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No full textOn the thermodynamic consistency of non-random hydrogen bonding lattice-fluid model for multicomponent mixtures
No full textCompressible 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*
Probing effect of solvent concentration on glass transition and sub-Tg structural relaxation in polymer solvent mixtures: The case of polystyrene-toluene system
No full textA 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
Water sorption thermodynamics in glassy polymers endowed with hydrogen bonding interactions
No full textIn this contribution, we review and critically compare the results of the analyses we have previously performed on water sorption thermodynamics in a series of polyimides. The experimental investigation was performed by combining gravimetric tests and in situ vibrational spectroscopy. A non-equilibrium theory, based on a compressible lattice framework accounting for the glassy state of the polymer and for the occurrence of hydrogen bonding interactions, has been used to interpret data. Information at a molecular level gained by vibrational spectroscopy has been used to tailor the model equations. The main features of water sorption thermodynamics are well captured, qualitatively and quantitatively, by the adopted model which displays a remarkable agreement with experimental results
Towards a predictive thermodynamic description of sorption processes in polymers: The synergy between theoretical EoS models and vibrational spectroscopy
No full textUnderstanding 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
Predictive Approach for the Solubility and Permeability of Binary Gas Mixtures in Glassy Polymers Based on an NETGP-NRHB Model
No full textThe 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
Combining FTIR spectroscopy and pressure-decay techniques to analyze sorption isotherms and sorption kinetics of pure gases and their mixtures in polymers: The case of CO2 and CH4 sorption in polydimethylsiloxane
Full text linkA 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
Modelling relative humidity and temperature effects on CO2 gas transport in polyetherimide
No full textThe aim of this work is to study the effect of relative humidity (RH) on CO2 gas transport in polyetherimide (PEI) membranes. The Non-Random Hydrogen Bonding model, extended to the case of non-equilibrium glassy polymers (NETGP-NRHB model), is used to interpret the sorption thermodynamics in glassy polymer/penetrant mixtures. Furthermore, a new diffusion model (namely NETGP-NRHB-DM), in the spirit of the Free Volume Theory, is used in combination with the NETGP-NRHB model to interpret the gas permeation. The parameters of the two models have been obtained partly from the literature and partly from a dedicated experimental campaign. The full set of parameters is used in a predictive manner to calculate the permeability coefficient of CO2 in PEI at different temperatures and relative humidity conditions. The model results are validated against a complete set of experimental data specifically carried out for the present investigation. The CO2 permeability predictions are satisfactory, but a slight deviation between the calculated results and the experimental data is observed when the average amount of water in the membrane is high, probably due to the onset of water clustering. In fact, the phenomenological expression of the mobility coefficient of NETGP-NRHB-DM is not properly suited to describe the complex picture involving different kind of water mers starting from the water clustering concentration onset
Sorption of CO2, CH4 and Their Mixtures in Amorphous Poly(2,6-dimethyl-1,4-phenylene)oxide (PPO)
Full text linkSorption of pure CO2 and CH4 and CO2/CH4 binary gas mixtures in amorphous glassy Poly(2,6-dimethyl-1,4-phenylene) oxide (PPO) at 35 °C up to 1000 Torr was investigated. Sorption experiments were carried out using an approach that combines barometry with FTIR spectroscopy in the transmission mode to quantify the sorption of pure and mixed gases in polymers. The pressure range was chosen to prevent any variation of the glassy polymer density. The solubility within the polymer of the CO2 present in the gaseous binary mixtures was practically coincident with the solubility of pure gaseous CO2, up to a total pressure of the gaseous mixtures equal to 1000 Torr and for CO2 mole fractions of ~0.5 mol mol-1 and ~0.3 mol mol-1. The Non-Equilibrium Thermodynamics for Glassy Polymers (NET-GP) modelling approach has been applied to the Non-Random Hydrogen Bonding (NRHB) lattice fluid model to fit the solubility data of pure gases. We have assumed here that no specific interactions were occurring between the matrix and the absorbed gas. The same thermodynamic approach has been then used to predict the solubility of CO2/CH4 mixed gases in PPO, resulting in a deviation lower than 9.5% from the experimental results for CO2 solubility
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