Permeability Sorption, and Diffusion

IV. Those connected with the Interplay between polymers and liquids or gases solubility, wetting and repulsion (Chaps. 7 and 8) permeability, sorption and diffusivity (Chaps. 9 and 18). 

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

Nonlinear, pressure-dependent sorption and transport of gases and vapors in glassy polymers have been observed frequently. The effect of pressure on the observable variables, solubility coefficient, permeability coefficient and diffusion timelag, is well documented (1, 2). Previous attempts to explain the pressure-dependent sorption and transport properties in glassy polymers can be classified as concentration-dependent and "dual-mode models. While the former deal mainly with vapor-polymer systems (1) the latter are unique for gas-glassy polymer systems (2). 

The second key factor determining permeability in polymers is the sorption coefficient. The data in Figure 2.18 show that sorption coefficients for a particular gas are relatively constant within a single family of related materials. In fact, sorption coefficients of gases in polymers are relatively constant for a wide range of chemically different polymers. Figure 2.25 plots sorption and diffusion coefficients of methane in Tanaka s fluorinated polyimides [23], carboxylated polyvinyl trimethylsiloxane [37] and substituted polyacetylenes [38], all amorphous glassy polymers, and a variety of substituted siloxanes [39], all rubbers. The diffusion... 

In terms of Eq. (1), the driving force is ApA and the resistance, f2 = L/Pa. Although the effective skin thickness L is often not known, the so-called permeance, PA/L can be determined by simply measuring the pressure normalized flux, viz., Pa/L = [flux of A]/A/j>a, so this resistance is known. Since the permeability normalizes the effect of the thickness of the membrane, it is a fundamental property of the polymeric material. Fundamental comparisons of material properties should be done on the basis of permeability, rather than permeance. Since permeation involves a coupling of sorption and diffusion steps, the permeability is a product of a thermodynamic factor, SA, called the solubility coefficient, and a kinetic parameter, DA, called the diffusion coefficient. 

Non-celluloslc Membranes. While the development of CA gas permeation membranes can be directly attributed to the development of water desalination membranes, the Invention of modified silicone membranes and polysulfone membranes was more Influenced by the extension of knowledge of transport, sorption and diffusion of gases In polymers (24-27). In principle, rubbery polymers exhibit the highest gas permeabilities at the lowest selectlvitles, and. 

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. 

The chemical structure of the polymer s constitutional unit is the fundamental determinant of the polymer s barrier behavior. In addition to chemical composition, polarity, stiffness of the polymer chain, bulkiness of side and backbone-chain groups, and degree of crystallinity significantly impact the sorption and diffusion of penetrants, and hence permeability. Of particular significance are influences on the free volume and molecular mobility of the polymer, and influences on the affinity between the permeant and the polymer. 

Gas permeability is also one of the parameters used to detect a change in the structure of a polymer. Since paraffins, such as propane, do not have any specific interaction with silver ions and thus only permeate via normal sorption and diffusion transport, the permeability behavior of propane is mostly determined by the microstructure and chain mobility of a polymer complex. As such, the propane permeabilities of POZ films decrease rapidly with AgCp3S03 concentration, which is consistent with the results of the d-spacings and glass... 

Molecular sieves such as zeolites or carbon molecular sieves show a much higher selectivity for many gas mixtures than polymeric membranes due to their very defined pore sizes. For example it can be calculated from reported sorption and diffusivity data that zeolite 4A has an oxygen permeability of 0.77 Barter and an O2/N2 selectivity of approximately 37 at 35 °C [308]. 

A similar result can be concluded from the hydrophilicity of hydrophilic-hydrophobic copolymers. For example, it is well- known that at least 10 % hydrophilic segments is needed to disperse a statistical hydrophilic-hydrophobic copolymer in water. Whereas, in our work with vinyl acetate-neutralized acrylic acid block copolymers, stable dispersion in water was achieved even at 4 wt % acrylic acid content (Caneba and Dar, 2005). Finally, a comparative study of permeabilities has been made between block and random copolymers for sorption and diffusion of cyclohexane in styrene-butadiene copolymers (Caneba et al., 1983-1984). Since the permeability is proportional to the product of the diffusivity and solubility, numerical results for 10 wt % S contents indicate an increase in permeability for the block copolymer membrane compared to the random copolymer membrane. 

Diffusion coefficient D) is the ability of the penetrant to move among the polymer segment. It is a kinetic parameter which depends on the polymer segment mobility. Sorption is a surface phenomenon, and it is an indication of the tendency of the penetrant to dissolve into the polymer. Permeation on the other hand, can be considered as the combined effect of sorption and diffusion process. From equation 22.5, it can be inferred that the sorption process controls the permeability. 

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