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This contribution aims at an understanding, at a molecular scale, of the state of CO2 molecules absorbed in glassy poly(ether imide) (PEI). This issue has been challenged by combining different approaches that tackle the problem from both the experimental and the theoretical viewpoints and providing a comprehensive physicochemical picture. In situ FTIR spectroscopy and gravimetry were exploited to gather relevant experimental information, while molecular dynamics (MD), density functional theory (DFT), and statistical thermodynamics approaches were used to model the behavior of the binary system at different scales. Based on the findings of FTIR spectroscopy and on DFT and MD calculations, it was determined that, among the possible interaction configurations, some are prevailing. In particular, the carbon atom of carbon dioxide molecules establishes relatively weak interactions prevalently with the carbonyl groups of PEI. A quantitative estimate of such interaction has been provided by MD calculations. The system was also analyzed using a lattice fluid model, specifically developed to deal with sorption of low molecular weight compounds in glassy polymers, that is rooted on statistical thermodynamics, determining the values of the isosteric heat of sorption and carbon-dioxide-polymer interaction energy. Finally, experimental data of CO2-PEI mutual diffusivity have been interpreted using a semiempirical theoretical model accounting for the effects of the penetrant concentration, of energy barriers associated with the occurrence of an effective diffusive jump, and of a thermodynamic factor.

Polymer matrices, when placed in contact with a fluid phase made of low molecular weight compounds, undergo a depression of their glass transition temperature ( T g ) determined by the absorption of these compounds and the associated plasticization phenomena. Frequently, this effect is coupled with the mechanical action of the compressive stress exerted by the pressure of the fluid phase that, in contrast, promotes an increase in the T g . This issue is relevant for technological and structural applications of composites with high-performance glassy polymer matrices, due to their significant impact on mechanical properties. We propose an approach to model and predict rubbery-glassy states maps of polymer–penetrant mixtures as a function of pressure and temperature based on the Gibbs–Di Marzio criterion. This criterion establishes that a ‘thermodynamic’ glass transition does occur when the configurational entropy of the system vanishes. Although questioned and criticized, this criterion constitutes a good practical approach to analyse changes of T g and, in some way, reflects the idea of an ‘entropy catastrophe’ occurring at the glass transition. Several polymer–penetrant systems have been analysed modelling configurational entropy by means of the Non-Random Hydrogen Bond lattice fluid theory, able to cope with possible non-random mixing and occurrence of strong interactions. This article is part of the theme issue 'Ageing and durability of composite materials'.

The study of the reinforcement network in elastomer compounds is one of the most relevant issues for the application of these materials because their properties are strongly dependent on the obtained morphology. To this regard, the viscoelastic and dielectric behavior of vulcanized styrene butadiene rubber (SBR) reinforced with different amounts of carbon nanotubes (CNT) have been investigated and compared with the vulcanized unfilled SBR and the vulcanized SBR samples reinforced with a conventional amount of carbon black (40 phr). Differential scanning calorimetry (DSC) measurements have been carried out to highlight possible differences of the glass transition temperatures for all the reinforced compounds. The percolation threshold value of the nanocomposite samples has been estimated by dielectric analysis. Finally, dynamic mechanical analysis (DMA) measurements have been performed in tensile mode in the temperature range of −60 to 80 °C to obtain both E′ and E′′. From these experimental data, the master curve for each sample has been estimated by using the time–temperature superposition principle in combination with the vertical shift approach. From the analysis of this latter, the activation energy, associated to the thermal movement of the reinforcement network, has been calculated to better elucidate the reinforcement mechanism in the nanocomposites.

The NETGP-NRHB lattice-fluid model describes the sorption thermodynamics of penetrants in amorphous polymer-penetrant mixtures locked in an out-of-equilibrium “glassy” state. It accounts for the nonrandom distribution of mean-field contacts and voids and for the possible occurrence of specific interactions. In this contribution, we assess the suitability of the NETGP-NRHB model to interpret the sorption thermodynamics of binary penetrant mixtures in glassy polymers. Moreover, adopting the gradients of NETGP-NRHB penetrant chemical potentials as driving forces for their diffusive fluxes, a self-consistent framework is proposed to predict the permeability of light gas binary mixtures in glassy polymer membranes once all of the model parameters are obtained by nonlinear regression of data of the corresponding binary and pure component subsystems. This approach is validated against solubility data of CO2/CH4 and CO2/C2H4 mixtures in glassy amorphous poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) and poly(methyl methacrylate) (PMMA), respectively, and permeability data of CO2/CH4 mixtures in three glassy amorphous polymer membranes (PAr, PSf, PH); all of the data are taken from the literature. In particular, solubility data are investigated up to a CH4 partial pressure of 15 atm at a fixed CO2 partial pressure equal to 5.1 atm for the system CO2/CH4/PPO and up to a CO2 partial pressure of 4 atm at a fixed C2H4 partial pressure equal to 2.09 atm for the system CO2/C2H4/PMMA. Permeability data are investigated at a fixed upstream molar concentration of the binary gas mixture equal to 0.5 by changing the total pressure up to 18 atm for the systems CO2/CH4/PAr and CO2/CH4/PSf and up to 14 atm for the system CO2/CH4/PH; the downstream total pressure is equal to 0 atm for all of the systems. All of the experimental sets of data are obtained at 35 °C. Solubility and permeability predictions for the ternary systems compare very well with all experimental literature data without additional parameters besides those required for the corresponding binary subsystems.

This contribution aims at providing a critical overview of experimental results for the sorption of low molecular weight compounds in the Cu-BTC Metal–Organic Framework (MOF) and of their interpretation using available and new, specifically developed, theoretical approaches. First, a literature review of experimental results for the sorption of gases and vapors is presented, with particular focus on the results obtained from vibrational spectroscopy techniques. Then, an overview of theoretical models available in the literature is presented starting from semiempirical theoretical approaches suitable to interpret the adsorption thermodynamics of gases and vapors in Cu-BTC. A more detailed description is provided of a recently proposed Lattice Fluid approach, the Rigid Adsorbent Lattice Fluid (RALF) model. In addition, to deal with the cases where specific self- and cross-interactions (e.g., H-bonding, Lewis acid/Lewis base interactions) play a role, a modification of the RALF model, i.e., the RALFHB model, is introduced here for the first time. An extension of both RALF and RALFHB is also presented to cope with the cases in which the heterogeneity of the rigid adsorbent displaying a different kind of adsorbent cages is of relevance, as it occurs for the adsorption of some low molecular weight substances in Cu-BTC MOF.

Compressible lattice-fluid Equation of State (EoS) models have been widely used to interpret phase equilibria and related properties of pure fluids and their mixtures, including polymer solutions. One of the first models of this family has been proposed by Sanchez and Lacombe (SL), providing useful expressions for EoS and chemical potentials for both pure components and mixtures. The assessment of the thermodynamic consistency of the expressions provided by these models for the chemical potential of each component in a mixture is a relevant issue, to which has seldom been devoted the attention it deserves. In fact, it has been demonstrated in the literature that the equations provided by the SL theory for the equilibrium chemical potential of a component in a mixture exhibits a thermodynamic inconsistency emerging from the adopted mixing rules for the close packed volume. Consequently, these expressions do not converge to the proper form in the limit of ideal gas mixtures. Later, the Non-Random Hydrogen Bonding (NRHB) lattice-fluid model was introduced to overcome some limitations of the SL model, by accounting for possible presence of strong specific intermolecular interactions, such as hydrogen bonding, as well as for non-random distribution of intermolecular contacts. In the present work, using a thermodynamic framework endowed with internal state variables, it is shown that the expressions of the chemical potential provided by the NRHB model for a multicomponent mixture at equilibrium, converge consistently to the correct form in the limit of ideal gas mixtures, thus overcoming the inconsistency implicit in the most common corresponding formulations of the SL model. We demonstrate that this feature is essentially related to the assumption of a constant value of the segmental volume, v*, that takes the same ‘universal’ value (9.75/NA cm3/molecular segment, where NA is the Avogadro number) for all pure fluids as well as for their mixtures. In addition, we have re-examined also the inconsistency issue of the SL model proving that this model recovers the thermodynamic consistency if it is assumed again a constant value of v* or if a particular type of mixing rule is assumed for v*.

A hyphenated technique combining FTIR Spectroscopy and Barometry is implemented to study transport properties of pure and mixed gases in rubbery polymers. FTIR spectroscopy is operated in situ and in the transmission mode. The specific case of transport of pure CO2 and CH4 in polydimethylsiloxane (PDMS) was addressed by performing the experimental investigation at ambient temperature and pressure values up to 9 bar, analyzing quantitatively both the gas phase and the solid polymer phase. The IR signals of each species in the gaseous phase were first calibrated against density data of each pure gas. Then, sorption experiments from a unary gas phase were conducted increasing the pressure stepwise and the amount of gas sorbed at each pressure within the polymer was quantitatively determined by measuring the absorbance decay within the gas phase. From these measurements, equilibrium sorption isotherms and sorption kinetics of both pure gases in PDMS have been evaluated. At the same time, FTIR spectra of pure CO2 absorbed within the polymer phase were collected and calibrated. The spectroscopic contrast in the gas and the polymer phase allowed us to apply the same approaches to sorption of gas mixtures, a very difficult task with the techniques currently available. Preliminary results for the sorption of carbon dioxide from CO2/CH4 gas mixtures are presented.

A new hyphenated technique based on simultaneous in situ FT-NIR spectroscopy and pressure-decay measurements has been implemented to study sorption of low-molecular-weight compounds in polymeric membranes and the induced swelling of the matrix. The FT-NIR measurements are performed in the transmission mode and, besides sorption equilibrium and kinetics, allow also the straightforward measurement of polymer swelling. The pressure decay method is used to provide quantitative information on the concentration of penetrant sorbed in the polymer. This measurement, once combined with the photometric data, allows an accurate estimation of the molar absorptivity of the analytical peaks as well. To validate the new experimental approach, sorption of CO₂ in polydimethylsiloxane at 35 °C and at pressures up to 9 bar has been investigated and the results are compared with available literature data.

Lattice fluid theory is used to develop transport property–structure correlations for glassy perfluoropolymers with dioxolane pendant rings, a new class of membrane materials for gas separation. Poly(perfluoro-2-methylene-1,3-dioxolane) (poly(PFMD)) and poly(perfluoro-2-methylene-4-methyl-1,3-dioxolane) (poly(PFMMD)) exhibit lower permeability but much higher selectivity than commercial fluoropolymers, such as Teflons AF. Their enhanced separation performance is due to the combined effect of solubility- and diffusivity-selectivity. Moreover, poly(PFMD) and poly(PFMMD) exhibit enhanced CO2-philicity as compared to Teflons AF, which can be ascribed to the higher oxygen/carbon ratio exhibited by the former materials. To provide rational guidelines to maximize the solubility-selectivity, the enthalpic and entropic contributions to sorption coefficient were calculated and compared for several polymers of practical interest for gas separation. In the absence of localized penetrant–polymer interactions, gas sorption is controlled essentially by the free volume and solubility-selectivity is controlled by the polymer cohesive energy density.