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The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO$_\text{2}$/N$_\text{2}$ separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes.

Background to date, more than 243 million COVID-19 cases have been diagnosed globally, with 4.94 million deaths, 489.000 new cases and 8.474 deaths per day. In Italy there are currently 4.73 million cases and 132.000 deaths. It is well known that the entry of the SARS- CoV-2 virus into cells is mediated by the binding between the virus Spike-glycoprotein (S) and the membrane ACE2-receptor (ACE2-R). When SARS-CoV-2 binds to ACE2-R, with subsequent membrane fusion and virus entry into the cell, a down-regulation of these receptors occurs. ACE2 –R downregulation plays a crucial role in the pulmonary and systemic inflammatory response. A serious clinical course appears to be associated with some factors such as age, previous pathologies and comorbidities. However, also a dysregulation of the RAA system linked to a different expression of ACE-2 R and TMPRSS2 gene polymorphisms and different serum levels of soluble ACE2 (sACE2), could be associated with abnormal inflammatory and immune response to SARS-CoV-2 infection. Aim of the Study we aimed to verify whether there is an association between the clinical course of COVID-19 patients (pts) and the presence of more frequent ACE2 and TMPRSS2 single-nucleotide polymorphisms (SNPs) and if sACE2 levels are related to specific ACE2 and TMPRSS2 polymorphic variants. Methods we consecutively enrolled subjects with previous documented SARS-CoV-2 infection and divided our sample into three groups: pts with asymptomatic course; pts with symptomatic course but without the need for hospitalization for COVID-19; pts with severe symptomatic course requiring hospitalization in intensive care unit. Data about age, clinical course, comorbidities, and therapies were collected. Blood samples were taken for the genetic analysis of the most frequent SNPs of the ACE2-R and TMPRSS2 detected in Italian population, in particular genotypic variants TT and CC of ACE2 SNPs 1 and 5 (rate of 5% and 14% respectively) and genotypic variants TT and CC of TMPRSS2 SNPs 2 and 3 (rate of 50% and 30% respective). Results among 178 pts enrolled up to March 2022, we have so far analyzed the genetic polymorphisms of 74 pts.; 21 (28%) were hospitalized for COVID-19, 38 (51%) had symptomatic course without hospitalization and 15 (21%) were completely pauci-asymptomatics. Serum concentrations of sACE2 and distribution of polymorphic variants in the three groups are summarized in Table 1. We found that sACE2 levels were higher in genotypic variant CC of SNP 1 of TMPRSS2 gene (Table 2). Considering that a high concentration of sACE2 outlines a proinflammatory condition, it could be hypothesized that the CC genotype may be a predisposing condition to the cytokine storm of COVID-19. Perspectives: Genetic analysis of ACE2 and TMPRSS2 SNPs will help to clarify the relationship between these polymorphic variant, sACE2 levels, risk of SARS-CoV2 infection and severity of clinical presentation of COVID-19 in patients with or without CV diseases.

Background It is well known that the entry of the SARS- CoV-2 virus into cells is mediated by the binding between the virus Spike-glycoprotein (S) and the membrane ACE2-receptor (ACE2R). When SARS-CoV-2 binds to ACE2R, with subsequent membrane fusion and virus entry into the cell, a down-regulation of these receptors occurs. ACE2R downregulation plays a crucial role in the pulmonary and systemic inflammatory response. Also ACE2 deficiency is thought to play an important role in the pathogenesis of SARS-CoV-2 infection. The down-regulation of ACE2 induced by viral infection could be particularly harmful in subjects with pre-existing ACE2 deficiency, for example due to advanced age, the presence of DM, arterial hypertension or pre-existing heart disease, including HF. Literature data suggest an association between the patient's age and comorbidities and a greater risk of severe clinical course and with a worse prognosis. However, serious clinical pictures requiring hospitalization or leading to death have also been observed in young subjects or subjects without comorbidities. Aim of the Study we aimed to identify predicting factors of a higher risk in terms of severity of the clinical course and worse prognosis in the population of the Brescia area, affected by a large number of cases in the first period of COVID-19 outbreak. In particular, we aimed to verify whether there is correlation between levels of serum ACE2 (sACE2) and the risk of SARS-CoV-2 infection, as well as between sACE2 and the different severity of the clinical manifestations of COVID-19 in patients with and without CV diseases. Methods we consecutively enrolled subjects with previous documented SARS-CoV-2 infection and divided our sample into three groups: pts with asymptomatic course; pts with symptomatic course but without the need for hospitalization for COVID-19; pts with severe symptomatic course requiring hospitalization in intensive care unit. Blood samples were taken for sACE2 dosage. We compared the concentrations of sACE2 in these groups in relation to the age, clinical course, comorbidities, and ongoing therapies. Results at March 2022, we enrolled 178 pts, 51 (28%) were hospitalized for COVID-19, whereas 78 (44%) had symptomatic course without hospitalization and 49 (28%) were completely pauci-asymptomatic. Only 6 pts (4%) had myocarditis or pericarditis SARS-CoV-2-related. Between hospitalized pts, male sex (67%), older age and higher BMI were most frequent. Moreover, chronic heart failure (20%), a diagnosis of cardiopathy (29%) and AF or atrial flutter (22%) were most frequent (Table 1). Plasma concentrations of sACE2 will be dosed and analyzed in relation to the clinical characteristics of each patient. Perspectives ACCEPT study will help to clarify the relationship between ACE2 molecule, the risk of SARS-CoV2 infection and the severity of clinical presentation of COVID-19 in pts with or without CV diseases.

The gas separation performance of biopolymers is still scarcely characterized, mostly because of their poor thermomechanical properties and high crystallinity which is associated to low permeability. In this work we characterize the gas transport in a poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) random copolymer, that has a relatively low crystallinity and good mechanical properties, combined with a renewable origin, biodegradability and biocompatibility. In the study we also compared several solvents for membrane casting, with different toxicity levels. We found that dimethyl carbonate allows the production of polymer films with transport properties similar to those obtained with the more toxic CHCl3, and it leads also to stable crystallinity of the samples over time. PHBV films show a size-sieving gas separation behaviour, as the permeability decreases significantly with the gas kinetic diameter. However, the strong energetic interactions of CO2 with the polymer matrix, confirmed by the Flory-Huggins model, induce a marked solubility-driven CO2/N2 and CO2/CH4 selectivity, which could make the material potentially interesting for CO2 removal processes.

Thermodynamics is the science of the interactions between energy and matter. It was formalized in the late 19th century and remains an essential piece in solving many technological challenges that society faces today. Yet, it is often considered complex and challenging, perhaps because it is often taught within a rigid mathematical framework, without highlighting the extensive range of applications and the tools that it offers for understanding and elaborating a sustainable future. The authors of this paper have performed an industrial survey (Kontogeorgis et al., Ind. Eng. Chem. Res., 2021, 60, 13, 4987-5013), which pointed out that thermodynamics is indeed a cornerstone of many processes in a large range of industries, but that as of today, many questions and needs remain unanswered. Some missing answers are caused by a lack of knowledge of the existing tools (educational issue), some by the unavailability of models, parameters or by the lack of transferability of the concepts from one system to another. In other cases, simply, no generally accepted approach exists, and fundamental research is required for understanding the phenomena. In all cases, data are needed, either to understand, develop, or validate the models. Specific recent examples of applied thermodynamics research relevant to industrial practice are discussed. This manuscript aims not only at promoting research but also at encouraging highly trained professionals to engage in education, laboratory work, fundamental developments, and/or model validation. Such professionals should find positions both in academia and in industry, as well as with software vendors. Collaboration between academia, industry, and software vendors is essential in order to foster new developments and serve the goals of sustainable development and circular economy.

The prediction of the solubility of gasses in semi-crystalline polymers is still a challenging task due to the difficulty in providing a comprehensive description of the morphological and mechanical perturbation felt by the amorphous phase intercalated with the impermeable crystal domains. Among the different modeling techniques, a frequently adopted strategy models the reduced solubility experienced by the confined amorphous phase via an additional pressure to the external gas pressure acting on the latter, the so-called constraint pressure ‘pc’. The work presented here is dedicated to a newly developed multi-scale modeling strategy, belonging to the aforementioned category, that innovatively couples Molecular Dynamics simulations with Lattice Fluid theory. The model was applied to carbon dioxide, ethylene, and propane solubility isotherms in High-Density Polyethylene, and validated against experimental literature data, confirming its ability to model the solubility in semi-crystalline polymers. In addition, it showed good accordance with a fully macroscopic model already present in the literature. The successful multi-scale coupling presented here paves the way for the development of a fully predictive modeling strategy.

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.

Aims To describe the characteristics of a cohort of patients with cardiac amyloidosis (CA) and to compare the two most common phenotypes of CA, transthyretin (ATTR) and immunoglobulin light-chain (AL). Methods and results One-hundred and eighty patients [n = 115 (64%) men, 74 ± 11 years] were retrospectively included from January 2013 to April 2021 in a single centre in Northern Italy. The majority [n = 102 (57%)] had ATTR-CA, whereas 78 patients (43%) had AL-CA. ATTR-CA patients were older (79 ± 7 vs. 66 ± 10 years, P Conclusions Despite ATTR-CA patients showed worse baseline characteristics, suggesting a more advanced disease at presentation, AL-CA phenotype was associated with a higher risk of all-cause death. Of note, CV mortality was comparable between the two groups.

Aims HFA-PEFF and H2FPEF scores were developed to aid the diagnosis of heart failure with preserved ejection fraction (HFpEF) and have been associated with outcomes. We aimed to investigate the diagnostic and prognostic significance of these scores in patients with a specific phenotype of HFpEF, cardiac amyloidosis (CA). Methods and results In a retrospective, double-centre, observational study we included 171 patients with either transthyretin (ATTR) (n = 89, 52%) or light-chain (AL) (n = 82, 48%) cardiac amyloidosis and preserved left ventricular ejection fraction (LVEF). Patients were divided into three groups according to HFA-PEFF score (low, 0–1; intermediate 2–4; high 5–6) and H2FPEF score (low, 0–1; intermediate 2–5; high 6–9). None of the patients had a HFA-PEFF score of 0 or 1 (n = 0, 0%); 57 (33.3%) patients had HFA-PEFF score 2–4 and the majority (n = 114, 66.7%) had a high HFA-PEFF score. Twenty-eight (16.4%), 104 (60.8%), 39 (22.8%) patients had low, intermediate, and high H2FPEF score, respectively. During a median follow-up of 14.5 (6.5–30.2) months after diagnosis, 61 (35.7%) patients died. Patients with a high HFA-PEFF score had higher mortality, compared to those with an intermediate score (47.4% vs. 12.3%, P Conclusions Our results suggest that a low HFA-PEFF score successfully rules out CA diagnosis, whereas some CA patients present a low H2FPEF score, potentially misleading the diagnosis. HFA-PEFF but not H2FPEF score was associated with outcome in patients with CA.

Polyxydroxyalkanoates (PHA) are a family of linear optically active semi-crystalline polyesters produced by bacterial fermentation, known for their overall sustainability, including biodegradability and biocompatibility. PHA are also characterized by thermoplasticity and good mechanical properties, comparable to those of commercially relevant standard polymers. The gas transport properties of these materials are still scarcely characterized experimentally, and their determination is complicated by a number of uncertainty sources, such as a time-dependent degree of crystallinity. In this study we aim at evaluating the physicochemical and transport properties of such materials with molecular simulations, to gain information about their applicability in the membrane gas separation field. In order to draw correlation between the molecular structure and the performance of these materials, three homopolymers and two copolymers of the PHA family were considered: • poly(3-hydroxybutyrate) (P3HB); • poly(3-hydroxyvalerate) (P3HV); • poly(4-hydroxybutyrate) (P4HB); • poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV); • poly(3-hydroxybutyrate-co-4-hydroxybutyrate) (PHBB). Molecular models of each material were simulated using Molecular Dynamics (MD), obtaining amorphous density and solubility parameter values, that were successfully validated with experimental data found in literature2,3. The simulated values of radius of gyration, accessible free volume, density, cohesive energy and elastic modulus in the different copolymers were correlated to their chemical composition. Sorption and diffusion in the polymers were then analysed for three gases, O2, CH4 and CO2, by means of Grand Canonical Monte Carlo (GCMC) and MD simulations. The results were compared with experimental values, obtained through permeation tests at different temperatures, performed on PHBV with 8% of 3-hydroxyvalerate monomers purchased from Merck-Sigma.

This work aims at obtaining a systematic description and prediction of the multicomponent gas separation behavior of membranes, using the Non-Equilibrium Lattice Fluid (NELF) model for gas sorption and the Standard Transport (ST) model for gas permeation. The scheme is applied to a comprehensive analysis of CO2/CH4 separation with cellulose acetate membranes. A dedicated experimental campaign (pressure-volume-temperature (pVT), differential scanning calorimetry (DSC) and pure gas sorption tests) was performed to obtain reliable model parameters, accounting also for crystallinity. The approach was validated against a complete set of literature data, including mixed gas sorption and permeation.The parameters obtained were used to perform predictive simulations of mixed CO2/CH4 sorption and permeation in a wide mixture composition range. The NELF model accurately predicts the effect of temperature on sorption, as well as the strong competitive exclusion of CH4 when CO2 is present, that enhances the solubility-selectivity. The ST model correctly estimates the experimentally observed lower-than-ideal CO2/CH4 perm-selectivity. The model shows that low perm-selectivity is due to mixed gas diffusivity-selectivity (which is not available experimentally): even though solubility-selectivity increases in the mixed gas case, diffusivity-selectivity suffers a larger departure from pure gas conditions, ultimately leading to a lower perm-selectivity under multicomponent conditions.

The sorption and transport of CO2 in two polymers, Matrimid and PDMS, were modelled using data available across the critical region, at various temperatures and up to 18 MPa. The experimental trends show a complex behavior that is affected by the transition from gas-like to liquid-like density of CO2, as well as by the sorption induced glass transition of the polymer. The Non Equilibrium Thermodynamics (NET-GP) approach for the solubility, coupled to its complementary tool for the permeability, the Standard Transport Model (STM), allows to represent thoroughly the complexity of CO2 sorption and permeation in this operative range with a selfconsistent set of parameters. Furthermore, the model offers a deep insight in the swelling induced by CO2 in the different states of the polymers, and allows to decouple the kinetic and thermodynamic contributions to the transport phenomena in a meaningful way. This work takes a step forward in the understanding and simulation of the complex interactions between high pressure, supercritical CO2 and industrially relevant polymeric materials.

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%.

We used catalytic arene−norbornene annulation (CANAL) polymerization to synthesize high-molecular weight (degree of polymerization 500−800 based on Mn) rigid ladder polymers with methyl, ethyl, and isopropyl substituents that can form self-standing films. The short alkyl substitution on CANAL ladder polymers significantly impacted gas transport properties and their chain packing as revealed by variable-temperature pure-gas permeation and high-pressure sorption experiments as well as wide-angle X-ray scattering. Interestingly, a combination of methyl and isopropyl substituents enhanced both the sorption capacity and permeation of all gases tested without compromising permselectivity. Our findings suggest that varying short alkyl substitutions on ladder polymers with high fractional free volume represents an effective strategy to tune their chain packing and fractional free volume, which can enhance permeability without compromising permselectivity.

A simulation strategy encompassing different scales was applied to the systematic study of the effects of CO2 uptake on the properties of atactic polystyrene (aPS) melts. The analysis accounted for the influence of temperature between 450 and 550 K, polymer molecular weights (Mw) between 2100 and 31000 g/mol, and CO2 pressures up to 20 MPa on the volumetric, swelling, structural, and dynamic properties of the polymer as well as on the CO2 solubility and diffusivity by performing molecular dynamics (MD) simulations of the system in a fully atomistic representation. A hierarchical scheme was used for the generation of the higher Mw polymer systems, which consisted of equilibration at a coarse-grained level of representation through efficient connectivity-altering Monte Carlo simulations, and reverse-mapping back to the atomistic representation, obtaining the configurations used for subsequent MD simulations. Sorption isotherms and associated swelling effects were determined by using an iterative procedure that incorporated a series of MD simulations in the NPT ensemble and the Widom test particle insertion method, while CO2 diffusion coefficients were extracted from long MD runs in the NVE ensemble. Solubility and diffusivity compared favorably with experimental results and with predictions of the Sanchez-Lacombe equation of state, which was reparametrized to capture the Mw dependence of polymer properties with greater accuracy. Structural features of the polymer matrix were correctly reproduced by the simulations, and the effects of gas concentration and Mw on structure and local dynamics were thoroughly investigated. In the presence of CO2, a significant acceleration of the segmental dynamics of the polymer occurred, more pronouncedly at low Mw. The speed-up effect caused by the swelling agent was not limited to the chain ends but affected the whole chain in a similar fashion.

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 &deg, 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 &deg, 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.

CO2 and CH4 mixed-gas solubility was measured in 3,3′-dihydroxy-4,4′-diamino-biphenyl (HAB) 2,2′-bis-(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) polyimide and in its thermally rearranged (TR) derivative, TR450. Due to competitive sorption effects, the solubility of both species in mixed-gas conditions is lower than the corresponding pure-gas solubility at the same fugacity. CH4 sorption is significantly affected by the presence of the second gas, while CO2 behavior is hardly altered. Therefore, the multicomponent solubility-selectivity is higher than the ideal value calculated from pure-gas sorption data, and this has a positive impact on CO2/CH4 separation properties. The multicomponent solubility data were modelled with the Non-Equilibrium Lattice Fluid (NELF) model, using only pure component parameters and binary interaction parameters obtained from pure-gas sorption data available in the literature, with no parameters determined from the mixed-gas sorption data. Although it is easier to use, the multicomponent Dual Mode Sorption (DMS) model yielded less accurate predictions of mixed-gas sorption. Mixed-gas sorption experiments and modelling, coupled with mixed-gas permeation data, enabled a better fundamental understanding of the separation properties of these materials. Unlike the case of pure-gas experiments, where diffusivity contributes more to the overall ideal selectivity, competitive sorption is the main effect governing the permselectivity of these membrane materials at multicomponent conditions. A systematic comparison with literature data on mixed-gas CO2/CH4 sorption and permeability revealed these to be generalized trends, obeyed by materials of very different chemical constitution. This finding can inform on the criteria that make polymers performing better in multicomponent scenarios, with potential impact on the design and synthesis strategies of new materials.

In this work, a new experimental protocol was designed to measure sorption of ternary gas mixtures in polymer membranes for the first time. We measured the sorption isotherms of binary and ternary mixtures of C2H6, CO2, and CH4 in PIM-1, using a pressure decay apparatus, working at constant composition and variable pressure of the gas phase. The results show competitive sorption effects in all gas mixtures analyzed, affecting each species in proportion to the total sorbed concentration of the other components. It was found that the presence of C2H6 in the mixture reduces the sorption of both CH4 and CO2 to a similar extent, so that the CO2/CH4 solubility-selectivity is not markedly affected. The experimental data were used to validate predictions of the Non-Equilibrium Lattice Fluid (NELF) model of binary and ternary sorption isotherms. The NELF model is generally in close agreement, both in the prediction of pressure and mixture composition effects, proving to be a reliable tool to assess mixed-gas sorption, even in complex scenarios.

The gas solubility in polymeric membranes affects the separation performance, particularly in the case of CO2 capture processes. Solubility and solubility-selectivity in membranes of multicomponent mixtures can deviate rather markedly from the corresponding pure gas values, due to swelling and competition phenomena, and require dedicated time-consuming measurements. Many experiments can be avoided by using a suitable thermodynamic tool, such as an Equation of State (EoS) model, to represent the gases sorption in the membrane. Such models require, for parameterization, knowledge of the polymer behavior above the glass transition Tg, which is a limit for membrane modeling, because the most attractive polymers for gas separation are rigid matrices characterized by very high Tg values, difficult to reach experimentally. In this work, we study the sorption of CO2/CH4 mixtures in a high-Tg polyimide membrane (Matrimid®) using a bottom-up approach. Pressure-volume-temperature data for Matrimid® above Tg are generated using NPT Molecular Dynamics simulations: the results are regressed to find Matrimid® parameters for the PC-SAFT Equation of State. Finally, the Non Equilibrium PC-SAFT macroscopic model (NE-PC-SAFT) is used to calculate CO2 and CH4 solubility and solubility-selectivity as a function of gas mixture pressure, composition and temperature. The approach is tested successfully over many experimental pure gas and vapor sorption data in Matrimid®. Mixed gas calculations predict a marked competition, which affects more methane than CO2 sorption, and results in a higher-than-ideal value of solubility-selectivity. Combined with the fact that experimental mixed gas permeability-selectivity is lower than the ideal value, such results indicate that the diffusivity of CH4 in Matrimid is significantly enhanced in presence of CO2, causing a decrease of diffusivity-selectivity. The gas solubility in polymeric membranes affects the separation performance, particularly in the case of CO2 capture processes. Solubility and solubility-selectivity in membranes of multicomponent mixtures can deviate rather markedly from the corresponding pure gas values, due to swelling and competition phenomena, and require dedicated time-consuming measurements. Many experiments can be avoided by using a suitable thermodynamic tool, such as an Equation of State (EoS) model, to represent the gases sorption in the membrane. Such models require, for parameterization, knowledge of the polymer behavior above the glass transition Tg which is a limit for membrane modeling, because the most attractive polymers for gas separation are rigid matrices characterized by very high Tg values, difficult to reach experimentally. In this work, we study the sorption of CO2/CH4 mixtures in a high-Tg polyimide membrane (Matrimid®) using a bottom-up approach. Pressure-volume-temperature data for Matrimid® above Tg are generated using NPT Molecular Dynamics simulations: the results are regressed to find Matrimid® parameters for the PC-SAFT Equation of State. Finally, the Non Equilibrium PC-SAFT macroscopic model (NE-PC-SAFT) is used to calculate CO2 and CH4 solubility and solubility-selectivity as a function of gas mixture pressure, composition and temperature. The approach is tested successfully over many experimental pure gas and vapor sorption data in Matrimid®. Mixed gas calculations predict a marked competition, which affects more methane than CO2 sorption, and results in a higher-than-ideal value of solubility-selectivity. Combined with the fact that experimental mixed gas permeability-selectivity is lower than the ideal value, such results indicate that the diffusivity of CH4 in Matrimid® is significantly enhanced in presence of CO2, causing a decrease of diffusivity-selectivity.

We have explored the effect of temperature, in the range between 25 and 50 °C, on the mixed gas CO2/CH4 sorption in a polymer of intrinsic microporosity (PIM-1), that has a solubility-selectivity higher than diffusion-selectivity for this mixture. The new data obtained in this work at 25 and 50 °c were combined with previously published data obtained at 35 °C to determine the temperature-dependence of mixed gas solubility and solubility-selectivity, a type of information that has not been obtained before in the literature. The data were collected at different total pressures and gas mixture compositions using a pressure decay − gas chromatographic device. The data collected indicate that the sorption of such mixture in PIM-1 is dominated by competition, whose major effect is to reduce the solubility of gases with respect to the pure gas value at same fugacity. The competitive phenomena follow a generalized trend that is not dependent on total gas pressure, composition and gas type but is only a function of the second gas concentration in the polymer and temperature. In particular the competition, expressed as reduction of gas solubility with respect to pure gas value, decreases with the concentration of the second gas, and increases with increasing temperature. Such effects are however generally favourable to separation, with positive deviations of the CO2/CH4 solubility-selectivity from ideal values calculated from pure gas solubility, by factors as high as 4. As a rule of thumb, observed at all temperatures and also in other glassy polymers, the real solubility-selectivity deviates positively from ideal value calculated from pure gas behaviour if the molar content of CO2 in the membrane is higher than that of methane, which is usually the case, unless low CO2 gas fractions are considered. A new type of generalized plot, reporting departures of multicomponent properties from the corresponding pure gas values, has been traced for this system and indicates that solubility selectivity departure is univocally correlated to CH4 solubility departure, independent of the operative conditions (pressure, composition, temperature) explored during the experiments.