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The non-equilibrium thermodynamic approach to describing properties of glassy polymers, earlier applied in the so-called NELF model using Lattice Fluid Theory, is generalized to the use of arbitrary equations of state. Application to Statistical Associating Fluid Theory (SAFT) is discussed in detail and use of this approach to predict opr correlate gas solubility in glassy polymers is presented for the case of low-pressure sorption. Prediction procedures rely on volumetric data for the pure polymer and gaseous species, while for data correlation a temperature independent binary interaction coefficient is used as an adjustable parameter. Results from model calculations are compared with literature data for gas solubility in polycarbonate and polysulfone. Analysis of solubility coefficient variations above and below the glass transition temperature indicates thet the non-equilibrium approach is the proper procedure to extend an EoS description of thermodynamic properties to the glassy state.

The diffusion coefficient of ethanol and of n-pentane in PTMSP, at 27°C, was measured as a function of concentration up to a penetrant content of about 12% by weight, for polymer samples obtained through different processes; differential sorptions and desorptions with vapor phases were considered. In the case of ethanol a nonmonotonous behavior was observed for the diffusivity, while in the case of n-pentane the same property was found to monotonously decrease with increasing the penetrant content. The sorption isotherms were also reported, indicating that n-pentane exhibits a typical dual mode behavior, while ethanol follows an unusual s-shape curve. The chemical potential of the dissolved penetrants, calculated directly from the isotherms, shows the very different importance of the energetic interactions of the two penetrants with the polymer units. In spite of the remarkably different concentration dependencies observed for both solubility and diffusivity of the two penetrants, the mobility factors are in both cases monotonously decreasing with the penetrant concentration, and follow very similar trends. The significant differences observed for the concentration dependence of the diffusion coefficients are, thus, associated to the thermodynamic contributions, which are very different for n-pentane and ethanol. Different polymeric films, obtained through different solvent evaporation processes, show quite different solubility, diffusivity and mobility for both ethanol and n-pentane. On the other hand, the ratio between the mobility of the two penetrants as well as the slope of mobility as function of the concentration remains the same for all the different samples inspected. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2245–2258, 1997

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 present work is focused on the characterization of the sorption properties of gaseous mixtures of CO2 and C2H6 in a crosslinked poly(ethylene oxide) copolymer, XLPEO, in a wide range of temperatures from a modeling point of view, by the use of Sanchez Lacombe EoS

The nonequilibrium thermodynamics of glassy polymers (NET-GP) approach (Macromolecules 2005, 38, 10299.) has been applied to the development of a one-dimensional transport model aimed at describing the kinetics of sorption and dilation of polymeric films in supercritical carbon dioxide. The NET-GP model was combined with a simple rheological constitutive equation to build a sorption-diffusion-relaxation model able to describe mass uptake and swelling kinetics of polymeric films in contact with carbon dioxide over a wide range of pressures and temperatures. The model calculations are compared with data on mass sorption kinetics for CO2 in supported glassy poly(methyl methacrylate) (PMMA) films, measured in a high-pressure quartz crystal microbalance (QCM).

A new experimental apparatus has been set up to analyze the polymer dilation as well as the stress profile induced by vapour sorption in constrained films. The device couples the bending cantilever technique with a new digital micrometer which allows to measure both deflection and polymer swelling at the same time. The apparatus has been applied to study the effects of acetonitrile mass uptake in polycarbonate at 40°C, obtaining the time evolution of swelling and of cantilever deflection during integral sorption tests, in the activity range from zero up to 0.35. A simulation model is also proposed, which couples Fick’s law for diffusion to the study of strain and stress distributions in the cantilever; the mechanical problem has been formulated following the classical laminate theory. The relevant values of the material properties entering the model, as solubility, diffusivity and penetrant induced dilation, have all been determined through separate independent measurements, and the results obtained are in good agreement with the corresponding values reported in the literature. The simulation model is able to predict with good precision both the kinetics of deflection during sorption and its final equilibrium value, as well as the overall swelling kinetics, with no need of any adjustable parameters. The model allows also to calculate the time evolution of the stress profile in the polymer film during sorption/desorption steps.

Solubility isotherms for n-pentane and n-hexane were measured in pure poly[1-(trimethylsilyl)-1-propyne] (PTMSP) and in 1-trimethylsilyl-1-propyne/1-trimethylsilyl-1-n-hexyne 70/30 copolymer, using freshly prepared samples as well as aged films, at different temperatures. The experimental values of penetrant diffusivity, mobility and heat of mixing have been reported and discussed, based on direct positron annihilation lifetime spectroscopy information, Dual Mode Sorption Model and Non-Equilibrium Lattice Fluid model. The ageing effect is more pronounced in PTMSP, where it leads to a significant solubility and diffusivity reduction, than in the copolymer where the effect is less important. In the activity range inspected the diffusion coefficient and the heat of mixing are almost concentration independent for PTMSP, while they increase appreciably with concentration in the copolymer, as an effect of the great difference in the free volume present in the two matrices.

Cellulose-based nanocomposites are now emerging as promising new materials suitable for a variety of applications. One source for such new nanocomposites is microfibrillated cellulose (MFC), produced by delamination of cellulosic fibers in high-pressure homogenizers. MFC is an organic and biodegradable reinforcement in polymer nanocomposites because of its high aspect ratio, good mechanical properties and ability to form networks: promising properties that may make this material suitable for use in a number of industrial fields and products. The structure and transport properties of a four different films based on two different generations of microfibrillated cellulose (MFC), alone or in combination with glycerol as plasticizer, were investigated through FE-SEM analysis and sorption or permeation experiments. FE-SEM revealed the existence of complex structures in the different samples. A porous, closely packed fiber network, more homogeneous in the samples containing glycerol, was characteristic of the surface of MFC films; while film cross-sections presented a dense layered structure with no evidence of porosity. Water vapor sorption experiments confirmed the hydrophilic character of these cellulosic materials and showed a dual effect of glycerol, which reduced the water uptake at low water activity while enhancing it at high relative humidity, as showed in Figure 1. The observed trends of water sorption can be described considering that both physical adsorption on fiber surfaces and absorption in the cellulose amorphous phase takes place and therefore a dual-model sorption model was employed. The water diffusivity (in the panel in Figure 1) in dry samples was remarkably low for a porous material (10-11-10-12 cm2/s), confirming the existence of complex structures below the film surface; however, when water is present in the system, D rapidly increases with an exponential trend. Diffusivity is also definitely affected by plasticization, being higher for glycerol-containing samples. Similar behavior was observed in permeation experiments. Dry MFC films showed excellent oxygen barrier properties, comparable with those of polymers usually considered suitable for ultra-high barrier applications. Indeed, when dry, the cellulose network presents a particularly compact and stiff structure, causing the observed barrier effect. Furthermore, although MFC films are characterized by a certain porosity, FE-SEM images of sample surfaces suggests that the pores are not substantially interconnected When the water content in the membrane is raised, however, a dramatic decrease in these properties was observed (Figure 2).

Based on NonEquilibrium Thermodynamics (NET-GP) approach, a model is here presented and discussed, aimed to the prediction of anomalous characteristics in kinetics for differential sorption of swelling agents in amorphous glassy polymer films. For mentioned conditions, the “two-stage sorption” kinetics is typically observed, in which a first stage of Fickian character is followed by a second stage with kinetic order larger than 0.5 and characteristic time independent of film thickness. NET-GP model, which interprets the out of equilibrium conditions of polymer mixtures below Tg through the use of polymer mass density as order parameter, was successfully used since its introduction [Doghieri and Sarti, Macromolecules 1996, 29, 7885] to describe several non-equilibrium features in solubility isotherms for a number of glassy polymeric systems. By coupling the description of thermodynamic properties from NET-GP with simplified model for the bulk rheology of the system and generalized Fickian law for mass transport, a modeling tool is derived in this work which allows to satisfactorily describe results from experimental analysis of two stage sorption kinetics.

The sorption and diffusion properties of water vapor in a new, short-side-chain perfluorosulfonic acid ionomer (PFSI) membrane have been investigated at different temperatures in the range of 35÷120°C. Experiments show that pretreatment of the membranes under vacuum at low temperatures leaves in the polymer a residual amount of water, which decreases linearly with increasing evacuation temperature. The actual water content in the membrane, instead, is only slightly affected by temperature at fixed activity. For dry membranes, the sorption follows a dual mode behavior, with a downward curvature versus the activity axis. The water diffusivity increases with temperature and when plotted against water concentration shows a maximum. The higher value of the diffusion coefficient is reached at a water content which corresponds to a minimum of the solubility coefficient; such result suggests that different mechanisms take place during sorption of water molecules in PFSI, above and below a critical concentration value, which affect both the solubility and the diffusivity behavior.

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 approach for modeling sorption and swelling of glassy polymer matrix with carbon dioxide at high pressure has been developed. The ability of the model to predict gas solubility at different operative conditions, with only one adjustable parameter, was investigated through the comparison with experimental data in a wide pressure range.

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).