A FREE-VOLUME DISTRIBUTION MODEL OF GAS SORPTION AND DILATION IN GLASSY-POLYMERS

A new approach is employed to model the sorption of gases in glassy polymers. The dual-mode concept that sorption occurs in both ''equilibrium'' (Henry's law) sites and ''nonequilibrium'' (Langmuir) sites is used to separate the two contributions. The Sanchez-Lacombe equation of state is applied to predict the sorption in the Henry's law region of the polymer matrix. Characteristic parameters for the polymer liquid are used at glassy temperatures to provide a description of sorption in a hypothetical ''equilibrium'' state. The additional contribution provided by sorption into the regions of excess free volume that arise from the glassy state is addressed using a modified version of an approach first proposed by Kirchheim. The excess free volume is presumed to exist in a distribution of sizes, which in turn gives rise to a distribution of sorption energies. Positron annihilation lifetime spectroscopy data are used in conjunction with PVT data to characterize the glassy polymer. This independent description of the glassy state is then used to calculate the Langmuir-type sorption. The resulting model uses only one adjustable parameter to provide excellent descriptions of the sorption of several gases in three polycarbonates, as well as the volume dilation caused by the sorbed gas.