Thermodynamics of the Glassy Polymer State: Equilibrium and Non-Equilibrium Aspects

This work examines, first, the non-equilibrium character of the glassy state of polymer systems and its significance in the development of novel materials for important technological applications. Subsequently, it summarizes the essentials of the generalized lattice fluid approach for the description of this highly complex non-equilibrium behavior with an approximate and simple, yet analytically powerful formalism. The working equations are derived in a straightforward and consistent manner by clearly defining the universal and specific variables needed to describe the discussed properties. The role of the non-random distribution of molecular species and free volume in the glassy system is also examined, as is the role of strong specific interactions, such as hydrogen-bonding networks. This work also reports examples of applications in a variety of representative systems, including glass densification, retrograde vitrification, increase in glass-transition temperature in hydrogen-bonded polymer mixtures, and hysteresis phenomena in sorption-desorption from glassy polymer matrices.

Cooperativity in Sorption Isotherms

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Water Sorption in Rubbery and Glassy Polymers, Nifedipine, and Their ASDs

Polymers like poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA) or hydroxypropyl methylcellulose acetate succinate (HPMCAS) are commonly used as a matrix for amorphous solid dispersions (ASDs) to enhance the bioavailability of the active pharmaceutical ingredients (APIs). The stability of ASDs is strongly influenced by the water sorption in the ASD from the surrounding air. In this work, the water sorption in the neat polymers PVPVA and HPMCAS, in the neat API nifedipine (NIF), and in their ASDs of different drug loads was measured above and below the glass-transition temperature. The equilibrium water sorption was predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) combined with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP).The water-sorption kinetics were modeled using the Maxwell-Stefan approach whereas the thermodynamic driving force was calculated using PC-SAFT and NET-GP. The water diffusion coefficients in the polymers, NIF, or ASDs were determined using the Free-Volume Theory. Using the water-sorption kinetics of the pure polymers and of NIF, the water-sorption kinetics of the ASDs were successfully predicted, thus providing the water diffusion coefficients in the ASD as a function of relative humidity and of the water concentration in polymers or ASDs.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

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

Dry Glass Reference Perturbation Theory Predictions of the Temperature and Pressure Dependent Separations of Complex Liquid Mixtures Using SBAD-1 Glassy Polymer Membranes

In this work we apply dry glass reference perturbation theory (DGRPT) within the context of fully mutualized diffusion theory to predict the temperature and pressure dependent separations of complex liquid mixtures using SBAD-1 glassy polymer membranes. We demonstrate that the approach allows for the prediction of the membrane-based separation of complex liquid mixtures over a wide range of temperature and pressure, using only single-component vapor sorption isotherms measured at 25 °C to parameterize the model. The model was then applied to predict the membrane separation of a light shale crude using a structure oriented lumping (SOL) based compositional model of petroleum. It was shown that when DGRPT is applied based on SOL compositions, the combined model allows for the accurate prediction of separation performance based on the trend of both molecular weight and molecular class.

Predicting the Water Sorption in ASDs

Water decreases the stability of amorphous solid dispersions (ASDs) and water sorption is, therefore, unwanted during ASD storage. This work suggests a methodology to predict the water-sorption isotherms and the water-sorption kinetics in amorphous pharmaceutical formulations like ASDs. We verified the validity of the proposed methodology by measuring and predicting the water-sorption curves in ASD films of polyvinylpyrrolidone-based polymers and of indomethacin. This way, the extent and the rate of water sorption in ASDs were predicted for drug loads of 0.2 and 0.5 as well as in the humidity range from 0 to 0.9 RH at 25 °C. The water-sorption isotherms and the water-sorption kinetics in the ASDs were predicted only based on the water-sorption isotherms and water-sorption kinetics in the neat polymer on the one hand and in the neat active pharmaceutical ingredient (API) on the other hand. The accurate prediction of water-sorption isotherms was ensured by combining the Perturbed-Chain Statistical Association Theory (PC-SAFT) with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP) approach. Water-sorption kinetics were predicted using Maxwell–Stefan diffusion coefficients of water in the ASDs.

Water Sorption in Glassy Polyvinylpyrrolidone-Based Polymers

Polyvinylpyrrolidone (PVP)-based polymers are excellent stabilizers for food supplements and pharmaceutical ingredients. However, they are highly hygroscopic. This study measured and modeled the water-sorption isotherms and water-sorption kinetics in thin PVP and PVP-co-vinyl acetate (PVPVA) films. The water sorption was measured at 25 °C from 0 to 0.9 RH, which comprised glassy and rubbery states of the polymer-water system. The sorption behavior of glassy polymers differs from that in the rubbery state. The perturbed-chain statistical associating fluid theory (PC-SAFT) accurately describes the water-sorption isotherms for rubbery polymers, whereas it was combined with the non-equilibrium thermodynamics of glassy polymers (NET-GP) approach to describe the water-sorption in the glassy polymers. Combined NET-GP and PC-SAFT modeling showed excellent agreement with the experimental data. Furthermore, the transitions between the PC-SAFT modeling with and without NET-GP were in reasonable agreement with the glass transition of the polymer-water systems. Furthermore, we obtained Fickian water diffusion coefficients in PVP and in PVPVA from the measured water-sorption kinetics over a broad range of humidities. Maxwell-Stefan and Fickian water diffusion coefficients yielded a non-monotonous water concentration dependency that could be described using the free-volume theory combined with PC-SAFT and NET-GP for calculating the free volume.

The influence of additives on polymer matrix mobility and the glass transition

In the region near an interface, the microscopic properties of a glass forming liquid may be perturbed from their equilibrium bulk values. In this work, we probe how the interfacial effects of additive particles dispersed in a matrix can influence the local mobility of the material and its glass transition temperature, Tg. Experimental measurements and simulation results indicate that additives, such as nanoparticles, gas molecules, and oligomers, can shift the mobility and Tg of a surrounding polymer matrix (even for relatively small concentrations of additive; e.g., 5-10% by volume) relative to the pure bulk matrix, thus leading to Tg enhancement or suppression. Additives thus provide a potential route for modifying the properties of a polymer material without significantly changing its chemical composition. Here we apply the Limited Mobility (LM) model to simulate a matrix containing additive species. We show that both additive concentration, as well as the strength of its very local influence on the surrounding matrix material, will determine whether the Tg of the system is raised or lowered, relative to the pure matrix. We demonstrate that incorporation of additives into the simple LM simulation method, which has successfully described the behavior of bulk and thin film glassy solids, leads to direct connections with available experimental and simulation results for a broad range of polymer/additive systems.

A priori predictions of type I and type V isotherms by the rigid adsorbent lattice fluid

Adsorbents exhibiting non type I adsorption behaviour are becoming increasingly more important in industrial applications, such as drying and gas separation. The ability to model these processes is essential in process optimisation and intensification, but requires an accurate description of the adsorption isotherms under a range of conditions. Here we describe how the Rigid Adsorbent Lattice Fluid is capable of a priori predictions both type I and type V adsorption behaviour in silicalite-1. The predictions are consistent with experimental observations for aliphatic (type I) and polar (type V) molecules in this hydrophobic material. Type V behaviour is related to molecular clustering and the paper discusses the model parameters governing the presence/absence of this behaviour in the predicted isotherms. It is found that both the solid porosity and the adsorbate interaction energy/energy density are deciding factors for the isotherm shape. Importantly, the model, whilst thermodynamically consistent, is macroscopic and thus computationally light and requires only a small number of physically meaningful parameters.

Sorption Thermodynamics of CO₂, H₂O, and CH₃OH in a Glassy Polyetherimide: A Molecular Perspective

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.

Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag

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.

Effect of relative humidity on the gas transport properties of zeolite A/PTMSP mixed matrix membranes

Increasing the knowledge of the influence of water vapor in new mixed matrix membranes (MMMs) could favor the integration of novel membrane materials in the recovery of CO2 from wet industrial streams. In this work, the water vapor effect on the N2, CH4 and CO2 permeability through MMMs comprised of 20 wt% hydrophilic zeolite 4A in hydrophobic PTMSP polymer were investigated in the relative humidity range 0-75%. While in the pure PTMSP membranes, the permeability of all gases decreases with water vapor activity, with almost unchanged CO2/N2 and CO2/CH4 selectivities, in zeolite A/PTMSP MMMs, the CO2 permeability increases with increasing water content in the system up to 50% R.H., resulting in an increase in CO2/N2 and CO2/CH4 selectivities with respect to pure PTMSP. Gas sorption was studied so that the effect the residual humidity in the zeolite 4A has on the sorption of the different gases helped explaining the permeability observations. The sorption and humid permeation behavior were evaluated by a simple model equation based on the NELF theory, taking into account the multicomponent gas sorption and diffusion in the presence of humidity, as well as the counteracting effects of the hydrophobic PTMSP and hydrophilic zeolite A in a very accurate way.

Thermodynamic Modeling of Gas Transport in Glassy Polymeric Membranes

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.

Thermodynamic compatibility of actives encapsulated into PEG-PLA nanoparticles: In Silico predictions and experimental verification

Achieving optimal solubility of active substances in polymeric carriers is of fundamental importance for a number of industrial applications, including targeted drug delivery within the growing field of nanomedicine. However, its experimental optimization using a trial-and-error approach is cumbersome and time-consuming. Here, an approach based on molecular dynamics (MD) simulations and the Flory-Huggins theory is proposed for rapid prediction of thermodynamic compatibility between active species and copolymers comprising hydrophilic and hydrophobic segments. In contrast to similar methods, our approach offers high computational efficiency by employing MD simulations that avoid explicit consideration of the actual copolymer chains. The accuracy of the method is demonstrated for compatibility predictions between pyrene and nile red as model dyes as well as indomethacin as model drug and copolymers containing blocks of poly(ethylene glycol) and poly(lactic acid) in different ratios. The results of the simulations are directly verified by comparison with the observed encapsulation efficiency of nanoparticles prepared by nanoprecipitation. © 2016 Wiley Periodicals, Inc.

A predictive model for gas and vapor sorption into glassy membranes at high pressure

A predictive model was developed based on NELF model using FFV for gas and vapor sorption into glassy membranes at high pressure.

Vapor sensing characteristics of nanoelectromechanical chemical sensors functionalized using surface-initiated polymerization

Surface-initiated polymerization has been used to grow thick, uniform poly(methyl methacrylate) films on nanocantilever sensors. Cantilevers with these coatings yielded significantly greater sensitivity relative to bare devices as well as relative to devices that had been coated with drop-cast polymer films. The devices with surface-initiated polymer films also demonstrated high selectivity toward polar analytes. Surface-initiated polymerization can therefore provide a straightforward, reproducible method for large-scale functionalization of nanosensors.

Sharp diffusion front in diffusion problem with change of state

We propose an alternative model of diffusion in polymers, which may explain formation of propagating sharp diffusion fronts to be observed in some experiments. Differently from typical Case II or Stefan problem models, plasticisation of the polymer matrix is not necessarily required. Instead, diffusing small molecules are assumed to be captured by some specific sites of the polymer matrix for certain retention times. For example, they may become adsorbed at the surface of the holes and microvoids that are considered to be present in glassy polymer regions according to the well-known dual-sorption model and are attributed to excess free volume frozen into the glassy matrix. On the other hand, the small molecules may become bound to polymer chains. In this adsorbed/bound state they have much smaller movability and thus are effectively excluded from the diffusion. This adsorption/binding is considered to be a reversible process of state changing, but with asymmetric probabilities for direct and reverse events. With this assumption, taking into account that the amount of space available for such immobilised molecules is limited (limited free volume, limited number of anchoring sites) the model naturally results in the formation of sharp diffusion fronts or strong concentration gradients. Such a diffusion front is a region of effective immobilisation (adsorption/binding, though reversible) of the free diffusing molecules. For the simplest prescribed boundary conditions the diffusion front propagates linearly with the square root of time. By means of imposing generalised boundary conditions, it is possible to model other regimes of propagation of the diffusion front, including constant velocity.