NELF model prediction of the infinite dilution gas solubility in glassy polymers

It is observed in general that the solubility of gases and vapors in polymers, both in the rubbery and glassy phase, scales with measures of penetrant condensability, such as the Lennard-Jones parameter, the boiling temperature, or the critical temperature. For rubbery polymers, that behavior was found fully consistent with a simple equilibrium thermodynamic derivation, while no effective theoretical interpretation has been offered so far for the case of glassy polymers. On the other hand, a rigorous expression for the solubility coefficient S0 in the limit of low pressures can be found based on the NELF model for gas solubility in glassy polymers, which also indicates its dependence on the characteristic parameters of the penetrants, such as cohesive energy density, molar volume and molecular weight. The values of ln(S0) for a series of gaseous penetrants have been calculated with the NELF model for several common glassy polymers as polycarbonate (PC), polysulfone (PSf), poly(phenylene oxide) (PPO) and poly(methyl methacrylate) (PMMA). In all cases, ln(S0) is linear with the penetrant critical temperature, TC, and the dependence on temperature and on the polymer fractional free volume can easily be evaluated by the model. The analysis points out also the specific roles of the energetic and entropic contributions to the trend observed for the solubility coefficient in glassy polymers.