110th Anniversary: Gas and Vapor Sorption in Glassy Polymeric Membranes—Critical Review of Different Physical and Mathematical Models

Experimental Study for the Sorption and Diffusion of Supercritical Carbon Dioxide into Polyetherimide

Supercritical carbon dioxide (SCCO2) is a non-toxic and environmentally friendly fluid and has been used in polymerization reactions, processing, foaming, and plasticizing of polymers. Exploring the behavior and data of SCCO2 sorption and dissolution in polymers provides essential information for polymer applications. This study investigated the sorption and diffusion of SCCO2 into polyetherimide (PEI). The sorption and desorption processes of SCCO2 in PEI samples were measured in the temperature range from 40 to 60 °C, the pressure range from 20 to 40 MPa, and the sorption time from 0.25 to 52 h. This study used the ex situ gravimetric method under different operating conditions and applied the Fickian diffusion model to determine the mass diffusivity of SCCO2 during sorption and desorption processes into and out of PEI. The equilibrium mass gain fraction of SCCO2 into PEI was reported from 9.0 wt% (at 60 °C and 20 MPa) to 12.8 wt% (at 40 °C and 40 MPa). The sorption amount increased with the increasing SCCO2 pressure and decreased with the increasing SCCO2 temperature. This study showed the crossover phenomenon of equilibrium mass gain fraction isotherms with respect to SCCO2 density. Changes in the sorption mechanism in PEI were observed when the SCCO2 density was at approximately 840 kg/m3. This study qualitatively performed FTIR analysis during the SCCO2 desorption process. A CO2 antisymmetric stretching mode was observed near a wavenumber of 2340 cm-1. A comparison of loss modulus measurements of pure and SCCO2-treated PEI specimens showed the shifting of loss maxima. This result showed that the plasticization of PEI was achieved through the sorption process of SCCO2.

Simultaneous Water Sorption and Crystallization in ASDs 2: Modeling Long-Term Stabilities

The physical stability of amorphous solid dispersions (ASDs) is a major topic in the formulation research of oral dosage forms. To minimize the effort of investigating the long-term stability using cost- and time-consuming experiments, we developed a thermodynamic and kinetic modeling framework to predict and understand the crystallization kinetics of ASDs during long-term storage below the glass transition. Since crystallization of the active phrarmaceutical ingredients (APIs) in ASDs largely depends on the amount of water absorbed by the ASDs, water-sorption kinetics and API-crystallization kinetics were considered simultaneously. The developed modeling approach allows prediction of the time evolution of viscosity, supersaturation, and crystallinity as a function of drug load, relative humidity, and temperature. It was applied and evaluated against two-year-lasting crystallization experiments of ASDs containing nifedipine and copovidone or HPMCAS measured in part I of this work. We could show that the proposed modeling approach is able to describe the interplay between water sorption and API crystallization and to predict long-term stabilities of ASDs just based on short-term measurements. Most importantly, it enables explaining and understanding the reasons for different and sometimes even unexpected crystallization behaviors of ASDs.

A chemo-mechanical model for describing sorption hysteresis in a glassy polyurethane

Hysteretic sorption and desorption of water is observed from 0 to 95% relative humidity and 298-333 K on a glassy polyurethane foam. It is postulated that sorption-induced swelling of the glassy polyurethane increases the concentration of accessible hydrogen-bonding adsorption sites for water. The accessibility of sites is kinetically controlled due to the restricted thermal motions of chains in the glassy polymer, causing a difference in accessible site concentrations during sorption and desorption. This discrepancy leads to hysteresis in the sorbed concentrations of water. A coupled chemo-mechanical model relating volumetric strain, adsorption site concentration, and sorbed water concentration is employed to describe water sorption hysteresis in the glassy polyurethane. This model not only describes the final mass uptake for each relative humidity step, but also captures the dynamics of water uptake, which exhibit diffusion and relaxation rate-controlled regimes.

Simultaneous Water Sorption and Crystallization in ASDs 1: Stability Studies Lasting for Two Years

One way to increase the slow dissolution rate and the associated low bioavailability of newly developed active pharmaceutical ingredients (APIs) is to dissolve the API in a polymer, leading to a so-called amorphous solid dispersion (ASD). However, APIs are often supersaturated in ASDs and thus tend to crystallize during storage. The kinetics of the crystallization process is determined by the amount of water the ASD absorbs during storage at relative humidity (RH), storage temperature, polymer type, and the drug load of the ASD. Here, the crystallization kinetics and shelf life of spray-dried ASDs were investigated for ASDs consisting of nifedipine (NIF) or celecoxib (CCX) as the APIs and of poly(vinylpyrrolidone-co-vinyl acetate) or hydroxypropyl methylcellulose acetate succinate as polymers. Samples were stored over 2 years at different RHs covering conditions above and below the glass transition of the wet ASDs. Crystallization kinetics and onset time of the crystallization were qualitatively studied by using powder X-ray diffraction and microscopic inspection and were quantitatively determined by using differential scanning calorimetry. It was found that the NIF ASDs crystallize much faster than CCX ASDs at the same drug load and at the same storage conditions due to both higher supersaturation and higher molecular mobility in the NIF ASDs. Experimental data on crystallization kinetics were correlated using the Johnson-Mehl-Avrami-Kolmogorov equation. A detailed thermodynamic and kinetic modeling will be performed in Part 2 of this paper series.

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.

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.

The Rigid Adsorbent Lattice Fluid Model: Thermodynamic Consistency and Relationship to the Real Adsorbed Solution Theory

The Rigid Adsorbent Lattice Fluid model has been shown to comply with all the requirements for thermodynamic consistency in the case of an adsorbent that does not undergo structural changes. This is achieved by introducing a correction to the reduced density function that multiplies the combinatorial term. A procedure to calculate the predicted adsorbed mixture activity coefficients has been presented that allows the production of excess Gibbs energy plots at a constant reduced grand potential. The predicted nonideality is structurally consistent with the Non-Ideal Adsorbed Solution Theory of Myers in terms of both its dependence on concentration and reduced grand potential. The ability to generate excess Gibbs energy values allows linking the new Rigid Adsorbent Lattice Fluid model to the traditional Real Adsorbed Solution Theory providing an alternative approach to predicting multicomponent adsorption based solely on pure component data.

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.

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.