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

Abstract

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.

A model to predict the solubility and permeability of gaseous penetrant in the glassy polymeric membrane at high pressure

“…The solution‐diffusion mechanism 13 of gasses in the polymeric membrane is explained in several works. The gas solubility is described by various thermodynamic models, including the nonequilibrium lattice fluid (NELF), the nonequilibrium statistical‐associating‐fluid theory (NE‐SAFT), Flory‐Rehner theory, Sanchez‐Lacombe equation of state, and nonequilibrium perturbed‐hard spheres‐chain (NE‐PHSC) 14 . Moreover, the solubility of gasses in glassy polymer also can be described with the empirical approaches such as the dual mode sorption (DMS) model 15 .…”

“…The gas solubility is described by various thermodynamic models, including the nonequilibrium lattice fluid (NELF), the nonequilibrium statistical-associating-fluid theory (NE-SAFT), Flory-Rehner theory, Sanchez-Lacombe equation of state, and nonequilibrium perturbed-hard sphereschain (NE-PHSC). 14 Moreover, the solubility of gasses in glassy polymer also can be described with the empirical approaches such as the dual mode sorption (DMS) model. 15 For example, Koros and Paul investigated 16 the solubilities of CO 2 in poly (ethylene terephthalate) (PET) from 25 to 115 C. They also studied the effect of temperature on DMS parameters and observed all dual mode parameters decrease with temperature enhancement.…”

Elucidating the Role of Fluorine Content on Gas Sorption Properties of Fluorinated Polyimides

“…The dual-mode sorption model was chosen for sorption analysis in this study due to its widespread use in the current membrane literature, representing what we found to be the best compromise between scientific rigor and ease of communication. More specifically, the three model parameters possess a pedagogically compelling connection to physical meaning within the scope of model allowing for the development of structure–property relationships, such as relating changes in structure (e.g., addition of polar groups) to changes in the parameters. ,− It should be noted that the usefulness of the dual-mode model in describing the physical behavior of gas sorption in polymers has come into question, primarily due to its origin being a simple additive model between Henry and Langmuir sorption models . Additionally, the generation of inconsistent best-fit parameters resulting from nonlinear fitting has also been a concern of several researchers. , We address this concern in this article by reporting a novel method toward the nonlinear fitting and achieving reproducible dual-mode model parameters.…”

“…Additionally, the generation of inconsistent best-fit parameters resulting from nonlinear fitting has also been a concern of several researchers. , We address this concern in this article by reporting a novel method toward the nonlinear fitting and achieving reproducible dual-mode model parameters. More recently, models based on the nonequilibrium thermodynamics for the glassy polymer (NET-GP) framework have been extensively developed to describe gas sorption in glassy polymers starting from a thermodynamic basis, with the most well known being the nonequilibrium lattice fluid (NELF) model. , The NELF model, based on an assumption of a pseudo-equilibrium state in glassy polymers, has been successfully used in the fitting and prediction of gas sorption in glassy polymers given their respective lattice fluid parameters. − Interestingly, both the dual-mode sorption and NELF frameworks have shown reliable mixed-gas permeation and sorption predictions when compared to experimental results. ,,,− Both models capture the physical nature of competitive phenomena. In particular, it has been observed that when dual-mode sorption parameters are retrieved from data sets at multiple temperatures, , as done in this work, the prediction of multicomponent sorption is much more in line with that of more sophisticated models …”

“…19,26−37 It should be noted that the usefulness of the dual-mode model in describing the physical behavior of gas sorption in polymers has come into question, primarily due to its origin being a simple additive model between Henry and Langmuir sorption models. 38 Additionally, the generation of inconsistent best-fit parameters resulting from nonlinear fitting has also been a concern of several researchers. 39,40 We address this concern in this article by reporting a novel method toward the nonlinear fitting and achieving reproducible dual-mode model parameters.…”