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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Understanding the dynamics of water in solid-state polymer electrolytes (e.g., Nafion) is important for a variety of applications ranging from membrane-based water purification to hydrogen fuel cells. In this study, the dynamics of water in Nafion was investigated at both low and high humidities with time-resolved Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy; a technique that provides a molecular fingerprint of both the diffusant and the polymer simultaneously in real time. At low humidities (0-22% RH), an extended initial time lag resulted in non-Fickian behavior, where dynamic infrared data provided evidence for a reaction between water and sulfonic acid. A diffusion-reaction model was developed and predicted this anomalous behavior, where the time lag was a function of water content. At high humidities (0-100% RH), a slow approach to steady state resulted in non-Fickian behavior, where dynamic infrared data provided evidence of water-induced relaxation in the polymer backbone. A diffusion-relaxation model was developed and regressed well to both the polymer relaxation and water diffusion data, where only one fitting parameter was used for each data set to determine both a relaxation time constant and diffusion coefficient. This approach differs significantly from previous work on non-Fickian behavior in glassy polymers, which, consisted of regressing gravimetric data to models with a minimum of six fitting parameters. Not only do the diffusion coefficients from these two models compare well with Fickian diffusion coefficients from experiments with small water concentration gradients, but also the results in this study provide physical insight into the transport mechanisms of water and relaxation phenomena in solid-state polymer electrolytes.

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