Permeability, glassy polymer transport

One can easily show that the appropriate equation derived from the dual mode sorption and transport models for the steady state permeability of a pure component in a glassy polymer is given by Eq (7) (18) when the downstream receiving pressure is effectively zero and the upstream driving pressure is p ... 

Nonlinear, pressure-dependent solubility and permeability in polymers have been observed for over 40 years. Meyer, Gee and their co-workers (5) reported pressure-dependent solubility and diffusion coefficients in rubber-vapor systems. Crank, Park, Long, Barrer, and their co-workers (5) observed pressure-dependent sorption and transport in glassy polymer-vapor systems. Sorption and transport measurements of gases in glassy polymers show that these penetrant-polymer systems do not obey the "ideal sorption and transport eqs. (l)-(5). The observable variables,... 

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 predicted effect of du mode sorption on the time lag and permeability vras derived by Paul using the total immobilization transport model and experimentally verified by Paul and Kemp using molecular sieves embedded in a silicone mbber. This was an excellent model system which fulfilled the postulate of complete inunobilization of the Langmuirian mode penetrant. The possibility that gas molecules sorbed in the Langmuirian mode may not necessarily be completely immobilized in glassy polymers was first raised by Petropoulos in 1970 Equations were developed and the possibility of these being used to check the assumption of immobilization by sorption and permeation data were described. The relaxation of the... 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

As a rule, permeability in glassy polymers (e.g. cellulose) is lower than in rubbery polymers (e.g. polydimethylsiloxane, PDMS) on the other hand, selectivity is dictated by the molecular dimensions of the permeating species [167]. The polymers used as membranes in analytical pervaporation are similar to those employed for gas separation and possess a dense, non-porous macroscopic structure. The difference between the two lies in the transport mechanism and arises mainly from a large affinity difference between the permeating molecules and the polymer membrane. 

Although no commercial examples exist currently in the gas separation field, thin film composite membranes such as those pioneered by Cadotte and co-workers (10) may ultimately permit the use of novel materials with unique transport properties supported on standard porous membranes. Therefore, the focus in this paper will be on suggesting a basis for understanding differences in the permeability and selectivity properties of glassy polymers. Presumably, if such materials prove to be difficult to fabricate into conventional monolithic asymmetric structures, they could be produced in a composite form. Even if thin film composite structures are used, however, the chemical resistance of the material remains an important consideration. For this reason, a brief discussion of this topic will be offered. 

Jacques, C.H.M., Hopfenberg, H.B. and Stannett, V. (1974) Super case 11 transport of organic vapors in glassy polymers, in Permeability of Plastic Films and Coatings to Gases, Vapors and Liquids (ed. H.B. Hopfenberg), Plenum Press, New York,... 

An overview of the physics of glassy polymers and the relationships between molecular mechanisms and macroscopic physical, mechanical and transport properties of polymer glasses is presented. The importance of local translational and/or rotational motions of molecular segments in the glass is discussed in terms of the implications for thermodynamic descriptions of the glass (configurational states and energy surfaces) as well as history dependent properties such as expansivity, refractive index, gas permeability, and viscoelastic mechanical behaviour. 

Transport Properties. Sorption and transport properties are highly dependent on the post-vitrification history of glassy polymers (77) hence one would expect parameters such as physical aging, antiplasticization and amorphous orientation to affect transport properties. The reduction in diffusivity and permeability due to aging, orientation, and antiplasticization can be modeled via entropy or fi ee volume arguments (77). In addition, diffusive jumps of penetrant molecules in glassy polymers can be affected by (facilitated by) the segmental mobility that is manifested in sub-Tg relaxations 78),... 

In contrast to the LCP results just presented, in glassy polymers used as gas separation membranes, free volume influences diffusion coefficients much more than solubility coefficients. Figure 6 provides an example of this effect. In this figure, the solubility, diffusivity, and permeability of methane in a series of glassy, aromatic, amorphous poly(isophthalamides) [PIPAs] are presented as a function of the fractional free volume in the polymer matrix. (More complete descriptions of the transport properties of this family of materials are available elsewhere (59, 40)). The fractional free volume is manipulated systematically in this family of glassy polymers by synthesizing polymers with different substituent and backbone elements as shown in... 

It is known that glassy polymer membranes can have a considerable size-sieving character, reflected mainly in the diffusive term of the transport equation. Many studies have therefore attempted to correlate the diffusion coefficient and the membrane permeability with the size of the penetrant molecules, for instance expressed in terms of the kinetic diameter, Lennard-Jones diameter or critical volume [40]. Since the transport takes place through the available free volume in the material, a correlation between the free volume fraction and transport properties should also exist. Through the years, authors have proposed different equations to correlate transport and FFV, starting with the historical model of Cohen and Turnbull for self diffusion [41], later adapted by Fujita for polymer systans [42]. Park and Paul adopted a somewhat simpler form of this equation to correlate the permeability coefficient with fractional free volume [43] ... 

It has been shown in a previous section that, in most cases of practical interest, the rate of gas permeation through nonporous polymer membranes is cOTitrolled by the diffusion of the penetrant gas in the polymer matrix. Many theoretical models have been proposed in the literature to describe the mechanisms of gas diffusion in polymers on a molecular level. Such models provide expressions for gas diffusion coefficients, and sometimes also for permeability coefficients, derived from free volume, statistical-mechanical, energetic, structural, or other considerations. The formulation of these coefficients is complicated by the fact that gas transport occurs by markedly different mechanisms in rubbery and glassy polymers. 

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