Transport mechanism, membranes surface diffusion

In many studies the separation factor, which is indicative of the membrane s ability to separate two gases in a mixture, is predominantly governed by Knudsen diffusion. Knudsen diffusion is useful in gas separation mostly when two gases are significantly different in their molecular weights. In other cases, more effective uansport mechanisms are required. The pore size of the membrane needs to be smaller so that molecular sieving effects become operative. Some new membrane materials such as zeolites and other molecular sieve materials and membrane modifications by the sol-gel and chemical vapor deposition techniques are all in the horizon. Alternatively, it is desirable to tailor the gas-membrane interaction for promoting such transport mechanisms as surface diffusion or capillary condensation. 

Selective surface flow is, as Knudsen diffusion, associated with transport through microporous membranes, usually inorganic materials. The mechanism of surface diffusion is disputed and several different approaches have been proposed in the literature. 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

The transport of gas in polymers has been studied for over 150 years (1). Many of the concepts developed in 1866 by Graham (2) are still accepted today. Graham postulated that the mechanism of the permeation process involves the solution of the gas in the upstream surface of the membrane, diffusion through the membrane followed by evaporation from the downstream membrane surface. This is the basis for the "solution-diffusion model which is used even today in analyzing gas transport phenomena in polymeric membranes. 

This complex barrier has to be crossed by drag molecules via passive diffusion or active transport in order to reach the brain compartment This is required for all drags acting on the central nervous system (CNS). The degree of uptake into the CNS or CSF can be quite different despite the similar mechanism involved in diffusion. This can be explained by the much greater surface of the blood-brain membrane compared to the surface of CSF and/or the existence of specific carrier proteins in the CNS. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

Figure 4.17 Transport mechanisms for gaseous mixtures through porous membranes (a) viscous How (b) Knudsen diffusion (c) surface diffusion (d) multi-layer diffusion (e) capillary condensation and (0 molecular sieving [Saracco and Specchia, 1994]...

There are, however, evidences that other more effective separating mechanisms such as surface diffusion and capillary condensation can occur in finer pore membranes of some materials under certain temperature and pressure conditions. Carbon dioxide is known to transport through porous media by surface diffusion or capillary condensation. It is likely that some porous inorganic membranes may be effective for preferentially carrying carbon dioxide through them under the limited conditions where either transport mechanism dominates. 

Molecular sieving and the interactions of gas molecules with the membrane are possible alternatives. As discussed in Chapter 4, if surface diffusion is operative on a gas but not the other, it can enhance the separation factor. Although surface diffusion contribution decreases with increasing temperature, it becomes more important as the pore diameter becomes smaller. Therefore, it is possible that as inorganic membranes with smaUer pore sizes become available their separation performance may increase not only due to molecular sieving effects but also surface diffusion or other transport mechanisms. 

A final application that can be envisaged for permselective IMRs concerns the enhancement of reaction selectivity toward intermediate products of consecutive reaction pathways. Such a goal could be attained by developing a membrane capable of separating the intermediate product from the reaction mixture [39,40]. The most critical point in this regard is that intermediate product molecules (e.g., partially oxidized hydrocarbons) are often larger in size than the complete reaction products (e.g., CO2) or the reactants themselves (e.g., O2). This seriously complicates the separation process, limiting the number of selective transport mechanisms that can be utilized for the purpose of capillary condensation, surface diffusion, or multilayer diffusion (described later in this chapter). 

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. 

The adsorption-surface diffusion-desorption mechanism of transport through the SSF membrane can simultaneously provide high separation selectivity between H2 and the impurities of the PSA waste gas and high flux for the impurities even when the gas pressure in the high-pressure side of the membrane is low to moderate (3-5 atm). 

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