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The majority of materials used for membrane-based separation of gas mixtures are non-renewable and non-biodegradable, and the assessment of alternative bio-based polymers requires expensive and time-consuming experimental campaigns. This effort can be reduced by adopting suitable modelling approaches. In this series of works, we propose various modelling approaches to assess the CO2/CH4 separation performance of eight different copolymers of 3-hydroxybutyrate and 3-hydroxyvalerate (PHBV) using a limited amount of experimental data for model calibration. In part 1, we adopted a fully atomistic approach based on Molecular Dynamics (MD), while, in this work, we propose a multiscale methodology where a molecular description of the polymers is bridged to a macroscopic prediction of its gas sorption behaviour. PHBV structures were simulated using MD to obtain pressure–volume–temperature data, which were used to parametrise the Sanchez–Lacombe Equation of State. This, in turn, allows for the evaluation of the CO2 and CH4 solubility in the copolymers at various pressures and compositions with little computational effort, enabling the estimate of the sorption-based selectivity. The gas separation performance obtained with this multiscale technique was compared to results obtained with a fully atomistic model and experimental data. The solubility–selectivity for the CO2/CH4 mixture is in reasonable agreement between the two models and the experimental data. The multiscale method presented is a time-efficient alternative to fully atomistic methods and detailed experimental campaigns and can accelerate the introduction of renewable materials in different applications.

In this work, we assessed the CO2 and CH4 sorption and transport in copolymers of 3-hydroxybutyrate and 3-hydroxyvalerate (PHBV), which showed good CO2 capture potential in our previous papers, thanks to their good solubility–selectivity, and are potential biodegradable alternatives to standard membrane-separation materials. Experimental tests were carried out on a commercial material containing 8% of 3-hydroxyvalerate (HV), while molecular modelling was used to screen the performance of the copolymers across the entire composition range by simulating structures with 0%, 8%, 60%, and 100% HV, with the aim to provide a guide for the selection of the membrane material. The polymers were simulated using molecular dynamics (MD) models and validated against experimental density, solubility parameters, and X-ray diffraction. The CO2/CH4 solubility–selectivity predicted by the Widom insertion method is in good agreement with experimental data, while the diffusivity–selectivity obtained via mean square displacement is somewhat overestimated. Overall, simulations indicate promising behaviour for the homopolymer containing 100% of HV. In part 2 of this series of papers, we will investigate the same biomaterials using a macroscopic model for polymers and compare the accuracy and performance of the two approaches.

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.

We developed Mixed Matrix Membrane Adsorbers (MMMAs) formed by cellulose acetate and various sorbent particles (activated carbon, zeolites ZSM-5 and clinoptilolite) for the removal of urea, creatinine and uric acid from aqueous solutions, to be used in the regeneration of spent dialysate water from Hemodialysis (HD). This process would allow reducing the disproportionate amount of water consumed and permits the development of closed-loop HD devices, such as wearable artificial kidneys. The strategy of MMMAs is to combine the high permeability of porous membranes with the toxin-capturing ability of embedded particles. The water permeability of the MMMAs ranges between 600 and 1500 L/(h m2 bar). The adsorption of urea, the limiting toxin, can be improved of about nine times with respect to the pure cellulose acetate membrane. Flow experiments demonstrate the feasibility of the process in a real HD therapy session.

Torlon® is a thermally and plasticization-resistant polyamide imide characterized by low gas permeability at room temperature. In this work, we aimed at improving the polymer performance in the thermally-enhanced He/CO2 and H2/CO2 separations, by compounding Torlon® with a highly permeable filler, ZIF-8, to fabricate Mixed Matrix Membranes (MMMs). The effect of filler loading, gas size, and temperature on the MMMs permeability, diffusivity, and selectivity was investigated. The He permeability increased by a factor of 3, while the He/CO2 selectivity decreased by a factor of 2, when adding 25 wt % of ZIF-8 at 65 °C to Torlon®; similar trends were observed for the case of H2. The MMMs permeability and size-selectivity were both enhanced by temperature. The behavior of MMMs is intermediate between the pure polymer and pure filler ones, and can be described with models for composites, indicating that such materials have a good polymer/filler adhesion and their performance could be tailored by acting on the formulation. The behavior observed is in line with previous investigations on MMMs based on glassy polymers and ZIF-8, in similar conditions, and indicates that ZIF-8 can be used as a polymer additive when the permeability is a controlling aspect, with a proper choice of loading and operative temperature.

The transport of H2, He, CO2, O2, CH4, and N2 at three temperatures up to 65 °C was measured in dense, thick composite films formed by amorphous Polysulfone (PSf) and particles of the size-selective zeolitic imidazolate framework 8 (ZIF-8) at loadings up to 16 wt%. The morphological and structural properties of the membranes were analyzed via SEM and density measurement. The addition of ZIF-8 to PSf enhances the H2 and He permeabilities up to 480% with respect to the pure polymer, while the ideal H2/CO2 and He/CO2 selectivities of MMMs reach values up to 30–40% higher than those of pure PSf. The relative permeability and diffusivity enhancements are higher than those obtained in other polymers, such as PPO, with the same amount of filler. The Maxwell–Wagner–Sillars model is able to represent the MMM H2/CO2 separation performance for filler volume fractions below 10%.

This Special Issue of Membranes provides an updated and comprehensive overview of the state of fundamental knowledge on the fluid sorption and transport in glassy polymers, combining original experimental and modeling works, as well as reviews, prepared by renowned experts [...]

In this study, we prepared and characterized composite films formed by amorphous poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and particles of the size-selective Zeolitic Imidazolate Framework 8 (ZIF-8). The aim was to increase the permselectivity properties of pure PPO using readily available materials to enable the possibility to scale-up the technology developed in this work. The preparation protocol established allowed robust membranes with filler loadings as high as 45 wt% to be obtained. The thermal, morphological, and structural properties of the membranes were analyzed via DSC, SEM, TGA, and densitometry. The gas permeability and diffusivity of He, CO2, CH4, and N2 were measured at 35, 50, and 65 °C. The inclusion of ZIF-8 led to a remarkable increase of the gas permeability for all gases, and to a significant decrease of the activation energy of diffusion and permeation. The permeability increased up to +800% at 45 wt% of filler, reaching values of 621 Barrer for He and 449 for CO2 at 35 °C. The ideal size selectivity of the PPO membrane also increased, albeit to a lower extent, and the maximum was reached at a filler loading of 35 wt% (1.5 for He/CO2, 18 for CO2/N2, 17 for CO2/CH4, 27 for He/N2, and 24 for He/CH4). The density of the composite materials followed an additive behavior based on the pure values of PPO and ZIF-8, which indicates good adhesion between the two phases. The permeability and He/CO2 selectivity increased with temperature, which indicates that applications at higher temperatures than those inspected should be encouraged.

Facilitated transport membranes are particularly promising in different separations, as they are potentially able to overcome the trade-off behavior usually encountered in solution-diffusion membranes. The reaction activated transport is a process in which several mechanisms take place simultaneously, and requires a rigorous theoretical analysis, which unfortunately is often neglected in current studies more focused on material development. In this work, we selected and reviewed the main mathematical models introduced to describe mobile and fixed facilitated transport systems in steady state conditions, in order to provide the reader with an overview of the existing mathematical tools. An analytical solution to the mass transport problem cannot be achieved, even when considering simple reaction schemes such as that between oxygen (solute) and hemoglobin (carrier) ( A + C ⇄ A C ), that was thoroughly studied by the first works dealing with this type of biological facilitated transport. Therefore, modeling studies provided approximate analytical solutions and comparison against experimental observations and exact numerical calculations. The derivation, the main assumptions, and approximations of such modeling approaches is briefly presented to assess their applicability, precision, and flexibility in describing and understanding mobile and fixed site carriers facilitated transport membranes. The goal is to establish which mathematical tools are more suitable to support and guide the development and design of new facilitated transport systems and materials. Among the models presented, in particular, those from Teramoto and from Morales-Cabrera et al. seem the more flexible and general ones for the mobile carrier case, while the formalization made by Noble and coauthors appears the most complete in the case of fixed site carrier membranes.

In an effort to reduce the experimental tests required to characterize the mixed-gas solubility and solubility-selectivity of materials for membrane separation processes, there is a need for reliable models which involve a minimum number of adjustable parameters. In this work, the ability of the Dual Mode Sorption (DMS) model to represent the sorption of CO2/CH4 mixtures in three high free volume glassy polymers, poly(trimethylsilyl propyne) (PTMSP), the first reported polymer of intrinsic microporosity (PIM-1) and tetrazole-modified PIM-1 (TZ-PIM), was tested. The sorption of gas mixtures in these materials suitable for CO2 separation has been characterized experimentally in previous works, which showed that these systems exhibit rather marked deviations from the ideal pure-gas behavior, especially due to competitive effects. The accuracy of the DMS model in representing the non-idealities that arise during mixed-gas sorption was assessed in a wide range of temperatures, pressures and compositions, by comparing with the experimental results available. Using the parameters obtained from the best fit of pure-gas sorption isotherms, the agreement between the mixed-gas calculations and the experimental data varied greatly in the different cases inspected, especially in the case of CH4 absorbed in mixed-gas conditions. A sensitivity analysis revealed that pure-gas data can be represented with the same accuracy by several different parameter sets, which, however, yield markedly different mixed-gas predictions, that, in some cases, agree with the experimental data only qualitatively. However, the multicomponent calculations with the DMS model yield more reliable results than the use of pure-gas data in the estimation of the solubility-selectivity of the material.

We fabricated novel composite (mixed matrix) membranes based on a permeable glassy polymer, Poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), and variable loadings of few-layer graphene, to test their potential in gas separation and CO2 capture applications. The permeability, selectivity and diffusivity of different gases as a function of graphene loading, from 0.3 to 15 wt %, was measured at 35 and 65 °C. Samples with small loadings of graphene show a higher permeability and He/CO2 selectivity than pure PPO, due to a favorable effect of the nanofillers on the polymer morphology. Higher amounts of graphene lower the permeability of the polymer, due to the prevailing effect of increased tortuosity of the gas molecules in the membrane. Graphene also allows dramatically reducing the increase of permeability with temperature, acting as a “stabilizer” for the polymer matrix. Such effect reduces the temperature-induced loss of size-selectivity for He/N2 and CO2/N2, and enhances the temperature-induced increase of selectivity for He/CO2. The study confirms that, as observed in the case of other graphene-based mixed matrix glassy membranes, the optimal concentration of graphene in the polymer is below 1 wt %. Below such threshold, the morphology of the nanoscopic filler added in solution affects positively the glassy chains packing, enhancing permeability and selectivity, and improving the selectivity of the membrane at increasing temperatures. These results suggest that small additions of graphene to polymers can enhance their permselectivity and stabilize their properties.