Surface diffusion separation

In which b° is the mechanical mobility for a molecule on an otherwise empty lattice, the concentration of available sites, R the universal gas eonstant, T absolute temperature, and 0 <6 < 1 is the average site occupation. Equilibrium between the site occupation and feed eoncentration on both sides of the membrane can be used as the boundary condition to solve the above eqnation. Non-eqnilibrinm correction factor 0 < j < 1 is often very close to nnity bnt can be very small for the molecule of low occupancy (low 0) when the other molecnle occnpies the sites strongly and hinders the movement of the former molecnle. The above generic expression leads to the following two types of microporous and surface diffusion separation ... 

By mixing an absorbing granulate or powder with the product to be dried, the distances the diffusion can become very small, or the water molecules may move by surface diffusion. In both cases, the problem is the same First to find an acceptable drying agent (absorber) and then to separate it quantitatively from the dried product. 

In the case of semi-infinite diffusion towards a spherical organism of radius r0, with the surface of separation (concentric with the organism s surface) at radius ra, the flux at the membrane surface is [26] ... 

In both situations the interaction of the medium inside the pore with the pore wall (1) is increased (2) or changed which affect the transport and separation properties (surface diffusion, multilayer adsorption) and/or help overcome equilibrium constraints in membrane reactors. Membrane modifications can be performed by depositing material in the internal pore structure from liquids (impregnation, adsorption) or gases. Several modification possibilities are schematically shown in Figure 2.3. Some results obtained by Burggraaf, Keizer and coworkers are summarized in Table 2.7. Composite structures on a scale of 1-5 nm were obtained. 

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. 

All the experimental data in Table 6.1 refer to pure gases. Separation experiments, in which surface diffusion is the separation mechanism, are scarcely reported. Feng and Stewart (1973) and Feng, Kostrov and Stewart (1974) report multicomponent diffusion experiments for the system He-Nj-CH in a y-alumina pellet over a wide range of pressures (1-70 bar), temperatures (300-390 K) and composition gradients. A small contribution of surface diffusion (5% of total flow) to total transport could be detected, although it is not clear, which of the gases exhibits surface difiusion. The data could be fitted with the mass-flux model of Mason, Malinauskas and Evans (1967), extended to include surface diffusion. 

In the eases reported previously, surface diffusion could have a pronounced effect and could increase the separation efficiency by a factor of 5. However, a sharp increase in the separation efficiency (a few orders of magnitude) is not to be exp>ected, due to the conflict between adsorption and mobility. A high heat of adsorption will invariably lead to a low mobility. Another drawback of surface diffusion is that it becomes less effective at high tempieratures. Therefore, it can be concluded that in order to employ surface diffusion as an eflectiye separation mechanism, the pores simuld be verx small (r iu < 3 nm) and the temperature should be kept low (T < 300°C), due to the necessary physical adsorption of the gas (Uhlhorn 1990). 

Membranes made from zeolite materials provide separahon properties mainly based on molecular sieving and/or surface diffusion mechanism. Separation with large pore zeolite membranes is mainly based on surface diffusion when their pore sizes are much larger than the molecules to be separated. Separation with small pore zeolite membranes is mainly based on molecular sieving when the pore sizes are smaller or similar to one molecule but are larger than other molecules in a mixture to be separated. 

Calculate the activation energy for diffusion of a Pt adatom on Pt(100) via direct hopping between fourfold sites on the surface and, separately, via concerted substitution with a Pt atom in the top surface layer. Before beginning any calculations, consider how large the surface slab model needs to be in order to describe these two processes. Which process would you expect to dominate Pt adatom diffusion at room temperature ... 

The density of the water employed as diffusion medium was raised by the addition of urea in order that the gold suspension could be run under a column of water without undue disturbance so as to obtain a uniform level surface of separation. 

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