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A new fitting model for sorption by glassy polymers is suggested based on the Flory–Huggins (FH) equation with a composite formula for the FH interaction parameter, χ, which is applicable if sorption experimental data shows a single-maximum variation of the FH parameter. Namely, a power-like and a linear approximation is assumed for χ ( φ 1 ) , as a function of solvent volume fraction φ 1 , before and after the point of its maximum. After determining the maximum point from a direct inspection of the sorption data, the three fitting parameters are evaluated by solving two independent least-square minimization problems. Several sorption studies of biopolymers taken from the literature show that the endset of the glass transition region is correlated with the position of the maximum of the FH interaction parameter. Based on this hypothesis and the Vrentas–Vrentas model for sorption of glassy polymers, a theoretical framework for the glass transition analysis is developed. In particular, the solvent-induced glass transition temperature variation can be estimated from the sorption isotherm as a function of the solvent content corresponding to temperatures above the temperature of sorption.

The local and cooperative dynamics of atactic PS (a- PS) were studied by broadband dielectric relaxation spectroscopy (BDRS) and attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR). The a-PS has been subjected to thermal rejuvenation and subsequent quenching, short-term aging (6 weeks), and long-term aging (1 year) at ambient conditions. Where for the rejuvenated sample only an α- and a γ-relaxation is observed, short-term aging results in an additional β*-relaxation that merges with the α-relaxation at longer aging times. The γ-relaxation is increasing in intensity and activation energy during aging. The α-process shows no spectral changes and shift in the relaxation time upon aging. This may be attributed to a possible erasure of history of the material during the temperature-sweep mode measurement. Fourier transform infrared spectroscopy (FTIR) results suggest that the energetically favorable trans-trans (tt) conformers are increased in population with aging. ispartof: JOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS vol:57 issue:20 pages:1394-1401 status: published

The effect of plastic deformation on the molecular dynamics of atactic polystyrene (a-PS) was studied by broadband dielectric relaxation spectroscopy (BDRS), Fourier-transform infrared spectroscopy (FTIR) and polarized-light microscopy. Sheets of a-PS have been subjected to cold rolling, that is, mechanical rejuvenation, followed by a quenching step and fast heating above its glass-transition temperature, resulting in thermal rejuvenation. Cold rolling revealed, in addition to the known α- and γ(I)-relaxations, four hitherto unknown relaxation processes (II, III, IV and V). Using the framework of craze formation and multiplicity of the glass transition (E. Donth, G. H. Michler, Colloid Polym. Sci. 1989, 267, 557–567), supported by an activation-enthalpy/entropy analysis (Starkweather, W. Howard, Macromolecules 1981, 14, 1277–1281), the following physical picture emerges: (a) processes I and II represent local conformation transitions γ referring to chains of two different degrees of stretching (T/G-ratio); and (ii) processes III and IV were identified as helix-inversion processes of T2G2 helices as reported earlier for syndiotactic-rich PS—an assignment supported by FTIR results. Finally, the relaxation V could be attributed to the onset of the fibrillar glass transition (within crazes), leading to stress release by collapse of the fibrils and hence dying out of process V. Polarized-light microscopy confirmed the creation of oriented structures and internal stresses upon cold rolling, and their removal upon thermal rejuvenation.

Antiplasticization of glassy polymers, arising from the addition of small amounts of plasticizer, was examined to highlight the developments that have taken place over the last few decades, aiming to fill gaps of knowledge in the large number of disjointed publications. The analysis includes the role of polymer/plasticizer molecular interactions and the conditions leading to the cross-over from antiplasticization to plasticization. This was based on molecular dynamics considerations of thermal transitions and related relaxation spectra, alongside the deviation of free volumes from the additivity rule. Useful insights were gained from an analysis of data on molecular glasses, including the implications of the glass fragility concept. The effects of molecular packing resulting from antiplasticization are also discussed in the context of physical ageing. These include considerations on the effects on mechanical properties and diffusion-controlled behaviour. Some peculiar features of antiplasticization regarding changes in Tg were probed and the effects of water were examined, both as a single component and in combination with other plasticizers to illustrate the role of intermolecular forces. The analysis has also brought to light the shortcomings of existing theories for disregarding the dual cross-over from antiplasticization to plasticization with respect to modulus variation with temperature and for not addressing failure related properties, such as yielding, crazing and fracture toughness.

Understanding and predicting sorption thermodynamics of low molecular weight compounds in rubbery and glassy polymers is of great relevance to elucidate important phenomena in areas at the interface of various scientific branches, such as the colloid and interface science, membrane science, polymer foaming, tissue engineering, scaffolding, microcellular materials, aerogels, and for the implementation of technological applications. The development of thermodynamic models for polymer-based mixtures, applicable over a wide range of conditions, remains an active and fascinating research area. Recent advances in statistical thermodynamics and a better understanding of intra- and inter-molecular interactions, thanks to accurate experimental measurements and molecular simulations using realistic force fields, have contributed significantly to this end. In fact, sorption thermodynamics in polymers plays a relevant role in describing phase equilibria of polymer mixtures, (hydro)gel swelling, intramolecular association, hydrogen-bonding cooperativity and polymer degradation and stability, in assessing durability of polymers exposed to aggressive environments, in predicting penetrant induced crystallization and plasticization phenomena in polymers, in designing polymer-based separation processes, in tailoring polymer foaming processes, in improving gas and vapor barrier properties of polymer packaging, in modelling devolatilization of polymer solutions and migration phenomena of additives, in designing drug delivery systems, to mention a few. In the last decades, models have been introduced rooted on Equation of State theories, some of them based on compressible lattice frameworks. Notably, these models have been structured to specifically account for non-random distribution of molecular species and for dealing with several kinds of self-interactions that establish between polymer molecules and between penetrant molecules as well as cross-interactions that establish between moieties present on polymer backbone and penetrants. These models have been built to describe the behaviour of both rubbery polymers and out-of-equilibrium glassy polymers. Towards the further development of these approaches to gain an increased predictive capability of this thermodynamic description, recently have been also introduced approaches aimed at the estimation of relevant parameters based on molecular descriptors for calculations of properties of pure-components bulk phases and solutions. Such a quantitative description of the sorption process by use of advanced thermodynamic theories invariably relies on a molecular-level characterization of the system under scrutiny to validate and support the theoretical framework. Information is required on the molecular aggregates formed in the system, their structure, stoichiometry and, whenever possible, their population. In this respect, vibrational spectroscopy (FTIR, Raman) has demonstrated to be among the most powerful techniques, due to its sensitivity towards H-bonding detection and to its sampling flexibility, which allows the development of in-situ, time-resolved measurements. In the last ten years, significant advancements have occurred in terms of both experimental approaches and data analysis techniques, which considerably contributed to deepening the interpretation of the molecular interactions scenario. In particular, Two-dimensional correlation spectroscopy (2D-COS), Difference spectroscopy (DS) and first-principles quantum chemistry calculations have made a strong impact on the amount and quality of the acquired information. In view of the progress in this rapidly advancing and technologically relevant subject, this review article summarizes the state of the art on sorption thermodynamics modelling and on synergic combination with the wealth of information recently made available thanks to advanced vibrational spectroscopy techniques.

For the past few decades, researchers have been intrigued by glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers over the last few years. This review also includes the applications of glassy polymers. Despite having many applications, current researchers still have difficulty in implementing coating challenges due to issues such as physical ageing, brittleness, etc., which are briefly discussed in the review.

In this paper, the sorption thermodynamics of low-molecular-weight penetrants in a glassy polyetherimide, endowed with specific interactions, is addressed by combining an experimental approach based on vibrational spectroscopy with thermodynamics modeling. This modeling approach is based on the extension of equilibrium theories to the out-of-equilibrium glassy state. Specific interactions are accounted for in the framework of a compressible lattice fluid theory. In particular, the sorption of carbon dioxide, water, and methanol is illustrated, exploiting the wealth of information gathered at a molecular level from Fourier-transform infrared (FTIR) spectroscopy to tailor thermodynamics modeling. The investigated penetrants display a different interacting characteristic with respect to the polymer substrate, which reflects itself in the sorption thermodynamics. For the specific case of water, the outcomes from molecular dynamics simulations are compared with the results of the present analysis.

A triptycene-based diamine, 1,3,6,8-tetramethyl-2,7-diamino-triptycene (TMDAT), was used for the synthesis of a novel solution-processable polyamide obtained via polycondensation reaction with 4,4&prime, (hexafluoroisopropylidene)bis(benzoic acid) (6FBBA). Molecular simulations confirmed that the tetrasubstitution with ortho-methyl groups in the triptycene building block reduced rotations around the C&ndash, N bond of the amide group leading to enhanced fractional free volume. Based on N2 sorption at 77 K, 6FBBA-TMDAT revealed microporosity with a Brunauer&ndash, Emmett&ndash, Teller (BET) surface area of 396 m2 g&minus, 1, to date, this is the highest value reported for a linear polyamide. The aged 6FBBA-TMDAT sample showed moderate pure-gas permeabilities (e.g., 198 barrer for H2, ~109 for CO2, and ~25 for O2) and permselectivities (e.g., &alpha, H2/CH4 of ~50) that position this polyamide close to the 2008 H2/CH4 and H2/N2 upper bounds. CO2&ndash, CH4 mixed-gas permeability experiments at 35 &deg, C demonstrated poor plasticization resistance, mixed-gas permselectivity negatively deviated from the pure-gas values likely, due to the enhancement of CH4 diffusion induced by mixing effects.

An analysis of the diffusivity of light gases through Polymers of Intrinsic Microporosity (PIMs) shows that smaller H-2 and He gas molecules have a transport mechanism that is similar to that of porous materials, whereas larger gas molecules, CH4, N-2, O-2 and CO2, show activated transport similar to that of conventional dense polymers. A typical and defining feature of PIMs, which differentiates their properties from other high free volume polymers, glassy polymers and rubbers, is the change in slope of the plot of the diffusion coefficient as a function of the gas diameter, with a stronger size-selective trend for the larger gas molecules than for He and H-2. Deviation from this trend is observed for a polymer-gas combination with strong mutual affinity (i.e. an amine modified PIM with CO2). Molecular modelling shows that size selectivity in PIMs originates from the presence of bottlenecks between the individual free volume elements. For the latest generation of highly rigid PIMs, ageing studies show that diffusivity is differentially reduced for larger gas molecules, thus further enhancing their size-selectivity.

Global warming by greenhouse gas emissions is one of the main threats of our modern society, and efficient CO2 capture processes are needed to solve this problem. Membrane separation processes have been identified among the most promising technologies for CO2 capture, and these require the development of highly efficient membrane materials which, in turn, requires detailed understanding of their operation mechanism. In the last decades, molecular modeling studies have become an extremely powerful tool to understand and anticipate the gas transport properties of polymeric membranes. This work presents a study on the correlation of the structural features of different membrane materials, analyzed by means of molecular dynamics simulation, and their gas diffusivity/selectivity. We propose a simplified method to determine the void size distribution via an automatic image recognition tool, along with a consolidated Connolly probe sensing of space, without the need of demanding computational procedures. Based on a picture of the void shape and width, automatic image recognition tests the dimensions of the void elements, reducing them to ellipses. Comparison of the minor axis of the obtained ellipses with the diameters of the gases yields a qualitative estimation of non-accessible paths in the geometrical arrangement of polymeric chains. A second tool, the Connolly probe sensing of space, gives more details on the complexity of voids. The combination of the two proposed tools can be used for a qualitative and rapid screening of material models and for an estimation of the trend in their diffusivity selectivity. The main differences in the structural features of three different classes of polymers are investigated in this work (glassy polymers, superglassy perfluoropolymers and high free volume polymers of intrinsic microporosity), and the results show how the proposed computationally less demanding analysis can be linked with their selectivities.

In gas separation membrane processes, CO2 may induce the plasticization of glassy polymer, lowering its the mechanical rigidity and reducing the glass transition, with a loss of separation performances. Such mechanism is often associated to gas permeability behavior in glassy membranes vs. upstream p, and increasing trends are considered as the footprint of the plasticization onset. However, there is no clear correlation between gas permeability and the effects of CO2 on mechanical behavior. The CO2 induced plasticization in glassy membranes is investigated by direct DMA analysis of polymers saturated at different CO2 pressures. Matrimid polyimide is considered, as it shows a non-monotonous CO2 permeability behavior, and compared to PS (decreasing behavior) and PMMA (increasing).CO2 lowed the elastic modulus of all materials investigated, while the relaxation dynamics revealed a strong enhancement of tan δ, even in absence of a second order transition. The same qualitative behaviors are observed for all glassy systems investigated, and in Matrimid, no apparent change is identified around the pressure value corresponding to the minimum in CO2 permeability, excluding the presence of a new phenomenon onset. Results suggest that increasing permeability behaviors and non-monotonous trends, are not directly related to softening effect induced by CO2 in the polymer matrix, and such features have to be ascribed to the combination of solubility and diffusivity coefficients.In gas separation membrane processes, CO2 may induce the plasticization of glassy polymer, lowering its the mechanical rigidity and reducing the glass transition, with a loss of separation performances. Such mechanism is often associated to gas permeability behavior in glassy membranes vs. upstream p, and increasing trends are considered as the footprint of the plasticization onset. However, there is no clear correlation between gas permeability and the effects of CO2 on mechanical behavior. The CO2 induced plasticization in glassy membranes is investigated by direct DMA analysis of polymers saturated at different CO2 pressures. Matrimid polyimide is considered, as it shows a non-monotonous CO2 permeability behavior, and compared to PS (decreasing behavior) and PMMA (increasing).CO2 lowed the elastic modulus of all materials investigated, while the relaxation dynamics revealed a strong enhancement of tan δ, even in absence of a second order transition. The same qualitative behaviors are observed for all g...

The transport of CO2, CH4, N2 and He in films of polyimide 6FDA–6FpDA was studied at different temperatures, from 25 to 45 °C, and Relative Humidity (RH) from 0% to 90%. The permeability of all gases decreases with increasing RH, by factors as high as 44% for CH4 and 35% for the other gases; moreover, the relative decrease of gas permeability with respect to the dry polymer value is constant with temperature and just weakly dependent on the gas type. Pure water vapour sorption experiments were also conducted on the polymeric films in the same RH and temperature range, showing that water solubility in 6FDA–6FpDA is almost temperature-independent. A strong correlation therefore seems to exist between gas permeability decrease and water content in the membrane, due to the fact that absorbed water molecules occupy a portion of the polymer free volume, that is no longer available for gas permeation. Based on these considerations, the humid permeation results were analysed quantitatively and modelled with a simple approach based on free volume theory.

The influence of water vapor on the gas permeability of a commercial polyimide, Matrimid ® 5218, has been extensively investigated at three different temperatures (25, 35 and 45 °C), and with four different penetrant gases (CH 4 , N 2 , CO 2 and He), varying the relative humidity in the range 0–75%. In all tests performed, the permeability coefficient decreases as the concentration of water vapor in the membrane increases. In particular, the influence of the presence of water on gas permeability is very similar for all penetrants, as the same permeability decrease is found, at a given relative humidity, despite the different thermodynamic and kinetic characteristics of the probe gases considered. As temperature is raised, the gas permeability is enhanced, as expected. On the other hand, its decrease with respect to the dry polymer values, as relative humidity increases, is not affected by temperature, and it remains substantially unaltered from 25 to 45 °C, suggesting that such phenomenon can be directly related to the amount of water dissolved in the membrane, which is also unaffected by temperature. Based on the experimental evidence, a simple model is proposed to describe the permeation process under humid conditions, in the framework of the free volume theory. In particular, it has been considered that absorbed water molecules influence gas permeability by occupying polymer free volume, reducing its availability to other penetrants with lower condensability. The model describes accurately the experimental data using only two adjustable parameters for the polymer-water-penetrant system, once the water solubility is estimated from sorption measurements.

An extensive analysis is performed for the use of a model recently introduced for sorption induced volume dilation in glassy polymers, which can be combined with the nonequilibrium lattice fluid model (NELF) for the description of gas and vapor solubility in glassy polymers in a wide temperature range below the glass transition, from dry to fully plasticized conditions. The procedure extends the capability of previous versions of NELF model, as it refers to correlation and prediction of solubility of vapors and swelling agents. To this aim, the model counts on an additional out-of-equilibrium parameter for the polymeric species that interprets its pseudoequilibrium compressibility, and it can be retrieved from the analysis of pure component pressure–volume–temperature data below T g . The examples discussed in this work show that the overall procedure is highly reliable and addresses the key properties of the system for the direct interpretation of the effect of temperature, solute fugacity and state of glassy polymers on pseudoequilibrium volume swelling and solute content.

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.

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

The sorption of organic vapors of different chemical nature, molecular weight and polarity in glassy Matrimid 5218 polyimide films is measured and modeled in the entire activity range up to saturated vapor conditions. Experimental isotherms show several different peculiarities according to the nature of the solute component, consistent with the glassy character of the polymeric matrix. These features range from high vapor solubility coefficient at infinite dilution to swelling and plasticization of the polymer matrix depending on temperature and solute affinity. The various behaviors are then discussed by means of a thermodynamic model for properties of glassy polymeric phases. Indeed, the Non-Equilibrium Lattice Fluid (NELF) model is used to interpret the Vapor-Liquid-Equilibrium below Tg, while the corresponding equilibrium Lattice Fluid model was considered to the same purpose for the case of plasticization conditions in the system. This representation is able to describe consistently all different observed features and allows for a predictive procedure to reproduce solubility isotherms over a wide activity range.

The nonequilibrium lattice fluid (NELF) model is here implemented with a simplified relation for bulk rheological behavior of glassy polymers, to obtain a predictive model for pseudoequilibrium solute content and volume dilation induced by swelling agents. The rheological model discussed in this work is ultimately used to derive a relation for the pseudoequilibrium volume of the polymeric system as a function of temperature and solute fugacity. The model makes use of two nonequilibrium parameters which, in turn, can be determined through the analysis of nonequilibrium pVT properties of the polymeric species. The predictive ability of the new model for solubility and volume swelling was tested by means of the comparison of model predictions and correlations with experimental data, available in the literature, for different polymer/penetrant pairs. The results obtained from the comparison allow one to conclude that the model is not just useful to describe the swelling effect of penetrants but also to recognize conditions at which plasticization by solute species induces a glass to rubber transition in the polymeric system.

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

cited By 8; International audience; Physical ageing of amorphous polymers well below their glass transition temperature leads to changes in almost all physical properties. Of particular interest is the increase in yield stress and post-yield strain softening that accompanies ageing of these materials. Moreover, at larger strain polymers seem to rejuvenate, i.e. aged and non-aged samples have identical stressstrain responses. Also, plastically deforming an aged sample seems to rejuvenate the polymer. In this work we use molecular dynamic simulations with a detailed force field suitable for macromolecular ensembles to simulate and understand the effects of ageing on the mechanical response of these materials. We show that within the timescales of these simulations it is possible to simulate both ageing and rejuvenation. The short range potentials play an important role in ageing and rejuvenation. A typical yield drop exhibited by glassy polymers is a manifestation of a sudden relaxation in the short range structure of an aged polymer. Moreover, the aged polymers are known to be brittle. We show that this is intimately related to its typical stressstrain response which allows it to carry arbitrarily large mean stresses ahead of a notch. © 2010 Elsevier Ltd. All rights reserved.

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.

The competition between crazing and matrix shear yielding in rubber-toughened glassy polymers is investigated by detailed finite element simulations. To this end the microstructure is represented by an axisymmetric unit cell of glassy matrix containing a single cavitated rubber particle which is modeled as a void. The behavior of the matrix material is described in the framework of finite strain viscoplasticity, while a cohesive surface model is employed for crazing. The influence of the matrix yield behavior, the craze response, the rubber content, and the overall loading state are analyzed. (C) 2008 Elsevier B.V. All rights reserved.

An analysis of the empirical correlations that relate the solubility coefficient of gases at infinite dilution in glassy polymers to penetrant properties has been performed, by considering gas sorption as a succession of three steps: condensation of the penetrant, dissolution in the equilibrium polymeric phase, and departure of the system from equilibrium. The infinite dilution solubility coefficient is obtained from the contributions of the three steps, the first two of which involve standard equilibrium thermodynamics, while the latter requires nonequilibrium considerations and is described by using the nonequilibrium lattice fluid (NELF) model. The various terms have been evaluated for several gases in polycarbonate, polysulfone, poly(phenylene oxide), and poly(methyl methacrylate). It has been found that the largest term in the expression of solubility is due to condensation, which explains the observed correlation between solubility and critical temperature, while the out of equilibrium contribution to solubility, which generally gives numerical values lower than the condensation term, is in turn more strongly correlated to the penetrant critical volume.

The deformation of polymers under high-rate loading conditions is a governing factor in their use in impact-resistant applications, such as protective shields, safety glass windows and transparent armor. In this paper, Taylor impact experiments were conducted to examine the mechanical behavior of polycarbonate (PC), under conditions of high strain rate (∼105 s−1) and inhomogeneous deformation. High-speed photography was used to monitor the progression of deformation within the sample. A recently developed three-dimensional large strain rate-dependent elastic–viscoplastic constitutive model which describes the high-rate behavior of glassy polymers was used together with the ABAQUS/Explicit finite-element code to simulate several Taylor impact conditions. The simulation results are compared directly with experimental images for a range in initial rod dimensions and velocities. Final deformed shapes are found to correspond with those obtained experimentally, demonstrating the ability to predict complex inhomogeneous deformation events during very high-rate impact loading scenarios. The dependence of the observed behaviors on the various features of the polymer stress–strain behavior are presented in detail revealing the roles of strain softening and strain hardening in governing the manner in which deformation progresses in a polymer during dynamic inhomogeneous loading events.

It is observed in general that the solubility of gases and vapors in polymers, both in the rubbery and glassy phase, scales with measures of penetrant condensability, such as the Lennard-Jones parameter, the boiling temperature, or the critical temperature. For rubbery polymers, that behavior was found fully consistent with a simple equilibrium thermodynamic derivation, while no effective theoretical interpretation has been offered so far for the case of glassy polymers. On the other hand, a rigorous expression for the solubility coefficient S 0 in the limit of low pressures can be found based on the NELF model for gas solubility in glassy polymers, which also indicates its dependence on the characteristic parameters of the penetrants, such as cohesive energy density, molar volume and molecular weight. The values of ln( S 0 ) for a series of gaseous penetrants have been calculated with the NELF model for several common glassy polymers as polycarbonate (PC), polysulfone (PSf), poly(phenylene oxide) (PPO) and poly(methyl methacrylate) (PMMA). In all cases, ln( S 0 ) is linear with the penetrant critical temperature, T C , and the dependence on temperature and on the polymer fractional free volume can easily be evaluated by the model. The analysis points out also the specific roles of the energetic and entropic contributions to the trend observed for the solubility coefficient in glassy polymers.

A model is introduced here for volume relaxation in glassy polymers, induced by sorption of low molecular weight species. The model relies on description of thermodynamic properties of glassy mixtures obtained through NET-GP model and it considers simple linear viscoelastic laws to interpret the stress–strain relation for the polymeric material. Results for the case of sorption kinetics in constant fugacity processes, obtained from the model, are compared with experimental values for vapour sorption in glassy polymeric microspheres. Satisfactory representations were obtained both for instant solute content measured in experimental run and for mass uptake registered in ‘relaxation stage’ of sorption processes. Viscosity data obtained from fitting of sorption experimental results are finally discussed in terms of temperature dependence and compared with values obtained form purely mechanical volume relaxation experiments.

The application area of existing gas separation membranes is limited by commercially available polymers for their preparation. In many cases the separation selectivity of these polymers is not sufficient for effective separation processes. One of the ways to improve the separation effectivity of existing membranes from glassy polymers is gas phase fluorination. It is very important to note that this method can be successfully used for modification of polymeric films, different types of membranes (flat sheet and hollow fiber) and membrane modules. The hollow fibers produced from Matrimid 5218 in Twente University and a flat-sheet membrane from polyvinylthrimethilsilane (PVTMS) produced in Russia were investigated. The treatment of samples by fluorination was carried out in closed reactor at 20–22 °C with gaseous mixtures of F2/He of different composition. A gas mixture of different concentrations (2–10 vol.% of F2) at 1 atm was used The time of fluorination was from 2 min to 265 min. The dependence of the structure of the PVTMS and Matrimid 5218 on gas phase fluorination by IR-spectroscopy and the influence of modification on membrane structure by SEM were studied. The productivity of He, CO2, N2 and CH4 through the membranes modified at different conditions of fluorination was measured, and it was shown that it is possible to achieve a significant increase of He/CH4, CO4/CH4 and He/N2 selectivity at high level He and CO2 productivity by this type of modification. Thus, modified membranes and membrane modules can be successfully used for separation of components of biogas in membrane contactors and selective membrane valves for extraction of He/Ne fraction from waste in the metallurgy industry and separation of natural gas components.

The description of permeability and solubility of CO 2 in poly(ethylene terephthalate) both in the glassy and in the rubbery state is analyzed by means of thermodynamic based models for solubility and diffusivity. The Non-Equilibrium Thermodynamic approach for Glassy Polymers (NET-GP), together with the Sanchez Lacombe equation of state, provides the description of the solubility isotherms above and below the glass transition temperature (NELF model). The penetrant diffusion coefficient is then taken as the product of a kinetic factor, the mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species. The thermodynamic factor is predicted by the NELF model, while 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 model analysis shows that, in all the cases examined, the model used is able to describe carefully the experimental trends in a simple and effective way, accounting for all the different behaviors observed, for both solubility and permeability.

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

The 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.

As a new solvent free method for membrane formation, we have investigated the foaming of high-Tg polymers. We report two different routes for the formation of open-microcellular and open-nanoporous membrane morphologies. Porosity is introduced by expansion of carbon dioxide saturated films and hollow fibers at elevated temperatures. The microcellular structure manifests itself by small spot-like openings with diameters between 50 and 200 nm in the cell walls. The nanoporous structures exhibit a lacy structure with pore sizes between 2 and 50 nm. The mass transport resistance of the membrane structures is characterized in detail on the basis of gas permeation measurements.

Giulio C. Sarti and Maria Grazia De AngelisDipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali (DICMA), Alma MaterStudiorum-Universita` di Bologna, via Terracini 28, 40131 Bologna, ItalyDOI 10.1002/aic.12571Published online March 2, 2011 in Wiley Online Library (wileyonlinelibrary.com).The solubility of liquid molecules in glassy polymers has been considered by using thegeneral results of the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP),which proved successful to calculate solubility isotherms of gases in glassy polymers forrather different situations, including polymer blends, mixed gases, and mixed matrices. Itis shown that the existing model is suitable also for liquid penetrants in a glassy phase:water and ethanol sorption in polycarbonate (PC) and water sorption in polysulfone(PSf) have been examined as examples. The model’s ability to predict the solubilityfrom both liquid and vapor phases was tested successfully, using the same values of theparameters for both phases. In the case of PC, the model was also applied to calculatesuccessfully the solubility of liquid water at different temperatures from 25 to 130 C,with a single value of the energetic binary parameter.

The enhancement of gas and vapor transport rates induced by the addition of fumed silica nanoparticles to fluorinated glassy polymers is interpreted and quantitatively modeled considering the additional free volume created by incorporation of filler. That effect can be evaluated accurately from gas solubility data, using the NELF model. The solubility of CH4 and CO2 in matrices of Teflon AF1600 and AF2400, filled with variable amounts of fumed silica nanoparticles, was measured at 35 °C; the solubility of n-C4 and n-C5 vapors, as well as their diffusivity and the dilation induced in the same polymer matrices, was also measured at 25 °C. The fractional free volume (FFV) values, estimated on the basis of CH4 solubility data, were used to predict the solubility of the other penetrants inspected, with excellent agreement with experimental data. In addition, a single empirical correlation can be drawn, for both AF1600 and AF2400-based mixed matrices, between the infinite dilution diffusivity of vapors and the FFV value calculated from solubility data. Similarly, a simple correlation valid for both matrices is obtained as well for the dependence of diffusivity on penetrant concentration. Finally, use of the NELF model also allows an estimate of the swelling induced by the sorption process on the basis of virtually one simple data point of gas solubility.

We investigate evidences of diffusion controlled by mechanical relaxation of the glassy matrix, i.e. Case-II mechanism, in a series of liquid/glassy interphases formed by polystyrene (PS) and poly (phenylene oxide) (PPO) as liquid and glassy components respectively. Diffusion experiments were performed in conditions of unlimited supply of the liquid polymer, parallel to those in which Case-II has been effectively verified. Interphase profiles were obtained via optical sectioning with confocal Raman microspectroscopy. We observed that interphase diffusion kinetics were markedly Fickean, in contrast with interpretations from other authors that invoke Case-II to explain the mechanisms that rule interphase evolution in these systems. Fil: Tomba, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina Fil: Carella, Jose Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina Fil: Pérez, Claudio Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones en Ciencia y Tecnología de Materiales. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones en Ciencia y Tecnología de Materiales; Argentina Fil: Pastor, José M.. Universidad de Valladolid; España

A theoretical insight into the generally used correlations between infinite dilution gas solubility in glassy polymers and gas parameters has been provided based on the NELF model.

Well established equation-of-state (EoS) models from Perturbed Hard Sphere Chain Theory have been adopted within the framework of non-equilibrium thermodynamics for glassy polymers (NET-GP) to describe the solubility of small penetrants in glassy polymers. The procedure presented here parallels the one already applied to the Lattice Fluid EoS, obtaining the Non-Equilibrium Lattice Fluid (NELF) model. The solubility is calculated as pseudo-equilibrium solute content in the glassy polymeric phase at fixed temperature and solute fugacity, and is compared to the experimental data. The NE-PHSC model predictions require pure component and binary EoS parameters, together with the value of the glassy polymer density during sorption. Several common glassy polymers, as well as a high free volume fluoropolymer, have been considered to test the model ability to represent the thermodynamic properties of glassy gas–polymer mixtures. A comparison between the performance of two NE-PHSC models, endowed with different expressions for the interaction potential, is also presented, offering interesting conclusions on their accuracy in the representation of the thermodynamic properties of relatively high-density systems. The results obtained in this work show that the NET-GP approach provides a reliable description of the properties of homogeneous glassy mixtures.

The solubility of C2H6 and C2F6 in two amorphous glassy fluoropolymers, Teflon® AF1600 and AF2400, has been modeled with the non equilibrium statistical associating fluid (NE-SAFT) and non equilibrium perturbed hard sphere chain (NE-PHSC) theories. Experimental swelling data during sorption are available to obtain a complete prediction of the solubility isotherms at 35°C. The solubility of C2F6 in both fluoropolymers is rather satisfactorily predicted by the models with no adjustable parameters, while that of C2H6 is overestimated, and a correction factor equal to about 0.90 must be applied on the binary energetic interactions estimated with the first approximation mixing rule. This result, combined with what previously obtained with the NE-lattice fluid (NE-LF) model, reveals inadequate representation of the hydrocarbon solubility in fluoropolymers by the geometric mean rule used to estimate the binary energetic interactions.

A new procedure is introduced for the calculation of solubility isotherms of plasticizing agents in glassy polymer matrices with particular application to the case of absorption of supercritical gases in bulk glassy polymer films. The model presented is an extension of the nonequilibrium thermodynamics for glassy polymers (NET-GP) approach, modified to allow for the calculation of the effects of pressure, temperature, and gas concentration on the glass transition. Mass sorption and one- dimensional swelling behavior are analyzed for the carbon dioxide (CO2)-poly(methyl methacrylate) (PMMA) system at high pressure. A quantitative comparison is presented between the model performance and experimental data measured using quartz crystal microbalance (QCM) and high-pressure ellipsometry (HPE).

An explicit numerical implementation is described, for a constitutive model of glassy polymers, previously proposed and validated. Then it is exploited within a Finite Element continuum model, to simulate spontaneous strain localization (necking) occurring during extension of a prismatic bar of a typical glassy polymer. Material parameters for atactic polystyrene are employed. The material model is physically based and highly non-linearly viscoelastic. Three of its principal features are critical in simulations of strain localization: rate-dependence of plastic flow stress; strain-induced structural rejuvenation, represented by increase of Tool's fictive temperature and leading to pronounced post-yield strain softening; and molecular alignment during extension, giving rise to strain-hardening. In all simulations there is a peak in nominal stress, satisfying the condition for localization to occur. Nevertheless, the simulations show that the process of strain localization varies considerably, depending on details of the extension sequence and on assumed values for certain material parameters. A characteristic feature observed is that strain localization in such a material occurs in two stages. There is an initial spurt associated with strain-softening, followed by a slower growth of localization that eventually subsides, ultimately giving way to uniform extension of the neck. But the details of evolution of the strain distribution vary greatly. The rapidity and severity of localization are increased by decreased temperature, increased strain-rate or greater structural rejuvenation. A simple one-dimensional stability analysis is successful in explaining the results. © 2008 Elsevier Ltd. All rights reserved.

This paper deals with the volume relaxation and simultaneous changes in mechanical properties that occur after complicated thermal histories. The histories were chosen such that, at the final measuring temperature, the specific volume v passes through a maximum with increasing time. It is shown that, for polystyrene, poly(vinyl chloride) and polycarbonate, the mechanical creep properties change as if the position on the log time scale of the creep curve is uniquely determined by the momentary value of v. Thus, a maximum in the volume relaxation curve implies that the creep curve first shifts to the left and later to the right.