Surface diffusion and capillary condensation

The hydrodynamic model In this model the adsorbed gas is considered as a liquid film, which can glide along the surface under the influence of a pressure gradient. 

9 — TRANSPORT AND SEPARATION PROPERTIES OF MEMBRANES WITH GASES AND VAPOURS 

The hopping model This model assumes that the molecules can move over the surface by hopping over a certain distance with a certain velocity. 

The random walk model This model is based on the two-dimensional form of Pick s law and is most frequently used in the literature. 

For relatively low surface concentrations, the surface flux Jg for a single gas is generally described by the two-dimensional Pick law  

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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. 

Separation with Surface Diffusion and Capillary Condensation... 

The permeation of gases in membranes due to surface diffusion and capillary condensation has been discussed in Section 9.2.3.S. together with some illustrative data. The total flux of a single gas is usually calculated as the sum of the flux by surface diffusion and the flux through the gas phase. As shown the surface flux can contribute considerably to the total flux (increased by factor 2-3 of gas diffusional flux), especially with smaller and uniform pore sizes (compare Eqs. (9.9a) and (9.15). With decreasing pore size the flux through the bulk gas decreases while the surface diffusional flux increases. With very small pore diameter (< 2-3 nm) the effective diameter for bulk gas transport is less than the geometric pore diameter due to the thickness of the absorbed layer which... 

Four types of diffusion mechanisms can be utilized to effect separation in porous membranes. In some cases, molecules can move through the membrane by more than one mechanism. These mechanisms are described below. Knudsen diffusion gives relatively low separation selectivities compared to surface diffusion and capillary condensation. Shape selective separation can yield high selectivities. The separation factor for these mechanisms depends strongly on pore-size distribution, temperature, pressure, and interactions between the solute being separated and the membrane surfaces. 

Multi-layer diffusion is developed when the molecule/surface interactions are strong. This mechanism is like to an intermediate flow regime between surface diffusion and capillary condensation [18]. 

Among these mechanisms, viscous flow is non-selective while Knudsen diffusion is selective to smaller molecules. At high temperature, gas adsorption becomes weak and thus the surface diffusion and capillary condensation may be negligible. In fact, the perm-selectivity in micropo-rous membranes is a complex function of the temperature, pressure, and gas composition. Therefore, it is necessary to evaluate the perm-selectivity of the porous membranes using a gas mixture under similar operating conditions [3]. Table 2.2 gives an overview of the transport mechanisms in porous membranes. Note that the perm-selectivity is not always a key factor in MRs. 

First, porous membranes will be discussed. Gases can be separated due to differences in their molecular masses (Knudsen diffusion), due to interaction (surface diffusion, multilayer diffusion and capillary condensation) and due to their size (molecular sieving). All these mechanisms and their possibilities will be discussed. For the sake of simplicity, theoretical aspects are not covered in detail, but examples of separations in literature will be given. The next section deals with nonporous membranes. Here the separation mechanism is solution-diffusion, e.g. solution and diffusion of hydrogen through a platinum membrane. This section is followed by an outline of some new developments and conclusions. 

Surface diffusion (Fig. 4(c)) can lead to high separation factors when one of the components interacts strongly with the surface multilayer diffusion and capillary condensation (d) have also been proposed [38]... 

Thus Eq. (4-13) implies that Knudsen diffusion is practical only when those gases with large differences in their molecular weights are to be separated. For applications where this mechanism poses as a severe limitation, other more effective separation mechanisms would be necessary. Two such possibilities are surface diffusion (and multi-layer diffusion) and capillary condensation, both of which are dependent on the chemical nature of both the membrane material and pore size and the species to be separated. 

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. 

For molecule-surface interactions that are particularly strong, Ulhom and co-workers [53] proposed the existence of another flow mechanism, the multilayer diffusion (Fig. 9), a sort of intermediate regime between surface flow and capillary condensation. 

Diffusion and Flow in Surface Adsorbed and Capillary Condensed Adsorbate... 

There are many transport mechanisms Poiseuille, Knudsen, molecular sieving, surface diffusion, multilayer diffusion, and capillary condensation. 

FIGURE 11.9 Schematic representation of membrane-based gas separations, (a) Knudsen-flow separation, (b) surface-diffusion, (c) capillary condensation, (d) molecular-sieving separation, and (e) solution-diffusion mechanism. 

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]...

Although Knudsen diffusion, shape selectivity, and molecular sieving play an important role in the separation of mixtures, the mechanisms which control the majority of the multicomponent separations in zeolite membranes are surface diffusion, and sometimes, capillary condensation. In addition, molecular simulations and modeling of M-S diffusion in zeolites [69,70] show that the slower moving molecules are also sped up in some mixtures [71,72] in the presence of fast-diffusing molecules and other times, slower molecules inhibit diffusion of faster molecules because molecules have difficulty passing one another in zeolite pores [73]. 

When the pore walls strongly absorb gas molecules, surface diffusion and/or capillary condensation accompanied by (surface) flow occurs. Usually this is the case with gases which condense rather easily at moderate temperature-pressure conditions (in any case being below their critical point) and we are dealing with vapour flow. 

To increase the separation factor above the ideal Knudsen separation factor requires contribution of surface diffusion and/or capillary condensation or the presence of micropore systems. 

Pore migration mechanisms include surface diffusion, lattice diffusion, gas diffusion and evaporation/condensation, as shown schematically in Figure 11.1. Under a capillary driving force of grain boundary migration, the atoms in front of the moving boundary around the pore are under compression while those behind the boundary are under tension. This pressure distribution results in a... 

Apart from diffusion in continuum phase, the transport of surface-adsorbed molecules and capillary condensate takes place in meso- and macroporous media. In order to model transport of adsorbable vapor at elevated pressure, it is necessary to consider the type of adsorption occurring monolayer adsorption, multilayer adsorption, or capUlary condensation [38]. Models for surface diffusion have been proposed... 

The typical gas transport mechanisms in porous membranes are molecular diffusion and viscous flow, capillary condensation, Knudsen diffusion, surface diffusion, and configurational or micropore-activated diffusion. The contributions of these different mechanisms depend on the properties of both the membrane and the gas under the operating temperature and pressure. Figure 2.3 illustrates schematically the gas transport mechanisms in a single membrane pore. 

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