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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.

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 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.

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.

The sorption of CO2, CH4 and CO2/CH4 mixtures in poly(trimethylsilyl propyne) (PTMSP) and PIM-1 (the first reported polymer of intrinsic microporosity) measured in previous works revealed that, in the multicomponent case, significant exclusion effects cause a decrease in solubility with respect to the pure-gas case, and this effect is more pronounced for the less soluble gas (CH4). In this work we perform a similar experimental analysis on the tetrazole-modified PIM-1 (TZ-PIM), at three mixture compositions (10, 30, 50 mol.% CO2) and three temperatures (25, 35, 50 °C), up to 35 bar. The obtained trends for solubility and solubility-selectivity of CO2, CH4, and their mixtures in TZ-PIM are found to be qualitatively and quantitatively comparable to those obtained for other high free volume polymers. Moreover, mixed-gas sorption data collected so far for three materials (TZ-PIM, PIM-1 and PTMSP) are modelled by means of the Non-Equilibrium Lattice Fluid (NELF) model and compared with experimental results. The model was found capable of representing the competitive effects in solubility and solubility-selectivity, in a wide range of temperature and pressure, with a better quantitative accuracy attained at higher temperatures. Finally, by coupling these results with mixed-gas permeation data, an estimate of the mixed-gas diffusivity was obtained, and it was revealed that, in multicomponent conditions, sorption provides a greater contribution to the selectivity than diffusivity, in agreement with experimental findings for similar materials.

Increasing the knowledge of the influence of water vapor in new mixed matrix membranes (MMMs) could favor the integration of novel membrane materials in the recovery of CO2 from wet industrial streams. In this work, the water vapor effect on the N2, CH4 and CO2 permeability through MMMs comprised of 20 wt% hydrophilic zeolite 4A in hydrophobic PTMSP polymer were investigated in the relative humidity range 0-75%. While in the pure PTMSP membranes, the permeability of all gases decreases with water vapor activity, with almost unchanged CO2/N2 and CO2/CH4 selectivities, in zeolite A/PTMSP MMMs, the CO2 permeability increases with increasing water content in the system up to 50% R.H., resulting in an increase in CO2/N2 and CO2/CH4selectivities with respect to pure PTMSP. Gas sorption was studied so that the effect the residual humidity in the zeolite 4A has on the sorption of the different gases helped explaining the permeability observations. The sorption and humid permeation behavior were evaluated by a simple model equation based on the NELF theory, taking into account the multicomponent gas sorption and diffusion in the presence of humidity, as well as the counteracting effects of the hydrophobic PTMSP and hydrophilic zeolite A in a very accurate way. Financial support is gratefully acknowledged to the Spanish Ministry of Economy and Competitiveness (MINECO) under projects CTQ2016-76231-C2-1-R and CTQ2012-31229 at the University of Cantabria. A. F. B. also thanks the MINECO for the Early Stage Researcher (BES2013-064266) contract and the short stay grant to work at the University of Bologna for 3 months (EEBB-I-17-12097).

It was previously proven that small loadings of few-layer graphene (G) and monolayer graphene oxide (GO) adjust the permselectivity and reduce the ageing of thick poly(trimethyl silyl propyne) (PTMSP) membranes, which currently inhibits their application in real separations. In this work, we extend the analysis to thin film composite membranes with top layers of PTMSP/G and PTMSP/GO between 1 and 7 µm. The good quality of the films, obtained by spin coating the polymer solution on porous flat supports, indicates that graphenic sheets are aligned parallel to the film surface, without defects, and that the large-scale production of such composite films is feasible. The addition of G and GO to PTMSP can improve the gas permeability and selectivity, and even change the behaviour from CO2-selective to He-selective. GO produces more repeatable effects than graphene, and it generally enhances the PTMSP permeability. The ageing was studied by tracking permeability of 4 gases with time: thin films age faster than thick ones, because ageing is due to free volume diffusion across the film. Incorporation of 1 wt% of G and GO visibly reduces the ageing of thin PTMSP films, and the effect is repeated on many different samples. The ageing can be correlated, with a single power law, to the ratio between time and squared film thickness. The exponent of such function, that quantifies the ageing rate, decreases when G and GO are added to PTMSP thin films, by factors as high as 40%. The temperature effect was studied, up to 60 °C, on annealed samples: the membranes, CO2-selective at room temperature, can become easily He-selective by raising the temperature. The He/CO2 selectivity increases with temperature: such effect could be exploited syngas purification and pre-combustion capture processes.

Novel composite Mixed Matrix Membranes (MMM) were fabricated by dispersion of different loadings of graphene nanoparticles (from 0.3 to 15 % weight percentage) in a dense permeable glassy polymer, poly (2,6-dimethyl-1,4-phenylene oxide), PPO, by solvent casting procedure. The permeability, selectivity and diffusivity of helium, nitrogen and carbon dioxide have been measured at two different temperatures, 35° and 65°C and the effect of graphene loading was studied. (R. Rea et al. 2018).

We fabricated a new type of nanostructured materials for CO2 capture processes, based on poly (acrylonitrile), PAN, a polymer almost impermeable to CO2, but easily functionalizable and spinnable. The preparation involved amine functionalization of PAN powder, electrospinning of the powder to form a nanofibrous mat with a large surface area, and compression of the mat to obtain dense membranes for facilitated transport of humid CO2. The functionalization step was carried out with different routes: amination with hexamethylene diamine or ethylene diamine, and basic hydrolysis. The final amine content in the polymer could be tuned varying the reaction type and conditions, although high functionalization degrees led to crosslinking, which made the powder insoluble. The dry CO2 uptake was measured at various stages of the preparation, in order to assess separately the effect of chemical functionalization and surface area enhancement on the material capture ability. Such tests indicated that both chemical and morphological changes of the neat polymer enhanced the dry CO2 sorption capacity, although the increase of surface area yielded the largest improvement. CO2 permeation tests in humid conditions were carried out on the compacted membranes, indicating that the materials functionalized via direct amination exhibit a behavior compatible with the facilitated transport mechanism, with CO2 permeability reaching 83 Barrer, increasing by 17 times with respect to the dry state value, at a relative humidity of 50%. Membranes functionalized via hydrolysis did not show such a behavior, maybe because the amine functionalities were consumed by an unwanted reaction. The procedure can be further improved by optimizing each processing step, or changing the order of the steps. The electrospinning process seemed the key factor of the approach, as the large surface area of electrospun mats allowed to obtain membranes with a higher permeability than the original ones, and a large availability of amine groups useful for humid CO2 capture.

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 degrees 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/N-2 and CO2/N-2, 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.

The aim of this work is to study in detail the sorption of binary gas mixtures containing methane into polymers suitable for membrane separations. A novel measuring procedure has been developed and validated by performing mixed gas sorption tests on the n -C 4 /CH 4 mixture in films of poly(1-trimethylsilyl-1-propyne) (PTMSP), for which literature data are available. Then, individual uptakes of CH 4 and CO 2 from binary gas mixtures were measured at 35 °C and up to 35 bar in PTMSP, in the whole gas composition range. The experiments were conducted on a pressure-decay apparatus equipped with a gas chromatographic device. The novel experimental procedure was set up in order to obtain data either at constant partial pressure of one gas, as done by previous authors, or at constant gas composition and variable total pressure. The latter protocol allows to mimic more closely the real membrane separation processes, where only the total pressure of the mixture can be varied arbitrarily. It was observed that the presence of CH 4 does not alter significantly the sorption of CO 2 and of n -C 4 in PTMSP, while the mixed gas solubility of CH 4 is lower than the pure gas value at the same CH 4 fugacity. In particular, the CH 4 solubility coefficient, as well as the mixed gas solubility selectivity are univocal functions of CO 2 fugacity (or concentration) and are otherwise independent of the gas phase composition. The real CO 2 /CH 4 solubility-selectivity of PTMSP is similar to the ideal value at low CO 2 fugacity but it becomes significantly higher, up to 4.5 times, at 25 bar of CO 2 fugacity. A quantitative rule can be drawn using data of several binary gas mixtures in glassy polymers, based on which the ratio between actual mixed gas and pure ideal solubility selectivity of CO 2 over CH 4 is a single, monotonously increasing function of the ratio between the concentration of the two components, c (CO 2 )/ c (CH 4 ), which becomes higher than unity as c (CO 2 )> c (CH 4 ). In other words, the competition effects depress more significantly the less abundant penetrant in the polymer, that is usually CH 4 .

The effects of adding fumed silica (FS) nanoparticles on the gas permeability, solubility, diffusivity and selectivity of a polymer of intrinsic microporosity (PIM-1) are modeled considering the density of the composite matrix as the key input information. PIM-1 is treated as a homogeneous glassy polymer endowed with a specific free volume that increases with the amount of nanoparticles loaded, as indicated by the experimental values of mixed matrix density. The solubility isotherms of H2, He, O2, N2, CH4 and CO2 in matrices of PIM-1 with different FS loadings are calculated with the Nonequilibrium Lattice Fluid (NELF) model. The gas diffusivity and permeability variation due to FS addition are related to the fractional free volume of the polymer phase according to the semiempirical free volume theory equation. Remarkably, the coefficient amplifying the free volume effect increases with the molecular size of the gas, expressed by the van der Waals volume, thus allowing to estimate the transport properties of gases not investigated experimentally, such as methane. The behavior inspected differs from the one observed in Mixed Matrix Membranes (MMM) formed by PIM-1 and porous selective fillers, that show higher selectivity towards smaller penetrants than the pure polymer, because the effect of silica nanoparticles is only represented by an enhancement of the large free volume domains. The model allows to estimate the ideal selectivity together with its solubility and diffusivity contributions, at various FS contents, for several gas pairs (O2/N2, CO2/N2, CO2/CH4, CO2/H2), which are then compared to the experimental trends available.

none 6 si In this work, we studied two copolymers formed by segments of a rubbery polyether (PPO or PEO) and of a glassy polyimide (BPDA-ODA or BKDA-ODA) suitable for gas separation and CO2 capture. Firstly, we assessed the absorption of water vapor in the materials, as a function of relative humidity (R.H.), finding that the humidity uptake of the copolymers lies between that of the corresponding pure homopolymers values. Furthermore, we studied the effect of humidity on CO2 and N2 permeability, as well as on CO2/N2 selectivity, up to R.H. of 75%. The permeability decreases with increasing humidity, while the ideal selectivity remains approximately constant in the entire range of water activity investigated. The humidity-induced decrease of permeability in the copolymers is much smaller than the one observed in polyimides such as Matrimid® confirming the positive effect of the polyether phase on the membrane performance. Finally, we modeled the humidity-induced decrease of gas solubility, diffusivity and, consequently, permeability, using a suitable approach that considers the free volume theory for diffusion and LF model for solubility. Such model allows estimating the extent of competition that the gases undergo with water during sorption in the membranes, as a function of the relative humidity, as well as the expected reduction of free volume by means of water molecules occupation and consequent reduction of diffusivity. open Olivieri, Luca; Tena, Alberto; De Angelis, Maria Grazia; Giménez, Antonio Hernández; Lozano, Angel E.; Sarti, Giulio Cesare Olivieri, Luca; Tena, Alberto; De Angelis, Maria Grazia; Giménez, Antonio Hernández; Lozano, Angel E.; Sarti, Giulio Cesare

The improvement of the separation performance of polymeric membranes for gas separations has been pursued by the addition of specific fillers, which produced diverse and even unexpected behaviors, hard to rationalize and to predict, both quantitatively and qualitatively. In particular, the addition of fumed silica nanoparticles in glassy polymeric membranes has shown unusual properties that apparently lead to the indication that only a specific experimental analysis could provide the information required for the permeability and separation of the gases of interest. We review transport properties, solubility and permeability in mixed matrix membranes obtained by loading fumed silica nanoparticles in different glassy polymers, interesting for membrane separations, and revise the main modeling procedure suitable to calculate and predict the relevant transport properties in such mixed matrix membranes.

The sorption and transport properties of n -alkane and alkyl-alcohol vapors in addition-type poly(trimethyl silyl norbornene) (PTMSN) were studied at 35 °C and at various activity values. PTMSN is a high free volume polymer that shows very high solubility to the condensable vapors and can be considered a promising material for several applications, such as gas/vapor membrane separations. Sorption and diffusion experiments with n -alkanes ( n -C 4 , n -C 5 , n -C 6 ) and alkyl alcohols (CH 3 OH, C 2 H 5 OH, n -C 3 H 7 OH) were performed as well as dilation measurements with n -C 5 and n -C 6 , at 35 °C. The behavior of the alcohol vapors differs from that of alkanes, mainly for the shape of the solubility, diffusivity and mobility isotherms: this phenomenon, as well as the diffusion trend of the different vapors, was explained by the different interactions between the penetrants and the hydrocarbon-based polymer. The permeability isotherms were also estimated from solubility and diffusivity data, showing that the permeability of PTMSN lies in between those of AF2400 and PTMSP. Finally, the dependence of the transport parameters of n -alkanes in PTMSN on penetrant pressure and molecular weight was analyzed, and compared to that observed in other high free volume glassy polymers. The activity-based solubility coefficients as well as permeabilities of alkanes in PTMSN show a weak dependence on molecular weight, while in PTMSP permeability increases and in AF2400 decreases with increasing the number of carbon atoms.

Solubilities of N2, CO2 , C1-C3 saturated hydrocarbons, C1-C3 saturated fluorocarbons, and normal- and cyclo-C5 and -C6 alkanes at 35 °C are reported in an amorphous, rubbery, random copolymer composed of 50.7 mol % tetrafluoroethylene and 49.3 mol % perfluoromethyl vinyl ether, TFE/ PMVE49. Permeabilities of N2, O2, CO2, and C1-C3 saturated hydrocarbons in this polymer at 35 °C are also presented. Solubilities of hydrocarbon vapors in this fluoropolymer are lower than those of their corresponding fluorocarbon analogues due to less favorable interactions of the fluorinated polymer with hydrocarbon vapors than with fluorocarbon penetrants. Polymer density was measured over a wide temperature and pressure range to estimate parameters for equation-of-state modeling of gas sorption. Modeling the sorption isotherms with the Sanchez-Lacombe equation-of-state model requires a reduction of approximately 10% in the cohesive energy density of the gas-polymer mixture from that predicted by the geometric mean mixing rule for all hydrocarbon penetrants other than CH4. Sorption of CH4 and fluorocarbon penetrants is well described with little or no variation in the geometric mean rule estimate of interaction energy. While linear correlations between the natural logarithm of hydrocarbon gas solubility and penetrant critical temperature in hydrocarbon polymers often have slope values of about 0.019 K-1 at 35 °C, this fluoropolymer has a much lower slope value, 0.011 K-1. Hydrocarbon/nitrogen permeability selectivity is much lower in TFE/PMVE49 than in hydrocarbon-based rubbery polymers such as poly- (dimethylsiloxane). This effect is, to a very large extent, a result of hydrocarbon solubility suppression in the fluoropolymer, due to less favorable hydrocarbon-fluorocarbon interactions.

Hybrid silica/poly(trimethylsilyl propyne) (PTMSP) membranes, in which the silica particles are generated in the polymer solution with a sol-gel reaction from a tetraethoxysilane (TEOS) precursor, were fabricated with silica loadings up to 30 wt%. The membranes are characterized with microscopic, thermogravimetric and pycnometric analysis; their sorption and diffusion properties with respect to n-C4 and n-C5 vapors are also measured at 25°C. A significant reduction of the polymer specific volume, organic vapour solubility and diffusivity is observed after incorporation of silica, according to a combination of free volume filling and compressive constraints. The behaviour of the hybrid membranes (HM) is opposite to that of mixed matrix membranes (MMM) obtained by physical mixing of preformed silica nanoparticles into PTMSP solutions, which show, on the contrary, free volume, vapour solubility and diffusivity values higher than pure PTMSP. The hybrid membranes are characterized by larger silica domains (around 1 m) than mixed matrix ones. Remarkably, however, the transport behaviour of both type of membranes can be interpreted, by the same theoretical background, on the basis of a single structural parameter, namely the density of the polymer phase. This parameter allows a direct estimation of the variation of free volume and vapour solubility and diffusivity in both type of membranes, through a NELF/free volume approach.

The enhancement of gas diffusivity observed after addition of fumed silica nano-particles to glassy polymers can be described and modeled by considering the additional fractional free volume (FFV) created by filler insertion, which can be evaluated from gas solubility data in the composite matrix by means of the NELF model. In this work, a detailed characterization of the solubility of n-C4 and n-C5 vapors, as well as of their diffusivity in matrices of AF 2400 filled with variable amounts of fumed silica has been performed at 25°C. On the bases of n-C4 solubility in the mixed matrix the FFV variation due to filler loading can be estimated and then used to predict the solubility of n-C5 that is found in good agreement with experimental data. Finally, an empirical correlation can be drawn between the FFV value obtained from solubility data and the infinite dilution diffusivity of the penetrants, as well as with the concentration dependence of the penetrant diffusivity.

The vapor transport properties of nanocomposite materials obtained with different techniques and based on a high free volume glassy polymer suitable for membrane separations, poly[1-(trimethylsilyl)-1-propyne] (PTMSP), have been determined and modeled. The simple mixing in solution of hydrophobic fumed silica nanoparticles with PTMSP leads to mixed matrix membranes, which show higher free volume and higher values of diffusivity and permeability than the pure polymeric material. If a sol-gel route is followed, with PTMSP and Tetraethoxysylane (TEOS) as precursor of the silica phase, one obtains hybrid matrices characterized by lower vapor diffusion and sorption values with respect to the pure polymer. Although the trends observed are very regular functions of the silica content in the composite, none of the behavior observed obeys traditional models for composites permeability, such as the Maxwell’s one. Both types of behaviors were modeled considering the variation of polymer fractional free volume induced by the inorganic phase: in the mixed matrices the poor interactions between silica and polymer chains favor the formation of nanovoids at the interface, increasing the free volume and the vapor diffusivity, while in the more interconnected hybrid matrices the inorganic domains act as constraints, reducing the volume occupied by the polymeric phase, which is naturally endowed with a very high excess free volume.

The addition of fumed silica particles to glassy polymers such as PTMSP and Teflon AF 2400 results in an enhancement of gas diffusivity and permeability that is not captured by traditional models for composites because both volume and gas solubility of the composite material are underestimated by the additive rule based on pure component properties. Such effects have been attributed to the creation of additional free volume due to the insertion of filler in the polymeric matrix. In this work, we use the NELF model to relate gas solubility in the composite material to the variations induced by the addition of filler on polymer density and swellability. From these values, the fractional free volume (FFV) increase produced in the polymeric phase by filler incorporation may be evaluated and, in turn, also the diffusivity in the composite material can be calculated as a function of filler content on the basis of its relation to FFV. The gas diffusivity data for n-C4H10 in AF 2400 and AF 2400-based mixed matrices, as well as those relative to N2, CH4, C2H6, C3H8, and n-C4H10 in PTMSP, follow closely the correlation found, which contains only one adjustable parameter for each penetrant-polymer couple.

In this study we analyzed and compared the vapor transport behavior into two different composites based on PTMSP and obtained i) as mixed matrices by loading hydrophobic fumed silica nano-particles in PTMSP and ii) as hybrid matrices formed by PTMSP and SiO2 generated in situ from tetraethoxysilane (TEOS) via a sol-gel reaction. The experimental data show that n-butane solubility and diffusivity in the mixed matrices increase monotonously with the silica fraction, while the transport rates in hybrid matrices are lower than those of the pure polymer and much lower than those observed in mixed matrices at equal content of silica. None of these trends can be described by the Maxwell's model, which assumes absence of interactions between polymer and filler: in particular, the diffusivity in the mixed matrices is higher than predicted, while that in hybrid matrices is lower than the estimated value. The data were thus modeled using a different approach that is able to represent the transport behavior of both types of composite membranes, based on a small set of physical and empirical parameters. The model adopted describes the gas diffusion as a function of one parameter, i.e. the fractional free volume of the polymeric matrix, which can be estimated based on sorption data of one penetrant in the polymer and in the composite matrices, and the NELF model for glassy polymers. The data relative to hybrid and mixed matrices lie on a same mastercurve when the diffusivity in the matrix is plotted against the fractional free volume estimated by means of the NELF model. It was concluded that, in mixed matrices additional free volume is created at the interface between polymer and filler, maybe due to poor interactions between the phases; for hybrid matrices the inorganic phase is deeply interconnected to polymeric chains and acts as an additional constraint on the open structure of PTMSP, lowering its fractional free volume.

Polymer membranes with ultrahigh CO2 permeabilities and high selectivities are needed to address some of the critical separation challenges related to energy and the environment, especially in natural gas purification and post-combustion carbon capture. However, very few solution-processable, linear polymers are known today that access these types of characteristics, and all of the known structures achieve their separation performance through the design of rigid backbone chemistries that concomitantly increase chain stiff-ness and interchain spacing, thereby resulting in ultramicroporosity in solid-state chain-entangled films. Herein, the separation performance of a porous polymer obtained via ring-opening metathesis polymerization is reported, which possesses a flexible backbone with rigid, fluorinated side chains. This polymer exhibits ultrahigh CO2 permeability (>21 000 Barrer) and exceptional plasticization resistance (CO2 plasticization pressure > 51 bar). Compared to traditional polymers of intrinsic microporosity, the rate of physical aging is slower, especially for gases with small effective diameters (i.e., He, H2, and O2). This structural design strategy, coupled with studies on fluorination, demon-strates a generalizable approach to create new polymers with flexible backbones and pore-forming side chains that have unexplored promise for small-molecule separations.