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.     

Impact of thermal ageing on sorption and diffusion properties of PTMSP

Gas and vapour permeability in both freshly cast and aged poly(1-trimethylsilyl-1-propyne) (PTMSP) membranes were investigated in terms of solubility and diffusion coefficients for two probe molecules, a permanent gas (nitrogen) and an organic vapour (dichloromethane). To get reliable data for this study, we set up a fast and reproducible ageing procedure consisting of thermal treatment of the polymer films (100 °C during 24 h under vacuum). As expected, measurements recorded from time-lag experiments and isothermal sorption showed strong variations of the PTMSP transport properties before and after the thermal ageing procedure. Freshly cast membranes exhibited high permeability, whereas after ageing a 40–45% decrease of the permeability was recorded for both probes. The results demonstrated that only the glassy physical microstructure of PTMSP was affected by the ageing procedure, while the chemical structure was unchanged. Based on a dual-mode model for sorption and a Long's model for diffusion, the analysis of the data showed that the solubility and diffusion coefficients of the gas and the vapour were not affected in the same way. For nitrogen, only the diffusion coefficient decreased, whereas for dichloromethane, the thermal treatment mainly influenced the sorption coefficient. The lower permeability due to the combination of sorption and diffusion parameters could be attributed to a change of the PTMSP hole geometry or the hole connections.     

Dual-mode sorption kinetics of gases in glassy polymers

The transport of gases in many glassy polymers can be described satisfactorily by means of a “dual-mode sorption” model. The transport behavior observed with a given gas/polymer system can be characterized by the model parameters, which are obtained from solubility measurements in conjunction with absorption/desorption or permeability measurements. The present study discusses the inverse problem, namely, the prediction of the absorption/desorption behavior of a gas in a glassy polymer from a specified set of dual-mode sorption parameters. Satisfactory agreement is obtained between reported absorption rates of sulfur dioxide in glassy polycarbonate and of water vapor in Kapton® ?

1 ?Trademark of E. I. du Pont de Nemours & Co.

and the rates predicted by the dual-mode sorption model. This study also confirms the consistency of the model.     

The transport of gases in synthetic polymeric membranes — an historic perspective

The early history of gas transport studies is briefly reviewed. These studies were almost entirely concerned with natural rubber membranes. By 1880 the simple form of the solution-diffusion model had been derived and checked and by 1920 the time lag method for determining diffusion coefficients had been developed. The work which followed, for the next thirty years, was mainly concerned with natural and synthetic elastomers all well above their glass transition temperature, mainly hydrocarbon in nature, and non-crystalline. p]A number of reasonably successful correlations were shown between the gas transport parameters and the physical and chemical properties of the polymers. It is clear now that these correlations break down with the polar polymers. p]Functional relationships which have stood the test of time are those between the force parameters of the gas and the logarithms of the solubility coefficients. The linear relationship between the pre-exponential factors (or the entropies) of the diffusion coefficients and the activation energies also holds for most polymers. The remarkable constancy of the ratios of the permeability coefficients for the atmospheric gases through a large number of different polymers also has continued to be valid. p]The arrival of numerous new polymers introduced the dual complications of crystallinity (and morphology) and the glassy state. The concept of dual mode sorption cast doubt on many of the results and conclusions reached with glassy polymers. Recent work, however, shows great promise that these difficulties can be overcome and attention can again be focused on the mechanism of such transport. Finally, the behavior of the gas transport parameters above and below the glass transition temperatures is discussed.     

“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.     

Modeling of penetrant diffusion in glassy polymers with an integral sorption deborah number

A mathematical model was developed to explain the anomalous penetrant diffusion behavior in glassy polymers. The model equations were derived by using the linear irreversible thermodynamics theory and the kinematic relations in continuum mechanics, showing the coupling between the polymer mechanical behavior and penetrant transport. The Maxwell model was used as the stress–strain constitutive equation, from which the polymer relaxation time was defined. An integral sorption Deborah number was proposed as the ratio of the characteristic relaxation time in the glassy region to the characteristic diffusion time in the swollen region. With this definition, an integral sorption process was characterized by a single Deborah number and the controlling mechanism was identified in terms of the value of the Deborah number. The model equations were two coupled nonlinear differential equations. A finite difference method was developed for solving the model equations. Numerical simulation of integral sorption of penetrants in glassy polymers was performed. The simulation results show that (1) the present model can predict Case II transport behavior as well as the transition from Case II to Fickian diffusion and (2) the integral sorption Deborah number is a major parameter affecting the transition. © 1993 John Wiley & Sons, Inc.     

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     

Analysis of hydrocarbon gas sorption and transport in ethyl cellulose using the dual sorption/partial immobilization models

Low pressure sorption and transport data reported by Barrer et al. [1] for various C₄ and C₅ hydrocarbons in ethyl cellulose are analyzed in terms of current models of sorption and transport in glassy polymers. The popular dual sorption model, which was first qualitatively justified by these investigators, is used to estimate the frozen free volume fraction in the polymer which can accommodate Langmuir sorption. New CO₂ sorption data in ethyl cellulose are also presented and shown to be consistent with the dual sorption model and the frozen free volume fraction estimated from the hydrocarbon sorption. p]Transport of the hydrocarbons in ethyl cellulose is adequately described in terms of the partial immobilization model which attributes mobilities to each of the two sorbed species. The ratio of the mobility of the Langmuir species to that of the Henry's law species was found to be considerably less than unity for all of the gases.     

Solution and Diffusion Behavior of Pure Gases and Gas Mixtures in Glassy Polymer Membranes

A general model for the solution and diffusion behavior in pure gas-polymer membrane systems and gas mixture-polymer membrane systems has been developed. Proved by experiments on different glassy and rubbery polymer membranes at various temperatures and pressures, this model can achieve the prediction of permeation behavior of pure gases and gas mixtures in polymer membranes only using the model parameters obtained from experiments on pure gases. The calculated results are in good agreement with experimental.     

Gas sorption in polymers based on bisphenol-A

Equilibrium gas sorption measurements for CO₂, CH₄, and N₂ were made with three polymers based on bisphenol-A, namely a polyhydroxyether, a polyetherimide, and a polyarylate. These data plus previous results for two other bisphenol-A polymers, polycarhonate and polysulfone, were analyzed using the dual-mode sorption model and the more recent gas-polymer-matrix model. The models were compared on the basis of physical interpretations of the resulting parameters. The Langmuir capacity from the dual-model model was related to the unrelaxed volume of the glassy polymer. The Henry's law sorption parameter from the dual-mode model was related to the internal pressure of the polymer and to its tensile stress at yield. The work suggests a means for estimation of gas sorption levels from thermal and mechanical properties of the polymer.     

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     

Permeation of CO2 and N2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions

Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time-dependent permeation of N₂ and CO₂ through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.     

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.     

Model for sorption of mixed gases in glassy polymers

A model is presented for analysis of the sorption of mixed gases in glassy polymers at concentrations below which significant plasticization occurs. The well-known dual-mode sorption model comprised of a Henry's law term and a Langmuir isotherm term, which has been used extensively for interpretation of single-component gas sorption data, forms the basis for the analysis of binary mixtures discussed here. Measurements using pure gases provide dual mode parameters which can then be used to predict the resultant sorption isotherms for binary mixtures of any of the pure gases. The proposed analysis is based upon recognition that the Langmuir component of the overall sorption concentration should be governed by competition between the two penetrants for the fixed unrelaxed volume in the polymer, which is believed to be the locus of the Langmuir capacity. This effect may result in a significant depression of the measured sorption of similar penetrants competing for the limited Langmuir capacity. A numerical example is considered which illustrates the range of behavior expected for CO₂ and CH₄ in polycarbonate. Deviations from the theoretical predictions of the simple dual-mode model for binary systems are discussed in terms of plasticizing effects on the Henry's law constant and the Langmuir affinity constant. The analyses proposed here are of direct and critical interest to the applied problems of migration of trace contaminants in glassy polymers and analysis of barrier packaging for foods since all of these applied problems involve mixed-penetrant sorption. Specifically, it is predicted that the presence of residual monomers or solvents in glassy polymers can produce both anomolously low Langmuir sorption affinity constants and sorption enthalpies compared with the residual-free case.     

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.     

Sorption and transport behavior of gasoline components in polyethylene glycol membranes

Desulphurization mechanism of polyethylene glycol (PEG) membranes has been investigated by the study of solubility and diffusion behavior of typical gasoline components through PEG membranes with various crosslinking degrees. The sorption, diffusion and permeation coefficients were calculated by the systematic studies of dynamic sorption curves of gasoline components such as thiophene, n-heptane, cyclohexane, cyclohexene and toluene in PEG membranes. Furthermore, the temperature dependence of diffusion and solubility coefficients and the influence of crosslinking degree on sorption and diffusion behaviors were conducted to elucidate the mass-transfer mechanism. According to the discussions on dynamic sorption curves, transport mode, activation energy and thermodynamic parameters, thiophene species were the preferential permeation components. Crosslinking is an effective modification way to improve the overall performance of PEG membranes applied in gasoline desulphurization. The pervaporation (PV) and gas chromatography (GC) experiments results corresponded to the conclusions. All these investigations will provide helpful suggestions for the newly emerged membrane desulphurization technology and complex organic mixture separation by pervaporation.     

Effect of antiplasticization on gas sorption and transport. I. Polysulfone

The addition of tricresyl phosphate, N-phenyl-2-naphthylamine, and 4,4′-dichlorodiphenyl sulfone to polysulfone causes changes in thermal and mechanical properties of the glassy mixtures associated with antiplasticization, i.e., reduction in glass transition temperature and increase in stiffness. These changes are also found to be accompanied by reductions in sorption of carbon dioxide and the permeability coefficients for helium, carbon dioxide, and methane at low diluent concentrations with reversal of these trends at higher levels as also occurs for the mechanical properties. Detailed analyses of data for carbon dioxide are given in terms of the dual sorption and mobility models often used for glassy polymers. The mobility for gas transport was found to decrease with diluent addition. The major cause for the decreased sorption is the reduction in glass transition temperature accompanying addition of the diluents. The changes in transport behavior approximately parallel the changes in mechanical behavior. These trends are not even qualitatively correlated with estimates of the excess volume changes associated with addition of the diluents to polysulfone.     

Concentration-dependent transport of gases and vapors in glassy polymers

The transport of gases and vapors in glassy polymers is analyzed on the basis of the “dual-sorption” model with partial immobilization and the assumption that the diffusion coefficient is an exponential function of concentration. Expressions are derived for the effective (apparent) permeability and diffusion coefficients, as well as for the diffusion timelag. These expressions reduce in limiting cases to forms reported by other investigators. The implications of these results to the separation of gas and vapor mixtures by permeation through glassy polymer membranes are discussed.