Diffusion in micropores

Anderson, JL KathawaUa, lA Lindsey, JS, Configurational Effects on Hindered Diffusion in Micropores, AIChE Symposium Series 84, 35, 1988. 

Shindo, Y., T. Hakuta, H. Yoshitome and H. Inoue. 1983. Gas diffusion in microporous media in Knudsen regime. J. Chem. Eng. Japan 16(2) 120-26. 

Application of Nuclear Shielding Surfaces to the Fundamental Understanding of Adsorption and Diffusion in Microporous Solids... 

Knudsen Diffusion and Surface Diffusion in Microporous Membranes... 

In the above considerations the total pressure should also be taken into account. With increasing pressure, the efficiency of a bidisperse catalyst decreases because diffusion in micropores turns from Knudsen to ordinary and the difference between Df n and Dejt disappears. At a pressure of 1-10 MPa, a uniform porous structure with a pore size close to the mean free path is the most favorable [6]. 

Another outstanding feature of TEOM is that it enables investigations of adsorption and diffusion in microporous and mesoporous materials as a function of the coke content (37,38). 

The heat of adsorption of Ar was also measured for acidity evaluation. In the case of Ar-TPD, an effect of the probe molecule diffusion in micropores is observed with some samples, such as zeoUtes, at high temperature-programmed rates. The adsorption method is not influenced by diffusion of the adsorbed molecule because the Ar isotherm is measured at static equilibrium. It is also advantageous that the usual BET apparatus can be used to obtain the adsorption isotherm. In addition, the adsorption behavior of Ar is of the Henry type at temperatures around room temperature. 

A summary of the major experimental techniques that have been applied to study diffusion in microporous solids is given in Table 1. These can be classified according to the nature of the measurement (transient or steady state), the scale of the measurement (micro, meso or macro) and the type of process (transport or self-diffusion). Additional details with complete references are given in recent reviews [10-12]. 

The principle of the Maxwell-Stefen diffusion equations is that the force acting on a species is balanced by the ffiction that is exerted on that species. The driving force for diffusion is the chemical potential gradient. The Maxwell-Stefan equations were applied to surface diffusion in microporous media by Krishna [77]. During surface diffusion, a molecule experiences friction from other molecules and from the surface, which is included in de model as a pseudo-species, n+1 (Dusty-gas model). The balance between force and friction in a multi-component system can thus be written as [77] ... 

In Fig. 9a and 9b the orders of magnitude of the different diffusion coefficients and the activation energy for diffusion are given as a function of pore size [36], For diffusion in micropores (<2 nm in diameter), the diffusivity can vary over several orders of magnitude, depending on the size and nature of the diffusing species and the microporous media. Diffusion in micropores is often referred to as configurational diffusion. 

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. 

Gibon J and Soffer A. Knudsen diffusion in microporous carbon membranes with molecular sieving character. J. Membr. Sci. 2002 209 339-352. 

In a series of papers, Ma and his co-workers [1 ] systematically examined the interrelationship between adsorption, permeation and diffusion in microporous silica membranes. Both equilibrium and nonequilibrium properties of the microporous inorganic gas separation membranes were studied. Both high pressure and low pressure gravimetric units were used in their adsorption measurements. 

Configurational diffusion in microporous (molecular sieve) membranes wiU be treated separately. Here the driving force must be described in terms of a chemical potential gradient, which is coupled to partial pressure via adsorption isotherms. In cases where several mechanisms operate simultaneously, the problem of additivity arises and in real membrane systems simplifying assumptions have to made. 

It is convenient to classify an overall soil reaction as a slow or rapid reaction. A soil reaction is slow when the kinetics are associated with an energy of activation. Slow reactions are those in which processes taking place at the solid phase are rate determining whether transport processes (such as surface diffusion, diffusion in micropores, penetration into the bulk, etc.), or chemical interactions. Mechanisms for slow soil reactions are discussed in detail in the following sections. 

Measurement of Diffusion in Microporous Solids by Macroscopic Methods... 

Abstract In this chapter the main macroscopic experimental methods for measuring diffusion in microporous solids are reviewed and the advantages and disadvantages of the various techniques are discussed. For several systems experimental measurements have been made by more than one technique, and in Part 3 the results of such comparative studies are reviewed. While in some cases the results show satisfactory consistency, there are also many systems for which the apparent intracrystaUine diffusivities derived from macroscopic measurements are substantially smaUer than the values from microscopic measurements such as PFG NMR. Recent measurements of the transient intracrystalline concentration profiles show that sirnface resistance and intracrystalline barriers are both... 

Tablet Classification of solids macroscopic methods for measuring diffusion in microporous ...

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