Apparent solubilities glassy polymers

The sorption isotherms for most gases in glassy polymers tend to have concave shapes l ke those shown in Figure 4. As a result, the apparent solubility (S = C2/p2) is a decreasing function of the upstream penetrant pressure. On the other hand, the diffusion coefficients, D, of gases in glassy polymers typically increase with sorbed concentration even in the absence of plasticization (17). 

The apparent solubilities and average diffusivities, S and D, for CO2 and CH in a number of glassy polymers at 30"C and 20 atm are shown in Table I. The values reported for cellulose acetate were estimated from various sources in the literature (., 6,37). In the case of cellulose acetate where C02 plasticization is apparently significant, it was assumed that the CH4 permeability in CO2/CH4 mixtures will increase by at least the same percentage as the CO2 permeability. This assumption seems reasonable since the plasticized matrix becomes more rubber-like and less discriminating for penetrants of different sizes and shapes (see Figure 1). 

Figure 5. Correlation of the apparent solubility at 20 atm and 35 °C with the critical temperatures of various penetrants in a number of glassy polymers polycarbonate,...

With rubbery polymers, the transport process is well described by Fick s laws and, at the low solubilities under consideration, with nearly concentration independent diffusion constants. The solubilities also are simple in that Henry s law is obeyed. Diffusion constants are usually in the 10-9 to 10-11 cm2/sec range for organic molecules at very low concentrations. With glassy polymers the transport at very low concentration is also Fickian but with the complications introduced by dual mode sorption as discussed in detail in the introductory section. Here, apparent diffusion constants in the range of 10 10 to 10"14 cm2/sec are often found. 

Total solubility of gases in glassy polymers is higher than in rubbers, which is consistent with the apparent existence of an additional sorption site in such polymers. The temperature dependence of Henry s law constant... 

The FFV value in the polymer phase of the mixed matrix can be calculated through Equation (7.11) based on the unpenetrated polymer density pi in the polymer phase of the MMM, obtained from the solubility data as indicated above. Since different filler loadings will induce different FFV in the polymer phase, one can use Equation (7.16) to obtain the parameters A and B virtually from as little as two different mixed matrices with two different filler loadings then the same Equation (7.16) can be applied to calculate or correlate the infinite dilution apparent diffusivity Dim for any other filler loading in the same glassy polymer. 

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