CO2 sorption in poly(ethylene terephthalate) above and below the glass transition

High-pressure CO₂ sorption data in semicrystalline poly(ethylene terephthalate) (PET) are presented for temperatures ranging from 25 to 115°C. The results are described by Henry's law above the glass-transition temperature of PET, while a dual-mode sorption model comprised of a Henry's law and a Langmuir isotherm applies in the glassy state. The disappearance of the Langmuir capacity of the polymer above T_g presumably results from the elimination of regions of localized lower density which are frozen into the glass upon quenching from the rubbery state. Exposure of PET to a high CO₂ pressure produced a systematic variation in the apparent sorption equilibria. Correlation of the Langmuir capacity of PET with the dilatometric parameters of the polymer provides a useful framework for understanding the origin of the Langmuir sorption mode and for interpreting annealing and conditioning effects in glassy polymers.     

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.     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

Sorption of carbon dioxide in fluorinated poyimides

Sorption isotherms of CO₂ for ten fluorinated polyimides measured at 35°C and up to about 25 atm are analyzed according to the dual-mode sorption model. Sorption properties for these polyimides are compared with those for other glassy Polymers including unfluorinated polyimides. The glassy polymers with higher glass transition temperatures T_g tend to show greater CO₂ sorption. Introduction of a ? C (CF₃)₂? linkage into the repeat unit of the main chain increases the sorption by 20–80%. For glassy polymers, including the fluorinated and unfluorinated polyimides, the Langmuir affinity constant b and Henry's law solubility constant k_D are correlated with the content of functional (carbonyl or sulfonyl) groups [FG], and composite parameter reflecting the magnitude of both [FG] and free-space fraction V_F, respectively, with some exceptions. The Langmuir capacity constant C′_H is correlated with T_g, but there are two correlation lines; one for unfluorinated polyimides and a different one for other glassy polymers including fluorinated polyimides. The slope of the former group is smaller probably because of smaller differences in thermal probably because of smaller differences in thermal expansion coefficients in rubbery and glassy states. Most fluorinated polyimides show greater solubility of CO₂ than unfluorinated polyimides and other glassy polymers, because of their larger C′_H and k_D. © 1993 John Wiley & Sons, Inc.     

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.     

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.     

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     

Sorption and partial molar volume of gases in poly (dimethyl siloxane)

Sorption of N₂, O₂, Ar, CH₄, CO₂, C₂H₄, and C₂H₆ in poly (dimethyl siloxane) liquid and rubber and the dilation of the polymers due to sorption of the gases are studied at 25°C under pressures up to 50 atm. In the liquid, the sorption isotherms for low-solubility and high-solubility gases are described by Henry's law and the Flory–Huggins equation, respectively. Gas sorption in the rubber, which contains a 29 wt % silica filler, follows the dual-mode sorption model, though marked hysteresis is observed in the sorption of O₂ and CH₄. The dilation isotherms increase linearly or exponentially in both polymers with increasing pressure. Considering that gas molecules adsorbed into micropores of the filler particles do not participate in the dilation, partial molar volumes of the dissolved gases in the rubber are determined from data of sorption and dilation. The values are nearly equal to the partial molar volumes in the liquid (48–60 cm³/mol).     

Argon sorption and partial molar volume in poly(ethyl methacrylate) above and below the glass transition temperature

Sorption and dilation isotherms for argon in poly(ethyl methacrylate) (PEMA) are reported for pressures up to 50 atm over the temperature range 5–85°C. At temperatures below the glass transition (T_g=61°C), sorption isotherms are well described by the dual-mode sorption model; and isotherms above T_g follow Henry's law. However, isotherms for dilation due to sorption are linear in pressure at all temperatures over the range investigated. Partial molar volumes of Ar in PEMA are obtained from these isotherms. The volumes are approximately constant above T_g (about 40 cm³/mol), whereas the volumes below T_g are smaller and dependent on both temperature and concentration (19–26 cm³/mol). By analyzing the experimental data according to the dual-mode sorption and dilation model, the volume occupied by a dissolved Ar molecule and the mean size of microvoid in the glass are estimated to be 67 129 ų, respectively. The cohesive energy density of the polymer is also estimated as 61 cal/cm³ from the temperature dependence of the dual-mode parameters.     

Gravimetric study of high-pressure sorption of gases in polymers

A gravimetric method for determining precisely the solubility of gases in polymers at high pressure is described. The solubilities of N₂ and CO₂ in low-density polyethylene (LDPE); CO₂ in polycarbonate (PC); and N₂, CH₄, C₂H₆, and CO₂ in polysulfone (PSUL) have been measured as a function of pressure up to 50 atm. Most of the measured sorption isotherms agreed closely with published data, but reproducible and time-dependent hysteresis in the sorption of CO₂, C₂H₆, and CH₄ in glassy polymers, PC, and PSUL, was observed in this study for the first time. Like the well known conditioning effect of high-pressure CO₂ on the sorption capacity of glassy polymers, these hysteresis phenomena are believed to be due to the plasticizing effect of sorbed gases. On the basis of the current data, the dual-mode sorption model including the plasticization by sorbed gas is discussed and a primitive equation for the concentration of sorbed gases in a quasiequilibrium state of sorption or desorption is proposed.     

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     

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.     

Effect of penetrant-induced isothermal glass transition on sorption,dilation, and diffusion behavior of polybenzylmethacrylate/CO2

The effect of a penetrant-induced isothermal glass transition on sorption, dilation, and diffusion behavior was studied in a single experimental run for CO₂ in cast polybenzylmethacrylate films. The dual-mode type sorption isotherms below the glass transition temperature of the polymer changed to linear ones above a certain concentration. Meanwhile, partial molar volume of CO₂ determined from the dilation of the films above the concentration gave a value very close to the one reported for rubbery polymers, and diffusion coefficients became less concentration-dependent. The results were conformable to the concept of unrelaxed volume in glassy polymers. © 1996 John Wiley & Sons, Inc.     

Sorptive dilation of polysulfone and poly(ethylene terephthalate) films by high-pressure carbon dioxide

Dilation of polysulfone (PSUL) and crystalline poly(ethylene terephthalate) (PET) films accompanying sorption of carbon dioxide is measured by a cathetometer under high pressure up to 50 atm over the temperature range of 35–65°C. Sorptive dilation isotherms of PSUL are concave and convex to the pressure and concentration axes, respectively, and both isotherms exhibit hysteresis. Each dilation isotherm plotted versus pressure and concentration for the CO₂-PET system shows an inflection point, i.e., a glass transition point, at which the isotherm changes from a nonlinear curve to a straight line. Dilation isotherms of PET below the glass transition point are similar to those of the CO₂-PSUL system, whereas the isotherms above the glass transition point are linear and exhibit no hysteresis. Partial molar volumes of CO₂ in these polymers are determined from data of sorptive dilation. On the basis of the extended dual-mode sorption model and the current data, primitive equations for gas-sorptive dilation of glassy polymers are proposed.     

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.     

Adsorption isotherms of CO2, CO,N2, CH4, Ar and H2 on activated carbon and zeolite LiX up to 1.0 MPa

The adsorption isotherms of CO₂, CO, N₂, CH₄, Ar, and H₂ on activated carbon and zeolite LiX were measured using a volumetric method. Equilibrium experiments were conducted at 293, 308, and 323 K and pressures up to 1.0 MPa. The adsorption isotherm and heat of adsorption were analyzed for two pressure regions of experimental data: pressures up to 0.1 MPa and up to 1.0 MPa. Each experimental isotherm was correlated by the Langmuir, Sips, Toth and temperature dependent Sips isotherm models, and the deviation of each model was evaluated. The Sips and Toth models showed smaller deviation from the experimental data of adsorbents than the Langmuir model. Isosteric heats of adsorption were calculated by the temperature dependent Sips model and are presented along with surface loading. From deviation analysis, it is recommended that the isotherm in the proper pressure range be used to appropriately design adsorptive processes.     

Sorption and transport of carbon dioxide in a polyimide from 3,3′4,4′-biphenyltetracarboxylic dianhydride and 4,4′-diaminodiphenyl sulfone

CO₂ sorption and transport were investigated for the polyimide prepared from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-diaminodiphenyl sulfone (DDS). The morphology of films did not change on annealing above the glass transition temperature and remained amorphous unlike the polyimide prepared from BPDA and 4,4′-oxydianilline (ODA). This seems to be due to the strong hindrance to rotation of the sulfonyl linkage. Sorption and transport data were analyzed according to the dual-mode model. Solubility, diffusion, and permeability coefficients at 20 atm and 80°C for BPDA-DDS polyimide were substantially equal between as-cast and annealed films and were 1.7, 2.2, and 3.7 times greater, respectively, than for the as-cast films of the BPDA-ODA polyimide. The higher solubility was due to larger values of the Henry's law solubility constant k_D, Langmuir capacity constant C, and the Langmuir affinity constant b. The sorption and transport properties were compared with those for amorphous glassy aromatic polymers including other polyimides. The relation of k, C, b, and the diffusion coefficients in the Henry's law population and the Langmuir population (D_D and D_H) with other properties of the polymers were discussed. Values D_D and D_H for BPDA-DDS polyimide were much larger than expected from the estimated free-volume fraction.     

Kinetics and equilibria of sulfur dioxide sorption in kapton polyimide

The kinetics and equilibria of SO₂ sorption in Kapton polyimide film have been measured at 25°C for pressures up to 58 cm Hg using a quartz spring balance. The observed equilibria are described well by the dual-mode model for sorption of penetrants in glassy polymers. Observed hysteresis in sorption-desorption cycling indicates that the diffusivity of SO₂ increases markedly with increasing local penetrant concentration in the polymer. The concentration dependence of the effective average diffusion coefficient is described well by an expression from dual-mode theory. The Langmuir component of the sorption population has an extremely low mobility compared to that of the Henry's law component; in fact, the so-called “total immobilization” limiting case, which assigns a zero diffusion coefficient to this component, appears to be satisfactory under the conditions studied. These results, coupled with published results for other penetrants, suggest that the degree of immobilization of the Langmuir population depends to a great extent on the condensability and/or the molecular size of the penetrant. Predictions of the SO₂ diffusion time lag and permeability in Kapton as functions of the upstream SO₂ pressure are presented and discussed in terms of the dual-mode theory.