Cryogenic gas sorption in high free volume glassy polymers: thermodynamic modeling and permeability correlations

Understanding the relationship between polymer structure, free volume, and gas-transport properties remains a central challenge in the design of membrane materials. In this concern, the fractional free volume (FFV), first outlined by Bondi's theory, is considered as the unoccupied space between the polymer chains in which the molecules of the penetrant gas can be accommodated. In recent years, the use of cryogenic N2 sorption in polymers has gained significant popularity for the characterization of gas separation membrane materials. In this work, cryogenic measurements, BET analysis, and the use of Equation of State (EoS) thermodynamic models are combined to establish a unified framework for quantifying free volume and its role in governing permeability. A wide range of polymer families is considered, including high-free-volume materials, the so-called intrinsically microporous systems, and conventional commercial polymers. Nitrogen sorption isotherms at 77 K provide experimentally accessible descriptors to estimate the polymer fractional free volume and to capture differences in backbones accessibility and polymer swellability. Furthermore, the FFV is evaluated by means of the Non-Equilibrium Lattice Fluid (NELF) model, which relates sorption behavior to the characteristic density of the polymer-penetrant system. The FFV values derived from NELF and from N2 sorption analysis show close agreement, indicating that cryogenic sorption data offer a reliable measure of thermodynamically accessible free volume. These parameters correlate well with gas permeability, demonstrating that low-temperature sorption can be effectively used to probe the free-volume architecture of dense polymers, i.e. in systems lacking well-defined porosity.