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Today, the most effective and suitable method to obtain molecular H2 is the extraction from mixtures where it is present, using gas‐sieving membranes. To this aim, the preparation and characterization of layered nano‐composites are described, made of alternated layers of positively charged Poly(Diallyl Dimethyl Ammonium chloride) (PDDA) and negatively charged graphene oxide (GO) nanosheets with high and tunable selectivity for H2 purification. The composites are assembled exploiting electrostatic interactions and the layer‐by‐layer technique; this study correlates permeance tests with changes in chemical composition and structure of the material using X‐rays Photoelectron Spectroscopy, X‐rays diffraction water contact angle, and surface zeta‐potential measurements. Thanks to its layered nature, the GO‐PDDA composite shows an excellent selectivity, allowing faster permeation of H2 as compared to CO2 and Argon. By transforming the GO to reduced GO, the porosity of the nanosheets can be further increased, in this way increasing the permeance of the material and its selectivity at the same time, thus allowing to overcome the Robeson limit, the technological upper boundary to the performance of actual membranes. [ABSTRACT FROM AUTHOR]

Abstract The effect of CO 2 on the mechanical properties of three different glassy polymeric materials, polystyrene (PS), polymethylmethacrylate (PMMA) and Matrimid polyimide (PI), has been investigated by dedicated Dynamic Mechanical Analysis (DMA) at 35 °C on samples equilibrated at different penetrant pressures (0–30 bar). The experimental campaign has been designed to inspect the mechanical properties associated to the so-called plasticization phenomenon, which has been invoked as responsible for the increase of gas permeability versus feed pressure in glassy polymeric membranes. The main aim of the work is to find if any correlation holds between the effects induced on polymer mechanical properties and on gas permeability by the presence of different amounts of penetrant gas. The DMA analysis revealed that CO 2 produces a decrease of polymer storage modulus E′ and an enhancement of tan δ factor. Experimental data for both E' and tan δ vary regularly and monotonically with CO 2 content in the membrane, with no indication of the onset of other new phenomena at pressures higher than the "plasticization pressure" associated to permeability data. The mechanical properties show very similar behaviors with CO 2 content for all polymers analyzed, notwithstanding their CO 2 permeability behaviors are different: decreasing with upstream pressure for PS, increasing for PMMA and nonmonotonous for Matrimid. The results obtained indicate that there is no direct correlation between gas permeation dependence on CO 2 content and the changes in the polymer mechanical properties induced by the same CO 2 content. Graphical abstract Image 10685098 Highlights • The mechanical behavior of glassy polymers saturated by CO 2 is investigated by DMA. • Different CO 2 pressures are considered in the range 0–30 bar at 35 °C. • The presence of CO 2 lowers the storage modulus and increases the tan δ coefficient. • No correlation is found between mechanical properties and CO 2 permeability behavior. [ABSTRACT FROM AUTHOR]

The transport of gaseous mixtures in glassy polymers is analyzed by means of a thermodynamic based model, which is applied to describe the permeability of CO 2 /CH 4 50/50 binary mixtures in various glassy polymeric membranes. The approach relies on the description of the solubility behavior of penetrant/polymer mixtures provided by the nonequilibrium thermodynamics for glassy polymers (NET-GP), and considers the gradient in penetrant chemical potential of each species as the actual driving force of the diffusive mass fluxes. Such an approach is specialized to dilute solutions conditions, as it is typically of interest for the transport of light gas (e.g. CO 2 , N 2 , CH 4 , O 2 ) in glassy polymeric membranes; that allows for the simple and successful prediction of the gas permeability of gas mixtures based on single component transport data, with no additional parameters required. The NET-GP model is used in combination with an equation of state (lattice fluid theory by Sanchez and Lacombe) to obtain the solubility of pure and mixed gases at various pressures and compositions, as well as the thermodynamic factors accounting for the dependence of chemical potentials of the solutes on the concentrations of both penetrants. An exponential dependence on penetrant concentration is used to describe the mobility coefficient behavior, so that only two adjustable parameters are required for the pure penetrant case (infinite dilution mobility and plasticization factor). A simple but effective linear mixing rule is considered to describe transport in the binary mixture case, which does not introduce any additional adjustable parameter due to the presence of a second penetrating species. The comparison with permeation data of gas mixtures in different polymers shows the good predictive ability of the model. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper presents an extended model for gas permeation through a filled polymer layer, and it is applied to the case of oxygen permeability through a poly(vinyl alcohol)/kaolin dispersion coating. The model is based on a description of polymer and penetrant properties in a thermodynamically consistent framework. The gradient in chemical potential is considered the driving force for the diffusion of the penetrating gas. The well-established nonequilibrium lattice fluid (NELF) model for the polymer phase is extended in order to account for the additional features of the polymer/filler system, such as the concentration and aspect ratio of the inorganic filler, which enhance the penetrant tortuosity. The model predicts the behavior of penetrant permeability with respect to polymer crystallinity and filler fraction. The calculated results are compared to experimentally obtained data for oxygen permeability through a dispersion coating layer consisting of poly(vinyl alcohol) (PVOH) and two types of kaolin with different aspect ratios. A good agreement is found in terms of the effects of polymer crystallinity, filler concentration, and filler aspect ratio. The experimental results also indicate a complex interplay between the polymer and the filler as the permeability of two differently surface modified kaolin clays was determined, displaying slight deviations from model predictions. Significant differences were observed in the experimental results between the two fillers investigated, and the one characterized by the smaller aspect ratio affects to a minor extent the oxygen permeability, as illustrated by the model. Furthermore, the lower hydrolysis degree of PVOH gives a reduced barrier performance, as expected. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44834. [ABSTRACT FROM AUTHOR]

The transport model proposed by Minelli and Sarti for the representation of gas and vapor permeability in glassy polymers has been extensively applied to various systems, and the model results are thoroughly analyzed. The approach is based on fundamental theory for the diffusion of low penetrant species in polymers, in which the diffusivity is considered as the product of the molecular mobility, and a thermodynamic coefficient, accounting for the concentration dependence of the chemical potential. The model relies on the thermodynamic description of the penetrant/polymer systems provided by the NonEquilibrium Thermodynamics for Glassy Polymers (NET-GP) approach. The penetrant mobility is assumed to depend exponentially on penetrant concentration, and the model contains two parameters only: mobility coefficient at infinite dilution and plasticization factor. The model parameters obtained from the analysis of the permeability behaviors of various systems have been examined and general correlations are derived. The mobility coefficient is indeed correlated to the properties of the pure penetrants (penetrant molecular size) and pure polymer (fractional free volume and characteristic energy). This allows the derivation of a simple and general expression for the prediction of the permeability of any penetrant species in glassy polymers in the range of low penetrant pressures, as well as the selectivity of any gas pair. Remarkably, the model predictions are able to represent quite accurately the experimental data available in the literature. Furthermore, the plasticization factor is correlated to the swelling produced by the penetrant into the glassy polymer matrix, obtaining thus a reliable tool for the estimation of the pressure dependence of gas permeability on upstream pressure. [ABSTRACT FROM AUTHOR]

The permeability of various low molecular weight species (both gases and vapors) in a series of glassy polymers has been extensively analyzed by means of a thermodynamic based approach for solubility and diffusivity, recently proposed and already applied to a few penetrant/polymer systems. The model relies on the thermodynamic description of the solubility behaviors of the solutes provided by the nonequilibrium thermodynamic model for glassy polymers (NET-GP), while the diffusivity is the product of the mobility coefficient, a purely kinetic quantity, and the thermodynamic factor, accounting for the dependence of the penetrant chemical potential on its concentration in the glassy polymer matrix. The model is applied to permeability data of many penetrant species from very light gases, such as hydrogen or helium, to hydrocarbons and fluorocarbons, in several different glasses, including very high free volume materials, polyimides and fluoropolymers. The model proved to be effective in the representation of all types of permeability behaviors with respect to penetrant upstream pressure, which may be either decreasing, increasing, or with a nonmonotonous trend showing a minimum value at the so-called plasticization pressure. [ABSTRACT FROM AUTHOR]

The permeability of light gases in a series of different glassy polymers is analyzed through a thermodynamic-based approach for solubility and diffusivity. The nonequilibrium thermodynamic model for glassy polymers describes the solubility of the different penetrants; diffusivity is given as the product of a mobility factor and a thermodynamic factor. The latter is predicted by the nonequilibrium lattice fluid thermodynamic model, while the mobility coefficient is determined using the experimental permeability data. For rather soluble penetrants (e.g., CO2), a plasticization factor is also accounted for, considering the mobility to depend exponentially on penetrant concentration, as often observed experimentally. The model is able to describe accurately the experimental behavior in a simple and effective way, considering only two adjustable parameters. The mobility coefficient is found to depend on the penetrant size (critical volume) and on the fractional free volume of the polymer matrix, following rather general and reasonable correlations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2776-2788, 2015 [ABSTRACT FROM AUTHOR]

The Maxwell equation relates the permeability P of a dispersion of particles A (modeled as hard congruent non-interacting spheres) in a continuous matrix B, to the ratio of the permeabilities of the components α = P A / P B and the corresponding volume fractions v A , v B (=1− v A ). Originally devised for use at v A →0, the validity of the said equation for practical purposes was shown, by analytical methods, to extend to congruent weakly interacting spheres packed in regular cubic lattices, in the low to medium v A range; while the equation itself extends further up to the correct upper limit P = P A at v A =1. Replacing a simple cubic (s.c.) lattice of spheres with an identical lattice of cubes, overcomes this limitation (because cubes can pack up to v A =1) but only at the expense of losing analytical mathematical tractability. However, an analytical limiting form of the s.c. lattice of cubes could be derived near the limit v A →1 and shown to agree with the Maxwell equation. Even so, a large gap of unexplored territory was obviously still left in the remaining medium to high v A range. The gap in missing data was successfully filled in Part I by the use of a numerical computation approach, which showed that the result obtained at v A →1 is valid for practical purposes throughout the medium to high v A range; thus confirming the applicability of the Maxwell equation to sc lattices of cubes (and correspondingly of the Wiener equation in the case of anisometric particles) in this v A region. The gap in analytical treatment is filled to a large extent, in the present companion paper, by the development of an approach combining two different analytical limiting forms of the s.c. lattice-of-cubes model (as well as comparable limiting forms applicable to anisometric particles treated by the Wiener equation). We show here that this approach (referred to in the main text as the BP II model) provides (to a high degree of approximation in the practically important region of 0≤ α ≤10) a satisfactory analytical theoretical basis for meaningful application of the Maxwell equation in the higher v A range, comparable with that afforded by the existing lattice-of-spheres analytical treatments in the lower v A region. [ABSTRACT FROM AUTHOR]

The vapor permeability in glassy Ethyl Cellulose may show rather different behaviors versus upstream pressure, depending on the penetrant considered, including a monotonous decrease as well as a monotonous increase with increasing pressure. Such a spectrum of behaviors, experimentally well known, is still needing a unifying interpretation and a mathematical description, which we are now proposing in the present work. For each solute, at all different temperatures, the permeability in Ethyl Cellulose is described by means of a simple model with a solid thermodynamic basis. The thermodynamic behavior of the polymer/penetrant mixture is given by the nonequilibrium lattice fluid model (NELF), which provides the vapor solubility at different values of T and p . The penetrant permeability is described considering the diffusion coefficient as the product of a purely kinetic factor, the mobility, and a thermodynamic factor related to the dependence of the chemical potential of the diffusing species on its concentration in the polymer. The thermodynamic factor is readily calculated from the NELF model, while the mobility factor is endowed with an exponential dependence on penetrant concentration, as often suggested by experimental data; its expression utilizes only two adjustable parameters: the infinite dilution mobility coefficient and the plasticization factor. The analysis indicates that this simple mathematical theory is able to describe accurately all the different behaviors observed experimentally, for all the penetrants inspected, at all temperatures. In addition, the two model parameters for mobility follow clear and simple correlations: the infinite dilution mobility coefficient scales with the penetrant size, and the plasticization factor is related to the ability of the penetrant to swell Ethyl Cellulose, as quantified by the volume swelling coefficient, which is available from independent information. [ABSTRACT FROM AUTHOR]

Abstract: In studies of the permeability of composite materials, consisting of solid isometric particles A dispersed in a polymeric matrix B, Maxwell's classical equation, rigorously valid only for very low fractional volumes (v A) of spherical particles, is often used for data analysis up to much higher v A values. Theoretical justification for this practice can be provided, only up to v A≈0.5, by current analytical models based on cubic lattices of congruent spheres. Replacing spheres by cubes yields a model covering the full composition range v A=0−1, but lacking convenient general analytical tractability. Accordingly, to explore unrestrictedly the practical validity of the Maxwell equation, a simple cubic lattice-of-cubes model was combined with an appropriate numerical computation tool. The results establish satisfactory applicability of the Maxwell equation for isometric particles A, at all compositions and over a wide range of component permeability ratios (α=P A/P B=0−100). The practical applicability of the corresponding classical equation of Wiener (which extends Maxwell's treatment to anisometric particles via the value of a single geometrical parameter A W ) was similarly explored, using appropriate model s.c. lattices of (a) unidimensionally anisometric particles (transverse square rods of varying length) or (b) bidimensionally anisometric particles (transverse square platelets of varying area). The computations covered the same v A and α ranges as above, as well as a range of aspect ratios in each of the cases (a) and (b). The results obtained enable determination of values of A W , independent of v A and α, linked directly to the aspect ratio of the embedded particles, and demonstrate very good practical applicability of the Wiener equation (with the proper A W value) under all conditions studied. [Copyright &y& Elsevier]

Abstract: The description of permeability and solubility of CO2 in different complex polymer matrices in the glassy state is analyzed by considering the diffusion coefficient as the product of a kinetic factor, mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species, according to what recently presented for different pure polymers [Minelli and Sarti, J. Membr. Sci. 435 (2013) 176–185]. The thermodynamic factor is calculated in a predictive way by using the nonequilibrium lattice fluid model (NELF) or is obtained directly from experimental solubility isotherms, when pure component parameters for the NELF model are not available. The mobility factor is considered to depend exponentially from penetrant concentration, following the usual trend commonly found experimentally, and its expression contains only two adjustable parameters. The permeability model is used to describe steady state permeation of CO2 in a series of complex glassy phases, formed by polysulfone (PSf) and polyphenylene oxide (PPO) with different plasticizers, glassy polymer blends, glassy random copolymers and crosslinked polyimides. The analysis shows that in all the cases examined, the model used is able to describe the experimental trends in a simple and effective way, accounting for all the different behaviors observed, in which permeability is either decreasing or increasing with upstream pressure and even when permeability is non-monotonous and presents a minimum value due to the so-called plasticization effect. A general correlation is also found for both model parameters: the infinite dilution mobility correlates well with the reciprocal fractional free volume, according to the FFV theory, while the plasticization factor is associated to the swelling coefficient of the polymer matrix. [Copyright &y& Elsevier]

Abstract: The description of permeability and diffusivity in glassy polymers has been revisited by considering the diffusion coefficient as the product of a kinetic factor, mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species. The latter term does not contain any adjustable parameter since it is obtained directly from solubility isotherm data or can be even calculated in a predictive way by using well established predictive procedures as the Non Equilibrium Thermodynamics for Glassy Polymers (NET-GP) models. The mobility factor considered is endowed with an exponential dependence on penetrant concentration, following the usual trend commonly found experimentally, thus containing only two adjustable parameters. The resulting expressions for diffusivity and for permeability describe rather carefully the pressure dependence observed in glassy polymers, both in steady state permeation and in transient mass uptake, in all the cases inspected, even in the presence of the so called plasticization effects. [Copyright &y& Elsevier]

Abstract: Pure gas permeability through a polystyrene-b-poly(ethylene oxide) block copolymer (SEO) membrane was measured between 20 and 80°C. The membrane comprised alternating polystyrene (PS) and poly(ethylene oxide) (PEO) lamellae; the average center-to-center distance between adjacent PS lamellae was 96nm. Among the different gases considered, carbon dioxide showed the highest permeability, with values up to 200Barrer, followed by helium, oxygen, methane and nitrogen. Gas permeability appeared to be controlled by condensability of the gas, molecular size, and molecular interactions. The melting of poly(ethylene oxide) (PEO) domains, which occurred between 40 and 60°C, caused deviation from Arrhenius behavior. A simple model that accounts for transport through a composite composed of semi-crystalline PEO lamellae and amorphous PS lamellae was developed. Model results and experimental data agreed fairly well considering the simplicity of the approach. The model can readily be used to predict pure gas permeabilities of SEO copolymers with arbitrary morphologies and crystallinity. The crystalline PEO volume fractions inferred from the permeation data are within 15% of those determined by differential scanning calorimetry. [Copyright &y& Elsevier]

Abstract: Relations between morphological characteristics and effective permeability in nanocomposite systems are here considered in details, both analyzing modeling results for simple systems as obtained in different past attempts and extending the applicability of the latter to more realistic configurations. In this perspective, the same mathematical tool and modeling approach used in a previous paper for the analysis of simple 2-D ordered systems [J. Membr. Sci. 327 (2009) 208–215] are here extended in several different respects. Predictions from numerical simulations for 3-D ordered and random systems, both for the case of low and high concentration of inclusions, are compared with results from previous works and with correlations offered by empirical approaches. A new model is finally proposed for the prediction of permeability in random systems which proves to be reliable in a rather large range of geometrical and morphological configuration. [Copyright &y& Elsevier]

Abstract: The structure and transport properties of a four different films based on two different generations of microfibrillated cellulose (MFC), alone or in combination with glycerol as plasticizer, were investigated through FE-SEM analysis and sorption or permeation experiments. FE-SEM revealed the existence of complex structures in the different samples. A porous, closely packed fiber network, more homogeneous in the samples containing glycerol, was characteristic of the surface of MFC films; while film cross-sections presented a dense layered structure with no evidence of porosity. Water vapor sorption experiments confirmed the hydrophilic character of these cellulosic materials and showed a dual effect of glycerol which reduced the water uptake at low water activity while enhancing it at high relative humidity. The water diffusion in dry samples was remarkably slow for a porous material, confirming the existence of complex structures below the film surface. In contrast, the diffusion coefficient was definitely affected by plasticization, being higher for glycerol-containing samples and showing in all cases an exponential increase when water was added to the system. Similar behavior was observed in permeation experiments. Dry MFC films showed excellent oxygen barrier properties; however, a dramatic decrease in these properties was observed when the water content in the samples was increased. [Copyright &y& Elsevier]

Abstract: The mass transport properties of composite systems resulting from the dispersion of impermeable platelets in a permeable matrix have been discussed on the basis of the results of a numerical analysis of the problem. In particular, 2-D ordered structures with platelets oriented normally to the average mass flux in the system have been analyzed by using a CFD algorithm, based on a finite volumes method, and the increase of barrier effect is discussed as function of filler loading, platelet shape and dimensions, and arrangement of platelet layers. The numerical solutions obtained were compared with the models most commonly used for correlations of apparent permeability and a new formulation capable to predict the gas transport properties in this simplified nanocomposite geometries has been proposed, based on revision of earlier theories. This relationship correctly describes the enhancement in barrier effect for the systems analyzed for a wide range of filler loading and platelet dimensions and can be reliably used to obtain relevant information on gas permeability in real nanocomposite systems. [Copyright &y& Elsevier]

The assessment of the transport properties of different substances in polymeric materials is of crucial importance for the evaluation of packaging performances, aiming to protect packed food products and ensure a prolonged shelf-life. The most relevant substances for such application can be identified in O 2 , CO 2 and C 2 H 4 (together with N 2 as control) as permanent gases, and water vapor as condensable species. All these penetrants are able to alter significantly food properties, in term of sensory characteristics, textures, and quality in general. All relevant techniques for the experimental characterization of mass transport properties in polymeric films or packages are critically reviewed, focusing in detail on standard methods. Each technique is briefly presented in terms of apparatus requirements and general procedures, followed by a discussion on its main features. • Standard methods for gas barrier characterization of polymer films are reviewed. • Relevant penetrants for food packaging application are O 2 , H 2 O, CO 2 , C 2 H 4 and N 2. • Test methodology, general setup and main procedures are analyzed. • The capabilities and the methods are illustrated together with their requirements. • The assessment of temperature and R.H. effect on permeation is also discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • A unified model strategy describes sub and supercritical CO 2 sorption and transport. • The model describes well both rubbery and glassy polymers in broad T and P ranges. • The model accounts for sorption induced glass transition and CO 2 phase transition. • The model predicts CO2 induced swelling induced to the polymer in different states. • The thermodynamic contribution influencing CO 2 diffusivity is inspected. The sorption and transport of CO 2 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 CO 2 , 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 CO 2 sorption and permeation in this operative range with a self-consistent set of parameters. Furthermore, the model offers a deep insight in the swelling induced by CO 2 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 CO 2 and industrially relevant polymeric materials. [ABSTRACT FROM AUTHOR]

The simple cubic lattice model of cubic particles A dispersed in a continuous (polymeric) matrix B (and occupying a volume fraction 0≤ v A ≤1 therein), introduced in Parts I and II to establish the meaningful applicability of the Maxwell and Wiener equations to binary composite-medium permeability properties up to v A →1, is here applied to modeling the practically important case of a three-phase composite medium, where the third phase is considered to take the (idealized) form of zones surrounding particles A which exhibit permeability properties differing substantially from those of the bulk matrix. It is shown, both theoretically and by application to various existing experimental data, that replacing the spherical particles, commonly assumed in such modeling, with cubic ones, leads to remarkable gains in model simplicity and internal consistency, in practical applicability, and ultimately in physical understanding of the observed variety of 3-phase composite-medium permeability behavior. [ABSTRACT FROM AUTHOR]