Solubility glassy polymers

A history independent sorption in a glassy polymer is represented by Eqs. (l)-(3), however, due to the microcavitational nature of the hypothesized polymer morphological modification, the history dependency of the solubility is assumed to affect the Languimir term only ... 

Table 4 contains some selected permeability data, including diffusion and solubility coefficients foT flavors in polymers used in food packaging. Generally, vtuylidene chloride copolymers and glassy polymers such as polyamides and EVOH are good barriers to flavor and aroma permeation, whereas the polyolefins are poor barriers. Comparison to Table 2 shows lhat the large-molecule diffusion coefficients are 1000 or more times lower tli an the small-molecule coefficients. 

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,... 

In the dual-mode sorption and transport model the pressure-dependence of a (= C/p), P and 0 in gas-glassy polymer systems arises from the pressure-dependent distribution of the sorbed gas molecules between Langmuir sites and Henry s law dissolution. Although k, Dg and are assumed to be constant, the average or effective solubility and diffusion coefficients of the entire ensemble of gas molecules change with pressure as the ratio of Henry s to Langmuir s population, C /C, changes continuously with pressure [eq. (14)]. 

In the following chapter we present the matrix model of gas sorption and diffusion in glassy polymers which is based on the observation that gas molecules interact with the polymer, thereby altering the solubility and diffusion coefficients of the polymer matrix. 

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 solubility coefficients of gases in glassy polymers are not constant, but decrease with increasing concentration of the gas in the polymers (2). Calculations of the isosteric enthalpy of sorption in several gas-polymer systems confirm that the gas-polymer affinity is reduced with increasing sorbed gas concentrations (24, 25, 26). The change in the isosteric enthalpy of sorption is a result of the changes in the polymer matrix induced by the presence of the sorbed gas. 

In the limit of zero-concentration, gas-glassy polymer systems behave "ideally. As the gas concentration in the membrane approaches zero the solubility coefficient becomes constant with the value ao [eqs. (1), (3) and (4)]. In the same limit, the diffusion coefficients are constant and equal to the diffusion coefficient Do, [eqs. (5), (7), (8) and (9)]. As typical of limiting values, ao and Do have no correspondence to... 

Figure 2.27 Solubilities as a function of critical temperature (Tc) for a typical glassy polymer (polysulfone) and a typical rubbery polymer (silicone rubber) compared with values for the ideal solubility calculated from Equation (2.97)[43]...

Figure 4.1 Schematic illustration of how the (a) diffusion coefficient of penetrants depend on their size in rubbery and glassy polymers and (b) solubility coefficients for penetrants depend on their condensability.

Table 4.2 illustrates the various selectivity factors for some typical rubbery polymers, that is, silicone rubber, poly(dimethyl siloxane), and natural rubber, polyiso-prene, and a glassy polymer, polysulfone. Here, we consider the important 02/N2 pair and several pairs involving C02 that will be our focus later. In all the cases, the solubility selectivity is greater than unity and there is not a large difference between rubbery and glassy polymers. For most of these pairs, the diffusion selectivity is greater than unity, but there are some exceptions for C02/02 and C02/N2 that reflect... 

A few general trends can be recognized from this table, in particular as far as the effect of diffusion is concerned. Rubbers, with their high free volume, allow a small molecule to diffuse much faster than a glassy polymer. With semi-crystalline polymers above Tg, such as PE and PP, the rubbery phase gives rise to a higher rate of diffusion than when the amorphous phase is in the glassy state. Deviations from this simple pattern can be attributed to differences in solubility (see also Qu. 8.16 and 8.17). 

However, the mathematical formulae of DST satisfactorily present the dependence of the solubility and diffusion coefficients for simple gases and organic vapors on the concentration of the penetrant in the glassy polymer (9,11,13,15,17,33,34,89). 

The average value of Tg = 90 °C for PS is used from Table 2-2. Using Table 9-4 and Eq. (9-19) for glassy polymers one can immediately calculate the solubility coefficients ... 

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