Zeolite transport theory

Transport Theory and Separation Capability of Zeolite Membranes... 

Inorganic membranes are made of inorganic materials such as metals, ceramics, zeolites, glasses, carbon, and so on. Actually, inorganic membranes usually consist of several layers from one or more different inorganic materials. Details of inorganic membranes with respect to their syntheses, characterizations, transport theories, and scaling-up problems have been well reviewed and summarized by several authors [5,6]. 

In the first chapter, Bates and van Santen summarize the theoretical foundations of catalysis in acidic zeolites. Being the most important crystalline materials used as catalysts, zeolites have been the obvious starting point for applications of theory to catalysis by solids and surfaces. Impressive progress has been made in the application of theory to account for transport, sorption, and reaction in zeolites, and the comparisons with experimental results indicate some marked successes as well as opportunities for improving both the theoretical and experimental foundations. 

The transport process within the zeolite pore system involves the passage of sorbate molecules through the windows between adjacent cavities. For molecules with critical diameters similar to the free aperture of the window ( 4.2 A for type A zeolites), an activated diffusion process is to be expected, and a molecule at the center of the window may be identified as the transition state. For the A-type lattice the following expression for the limiting diffusivity may be derived from absolute rate theory (14)... 

The application of the Maxwell-Stefan theory for diffusion in microporous media to permeation through zeolitic membranes implies that transport is assumed to occur only via the adsorbed phase (surface diffusion). Upon combination of surface diffusion according to the Maxwell-Stefan model (Eq. 20) with activated-gas translational diffusion (Eq. 12) for a one-component system, the temperature dependence of the flux shows a maximum and a minimum for a given set of parameters (Fig. 15). At low temperatures, surface diffusion is the most important diffusion mechanism. This type of diffusion is highly dependent on the concentration of adsorbed species in the membrane, which is calculated from the adsorption isotherm. At high temperatures, activated-gas translational diffusion takes over, causing an increase in the flux until it levels off at still-higher temperatures. 

A Bethe-tree is a particular case of more general networks considered in percolation theory, which is used to a growing extent to describe transport inside catalysts, as evidenced by a recent review by Sahimi et al [ref 26] Sahimi and Tsotsis [ref. 27] applied percolation theory and Honte Carlo simulation to deactivation in zeolites, represented by a simple cubic lattice. 

Membranes with ordered structures such as zeolites or nanotubes have considerable potential as gas separation membranes [46-48], In addition to having thermal and chemical stability, the porosity of these structures is ordered, and therefore there is usually more control over the separation properties. The pores within these structures are such that gas transport can not be completely explained by the transition state theory. This is because, in nanotubes for example, there is only one transition, from outside of the tube to inside of the tube. Two alternative models are outlined here, the parallel transport model and the resistance in series transport model, which are illustrated in Figure 5.5, and they are explained in detail by the work of Gilron and Softer [27]. 

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