The calculation of sorption isotherms for gases and vapors in glassy polymers is approached through a nonequilibrium equation of state procedure. The basic peculiar feature of the system, represented by the nonequilibrium structure of the mixture, is accounted for by introducing an order parameter for an isotropic glass. By revisiting the lattice fluid model by Sanchez and Lacombe (Macromolecules 1978, 11, 1145.), an expression for the Gibbs free energy of nonequilibrium lattice fluids is obtained in which the polymer species density in the solid mixture is considered as an order parameter and it is thermodynamically treated as an internal state variable. The absence of adjustable parameters makes the resulting model entirely predictive for the solubility, once the pseudoequilibrium volumetric data are available. The comparison of the predicted isotherms with the data for CO2−poly(carbonate) systems at 35 °C, obtained by Fleming and Koros (Macromolecules 1990, 23, 1353.) under different polymer prehistories, points out the remarkably good ability of the model to represent the sorption/desorption behavior and hysteresis experimentally observed.

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Polymer-based membranes play a key role in several industrially important gas separation technologies, e.g., removing CO 2 from natural gas, with enormous economic and environmental impact. Here, we develop a novel hybrid membrane construct comprised entirely of nanoparticles grafted with polymers. These membranes are shown to have broadly tunable separation performance through variations in graft density and chain length. Computer simulations show that the optimal NP packing forces the grafted polymer layer to distort, yielding regions of measurably lower polymer density. Multiple experimental probes confirm that these materials have the predicted increase in "polymer free volume", which explains their improved separation performance. These polymer-grafted NP materials thus represent a new template for rationally designing membranes with desirable separation abilities coupled with improved aging characteristics in the glassy state and enhanced mechanical behavior.

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