Sorption and mass transport of water in polyimides: quantifying first- and second-shell and their dynamics

Water sorption thermodynamics in glassy polymers is a salient issue in the context of accurately modeling membrane-based separation processes and tailoring the barrier properties of polymers for various technological applications. To this end, the water sorption thermodynamics of glassy polymers, two polyimides (6FDA-ODA and 6FDA-6FpDA), and a polyetherimide (Ultem®) have been interpreted within the framework of the Non-Equilibrium Thermodynamics Glassy Polymer-Perturbed Chain-Statistical Associating Fluid Theory (NETGP-PC-SAFT). This approach accounts for associative contributions, thereby enabling the quantitative reproduction of the complex interactional scenario exhibited by the three systems analyzed. This investigation also provided, for the first time, a validation of the NETGP-PC-SAFT model when self and cross-interactions occur in a polymer-penetrant system, by comparing model predictions with data from vibrational spectroscopy. Indeed, this theoretical approach enabled the quantitative estimation of the various types of sorbed water populations (i.e., water molecules that form the first and second hydration shells, respectively, related to water-polymer and water-water hydrogen bonding interactions) that successfully corresponded to the experimental outcomes. This interactional scenario has been further investigated through Density Functional Theory (DFT) calculations aimed at determining hydrogen-bonding energies and at confirming the involved interactive sites suggested by in situ Fourier-transform infrared spectroscopy. Following the validation of the NETGP-PC-SAFT model in terms of sorption thermodynamics, the model was implemented within the Standard Diffusion (SD) model to self-consistently describe water mass transport in the glassy PEI. This approach yielded a satisfactory data fit for the overall water sorption kinetics and concurrently predicted the time-evolution of the two distinct water populations with excellent concurrence to the experimental outcomes derived from in situ vibrational spectroscopy.