Sorption coefficient membranes

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

Plasticization and Other Time Effects Most data from the literature, including those presented above are taken from experiments where one gas at a time is tested, with Ot calculated as a ratio of the two permeabihties. If either gas permeates because of a high-sorption coefficient rather than a high diffusivity, there may be an increase in the permeabihty of all gases in contact with the membrane. Thus, the Ot actually found in a real separation may be much lower than that calculated by the simple ratio of permeabilities. The data in the hterature do not rehably include the plasticization effect. If present, it results in the sometimes slow relaxation of polymer structure giving a rise in permeabihty and a dramatic dechne in selectivity. 

At this point the superscript G is introduced to denote the gas phase. For example yp, the activity of component i in the gas phase, and Kf, the sorption coefficient of component i between the gas and membrane phases [Equation (2.56)]. 

The problem of predicting membrane permeability can be divided into two parts because permeability is the product of the diffusion coefficient and the sorption coefficient ... 

The sorption coefficient (K) in Equation (2.84) is the term linking the concentration of a component in the fluid phase with its concentration in the membrane polymer phase. Because sorption is an equilibrium term, conventional thermodynamics can be used to calculate solubilities of gases in polymers to within a factor of two or three. However, diffusion coefficients (D) are kinetic terms that reflect the effect of the surrounding environment on the molecular motion of permeating components. Calculation of diffusion coefficients in liquids and gases is possible, but calculation of diffusion coefficients in polymers is much more difficult. In the long term, the best hope for accurate predictions of diffusion in polymers is the molecular dynamics calculations described in an earlier section. However, this technique is still under development and is currently limited to calculations of the diffusion of small gas molecules in amorphous polymers the... 

As a general rule, membrane material changes affect the diffusion coefficient of a permeant much more than the sorption coefficient. For example, Figure 2.18 shows some typical gas permeation data taken from a paper of Tanaka et al. [23], The diffusion and sorption coefficients of four gases in a family of 18 related polyimides are plotted against each other. Both sorption and diffusion coefficients... 

Figure 8.4 Gas sorption coefficient as a function of molar volume for natural rubber membranes. Larger permeants are more condensable and have higher sorption coefficients [9]...

The selectivity (amcm) of pervaporation membranes critically affects the overall separation obtained and depends on the membrane material. Therefore, membrane materials are tailored for particular separation problems. As with other solution-diffusion membranes, the permeability of a component is the product of the membrane sorption coefficient and the diffusion coefficient (mobility). The membrane selectivity term amem in Equation (9.11) can be written as... 

Membrane phase concentration of component i in the feed side, Cg, can be calculated from its bulk concentration by Henry s equation (Equation 5.8) provided it is present in trace amount in the feed solution. For higher concentration of component i, Cg can be obtained from experimental sorption data. Membrane phase concentration on the permeate side of component i, i.e., Cpi may be neglected due to the low pressure the activity of the component in the downstream side is very low. Thus, Equation 5.28 can be readily solved to calculate the theoretical flux and diffusion coefficient of i or j component employing any of the above equations relating the diffusion coefficient and concentration. Equations 5.14 through 5.25 depending on its best matching with the experimental data. 

S is the sorption coefficient defined as the ratio of the membrane phase concentration and feed phase concentration... 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

Permeability According to the aforementioned, both the sorption and the diffusion of a solute determine the mass transfer across, and hence the separation characteristics of the membrane. The product of the diffusion coefficient and the sorption coefficient Sf is denoted the permeabihty of the membrane for component i and is commonly designated as Pf. In order to avoid confusing permeability and pressure, however, here it will be denoted (used commonly for the phenomenological constant)... 

The solution-difTusion model is valid only in strictly ideal systems, namely when dealing with solutions of infinite dilution. As soon as one departs from such ideal solutions, it becomes to some extent subjective what can still be considered as almost ideal and highly dilute . For the pervaporation of isobutyl alcohol, for example, a feed concentration of 50 mg kg would lead to a membrane surface concentration of 50 mg kg (according to the sorption coefficient listed in Table 3.6-2). For the same feed concentration, ethyl hexanoate would yield a membrane surface concentration about 240 times higher, namely 12 g kg which may not be considered ideal anymore. The stronger the (desired) solute-polymer affinity, the more pronounced can be the non-ideal phenomena, with the most relevant being discussed below. 

In pervaporation, as the feed fluid is a liquid, a thin, stagnant boundary layer always exists over the membrane surface in which the solute transport is diffusive (Fig. 3.6-11). The thickness of this boundary layer (stagnant liquid film) can be calculated from well-established boundary layer equations (for critical reviews on the use of the most common correlations see, for example, Gekas and Hallstrom, 1987 and Cussler, 1997). If the flux of a solute i across the concentration boundary layer toward the membrane is lower than the maximum (for the respective solute bulk feed concentration) attainable solute flux across the membrane, then solute i will be depleted in the boundary layer over the membrane upstream surface. As a consequence, the concentration of i in the membrane upstream surface will also be lower (assuming a constant sorption coefficient), the concentration gradient over the membrane will decrease and hence so will the trans-membrane flux. 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

Yawalkar et al. (2001) has developed a model for a three-phase reactor based on the use of a dense polymeric composite membrane containing discrete cubic zeolite particles (Fig. 4.5) for the epoxidation reaction of alkene. Catalytic particles of the same size are assumed vdth a cubic shape and uniformly dispersed across the polymer membrane cross-section. Effects of various parameters, such as peroxide and alkene concentration in liquid phase, sorption coefficient of the membrane for peroxide and alkene, membrane-catalyst distribution coefficient for peroxide and alkene and catalyst loading, have been studied. The results have been discussed in terms of a peroxide effidency defined as the ratio of flux of peroxide through the membrane utilized for alkene oxidation to the total flux of organic peroxide through the membrane. The paper aimed to show that, by using an organophilic dense membrane and the catalysts confined in the polymeric matrix, the oxidant concentration (in that reaction peroxides) can be controlled on the active site with an improvement of the peroxide efficiency and selectivity to desired products. 

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