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Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

The transport of gases in glassy polymeric membranes has been analyzed by means of a fundamental approach based on the nonequilibrium thermodynamic model for glassy polymers (NET-GP) that considers the penetrant chemical potential gradient as the actual driving force of the diffusional process. The diffusivity of a penetrant is thus described as the product of a purely kinetic quantity, the penetrant mobility, and a thermodynamic factor, accounting for the chemical potential dependence on its concentration in the polymer. The NET-GP approach, and the nonequilibrium lattice fluid (NELF) model in particular, describes the thermodynamic behavior of penetrant/polymer mixtures in the glassy state, at each pressure or composition. Moreover, the mobility is considered to follow a simple exponential dependence on penetrant concentration, as typically observed experimentally, using only two adjustable parameters, the infinite dilution penetrant mobility L10 and the plasticization factor β, both determined from the analysis of the dependence of steady state permeability on upstream pressure. The available literature data of diffusional time lag as a function of penetrant upstream pressure has been reviewed and compared with model predictions, obtained after the values of the two model parameters (L10 and β), have been conveniently determined from steady state permeability data. The model is shown to be able to describe very accurately the experimental time lag behaviors for all penetrant/polymer pairs inspected, including those presenting an increasing permeability with increasing upstream pressure. The model is thus more appropriate than the one based on Dual Mode Sorption, which usually provides an unsatisfactory description of time lag and required an ad hoc modification.