110th Anniversary: Gas and Vapor Sorption in Glassy Polymeric MembranesCritical Review of Different Physical and Mathematical Models

The analysis and modeling of the sorption behaviors in glassy polymers, of gases and vapors in particular, is of crucial relevance for a variety of different applications. Due to the peculiar behaviors associated with the nonequilibrium character of polymer glasses, different approaches have been used so far to describe gas solubility, whose dependence on penetrant pressure or activity shows a broad spectrum of experimental behaviors. In this work, three commonly used and completely different approaches (the Dual Mode Sorption (DMS), based on simultaneous adsorption and solubility; the Guggenheim–Anderson–de Boer (GAB) model, considering only adsorption; and the Nonequilibrium Thermodynamic model for glassy polymers (NET-GP), considering only solubility) have been critically reviewed and compared. The screening inspects the model ability to represent the different features shown by solubility isotherms in glassy systems, as well as their ability to provide reliable predictions with parameter values consistent with the underlying physical models. Finally, physical consistency issues have been also considered whenever appropriate. The analysis reveals that DMS and GAB describe well various experimental sorption behaviors, while they fail in representing other cases, such as those shown by the S-shaped isotherms of alcohols or those due to penetrants in supercritical conditions. More remarkably, both models reveal serious physical inconsistencies in the application to sorption–desorption hysteresis. Conversely, the NET-GP approach, combined with a Lattice Fluid model (NELF) shows a better predictive power, as it can naturally account for the S-shaped isotherms, and it is also physically consistent with the behavior observed in sorption–desorption hysteresis cycles.