Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

Sorption of light gases in glassy poly(ethyl methacrylate)

Although gas sorption in glassy polymers is a well‐studied phenomenon, no general microscopical model is developed which is able to describe the gas sorption in a wide temperature range using only characteristics of polymer and gas molecule. In this work, sorption isotherms and desorption kinetics of O₂, Ar, and N₂ for glassy poly(ethyl methacrylate) have been measured in the temperature range from 160 to 308 K. To describe both the phenomena, the model is developed which postulates that, in the frozen structure of glassy polymer, any cavities between macromolecules are the sorption sites for small molecules. The cavities of small size can expand elastically to accommodate a gas molecule. The sorption sites are considered to be the potential wells and their depths are distributed according to Gaussian law. The concentration of sorption sites, their mean depth and depths dispersion, and the frequency of molecules oscillations in the sorption sites are the only parameters which determine both the gas transport and sorption. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 288–296     

On the sorption of gas mixtures by polymer glasses

It was realized recently that various phenomena, related to the sorption of small molecules in polymer glasses could be described within the framework of a site distribution (SD) model. According to the SD model, non-equilibrium structure of glassy polymer leads to the distribution of sorption energies within the interchain holes. The parameters of the distribution for the given polymer–gas system could be expressed through the polymer–gas characteristics or evaluated from the experimental pressure–concentration isotherms. In this work we show how these parameters could be used to predict the sorption isotherms for gas mixtures. The suppression of solubility of each component by the other components, which is the main feature of mixed sorption by polymer glasses can be described within the SD model through the competitive occupancy of low-energy sorption sites. The clear physical meaning of the energy distribution parameters allows to analyze the role of different factors on the competitive sorption from gas mixtures. The comparison of SD model with the other theoretical approaches are given and new experiments, which could check the validity of our approach are proposed.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

A model incorporating reversible immobilization for sorption and diffusion in glassy polymers

A model incorporating reversible, bimolecular immobilization for diffusion and sorption in glassy polymers is developed. Sorption is considered to occur by two distinct mechanisms: ordinary diffusion-controlled sorption and sorption resulting from the immobilization of diffusing gas molecules by prexisting sites in the polymer. Expressions are obtained for equilibrium sorption, transient sorption, and time lag. The effects of kinetic parameters of the model are illustrated and discussed.     

Analysis of transport behavior in polymer powders

Vapor sorption studies on powder samples of glassy polymers have provided data which supplement results obtained on conventional film specimens and aid in the elucidation of glassy-state transport mechanisms. For uniform spherical particles of sub-micron size, sorption kinetics at very low activities of organic vapors follow a simple Fickian diffusion model. The short diffusion path in such samples allows determination of the very low diffusivities characteristic of the glassy state in experiments of conveniently short duration. Deviations from the Fickian, uniform-sphere model are observed in several circumstances: Particle size non-uniformity retards the approach to diffusion equilibrium. Sorption data at substantial vapor activities show an apparently similar slow approach to equilibrium which can be related to the contribution of a relaxation-controlled mode of sorption. The effects of particle non-uniformity and of relaxation processes can be distinguished by appropriate experimental design, and models for both have been developed. Sorption rate data obtained under Fickian diffusion conditions can be used to characterize particle size distribution. Sorption kinetics on uniform-sphere powders, conversely, can be analyzed through a diffusion-plus-relaxation model to distinguish and quantify the roles of the two transport modes more clearly than is possible with polymer film specimens. Polymer powder vapor solubility isotherms show significant variations with sample history which can be interpreted in terms of free volume changes and glassy state relaxations. This discussion, based on a study of vapor sorption by poly(vinyl chloride) samples, indicates that powder sorption measurements are also likely to be of general value in the study of other glassy polymers.     

Induction and measurement of glassy-state relaxations by vapor sorption techniques

Recent gravimetric studies of the sorption of organic vapors by poly(vinyl chloride) and polystyrene powders have demonstrated several features which promise to be generally useful in studying the structure and properties of the glassy state. The uptake of vapor can be significantly altered by prior thermal or vapor treatment of the polymer, apparently reflecting changes in the microvoid content or free volume of the polymer. Fickian sorption in sufficiently fine powders proceeds to equilibrium in a few minutes. Upon exposure of a polymer powder to an appreciable pressure of vapor, both a rapid Fickian sorption and a slower, relaxation-controlled sorption are observed. Superposition of these processes leads to widely varied sorption kinetics; a model comprising Fickian diffusion and first-order relaxation terms accurately describes the data and allows estimation of equilibrium and rate constants for both processes. After prolonged exposure, removal of a swelling vapor induces a slow reconsolidation of the polymer structure; this deswelling relaxation can be monitored by the decreasing amounts of vapor sorbed in repeated brief exposures to low vapor pressures, and can also be described by a first-order relaxation model. In this regard, the penetrant vapor serves as a molecular probe, monitoring glassy-state relaxation occurring in the absence of penetrant. The same, presumably true equilibrium is ultimately reached both by swelling from a low free-volume state and by consolidation from a preswollen state of high free volume. The rates of both swelling and consolidation relaxations appear to be retarded by the presence of low concentrations of vapor in the polymer, suggesting that vapor molecules may preempt some of the free volume required for relaxation.     

Evaluation of gas sorption parameters and prediction of sorption isotherms in glassy polymers

A model of continuous‐site distribution for gas sorption in glassy polymers is examined with sorption data of CO₂ and Ar in polycarbonate. A procedure is presented for determining from a measured isotherm the number of sorption sites in a polymer, an important parameter that previously had to be assumed. With this parameter value and solubility data obtained at zero pressure, the model can reasonably predict sorption isotherms of CO₂ in glassy polycarbonate for a wide temperature range. The number of sorption sites and the average site volume evaluated from CO₂ sorption isotherms are employed for the prediction of Ar sorption isotherms with zero‐pressure solubility data and the independently measured partial molar volume of Ar. A reasonable fit to the measured isotherms of Ar is achieved. With the proposed procedure, the continuous‐site model shows several advantages over the conventional dual‐mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 883–888, 2000     

The effect of lattice compressibility on the thermodynamics of gas sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration-dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory-Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Sorption of CO2 in polymers observed by positron annihilation technique

Positron annihilation lifetimes were measured for several polymers in the atmosphere of high pressure CO₂ gas. At low CO₂ pressured both ₃ andI ₃ decreased due to the Langmuir-type sorption, and at higher pressures their values recovered because the Henry-type sorption takes over. The amount of sorbed CO₂ and dilation of the bulk volume were measured simultaneously, and the free volume fraction was determined at each CO₂ pressure. The free volume fraction became smaller (for polyimide and polycarbonate) or slightly larger (for polyethylene) with the progress of sorption. However, the size of the o-Ps hole estimated from the ₃ value increased regardless of the change of the free volume fraction. It appears that o-Ps is selectively looking at larger holes or expanding the holes in which it is accommodated. For polycarbonate, which remains to be glassy even at the largest CO₂ sorption attained in the experiment, the o-Ps hole size became larger than that before sorption. This implies that, even if the polymer is glassy as bulk, the sorption site is strongly prone to molecular displacement by the pressure of the penetrating Ps. Cautious consideration is evoked about directly correlating the o-Ps lifetime and intensity with the free volume in general.     

“Second component” effects in sorption and permeation of gases in glassy polymers

Data for CO² permeability through Kapton polyimide at 60°C are reported for upstream pressures up to 240 psia (16.33 atm) in the presence and absence of water vapor in the feed. The carbon dioxide flux was depressed by the presence of the water vapor. This phenomenon is analyzed in terms of the dual mode sorption and transport models. Together with other recent sorption and permeation data, this study suggests that competition of mixed penetrants for sorption sites and transport pathways associated with unrelaxed volume in glassy polymers is a general feature of gas/glassy polymer systems. The permselectivity of a membrane to a mixture of penetrants is strongly related to its ability to maintain a size and shape differentiating matrix, that is, to remain essentially unplasticized under operating conditions. Under such conditions, competition among penetrants for excess volume will be a generally important consideration for modeling gas permeation in permselective membranes.     

Water sorption and transport in a series of polysulfones

Water sorption and transport properties for a series of polysulfones are presented and interpreted in terms of the changes in the structure of the repeat unit compared to that of bisphenol A polysulfone. The differences between the sorption and diffusion of water and of permanent gases in these materials are also discussed. Water has the ability to interact with the polymer and with itself through hydrogen bonding in a way that permanent gases cannot. The equilibrium solubility of water in the polymer, unlike permanent gases, does not have a simple dependence on free volume but correlates more strongly with the frequency of hydrogen bonding sites on the polymer. Analysis of the sorption isotherms using the method of Zimm and Lundberg suggests that water molecules cluster in these polysulfones to various extents. For each polysulfone except polyethersulfone, the water diffusion coefficient decreases with increasing activity, which also suggests water clustering. For most of these materials, the water diffusion coefficient is larger than that of bisphenol A polysulfone and is directly related to the polymer free volume. Water permeability in these materials broadly correlates with the polymer free volume, but a favorable water-polymer interaction can be an overriding factor. © 1996 John Wiley & Sons, Inc.     

Sorption of water and organic solutes in polyimide films and its effects on dielectric properties

The effect of structure on the sorption kinetics of water and of various organic solutes into polyimide (PMDA-ODA) thin films was studied. The major techniques employed include measurements of sorption kinetics, density, and dielectric relaxation. More solute uptake, lower densities and higher diffusivities were observed for films cured at lower temperatures. By measuring both changes of mass and of density, the volume expansion of the polymer due to each solute was obtained; this was found to be proportional to the molar volume of the solute. The two dielectric relaxation peaks (denoted by γ₁ and γ₂) due to water (and other solutes) were studied in detail to obtain the relevant activation energies and the separate dipole moments. While water and methylene chloride appear in both γ₁ and γ₂ configurations, methyl and ethyl alcohol appear mainly as γ₂, while acetic acid is primarily γ₁. It was concluded that the γ₁ configurations are relatively homogeneously distributed throughout the polymer, involving loose bonding to the polymer structure, while the γ₂ configurations involve small clusters, probably chains of molecules. © 1993 John Wiley & Sons, Inc.     

Sorption of water in hydrophilic polymers—I Sorption isotherms in copolymers of hydroxyethyl methacrylate and hydroxyethoxyethyl methacrylate

Sorption isotherms of water vapour were determined for crosslinked poly-2-hydroxyethyl methacrylate (PHEMA), poly-2-(2′-hydroxyethoxy)ethyl methacrylate (PHEOEMA) and statistical copolymers at 35°. In the case of PHEMA the amount sorbed does not depend on the porosity of structure: sorption is influenced by the crosslinking parameters only at higher activities. The isotherm of PHEMA is S-shaped, while that of PHEOEMA, is convex; at lower activities, the sorption in mol/mol is higher in PHEMA than in PHEOEMA, although the former has a lower content of polar groups per monomer unit. It seems that the differences between isotherms could be explained by the fact (in principle identical with Kargin's hypothesis) that PHEMA is in the glassy state at the temperature of measurement, while the state of PHEOEMA is viscoelastic. The sorption data were used to calculate the parameters of the B.E.T. equation modified by Anderson; the concentrations of the sorption sites thus determined do not oppose the view that strongly bound water molecules are sorbed between two hydroxyl groups. The dependence of the Flory-Huggins interaction parameter χ on the volume fraction of the polymer exhibits a marked change of slope at a concentration roughly corresponding to the water content needed to transform the polymer from the glassy into the viscoelastic state at 35°. The Zimm clustering function indicates, at a higher water content, a considerable tende`ncy towards clustering; however, for samples in the glassy state and at low amounts sorbed, this function assumes negative values, suggesting mutual isolation of the molecules of the sorbate.     

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S‐shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S‐shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999     

Pure hydrocarbon sorption properties of poly(1-trimethylsilyl-1-propyne) (PTMSP), poly(1-phenyl-1-propyne) (PPP), and PTMSP/PPP blends

Propane and n-butane sorption in blends of poly(1-trimethylsilyl-1-propyne) (PTMSP) and poly(1-phenyl-1-propyne) (PPP) have been determined. Solubilities of propane and n-butane increased as the PTMSP content in the blends increased. This result is consistent with the higher free volume of PTMSP-rich blends and the better thermodynamic compatibility between PTMSP and these hydrocarbons. Propane and n-butane sorption isotherms were well described by the dual-mode model for sorption in glassy polymers. PTMSP/PPP blends are strongly phase-separated, heterogeneous materials. A noninteracting domain model developed for sorption in phase-separated glassy polymer blends suggests that sorption in the Henry's law regions (i.e., the equilibrium, dense phase of the blends) is consistent with the model. However, Langmuir capacity parameters in the blends are lower than predicted from the domain model, suggesting that the amount of nonequilibrium excess free volume associated with the Langmuir sites depends on blend composition. © 1996 John Wiley & Sons, Inc.     

Dissipative particle dynamics simulations of polymer-protected nanoparticle self-assembly

Dissipative particle dynamics simulations were used to study the effects of mixing time, solute solubility, solute and diblock copolymer concentrations, and copolymer block length on the rapid coprecipitation of polymer-protected nanoparticles. The simulations were aimed at modeling Flash NanoPrecipitation, a process in which hydrophobic solutes and amphiphilic block copolymers are dissolved in a water-miscible organic solvent and then rapidly mixed with water to produce composite nanoparticles. A previously developed model by Spaeth et al. [J. Chem. Phys. 134, 164902 (2011)] was used. The model was parameterized to reproduce equilibrium and transport properties of the solvent, hydrophobic solute, and diblock copolymer. Anti-solvent mixing was modeled using time-dependent solvent-solute and solvent-copolymer interactions. We find that particle size increases with mixing time, due to the difference in solute and polymer solubilities. Increasing the solubility of the solute leads to larger nanoparticles for unfavorable solute-polymer interactions and to smaller nanoparticles for favorable solute-polymer interactions. A decrease in overall solute and polymer concentration produces smaller nanoparticles, because the difference in the diffusion coefficients of a single polymer and of larger clusters becomes more important to their relative rates of collisions under more dilute conditions. An increase in the solute-polymer ratio produces larger nanoparticles, since a collection of large particles has less surface area than a collection of small particles with the same total volume. An increase in the hydrophilic block length of the polymer leads to smaller nanoparticles, due to an enhanced ability of each polymer to shield the nanoparticle core. For unfavorable solute-polymer interactions, the nanoparticle size increases with hydrophobic block length. However, for favorable solute-polymer interactions, nanoparticle size exhibits a local minimum with respect to the hydrophobic block length. Our results provide insights on ways in which experimentally controllable parameters of the Flash NanoPrecipitation process can be used to influence aggregate size and composition during self-assembly.     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006