A Predictive Model for Solubility of Gases and Vapors In Swelling Glassy Polymers

The solubility of gases and vapors is of interest for many different applications, ranging from the fabrication of gas separation membrane to the development of barrier materials for packaging or sensors. For rubbery polymers, different equations of state have been developed following different approaches and provide reliable means for the calculation of the solubility of gases and vapors. On the other hand, glassy polymers are nonequilibrium systems and the same thermodynamic tool is not suitable. The general approach called Non Equilibrium Thermodynamics of Glassy Polymers (NET-GP) coupled to the Lattice Fluid (LF) was showed to be able to predict the solubility of gases and vapors in glassy polymers at various pressures based on pure component parameters. The NELF model relies on the hypothesis that the Gibbs free energy of a glassy polymer can be described by considering the density of the polymer as an internal state variable for the penetrant-polymer system. Therefore, in order to describe the complete sorption isotherm of a species in a glassy polymer, the model requires some information on its volumetric behavior during sorption, which might be a serious limitation to its predictive ability. In the present work, a new rheological assumption has been used to evaluate the swelling induced by the penetrating species, considering that the polymer relaxation occurs involving two characteristic times on fairly different scales. If temperature is appreciably below the glass transition of the polymer, only the short-time relaxation phenomena are involved during sorption within the usual experimental times, in which local rearrangements of the macromolecules take place. Much longer time would be instead required to have a noticeable relaxation for the second mode of rearrangement that involves the whole polymer chain, and therefore, in most of the cases this is not observed. In this concern, the polymer phase can be conveniently assumed as formed by two elements corresponding to the two characteristic times of relaxation; a soft part for which the equilibrium condition holds and a glassy hard part that does not contribute to the swelling. This assumption allows the estimation of the polymer swelling at increasing penetrant activity without specific experimental data and the calculation of the complete sorption isotherm by the NELF model in a purely predictive way. This tool was satisfactorily applied for many sorption isotherms of swelling gases (such as CO2 or C2H4) and organic vapors (xylene, toluene, or hydrocarbons) in glassy polymers such as polystyrene, polycarbonate or amorphous Teflon. The model was also able to capture complex behaviors such as those given by non linear trends of dilation or when a change in concavity of the sorption isotherm is observed due to a penetrant-induced glass transitions of the polymer. The experimental dilation isotherms, for those systems for which they were available, confirmed the reliability of the present model.