Permeation—Adsorption and Diffusion

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Permeation involves the transport of molecules across a membrane phase. The transport process involves either dissolution or adsorption within the substance of the membrane and then transport from regions of higher to lower potential (that is, concentration) within the membrane phase. The global measurement of the rate of transport across the membrane, given in terms of the measurable changes in the concentrations in the bulk above and below the membrane, is permeation. Transport within the membrane, described quantitatively in terms of the concentration within it, is diffusion. The processes that take gas phase species from the bulk either to the surface of the membrane or that lead to their dissolution within the near surface region are adsorption and partitioning (dissolution), respectively. 

The rate of transport across the membrane in units of mass (or moles) per unit time per unit area is termed a flux J and it is found to be proportional to the difference between the concentrations on either side of the membrane. The proportionality constant is called the permeability P with intrinsic dimensions of the same as the mass transfer coefficient and the same as velocity. 

Higher permeabilities make for higher fluxes as do higher concentrations and pressures. The high concentration side of the membrane from which mass typically flows is termed the retentate, while that side to which mass flows is the permeate. 

We will see how this factors into the analysis as we go through this material. 

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It might be thought as a consequence of measurements such as these that leakage factors are the main issues in fuel containment. However, although obviously important, in some cases a leak might occur only at intermittent intervals, and the associated problem might well be easily resolvable by component replacement. In contrast, the relevance of permeation to fluid containment is its continuous nature—its rate may be low, but it occurs all the time that fluid is contacting elastomer. Hence, this phenomenon is now considered in association with related processes absorption, adsorption, and diffusion. 

Permeation When a fluid contacts one side of an elastomer membrane, it can permeate right through the membrane, escaping on the far side. The process again combines adsorption and diffusion as above, but with the additional process eventually of evaporation—treated mathematically as negative adsorption. (Permeation could also be viewed as combining one-way absorption and evaporation.) Wherever these conditions for permeation exist the phenomenon occurs, whatever the shape of the elastomer barrier— but the associated mathematics becomes complex for irregular barrier shapes. 

Surface adsorption and diffusion add a second contribution to gas permeation that can occur in small-pore-diameter membranes. This phenomenon is shown schematically in Figure 2.38. Adsorption onto the walls of the small pores becomes noticeable when the pore diameter drops below about 100 A. At this pore diameter the surface area of the pore walls is in the range 100 m2/cm3 of material. Significant amounts of gas then adsorb onto the pore walls, particularly if the gas is condensable. Often the amount of gas sorbed on the pore walls is much greater than the amount of nonsorbed gas. Sorbed gas molecules are mobile and can move by a process of surface diffusion through the membrane according... 

Outside the Henry region calculation of the permeation from adsorption and diffusion data requires knowledge of the value of Especially for weakly adsorbing gases the value is not always known nor can be Ccisily determined from experiments. As discussed by Kapteyn et eil. [88] the value of tjsat can be estimated from the molar volume which is obtained from extrapolation of the liquid state [90] or from volume filling theory [91]. Some results will be discussed below (binary gas permeation). In the Henry regime separate values of q at are not necessary as discussed above and the product K-t/gat = b (Henry coef.)... 

A) Adsorption selectivity (from CCMC simulations for binary mixtures taking /j = 0.5 MPa at the upstream face), (B) diffusion selectivity sei/ 2seif> evaluated at the total mixture loading at the upstream face), and (C) resulting permeations selectivity (=product of the adsorption and diffusion selectivities) [2]. The graphs were constructed based on the data from [8]. 

As a rough estimate, the permeation through a molecular sieve membrane can be described by the permeation model for organic polymer membranes the membrane selectivity is the product of adsorption selectivity and diffusion selectivity. This means that a knowledge-based molecular sieve membrane development based on independent adsorption and diffusion data is possible. 

Flux through microporous membranes incorporates both adsorption and diffusion characteristics and as such the equations developed are modified based on the membrane material and pore structure. For example, the following expression (Equation [8.8]) for permeating flux through microporous silica membranes is accepted as an appropriate description of molecular sieving or activated transport (de Lange et al, 1995c) ... 

Figure 2.37 Permeability coefficients as a function of the gas kinetic diameter in micro-porous silica hollow fine fibers [58]. Reprinted from J. Membr. Sci. 75, A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Adsorption, Permeation, and Diffusion of Gases in Microporous Membranes, 233, Copyright 1992, with permission from Elsevier...

SEM and TEM images give detailed information about the porous structure of a supported heterogeneous catalyst (pore size distribution, typical sizes of the particles, etc.). The information from SEM and TEM images can be used in the reconstruction of porous catalytic medium. In the digitally reconstructed catalyst, transport (diffusion, permeation), adsorption, reaction, and combined reaction-diffusion processes can be simulated (Stepanek et al., 2001a). Parametric studies can be performed, and the resulting dependencies can serve as a feedback for the catalyst development. 

Adsorption plays an important role in permeation through microporous membranes. First of all, steps 1 and 5 involve adsorption and desorption processes. Second, the concentration dependence of the diffusion coefficient is often described by the adsorption isotherm. Some data on adsorption in zeolites will be presented in Section III.D. 

The different mechanisms that operate in the separation of gases have been previously described in Section 10.4.1. In pervaporation, the transport mechanism can be described by an adsorption-diffusion mechanism [74,114] similar to one for polymeric membranes [115]. However, it is necessary to consider that the specific interactions between the permeating component and the zeolitic material are different in zeolites. Moreover, the diffusion through the ordered zeolite nanopores is different than in the dense organic matrix. 

The mouth of the micropores may be narrowed by adsorbed CO2 molecules, which block N2 molecules from entering the pores. Furthermore, CO2 diffuses in pores of the zeolite membrane at a faster rate than Nj. This selection mechanism is plausible for micropores with a width of up to six molecules [7]. When CO2 molecules are strongly adsorbed on the pore wall, the COj permeation rate will be low even if CO2 is concentrated in the pore. If the pore size is close to the size of molecules, CO2 molecules cannot pass N2 molecules. Thus, balances between pore size and molecule size and between adsorptivity and mobility as well as difference in polarity of competitive species are important to attain both high permeance and selectivity. 

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. 

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