Search

In this study the effect of a high pressure homogenization (HPH) treatment, alone and in combination with a biodegradable polylactic acid (PLA) packaging activated with lysozyme on a smoothie made with apple, carrot and rice beverage was evaluated. In particular, the effects of treatments on the microbiological and quality characteristics of smoothies were assessed during storage at 4 and 10 ◦C in climatic chambers at RH of 50 %. Obtained results showed the efficacy of HPH at 100 MPa to reduce the initial cell load of mesophilic and psycothrophic aerobic bacteria, lactic acid bacteria, yeasts and aerobic spore-forming bacteria. Moreover, the combination of HPH and lysozyme activated packaging resulted in an increased antimicrobial effect against mesophilic, psychrotrophic and lactic acid bacteria during product storage at 10 ◦C. Yeast and spore forming bacteria showed, instead, lower cell loads independently from samples. Samples packed in active packaging, both treated and not, showed a better color retention in terms of lightness and red index, compared to control (C) ones both when stored at 4 and 10 ◦C. The HPH treated smoothies, both activated and not, at 4 ◦C remained microbiologically stable for more than 20 days. However, the use of active packaging has also allowed to reduce the microbiological proliferation during storage at 4 ◦C. Moreover, few differences in color indices were highlighted between samples stored at 4 ◦C. Obtained results indicate that the combination of HPH treatment and active packaging may represent a useful strategy to increase safety and shelf-life of vegetable smoothies.

The CO2/CO mixed-gas separation performance of a polyimide (Matrimid®), polyetherimide (PEI) and polylactic acid (PLA) membrane, were characterized in the presence of CO2 - rich ternary (CO2/ CO/ O2) and quaternary (CO2/ CO/ O2 / N2 ) feed gas mixtures mimicking the products of CO2 reforming conversion reactions. The membrane-based separation of this mixture is poorly characterized and original data were obtained in a novel mass spectrometric apparatus that permits to monitor the instantaneous permeate composition, thus allowing to evaluate both mixed gas diffusion and permeability coefficients of all gases. CO2 , CO, O2 and N2 permeability and diffusivity in single gas tests were measured between 298 and 353 K up to 1 atm feed pressure and relevantactivation energies were evaluated. At 298 K Matrimid® exhibits CO permeability of 0.50 ± 0.03 Barrer and an ideal CO2/ CO selectivity of 16 ± 1. PEI and PLA exhibit similar ideal selectivity values but lower CO transport rates. In all examined polymer films the CO2 / CO selectivity has absorption-selective character that favours the permeation of CO2 . The ideal CO2/ CO selectivity of all membrane samples decreases with temperature, reaching values of 10 ± 1 at 335 K in Matrimid®. The CO2 / CO selective performances of all examined membrane do not show markable variations exposing the membrane samples to CO2- rich gas mixtures as feed gas. The upper bound correlation among selectivity and permeability for the CO2/ CO gas couple is here for the first timeproposed.

La presente invenzione riguarda un materiale di rivestimento per migliorare le capacità filtranti di un tessuto o simili, detto materiale essendo ottenuto mediante la miscelazione di polivinilammina insieme ad uno o più composti che contengono particelle lamellari in grafene e suoi derivati, dispersi in un disperdente contenente: - un gruppo etossilico, e - almeno un gruppo fenolico e/o un gruppo fenolico sostituito. La presente invenzione riguarda inoltre un procedimento per il rivestimento di un tessuto con tale materiale e una mascherina facciale rivestita con tale materiale.

The aim of this work is the design of an apparatus which allows to measure the in plane stress that arises in polymer coating of commercial polystyrene (N2380) below the glass transition temperature (Tg) as result of vapor sorption/desorption processes and its evolution in time. The in plane stress is measured using bending beam cantilever technique. The experiments were performed at different temperatures, using different fugacity of n-pentane inside the system. From the stress state, knowing the material proprieties, the change in the volume recorded during the sorption/desorption process was derived. Through the use ofthe non-equilibrium lattice fluid model (NELF) it is then possible to estimate vapor mass uptake/release in the coating.

The solubility of several gases and vapors in glassy ethyl cellulose (EC) over wide ranges of temperature and pressure is described by means of a thermodynamic model, which specifically accounts for the nonequilibrium volumetric properties of EC. The behaviors of polymer/penetrant mixtures are repre- sented by the well-established nonequilibrium lattice fluid model (NELF) in its latest development, suitable to be used in a pure predictive fashion for the representation of the volume swelling of the polymer matrix, as induced by penetrant sorption. The analysis reveals the ability of the model to describe all the experimental trends, and a sole binary parameter for each polymer/penetrant couple is considered. The NELF model allows the satisfactory prediction of the thermodynamic properties of all polymer/solute systems examined, in the entire range considered for temperature and vapor fugacity.

The solubility of gaseous mixtures of CO2 and C2H6 in cross-linked poly(ethylene oxide) (XLPEO) has been 11 modeled over a wide range of temperatures, pressures, and compositions with the Sanchez−Lacombe lattice fluid equation of 12 state (LF EoS). The model binary gas−polymer parameters have been determined from pure gas solubility data and kept 13 constant with temperature and composition. Multicomponent solubility is then calculated with no additional adjustable 14 parameters, using a fully predictive procedure. The LF EoS model describes well the mixed gas solubility behavior data over wide 15 ranges of temperature (from −20 to 35 °C), pressure (0−20 atm), and composition. The model also allows representation of the 16 solubility selectivity behavior of XLPEO at different conditions, permitting an a priori determination that ethane solubility is 17 significantly enhanced by the presence of CO2, with a consequent reduction in CO2/C2H6 solubility selectivity relative to the 18 pure gas value. In this regard, the behavior of this rubbery polymer is opposite that of many glassy systems, in which competitive 19 sorption is often dominant, and the solubility of the less soluble gas (i.e., C2H6 in this case) is decreased by the presence of CO2, 20 and the CO2 solubility selectivity is enhanced with respect to the pure gas value.

The description of mass transport properties of low molecular weight species in heterogeneous polymeric systems is of great importance. The theoretical analysis of composite materials behaviors is indeed fundamental for the proper material design of such systems for a variety of different applications. Among the others, immiscible polymer blends as well as block copolymers are often of interest for their ability to combine properties of two or more materials. Semicrystalline polymers are also systems of great industrial importance, which require a two phases modeling in order to describe their behavior. In recent years, the development of nanocomposite materials was employed for barrier applications by incorporating impermeable platelets in the polymer phase. This technology is also suitable for the design of membranes for gas separation, and to this aim, particles selective to one or more gases, such as for instance zeolites or metallic organic frameworks, are dispersed in the polymer phase. All these examples are constituted by two, or more, well defined and well distinguished regions (of different length scale) characterized by their value of gas permeability Pi. The resulting permeability of the complete heterogeneous medium is then related to these Pi values but also to the relative weight of the two phases as well as the system morphology, i.e. the shape of the dispersed phase. The aim of this work is to develop a valuable tool for the description of transport properties in composite media, able to evaluate the permeability as function of system morphology. Numerical calculations are thus employed to model the two-phases system in a wide range of relative fraction of the two components and varying their characteristics. Results are then compared with existent model equations in order to investigate their predictive ability and ranges of validity.

The evaluation of the mixed gas solubility in glassy polymers is of fundamental importance in several applications such as in the development gas separation membranes. For rubbery polymers the usual equation of state (EoS) models, in their multicomponent version, can be applied to calculate multiple gas solubility in the equilibrium phases; for the case of glassy polymers, a different thermodynamic tool has to be used. The general approach called Non Equilibrium Thermodynamics of Glassy Polymers (NET-GP) [1], coupled to the Lattice Fluid (LF) model for the representation of substances [2], was showed to be able to predict the solubility of gases and vapors in glassy polymers at various pressures based on pure component parameters. The approach is here applied to the modeling of multicomponent gas solubility in a glassy polymeric matrix, to predict the solubility of CH4/CO2 mixtures in Poly(phenyleneoxide) (PPO), C2H4/CO2 and N2O/CO2 in poly(methylmetacrylate) (PMMA), at various pressures, for which experimental data are available. The data show that the solubility of mixed gases differ significantly from the corresponding pure component values: the N2O content in the PMMA is lowered by the increase of CO2 partial pressure; the same effect is observed for the CO2/CH4 pair in PPO. The NELF model is able to predict the experimental behavior observed for mixed gases solubility in both systems; the agreement is indeed remarkable in both cases in the whole pressure range investigated. The present approach allows also to estimate predictively the mixed gas solubility-selectivity of N2/CO2, CO2/CH4 and H2/CO2 mixtures in several glassy polymers including polyimides such as Matrimid, allowing to detect significant deviations from the ideal selectivity behavior and estimate the selectivity of membrane materials.

In this work, an atomistic approach is employed to simulate pvT data of polymers at high temperature (in the rubbery region), by using a molecular dynamics tool. Data are then regressed with the desired EoS to obtain the polymer characteristic parameters, which are used to evaluate the gas solubility in the polymer with NET-GP model.

The solubility of gases and vapors is of interest for many different applications, ranging from the fabrication of gas separation membrane to the development of barrier materials for packaging or sensors. For rubbery polymers, different equations of state have been developed following different approaches and provide reliable means for the calculation of the solubility of gases and vapors. On the other hand, glassy polymers are nonequilibrium systems and the same thermodynamic tool is not suitable. The general approach called Non Equilibrium Thermodynamics of Glassy Polymers (NET-GP) coupled to the Lattice Fluid (LF) was showed to be able to predict the solubility of gases and vapors in glassy polymers at various pressures based on pure component parameters. The NELF model relies on the hypothesis that the Gibbs free energy of a glassy polymer can be described by considering the density of the polymer as an internal state variable for the penetrant-polymer system. Therefore, in order to describe the complete sorption isotherm of a species in a glassy polymer, the model requires some information on its volumetric behavior during sorption, which might be a serious limitation to its predictive ability. In the present work, a new rheological assumption has been used to evaluate the swelling induced by the penetrating species, considering that the polymer relaxation occurs involving two characteristic times on fairly different scales. If temperature is appreciably below the glass transition of the polymer, only the short-time relaxation phenomena are involved during sorption within the usual experimental times, in which local rearrangements of the macromolecules take place. Much longer time would be instead required to have a noticeable relaxation for the second mode of rearrangement that involves the whole polymer chain, and therefore, in most of the cases this is not observed. In this concern, the polymer phase can be conveniently assumed as formed by two elements corresponding to the two characteristic times of relaxation; a soft part for which the equilibrium condition holds and a glassy hard part that does not contribute to the swelling. This assumption allows the estimation of the polymer swelling at increasing penetrant activity without specific experimental data and the calculation of the complete sorption isotherm by the NELF model in a purely predictive way. This tool was satisfactorily applied for many sorption isotherms of swelling gases (such as CO2 or C2H4) and organic vapors (xylene, toluene, or hydrocarbons) in glassy polymers such as polystyrene, polycarbonate or amorphous Teflon. The model was also able to capture complex behaviors such as those given by non linear trends of dilation or when a change in concavity of the sorption isotherm is observed due to a penetrant-induced glass transitions of the polymer. The experimental dilation isotherms, for those systems for which they were available, confirmed the reliability of the present model.

The object of the present study is the process of gas transport in nano-sized materials, i.e. systems having structural elements of the order of nanometers. The aim of this work is to advance the understanding of the gas transport mechanism in such materials, for which traditional models are not often suitable, by providing a correct interpretation of the relationship between diffusive phenomena and structural features. This result would allow the development new materials with permeation properties tailored on the specific application, especially in packaging systems. The methods used to achieve this goal were a detailed experimental characterization and different simulation methods. The experimental campaign regarded the determination of oxygen permeability and diffusivity in different sets of organic-inorganic hybrid coatings prepared via sol-gel technique. The polymeric samples coated with these hybrid layers experienced a remarkable enhancement of the barrier properties, which was explained by the strong interconnection at the nano-scale between the organic moiety and silica domains. An analogous characterization was performed on microfibrillated cellulose films, which presented remarkable barrier effect toward oxygen when it is dry, while in the presence of water the performance significantly drops. The very low value of water diffusivity at low activities is also an interesting characteristic which deals with its structural properties. Two different approaches of simulation were then considered: the diffusion of oxygen through polymer-layered silicates was modeled on a continuum scale with a CFD software, while the properties of n-alkanthiolate self assembled monolayers on gold were analyzed from a molecular point of view by means of a molecular dynamics algorithm. Modeling transport properties in layered nanocomposites, resulting from the ordered dispersion of impermeable flakes in a 2-D matrix, allowed the calculation of the enhancement of barrier effect in relation with platelets structural parameters leading to derive a new expression. On this basis, randomly distributed systems were simulated and the results were analyzed to evaluate the different contributions to the overall effect. The study of more realistic three-dimensional geometries revealed a prefect correspondence with the 2-D approximation. A completely different approach was applied to simulate the effect of temperature on the oxygen transport through self assembled monolayers; the structural information obtained from equilibrium MD simulations showed that raising the temperature, makes the monolayer less ordered and consequently less crystalline. This disorder produces a decrease in the barrier free energy and it lowers the overall resistance to oxygen diffusion, making the monolayer more permeable to small molecules.

The oxygen transport properties of LDPE films coated with different kinds of hybrid coatings were then obtained in terms of permeability and diffusivity at 35 and 50 °C, and their correlation to various structural and processing parameters is discussed. In this contribution, in particular, we report data obtained at different organic/inorganic (O/I) ratios and for different PE-PEG molecular weights. A second paper of this series re- ports the effects induced in the oxygen permeability by changing the organic phase composition with hydrogen bonding capable organics and by treating with plasma the LDPE surface prior to coating.

The mass transport properties of a system with impermeable platelets dispersed in a polymer matrix were investigated, through a numerical algorithm, based on finite volume method. Simulations were carried out on 3-D geometries where different shapes of the lamellae were considered, dispersed in both an ordered and random way; different volume fractions φ and aspect ratios α of the platelets were considered, and, in the ordered structures, also different values of the flakes spacing σ were investigated. In the case of random systems, multiple structures were analyzed for a given set of parameters and the results were treated statistically to obtain reliable information. The results show that the permeability in ordered geometries decreases with the product α φ and that the curves corresponding to different filler shapes have a similar qualitative behavior but quantitative differences in the enhancements of the material barrier properties; circular platelets in particular, showed to be less efficient than other geometries in decreasing the effective diffusivity of the composite. All 3-D structures then showed diminished barrier properties with respect to homologous 2-D structures suggesting that the use of the latter approach would lead to an overestimation of the barrier properties increases in real nanocomposites and thus, despite its simplicity, should not be used for this purpose. The data relative to 3-D random dispersions, that show barrier properties even worse than those of ordered dispersions of circular lamellae, can be accurately predicted by the Nielsen's model approach which therefore seems more suitable to describe the properties of real materials.

In the last years more and more interest has been devoted to the study of nanocomposite materials obtained through the addition of inorganic filler with, at least, one dimension in the scale of nanometer to a polymeric matrix. Continuum-based composite modeling reveals that the enhanced properties are strongly dependent on particular features of the second-phase “particles”; in particular, the particle volume fraction (φ) and the particle aspect ratio (α). A CFD algorithm was used to investigate the transport properties of a system with an impermeable phase dispersed in a polymer matrix; it is a pure diffusion phenomenon of small penetrant molecules in a composite media, simulated from a macroscopic point of view, using a finite volume algorithm. We invoke a simple model developed to describe the permeability in filled polymers; which strives to predict the observed permeability based strictly on tortuosity arguments. The reduction of permeability arises from the longer diffusive path that the pentrants must travel in the presence of the filler. The simulations are performed on these random geometries at different loading fractions and different aspect ratios, in order to have a fairly wide set of data. The results, averaged on the different geometries obtained, show that the permeability decays as function of the filler volume concentration, all the trends appear similar with similar behavior for different lamella characteristic parameters. As one can see analyzing the data set, there is a clear and unique trend considering α times φ as the ruling parameter. The permeability decay shows a power law dependence on α φ scaled with the inverse of the polymeric volume fraction; the exponent seems to have a value in between 1.0, as in Nielsen’s model, and 2.0, which is the one in the most famous Cussler’s formulation.

The permeability and diffusivity of oxygen in films of PET coated with a thin layer of a hybrid organic/inorganic (ceramer) material have been determined at 65°C. The permeability data are collected using a closed-volume permeation apparatus and the diffusivity has been calculated with the time-lag method. The addition of coating dramatically improves the oxygen barrier properties of the substrate, the apparent permeability of the multilayer film being up to 3 orders of magnitude lower than that of pure PET. The pure coating properties are opportunely calculated by taking into account the effect of the different diffusion resistances in the various layers. The effect of ageing has also been investigated, by comparing the oxygen permeability before and after immersion in water of the films that are suspected to be degraded by water.

Electrospinning is the most common and industrially scalable technique for the production of polymeric nanofibers. Currently, nanocomposites are drawing much interest for their excellent properties in terms of flexibility, electrical conductivity and high surface area, which enhances the interaction with the surrounding environment. The objective of this thesis was the optimization of different electrospinning setups for the production of nanostructured polymeric composites using graphene-related materials as nanofillers. Such composites were obtained using different polymers as matrix (polyamide 6, polyinylidene fluoride and polylactic acid) that were selected and combined with the appropriate reinforcements based on their properties and their interest for specific applications. Moreover, this study highlighted the possibility to tune the morphology and size of the produced nanofibers by the addition of appropriate nanofillers even in low amounts. The addition of only 0.5% of GO allowed the production of smooth nanofibers with diameters up to 75% thinner (in the case of PLA) than the ones obtained from the pristine polymer. PVdF was charged with GO to produce triboelectric materials that can be exploited in a wearable nanogenerator for the conversion of human motion energy in electrical energy. The addition of GO improved the open-circuit voltage and power-output of a generator prototype by 3.5 times. Electrospun PA6 membranes were coated with rGO using a simple two-step technique to produce conductive textiles for wearable electronic applications. The sheet resistance of the produced materials was measured in approximately 500 Ω/sq and their resistance to washing and bending was successfully tested. These materials could be exploited as strain sensors or heating elements in smart textiles. PLA was co-electrospun with GO and cellulose nanofibers to produce high-surface area and porosity mats that could be exploited for the production of functionalized highly selective adsorption membranes with low pressure drops.

The effect of CO2 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 degrees 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 CO2 produces a decrease of polymer storage modulus E' and an enhancement of tan delta factor. Experimental data for both E' and tan delta vary regularly and monotonically with CO2 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 CO2 content for all polymers analyzed, notwithstanding their CO2 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 CO2 content and the changes in the polymer mechanical properties induced by the same CO2 content.

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

The 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 modeling description of basic transport phenomena of either liquid, gas or vapor molecules in dense polymeric membranes is of tremendous impact for the separation industry, which relies on solid models for the design of optimal process conditions, for the selection of the most suitable membrane materials as well as for the development of novel ones. Such models need to deal with several physical aspects and phenomena, spanning over broad time and length scales, thus requiring multiple approaches. The solid frameworks now available mainly rely on the solution–diffusion theory, in which equation of state models and free volume theories are applied for the description of thermodynamic and kinetic properties, to be coupled in appropriate transport schemes.

Composite films based on poly(lactic acid) filled by 0.5 and 5 wt.% of Allium ursinum extract (wild garlic) for food packaging applications were prepared. Obtained films were examined from the view of characterization material properties and antimicrobial potential. The addition of two different amounts of A. ursinum extract improved thermal and mechanical properties of neat PLA (increase in Tgand tensile strength for both loadings). The oxygen barrier properties of the obtained hybrid films in dry condition were not significantly modified, while a slight increase of oxygen transmission rate was observed for the 5% loaded samples. Differences were detected in ΔE* values among the films containing A. ursinum extract in comparison with neat PLA. A marked difference between neat PLA and sample with 0.5 wt% of A. ursinum extract (3-6) was observed, while the color of the samples with 5 wt% was characterized by a completely different shade compared with neat PLA (>12). The antimicrobial activity of PLA films (neat and with 0.5 and 5 wt% of A. ursinum extract) was tested against Gram-negative bacterium Escherichia coli and both polymer composites with 0.5 and 5 wt% AU extract showed antimicrobial activity.

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.

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 N2, Ar, and CO2 in the glassy polymer with intrinsic microporosity PIM-1 has been investigated across a broad temperature range, from cryogenic (77 K) to near room temperature (275 K). The data obtained have been interpreted by the non-equilibrium thermodynamic model for glassy polymers (NET-GP), which accurately describes the experimental behaviors, and is used to predict the solubility of the same gases above room temperature. The analysis reveals that the same mechanism drives the sorption process over the broad temperature range inspected, with physical dissolution of the gas in the glassy matrix accompanied by significant swelling of the polymer occurring largely in the central portion of the isotherm at cryogenic temperatures. These findings clearly support the idea that calculation of the BET surface area for amorphous high free-volume glassy polymers does not represent an actual real physical property and suggest that its value is an unsuitable metric of polymer material properties. The gas uptake obtained in the cryogenic sorption isotherm is clearly related to the excess free volume and may instead serve as a more appropriate metric for comparison between different polymers.

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.

The use of Non-Equilibrium Thermodynamics for Glassy Polymers (NET-GP) model to predict infinite dilution gas solubility coefficient is revised in this work and its extension to the analysis of apparent constant pressure heat capacity in polymeric materials below the glass transition temperature Tg is developed. Use is made of different Equations of State (EoS), in the class of tangent-hard-spheres-chain theories, to predict the thermal expansion coefficient below Tg, resulting in consistent representations of the Henry's coefficient for gaseous species in the same temperature range, for the case of different versions of Statistical Associating Fluid Theory (SAFT) EoS. With reference to calorimetric properties, the analysis here performed indicates that NET-GP endowed with EoS tuned on melt phase equilibrium properties does not allow for the prediction of the bulk modulus of the glassy polymeric phase, and only qualitative behavior for the apparent heat capacity are reproduced. On the other hand, after the use of experimental data from structural relaxation experiments to evaluate the bulk modulus in glassy state, a satisfactory prediction of the excess heat capacity is obtained within the same framework, for the case of different non-equilibrium conditions. Conclusion are finally drawn for the need to account for additional order parameters in NET-GP approach in order to address the representation of the complex calorimetric behavior exhibited by glassy polymeric materials.

We used soluble graphene derivatives to fabricate gas barrier coatings on the surface of several industrially relevant commodity polymers. The coatings are prepared using electrochemically exfoliated graphene oxide, featuring both monoatomic thickness and micron-scale lateral size, showing better gas barrier performance as compared to films of commercial graphene products. A 74% decrease of oxygen transmission rate is found using loadings as low as 0.4 wt. % (0.2 vol. %). The coating process is performed using a combination of solution processing, filtering, and transfer. It is a robust and versatile approach, working with different transfer processes, different starting graphite materials and a wide range of well-known polymeric substrates: poly(ethylene terephthalate), poly(lactic acid), poly(hexamethylene adipamide), poly(propylene), and poly(vinyl chloride). The use of 2D sheets as surface coatings instead of bulk additives overcomes common issues related to dispersion of graphene in a polymer matrix, and gives a clear advantage in preserving the mechanical properties of the bulk polymer. Furthermore, it is a scalable approach able to significantly improve the barrier properties of polymeric films for large-scale applications.

Atactic polystyrene, as reported in a recent contribution by our group, displays a marked change in glass transition when exposed to toluene vapor due to plasticization associated with vapor sorption within the polymer. The dependence of the glass transition temperature of the polymer−penetrant mixture on the pressure of toluene vapor is characterized by the so-called “retrograde vitrification” phenomenon, in that, at a constant pressure, a rubber to glass transition occurs by increasing the temperature. In this contribution, we have used a theoretical approach, based on the nonrandom lattice fluid thermodynamic model for the polymer−toluene mixture, to predict the state of this system, i.e., rubbery or glassy, as a function of fluid pressure and system temperature. The experimentally detectable glass transition is assumed to be a kinetically affected evidence of an underlying II order thermodynamic transition of the polymer mixture. On the basis of this hypothesis, the Gibbs−Di Marzio criterion, stating that equilibrium configurational entropy is zeroed at the glass transition, has been applied to locate the transition. The working set of equations consists of the expression of configurational entropy obtained from the adopted lattice fluid model equated to zero, coupled with the equation expressing the phase equilibrium between the polymer phase and the pure toluene vapor phase in contact and with the equations of state for the two phases. Theoretical predictions are in good qualitative and quantitative agreement with the experimental results previously obtained gravimetrically performing “dynamic” sorption experiments, which represent a neat example of the occurrence of so-called “type IV” glass transition temperature vs pressure behavior. The peculiar retrograde vitrification phenomenon and the glass transition temperature vs pressure envelope determined experimentally are well described by the proposed theoretical approach.

Solubility and permeability of gases in glassy polymers have been considered with the aim of illustrating the applicability of thermodynamically-based models for their description and prediction. The solubility isotherms are described by using the nonequilibrium lattice fluid (NELF) (model, already known to be appropriate for nonequilibrium glassy polymers, while the permeability isotherms are described through a general transport model in which diffusivity is the product of a purely kinetic factor, the mobility coefficient, and a thermodynamic factor. The latter is calculated from the NELF model and mobility is considered concentration-dependent through an exponential relationship containing two parameters only. The models are tested explicitly considering solubility and permeability data of various penetrants in three glassy polymers, PSf, PPh and 6FDA-6FpDA, selected as the reference for different behaviors. It is shown that the models are able to calculate the different behaviors observed, and in particular the permeability dependence on upstream pressure, both when it is decreasing as well as when it is increasing, with no need to invoke the onset of additional plasticization phenomena. The correlations found between polymer and penetrant properties with the two parameters of the mobility coefficient also lead to the predictive ability of the transport model.

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.

The solubility of various gases in several glassy polymers has been analyzed by the nonequilibrium thermodynamics for glassy polymers (NET-GP) framework, coupled with a lattice fluid equation of state model. Moreover, a simple rheological tool recently introduced for the a priori evaluation of the penetrant induced swelling is employed to predict the volumetric behavior of the solute/polymer mixture below T g . Such model accounts for an additional nonequilibrium parameter for the description of polymer phase that represents its pseudoequilibrium compressibility, and it can be retrieved from pure component pressure–volume–temperature data below T g . More in detail, the effect of polymer pretreatment and its prior history (e.g. annealing or conditioning by preswelling) on the resulting solubility behavior has been thoroughly analyzed and discussed, and the experimental data obtained for several penetrant/polymer couples have been well described by the present model.

The possibility to evaluate in a predictive way the relevant transport properties of low molecular weight species, both gases and vapors, in glassy polymeric membranes is inspected in detail, with particular attention to the methods recently developed based on solid thermodynamic basis. The solubility of pure and mixed gases, diffusivity and permeability of single gases in polymer glasses are examined, considering in particular poly(2,6-dimethyl-1,4-phenylene oxide) as a relevant test case. The procedure clearly indicates what are the relevant physical properties of the polymer matrix and of the penetrants required by the calculations, which can be obtained experimentally through independent measurements. For gas and vapor solubility, the comparison with direct experimental data for mixed gases points out also the ability to account for the significant variations that solubility-selectivity experiences upon variations of pressure and/or feed composition. For gas and vapor permeability, the comparison with direct experimental data shows the possibility to account for the various different trends observed experimentally as penetrant pressure is increased, including the so-called plasticization behavior. The procedure followed for permeability calculations leads also to clear correlations between permeability and physical properties of both polymer and penetrant, based on which pure predictive calculations are reliably made. [Figure not available: see fulltext.]

The effect of block copolymer morphology on polymer crystallization and water sorption was investigated using two amphiphilic block copolymers with minority hydrophilic phase. Such polymers have many potential membrane applications, including CO 2 capture and water purification. A model block copolymer chemistry comprising polystyrene and poly(ethylene oxide) (PEO) is used in this work. Both block copolymers have strongly phase-separated order, one with lamellar morphology and another with cylindrical morphology. In addition to the block copolymer structure, the PEO phase is semicrystalline at room temperature. The block copolymer structure has dramatic consequences for the degree of PEO crystallinity even in the absence of water. Furthermore, the crystallinity is affected by water sorption. PEO melting and degree of crystallinity were determined as a function of water content. Water solubility was measured between 35 and 75 °C. Interestingly, water sorption properties are dictated almost exclusively by the amorphous PEO volume fraction, being low in the semicrystalline state (below 55 °C) and higher in the amorphous state (above 55 °C). At 55 °C, crystallite dissolution is observed with increasing water solubility. Water diffusion coefficient was also measured; it decreases monotonically with increasing water content. This concentration dependence of diffusion is explained by water clustering, which increases with increasing water content. In addition to block copolymer morphology playing a major role in PEO crystallinity, it has a significant effect on water diffusion in the amorphous polymers and is of practical importance as investigations at elevated temperature are not possible with homopolymer PEO.

The present invention relates to a process, and relevant plant (1), for separating at least one key component (KC) from a multicomponent gas stream (GS) that is caused to flow on a composite membrane (20) comprising dense domains (21) permeable to the key component (KC) and porous domains (22) intended to adsorb preferentially the key component (KC). A permeate stream (PS), separated from the multicomponent gas stream (GS) and containing the key component (KC), is extracted through a discharge line (5) depending on the measured value of the pressure (P) downstream the membrane (20), Upon reaching a predetermined maximum value (pmax) of such pressure (P), the permeate stream (PS) is extracted until reaching a predetermined minimum value (pmin) of such pressure (P) downstream the membrane (20), and upon reaching such predetermined minimum value (pmin), the extraction of the permeate stream (PS) is stopped. Thus by repeating such operations extracting and stopping the extraction downstream the membrane (20), alternated cycles are generated and a pseudo-steady state condition is accomplished, where the plant (1) receives the feed stream (GS) in the continuous mode and releases the permeate stream (PS) in an intermittent manner, while a retentate stream (RS), containing the components of the feed stream (GS) that have not been collected in the permeate stream (PS) is discharged with continuity. By handling the predetermined maximum value (pmax) and minimum value (pmin) of the pressure (P) downstream the membrane (20), that is of the extraction cycle of the permeate stream (PS), it is possible to considerably vary the efficacious permeance value and the separation factor of the process without modifying the membrane (20), the module (10) where it is contained or the feeding conditions.

Sorption data of nitrogen, argon and krypton in different glassy polymers at different cryogenic temperatures are analyzed, including hydrogen in PIM-1; conventional and high free volume glassy polymers are included. A consistent interpretation of experimental data is obtained by considering penetrant dissolution in a uniform dense glassy polymer, undergoing volume swelling with all penetrants but hydrogen. All the data are properly described by using the NELF model which is appropriate for the solubility in glassy polymers. Remarkably, in each polymer the sorption isotherms of different penetrants are described well by using the same initial polymer density, and the same swelling coefficient value allows satisfactory description of the sorption behavior of one penetrant at different temperatures. For PIM-1, NELF model and molecular dynamics give exactly the same swelling, and desorption after sorption or subsequent sorption-desorption cycles show hysteresis effects clearly associated to irreversible volume changes; in addition, hydrogen sorption in PIM-1 is fully predicted by the NELF model, simply based on nitrogen sorption, as opposed to BET theory. On the bases of the above results the conclusion is drown that BET theory is not applicable to the cryogenic sorption isotherms in glassy polymers.

Polymer-based membranes play a key role in several industrially important gas separation technologies, e.g., removing CO2 from natural gas, with enormous economic and environmental impact. Here, we develop a novel hybrid membrane construct comprised entirely of nanoparticles grafted with polymers. These membranes are shown to have broadly tunable separation performance through variations in graft density and chain length. Computer simulations show that the optimal NP packing forces the grafted polymer layer to distort, yielding regions of measurably lower polymer density. Multiple experimental probes confirm that these materials have the predicted increase in “polymer free volume”, which explains their improved separation performance. These polymer-grafted NP materials thus represent a new template for rationally designing membranes with desirable separation abilities coupled with improved aging characteristics in the glassy state and enhanced mechanical behavior.

Exposing a glassy polymer to a fluid phase (in gaseous or liquid state) containing a low molecular weight compound results in the sorption of the latter within the polymer, inducing, among other effects, the plasticization of the material which also promotes a change in the glass transition temperature. The amount of sorbed penetrant is often related in a complex fashion to the temperature and pressure of the fluid, thus determining that the locus of glass transition, when represented in pressure−temperature coordinates, may display as well rather complex patterns. This is an issue of particular importance in several applications of glassy polymers. In particular, we investigated the behavior of polystyrene in contact with toluene vapor by performing several modes of dynamic sorption experiments, in which the rate of change of the temperature of the system and/or of the pressure of the vapor phase are controlled with high accuracy, with the aim of creating a map of rubbery and glassy states of the polymer as a function of temperature and pressure of the toluene vapor. Isothermal tests were performed by changing the pressure at a controlled rate, isobaric tests were performed by changing the temperature at a controlled rate, and isoactivity tests were performed by concurrently changing, in a proper way, both temperature and pressure. A relevant feature resulting from these experiments is the presence of a discontinuity in the slope of the mass of toluene sorbed within polystyrene reported as a function of temperature and/or pressure. This discontinuity has been interpreted as the indication of the occurrence of a glass transition. The elaboration of the experimental results allowed identification of the pressure/temperature conditions at which rubbery or glassy states of the polymer mixture are established. Quite interestingly, the system displays the so- called “retrograde vitrification” phenomenon, which consists of the occurrence of a rubbery-to-glassy state transition as the temperature increases at a fixed pressure. The whole set of results has been successfully interpreted on the basis of thermodynamics of II order transitions accounting for the fact that experimental evidence of such transitions is significantly affected by the kinetics of polymer relaxation.

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.

Water sorption behavior of two different microfibrillated cellulose (MFC) films, produced by delamination of cellulose pulp after different pretreatment methods, is examined at various temperatures (16–65°C) and up to 70% RH. The effect of drying temperature of MFC films on the water uptake is also investigated. The obtained solubility isotherms showed the typical downward curvature at moderate RH, while no upturn is observed at higher RH; the uptakes are in line with characteristic values for cellulose fibers. Enzymatically pretreated MFC dispersion showed lower solubility than carboxymethylated MFC, likely due to the different material structure, which results from the different preparation methods The experimental results are analyzed by Park and GAB models, which proved suitable to describe the observed behaviors. Interestingly, while no significant thermal effect is detected on water solubility above 35°C, the uptake at 16 and 25°C, at a given RH, is substantially lower than that at higher temperature, indicating that, in such range, sorption process is endothermic. Such unusual behavior for a cellulose-based system seems to be related mainly to the structural characteristics of MFC films, and to relaxation phenomena taking place upon water sorption. The diffusion kinetics, indeed, showed a clear Fickian behavior at low temperature and RH, whereas a secondary process seems to occur at high temperature and higher RH, leading to anomalous diffusion behaviors.

Geopolymer materials, a new class of alkali-bonded ceramics, have been prepared in monolith porous form, in order to investigate the adsorptive performances of CO 2 and light gases (CH 4 and N 2 ) by means of a volumetric method in the sub-atmospheric pressure range. The samples have been produced by reacting an aluminosilicate powder with an aqueous alkali silicate solution, in different dilution proportions, achieving very high geopolymerization conversion (higher than 97%). The monoliths microstructural and textural properties have been first characterized by SEM and porosimetric measurements, which revealed the structure of the geopolymer as mainly consisting of nanoprecipitates and mesopores, with overall porosity from 30% up to 60%, and BET surface area up to 50 m 2 /g. The analysis of the gas adsorption properties showed a quite good capacity for CO 2 in the geopolymer monoliths, remarkably higher than those of CH 4 and N 2 , pointing out the significant ability in the selective capture of CO 2 of these geopolymers. The values of selectivity in capacity obtained from the adsorption measurements, up to 200 and 100 for CO 2 /N 2 and CO 2 /CH 4 separation, respectively, are considerably higher than those of most of the adsorbent materials commonly accounted for in such applications.

Fully bio-based and biodegradable materials, such as polylactic acid (PLA) and microfibrillated cellulose (MFC), are considered in order to produce a completely renewable packaging solution for oxygen barrier applications, even at medium-high relative humidity (R.H.). Thin layers of MFC were coated on different PLA substrates by activating film surface with an atmospheric plasma treatment, leading to the fabrication of robust and transparent multilayer composite films, which were then characterized by different experimental techniques. UV transmission measurements confirmed the transparency of multilayer films (60% of UV transmission rate), while SEM micrographs showed the presence of a continuous, dense and defect free layer of MFC on PLA surface. Concerning the mechanical behavior of the samples, tensile tests revealed that the multilayer films significantly improved the stress at break value of neat PLA. Moreover, the oxygen barrier properties of the multilayer films were improved more than one order of magnitude compared to neat PLA film at 35 °C and 0% R.H. and the permeability values were maintained up to 60% R.H. The obtained materials therefore showed interesting properties for their possible use in barrier packaging applications as fully biodegradable solution, coupling two primarily incompatible matrices in a multilayer film with no need of any solvent or chemical.

A novel experimental method for the analysis of volume relaxation induced by solvents in glassy polymers is presented. A gravimetric technique is used to evaluate the isothermal solvent mass uptake at controlled increasing/decreasing solvent pressure at constant rate. Fundamental properties of the solvent/polymer system can be obtained directly, and models can be applied, combining both nonequilibrium thermodynamics and mechanics of volume relaxation contribution. The fundamental case of polystyrene and toluene mixtures are thus accounted for, and various experimental conditions have been explored, varying the temperature, and spanning over different pressure increase/decrease rates. The results obtained allowed to evaluate the isothermal second order transition induced by solvent sorption, as well as the determination of the effect of the pressure rate. Therefore, this work proposes a new standard for the characterization and the understanding of the relaxational behavior of glassy polymers.

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