to these random motions of a mobile component in a chemically homogenous host is referred to
AA8.12.2
as self diff
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