Diffusion and Permeability in Polymers

Factors affecting permeability include the solubility and diffusivity of the penetrant into the polymer, polymer packing and side-group complexity. 

The concept of holes, or free volume, in polymers has already been introduced in relation to phase diagrams. It must be emphasized that holes in materials are required for all types of molecular motion beyond simple vibrational and rotational states. One must ask the question When a molecule moves from position A to position B, into what does it move, and what does it leave behind The answer is that it moves into a hole. The hole and the molecule are transposed, so the hole is where the molecule was before the action started. The general concept of free volume is developed in Chapter 8, in relation to the glass transition. 

Consider a polymer in contact with a solvent. Diffusion takes place in both directions, the polymer into the solvent, and vice versa. However, the rate of diffusion of the solvent, being a small molecule, is much faster. Hence, for a time, the polymer really acts as the solvent. 

If the polymer is glassy, the solvent lowers the Tg by a plasticizing action. Polymer molecular motion increases. Diffusion rates above Tg are far higher than below Tg. Thus diffusion may depend on the concentration of the diffusing species (63,64). 

Perhaps one of the most interesting cases of the polymer behaving as the solvent has to do with permeability of water and gases. Often polymers, in the form of films, are used as barriers to keep out water and air. In the case of food wrappers, it is often desired to keep in water but keep out oxygen. 

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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,... 

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]. 

The influence of chain packing (Le. free volume) on solubility, diffusivity and permeability in liquid crystalline polymers can be studied by comparing properties of LCPs in the disordered, isotropic state with those in the ordered, liquid crystalline state. HIQ-40 is a random, glassy, thermotropic, nematogenic terpolymer synthesized from 40 mole percent p-hydroxybenzoic acid and 30 mole percent each of isophthalic acid and hydroquinone. The chemical structures of the constituent monomers for fflQ-40are ... 

Marais, S., Metayer, M., and Labbe, M. (1999), Water diffusion and permeability in unsaturated polyester resin films characterized by measurements performed with a water-specific perme-ameter Analysis of the transient permeation. Journal of Applied Polymer Science 74(14), 3380-3395. 

Huggins interaction parameter, and prp is the equilibrium pressure of the coexistent sorbate gas and liquid at the temperature of the experiment. The fractional free volume f2 of the amorphous component of a semicrystalline polymer is increased by recoverable straining and decreased by plastic deformation. As a consequence one obtains a gradual increase of sorption, diffusion, and permeability in the former and a drastic decrease in the latter case. ... 

Diffusion and permeability are inversely related to the density, degree of crystallinity, orientation, filler concentration, and cross-link density of a polymeric film. Generally, the presence of smaller molecules, such as plasticizers, increases the rate of diffusion in polymers since they are more mobile and can create holes or vacancies within the polymer. The rate of diffusion or permeability is fairly independent of polymer chain length just as long as the polymer has a moderately high chain length. 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

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... 

The factors affecting the selectivity and permeability of polymer membranes to different gases are best discussed on the basis of Eqs. (12) and (14). As noted in Eq. (12), the permeability coefficient, P, of a penetrant gas in a polymer membrane is the product of a (concentration-averaged) diffusion coefficient, D, and of a solubility coefficient,... 

The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. 

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. 

The fit of these expressions to experimental results is very good. At low pressure regimes, the fit was shown to be even better than that of dual sorption expressions. Except for these regimes, the two models seem to do equally well in describing sorption and permeability data. Concentration dependent diffusivity and permeability have been considered before mainly for vapors. The new aspect of the matrix model is that it broadens these effects to fixed gases. The important difference between the matrix and dual sorption models is in the physical picture they convey of gas transport and interaction with the polymer. Additional experimental evidence will be needed to determine the preference of these different physical representations. 

As the molecular size of most gases is much smaller than any scale of structure expected in polymer blend morphology, diffusion and permeability of gases can be employed to determine the phase behavior of a polymer blend. Therefore, the study of transport phenomena in blends would be motivated not only by the requirements of producing improved barrier materials but also by the continuous interest in the nature and characterization of polymer blend morphology. 

In this chapter, we will explore the types of producl/package interactions that can occur between a plastic material and a product, as well as the factors that affect the sorption, diffusion, and permeability behavior of polymers. We will then examine how polymer and product mass transfer characteristics can be used to predict product shelf life, based on moisture and oxygen transport. 

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... 

PALS results allow a comparison of the effect of polymer substituent and backbone chemistry on the relative size and concentration of free volume elements. The methane solubility is not strongly correlated with the PALS free volume parameters (similar to the result shown for fractional free volume in Figure 6a). The methane diffusivity and permeability of these polyisophthalamides are strongly... 

Polymer nanocomposites find their first application in car hoods, which are easily attacked by NO pollutants since they are exposed to the exterior environment. NO at standard atmosphere and pressure is 29.5% NO and 70.5% N O. Polyamide-6 is highly sensitive to such pollutants. The infusion of nano-clay platelets in the polyamide matrix in general decreases the diffusivity and permeability of the nanocomposites to atmospheric oxygen... 

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