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.     

A Self-Consistent Model for Sorption and Transport in Polyimide-Derived Carbon Molecular Sieve Gas Separation Membranes

Demand for energy-efficient gas separations exists across many industrial processes, and membranes can aid in meeting this demand. Carbon molecular sieve (CMS) membranes show exceptional separation performance and scalable processing attributes attractive for important, similar-sized gas pairs. Herein, we outline a mathematical and physical framework to understand these attributes. This framework shares features with dual-mode transport theory for glassy polymers; however, physical connections to CMS model parameters differ from glassy polymer cases. We present evidence in CMS membranes for a large volume fraction of microporous domains characterized by Langmuir sorption in local equilibrium with a minority continuous phase described by Henry's law sorption. Using this framework, expressions are provided to relate measurable parameters for sorption and transport in CMS materials. We also outline a mechanism for formation of these environments and suggest future model refinements.     

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     

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.     

Dual-mode analysis of subatomspheric-pressure CO2 sorption and transport in Kapton H polyimide film

Sorption kinetics and equilibria as well as permeabilities and diffusion time lags for CO₂ in Kapton polyimide film have been studied at temperatures from 35 to 55°C and pressures up to 0.78 atm. The sorption/desorption cycles indicate that the diffusivity of CO₂ increases with increasing local penetrant concentration in the polymer. Both the permeability and time lag decrease with increasing upstream CO₂ pressure. All of these results are described well by theoretical expression based on the dual-mode theory of sorption and transport in glassy polymers.     

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.     

The solution and transport of gases in poly(N-butyl methacrylate) in the glass transition region. I. Absorption-desorption measurements

Solubility coefficients, S, and diffusion coefficients, D, have been determined for ethane and n-butane in poly(n-butyl methacrylate) (PnBMA) by the microbalance technique in the temperature range from ?14 to 50°C, which encompasses the glass transition of the polymer (22–35°C). S and D for ethane were found to be independent of penetrant pressure and concentration at all temperatures studied No transition to “dual-mode” sorption behavior, as reported for a number of penetrants in glassy polymers, was observed with ethane, even at the lowest experimental temperature. Plots of log S and log D versus 1-T, the reciprocal absolute temperature, were linear for the ethane-PnBMA system and did not exhibit discontinuities in the glass transition region. The above results suggest that the same mechanism of solution and transport of ethane in PnBMA is operative both above and below the glass transition of the polymer under the experimental conditions. This behavior is attributed to the low “excess” free volume of glassy PnBMA, as indicated by the small difference between the coefficients of thermal expansion of this polymer in its rubbery and glassy states. Possible conditions for the appearance of dual-mode gas sorption are discussed. A similar study with the n-butane-PnBMA system showed that the polymer was plasticized by the penetrant below 20°C, due to the higher solubility of n-butane compared with that of ethane in PnBMA.     

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     

Interface effects on moisture absorption in ultrathin polyimide films

Water absorption in thin films (<1000 Å) of a commercial polyimide was evaluated by monitoring dimensional changes induced by a humid environment. Film thickness was measured using x-ray reflectivity, which is a nondestructive technique offering angstrom resolution in the measurements of thin film or multilayer thickness. The effect of several variables on the absorption of moisture were monitored in polyimide films adhered to polished silicon substrates, including total dry film thickness, exposure time, and the contribution of a coupling agent. The percentage increase in film thickness due to moisture uptake is found to be a weak function of dry film thickness, decreasing as dry film thickness increases, and to be somewhat affected by the use of an interfacial coupling agent. The observed behavior points to the polymer/substrate interface as a strong factor controlling the absorption of moisture in the polyimide/silicon system, and is believed to reflect the presence of a highly moisture-saturated interfacial layer. A bilayer model is proposed, and the feasibility of using this model to describe the observed behavior is considered. Published 1998 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

J Polym Sci B: Polym Phys 36 : 155–162, 1998     

Model of sorption of simple molecules in polymers

A model of simple molecule sorption in polymers is proposed which embraces both the glassy and rubbery regions, and incorporates the successful dual-mode model below the glass-transition temperature. Hole filling is shown to be an important sorption mechanism both above and below T_g, although saturation effects do not occur in the rubbery polymer. The model interprets the “dual-mode” Langmuir and Henry's law parameters at the molecular level, and a simple statistical mechanical analysis allows estimation of the parameter values, as well as specifying certain interrelationships between the parameters. Applications of the model to gas solubility data in five polymers are considered [polyethylene (PE), poly(ethylene terephthalate) (PET), polystyrene (PS), polymethacrylate (PMA), poly(vinyl acetate) (PVAc)] and semiquantitative agreement is obtained for PE, PET, and to a lesser extent, PS. For PMA and PVAc, the agreement is qualitative only.     

Analysis of the kinetics of vapor absorption/desorption in/from silicone rubber and cellulose acetate membranes in the presence of stagnant boundary layers

The application of an interferometric technique (optical thickness meter, OTM) to the measurement of vapor sorption kinetics in both rubbery and glassy polymers is presented. In this technique, the membrane is formed by casting on a suitable glass surface and interferometry is applied in situ. The use of a carrier gas loaded with penetrant vapor introduced a stagnant boundary layer (SBL) effect which had to be corrected, in order to determine true sorption kinetics. The said SBL effect was estimated, on the basis of existing theory for the silicone rubber–methylene chloride (SR/MC) system and found to be more pronounced in the case of desorption. Upon correction for this effect, Fickian sorption curves were obtained; which yielded nearly constant values of the diffusion coefficient, not materially different for absorption and desorption, in line with theoretical expectation.Cellulose acetate–methylene chloride (CA/MC) was then studied as an example of a glassy polymer–vapor system, where the SBL effect distorts the absorption kinetic curve in the same way as the non-Fickian mechanism of sorption inherent in this kind of polymer–penetrant system. Here, the vapor sorption data were corrected using the results obtained from the Fickian SR/MC system. The corrected results were checked by comparison with independent data reflecting the true kinetic behavior of CA/MC, obtained with a vacuum balance apparatus (VBA), which is free of SBL effects. It is shown that this novel method of applying the SBL correction was reasonably successful in favorable circumstances, while a criterion is provided to identify cases where reasonably reliable correction is not possible.     

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.     

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.     

High-resolution solid-state 19F-NMR spectroscopy of the sorption and diffusion of fluorine-containing aromatic molecules in polymeric media

High-resolution ¹⁹F solid-state NMR spectroscopy was employed to study the sorption properties of hexafluorobenzene (HFB) and 3,5-bis (trifluoromethyl) aniline (TFMA) in polystyrene (PS) and butyl rubber (BR). The NMR spectra indicate that the penetrants undergo dual-mode sorption in the glassy polymer (PS), but are highly mobile in the rubbery polymer (BR). In addition, the NMR method was utilized in the experimental determination of diffusion coefficients for the HFB/PS, TFMA/PS, and HFB/BR systems through desorption studies. The diffusion results for the TFMA/PS case agree very well with those previously obtained via resonance nuclear reaction analysis. © 1993 John Wiley & Sons, Inc.     

Finite difference modeling of the gas transport process in glassy polymers

Finite difference modeling has been used to predict the results of gas transport experiments for a concentration-dependent diffusion coefficient. Experiments on the transport of CO₂ in poly(ethylene terephthalate) and poly(ethylene naphthalate) had previously shown a difference between the effective diffusion coefficients for absorption and desorption runs of a double-sided experiment, but this effect had not been seen for single-sided experiments. The finite difference calculations show that such results are to be expected, and the parameters included in the models that attempt to describe the diffusion process in glassy polymers, such as the dual-mode model, and which lead to concentration-dependent diffusion coefficients, can be found by fitting the experimental data for the double-sided experiment using finite difference modeling. The dependence of the effective diffusion coefficient on pressure for the single-sided experiment can be correctly predicted using results from the double-sided experiment for an identical sample. © 1996 John Wiley & Sons, Inc.     

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.     

Determination of dual-mode sorption and mobility parameters from permeation experiments

The precise pressure dependence of apparent diffusion and permeation coefficients was measured by using a microcomputer system for collecting and treating permeation data for CO₂ in glassy poly(ethylene terephthalate) below 1 atm between 15 and 40°C. The partial immobilization model was used to determine the dual-mode sorption and mobility parameters. The curves calculated with these parameters were in excellent agreement with experimental data. These parameters were also compared with sorption parameters obtained from measurements at 30°C. There was a small difference between the values of the parameters obtained from these permeation data and those from sorption data which we had previously obtained. Relations between this difference and the method of determination of the parameters are discussed.     

A method of validation and parameter evaluation for dual-mode sorption model

A method of visual validation of a widely used dual-mode model for sorption of gases in glassy polymers is presented. Instead of directly fitting the model equation to the sorption data to determine its three parameters, the method evaluates one of the parameters, Henry's law coefficient independently and then plot the data in a linear way. Good linearity was obtained from such plots for the sorption data of CO₂ in polycarbonate and polysulfone, which indicated the validity of the assumed model. Moreover, parameter values determined accordingly were seen to be reasonable and self-consistent. Applications of the method were also illustrated for detecting deviations from the dual-mode sorption. Finally, a normalized linear plot is discussed by which sorption isotherms obeying the dual-mode model could be transformed to parallel lines and be specified by a dimensionless parameter.