Carbon dioxide sorption and transport in polycarbonate

The solubility, permeability, and diffusion time lag for carbon dioxide in polycarbonate are reported at 35°C for pressures ranging from 1 atm to 23 atm. The solubility data are very well described by the dual sorption mechanism model, Henry's law plus Langmuir adsorption, proposed for glassy polymers. Both the permeability and time lag decrease with increased CO₂ pressure. These observations are not consistent with the proposal that CO₂ sorbed by the Langmuir contribution is totally immobilized; however, all of the results are entirely consistent with an extension of this proposal which considers partial immobilization. The data have been quantitatively analyzed in terms of this partial immobilization model, and the results suggest for polycarbonate at 35°C that the CC₂ sorbed by the Langmuir portion of the isotherm behaves as if it has only about 10% of the mobility of the gas sorbed by the Henry's law part of the isotherm. The results have also been interpreted in terms of a concentration-dependent diffusion coefficient which is shown to be mathematically equivalent to the partial immobilization model. The latter model was also formulated in thermodynamic terms, whereby fugacity was used rather than pressure, and diffusion coefficients were defined in terms of chemical potential gradients rather than concentration, but the consequences of these changes proved to be minor and no better. The significance of these observations and their interpretation is discussed.     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

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.     

Effects of carbon filler on sorption and diffusion of gases through rubbery materials

Effects of carbon filler on the sorption and diffusion of carbon dioxide in natural rubber and in styrene-butadiene rubber have been studied. Sorption isotherms conform to Henry's law in unfilled rubber and to Langmuir's law in carbon black. The isotherms in filled rubber exhibit a combination of the two sorption modes. The Henry's law solubility parameter k_D increases with carbon filler content; the Langmuir saturation constant C′_A initially is constant with filler level, but then decreases abruptly when carbon particles begin to aggregate. The diffusion coefficient decreases with increasing filler content, presumably owing to geometric effects and to polymer chain immobilization in the interfacial regions.     

Gas separation properties of aromatic poly(amide-imide) membranes

Aromatic poly(amide-imide)s were synthesized using direct 2,2-bis[N-(4-carboxyphenyl)-phthalimidyl] hexafluoropropane (6FDIA) polycondensation with various diamines containing flexible ether groups and bulky substituents. The oxygen and nitrogen gas transport in the poly(amide-imide) membranes was investigate at 35 °C with the pressure between the interval at 2-10 atm. The proposed method is expected to promote the gas permeability of the poly(amide-imide) membrane and maintain the gas selectivity. It was found that both gas permeability and selectivity of poly(amide-imide) membranes increased with increasing fractional free volume and d-spacing. The gas permeability had good correlation with the γ-transition temperature. The bulky pendent group introduced into diamine moiety of poly(amide-imide) could efficiently promote the gas permeability. For the behaviors of gas separation, the gas diffusivity coefficient and solubility selectivity controlled the gas permeability and selectivity, respectively. The sorption behavior of the aromatic poly(amide-imide) membranes can be well explained using the dual mode sorption model. The Langmuir capacity constant and Henry’s law constant increase with FFV increasing. 6F-TBAPS has the best O₂/N₂ separation performance among the poly(amide-imide) membranes.     

Permeation of carbon dioxide through homogeneous dense and asymmetric cellulose acetate membranes

Sorption isotherms for carbon dioxide in a homogeneous dense cellulose acetate membrane were measured by the pressure decay method at three temperatures between 20 and 40°C and gas pressures up to 1.7 MPa. Steady-state permeation rates for the same system at three temperatures between 24 and 40°C and gas pressures up to 2.2 MPa were measured by the variable volume method. The equilibrium sorption was described well in terms of the dual-mode sorption model. The pressure dependence of the mean permeability coefficient was interpreted by the total immobilization model, i.e., a limiting case of the dual-mode mobility model, where the diffusion coefficient for the Henry's law mode is not assumed to be constant but depends upon gas pressure via a modified free-volume theory. The observed pressure dependence of the mean permeability coefficient through an asymmetric cellulose acetate membrane was very similar to that through a homogeneous dense membrane. The thin skin layer in the asymmetric membrane can be simulated by a homogeneous dense membrane from the point of view of gas sorption and diffusion.     

Transient and steady-state permeation in poly(ethylene terephthlate) above and below the glass transition

Transient and steady-state permeation data are reported for CO₂ in semicrystalline poly(ethylene terephthalate) for temperatures ranging from 25 to 115°C over the pressure range from 1 to 20 atm. The pressure dependency of the time lag and permeability disappears completely above the glass transition of the polymer, and Fick's law with a concentration-independent diffusion coefficient applies. In the glassy state, a concentration-dependent diffusion coefficient is necessary to describe the data. The form of this concentration dependence is described well by the partial immobilization transport model that attributes a different mobility to each of the two populations of sorbed gas which exist in local equilibrium with each other in glassy polymers. The importance of reporting the pressure used in transport experiments involving glassy polymers is emphasized by comparing the difference in the activation energy of the apparent diffusivity calculated from the measured time lag at 1 and 20 atm. Also, the magnitude of the observed slope discontinuity at T_g in Arrhenius plots of these apparent diffusities is shown to be a function of the upstream pressure used in the experiment. The independently measured time lags are compared with the predicated values calculated from various transport models and found to be described best by the partial immobilization model.     

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.     

Uptake properties of Eu(III) on Na-attapulgite as a function of pH, ionic strength and temperature

Herein, the sorption properties of Eu(III) on Na-attapulgite were performed by using batch sorption experiments under different experimental conditions, such as contact time, pH, ionic strength, humic acid and temperatures. The results indicated that the sorption of Eu(III) on Na-attapulgite was strongly dependent on pH and temperature. At low pH values, the sorption of Eu(III) was influenced by ionic strength, whereas the sorption was not affected by ionic strength at high pH values. The sorption of Eu(III) was mainly dominated by ion exchange or outer-sphere surface complexation at low pH values, and by inner-sphere surface complexation or surface precipitation at high pH values. The sorption of Eu(III) onto Na-attapulgite increased with increasing temperature. The Langmuir and Freundlich models were applied to simulate the sorption isotherms, and the results indicated that the Langmuir model simulated the sorption isotherms better than the Freundlich model. The thermodynamic parameters (∆G ^o, ∆S ^o, ∆H ^o) were calculated from the temperature dependent sorption isotherms at 293, 313 and 333 K, respectively, and the results indicated that the uptake of Eu(III) on Na-attapulgite was an endothermic and spontaneous process. The results of high Eu(III) sorption capacity on Na-attapulgite suggest that the attapulgite is a suitable material for the preconcentration and immobilization of Eu(III) ions from large volumes of aqueous solutions.     

Sorption of radioeuropium onto attapulgite: effect of experimental conditions

Batch sorption experiments were performed to remove Eu(III) ions from aqueous solutions by using attapulgite under ambient conditions. Different experimental conditions, such as contact time, solid content, foreign ions, pH, ionic strength, fulvic acid and temperature, have been investigated to study their effect on the sorption property. The results indicated that the sorption of Eu(III) onto attapulgite was strongly dependent on pH, ionic strength and temperature. The sorption increased from about 8.9 to 90% at pH ranging from 2 to 6 in 0.01 mol/L NaNO₃ solution. The Eu(III) kinetic sorption on attapulgite was fitted by the pseudo-second-order model better than by the pseudo-first-order model. The sorption of Eu(III) onto attapulgite increased with increasing temperature and decreasing ionic strength. The Langmuir and Freundlich models were used to simulate the sorption isotherms, and the results indicated that the Freundlich model simulated the data better than the Langmuir model. The thermodynamic parameters (∆G ^o, ∆S ^o, ∆H ^o) were determined from the temperature dependent isotherms at 298.15, 318.15 and 338.15 K, and the results indicated that the sorption reaction was an endothermic and spontaneous process. The results suggest that the attapulgite is a suitable material as an adsorbent for preconcentration and immobilization of Eu(III) from aqueous solutions.     

GAS SORPTION AND TRANSPORT IN POLY (PHENYLENE OXIDE)(PPO)AND ARYL-BROMINATED PPO MEMBRANES

The apparent solubility (S), concentration-average diffusivity (D), and permeability (P), for C0_2, CH_4 and N_2 through PPO and aryl-brominated PPO at 35℃for pressure ranging from 1 to 26 atm are reported. It is found that P, D, and S of the membranes to all the three gases vary with the extent of bromination. S increases with the increase of the percent of bromine in each case, but D to CO_2 increases remarkably only at higher degree of brominafion, and therefore, P to CO_2 is increased by more than 100% over a wide range ofpressure in the case. The solubility data are well described by the dual mode sorption model. It is found that the gas molecules sorbed by the Langmuir mode are relatively more immobilized and the contribution of the nonequilibrinm character of the polymer to gas permeation increases obviously for CO_2 and is hardly changed for CH_4 with increasing bromine content. These observations are interpreted in terms of changes in specific free volume (SFV)and the cohesive energy density (CED) of the polymers.     

Gas transport properties of annealed polyimide films

Sorption and permeation of CO₂ in various annealed polyimide (PI) films were investigated. Dual-mode sorption and partial immobilization models were used to analyze the data. Sorption of CO₂ in PI film quenched from above the glass transition temperature (T_g) is greater than in film as received. In fact, sorption is decreased over the entire pressure range by cooling the film slowly. These changes in sorption of CO₂ can be attributed to a change in the Langmuir sorption capacity C′_H by annealing, since the other dual-mode sorption parameters, k_D and b, are almost independent of annealing. The value of C′_H is increased by quenching, and decreased by slow cooling from above T_g. The two diffusion coefficients D_D and D_H according to the Henry and Langmuir modes, respectively, for CO₂ also depend markedly on annealing. Diffusion coefficients of quenched PI films are increased and those of film cooled slowly are decreased compared with values for PI film as received. The change in D_H is larger than that in D_D. The permeability coefficient of quenched PI films at 100 cmH_g is about 1.7 times that of PI film as received. The film structure formed by quenching can enhance permselectivity.     

Sol-gel polyimide-silica composite membrane: gas transport properties

The effect of introduction of silica particles prepared by the sol-gel technique on the gas transport properties of a polyimide film was studied. The sorption and permeation of N₂, O₂, CO₂, H₂ and CH₄ were studied and correlated with morphological changes in the polymer structure. From sorption isotherms, we observed that the composite membrane presents higher solubility coefficients than the polyimide one. The solubility coefficient ratio between the composite and the polyimide is about 1.5–2.0. The isotherms were analyzed in terms of the dual mode sorption. The Henry's coefficient and the Langmuir's affinity and saturation constants were obtained allowing to calculate the Langmuir to Henry concentration ratios as function of the gas pressure. These ratios decrease until zero within a certain pressure range as long as the Langmuir's mode is acting and they are higher for the polyimide membrane when compared with the composite one. This study was completed with calorimetric measurements during the sorption. The gas interaction energy in kJ/mol decreases within the same pressure range as previously described. The measured energies are higher for the polyimide film when compared with the composite one because the polyimide membrane presents a stronger energetic effect caused by a higher Langmuir's contribution. From permeation studies at 3.15⁵ Pa, the composite membrane showed higher permeability coefficients and permselectivities than the polyimide one. All these results were explained, taking into account the difference on the imidization degree of both membranes and the morphological changes which may be induced by the silica nodules in the organic/inorganic interphases.     

Competitive permeation of gas and water vapour in high free volume polymeric membranes

Highly permeable glassy polymeric membranes based on poly (1‐trimethylsilyl‐1‐propyne) (PTMSP) and a polymer of intrinsic porosity (PIM‐1) were investigated for water sorption, water permeability and the separation of CO₂ from N₂ under humid mixed gas conditions. The water sorption isotherms for both materials followed behavior indicative of multilayer adsorption within the microvoids, with PIM‐1 registering a significant water uptake at very high water activities. Analysis of the sorption isotherms using a modified dual sorption model which accounts for such multilayer effects gave Langmuir affinity constants more consistent with lighter gases than the use of the standard dual mode approach. The water permeability through PTMSP and PIM‐1 was comparable over the water activities studied, and could be successfully model ed through a dual mode sorption model with a concentration dependent diffusivity. The water permeability through both membranes as a function of temperature was also measured, and found to be at a minimum at 80 ° C for PTMSP and 70 °C for PIM‐1. This temperature dependence is a function of reducing water solubility in both membranes with increasing temperature countered by increasing water diffusivity. The CO₂ ‐ N₂ mixed gas permeabilities through PTMSP and PIM‐1 were also measured and model ed through dual mode sorption theory. Introducing water vapour further reduced both the CO₂ and N₂ permeabilities. The plasticization potential of water in PTMSP was determined and indicated water swelled the membrane increasing CO₂ and N₂ diffusivity, while for PIM‐1 a negative potential implied that water filling of the microvoids hampered CO₂ and N₂ diffusion through the membrane. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 719–728     

On pressure dependence of the parameters of the dual-mode sorption model

Sensitivity of the parameters of the dual-mode sorption (DMS) model on the pressure range, in which sorption of gases in polymers have been studied, was analyzed. Different “gas-polymer” systems were considered but the most detailed analysis was performed for sorption of argon and nitrogen in poly[5,5-difluoro-6,6-bis(trifluoromethyl)] norbornene and polysulfone. It was shown that the model parameters depend upon the range of gas pressure studied. Expanding of the pressure range (0-p_i) results in an increase in the Langmuir adsorption capacity C′_H and in reduction of Henry's law solubility coefficient k_D and Langmuir affinity parameter b. These behaviors does not depend on a choice of an experimental apparatus or software and procedure of nonlinear least squares treatment of the data. As statistical analysis indicated, a systematic error of the measurement cannot call forth the observed dependencies of the model parameters. Different physical reasons of these behaviors were considered, among them: the pressure dependence of the affinity parameter, and the dilation of a polymer. The results obtained showed that although the DMS model, as a rule, gives an excellent fit of the experimental curves, and, hence, can be used as a form of compact storage of information on gas sorption in polymers, one should be careful in using it outside the pressure range in which its parameters have been determined. © 1996 John Wiley & Sons, Inc.     

Comparison of three models for permeation of CO2/CH4 mixtures in poly(phenylene oxide)

Two models for the permeability of pure gases have been extended to include binary gas mixtures. The first is an extension of a pure gas permeability model, proposed by Petropoulos, which is based on gradients of chemical potential. This model predicts the permeability of components in a gas mixture solely on the basis of competition for sorption sites within the polymer matrix. The second mixed gas model follows an earlier analysis by Barrer for pure gases which includes the effects of saturation of Langmuir sites on the diffusion as well as the sorption processes responsible for permeation. This generalized “competitive sorption/diffusion” model includes the effect of each gas component on the sorption and diffusion of the other component in the mixture. The flux equations from these two models have been solved numerically to predict the permeability of gas mixtures on the basis of pure gas sorption and transport parameters. Both the mixed gas Petropoulos and competitive sorption/diffusion model predictions are compared with predictions from the earlier simple competitive sorption model based on gradients of concentration. An analysis of all three models is presented for the case of CO₂/CH₄ permeability in poly(phenylene oxide) (PPO). As expected, the competitive sorption/diffusion model predicts lower permeability than either of the models which consider only competitive sorption effects. The permeability depression of both CO₂ and CH₄ predicted by the competitive sorption/diffusion model is roughly twice that predicted by the competitive sorption model, whereas the mixed gas Petropoulos model predictions for both gases lie between the other two model predictions. For the PPO/CO₂/CH₄ system, the methane permeability data lie above the predictions of all three models, whereas CO₂ data lie below the predictions of all models. Consequently, the competitive sorption/diffusion model gives the most accurate prediction for CO₂, while the simple competitive sorption model is best for methane. The effects of mixed gas sorption, fugacity, and CO₂-induced dilation were considered and do not explain the inaccuracies of any of the models. The relatively small errors in mixed gas permeability predictions using either of the three models are likely to be related to “transport plasticization” of PPO owing to high levels of CO₂ sorption and its effect on polymer segmental motions and gas diffusivity.     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

Pressure and temperature dependence of the gas‐transport properties of dense poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] membranes

The gas‐transport properties of poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] (6FDA‐2,6‐DAT) have been investigated. The sorption behavior of dense 6FDA‐2,6‐DAT membranes is well described by the dual‐mode sorption model and has certain relationships with the critical temperatures of the penetrants. The solubility coefficient decreases with an increase in either the pressure or temperature. The temperature dependence of the diffusivity coefficient increases with an increase in the penetrant size, as the order of the activation energy for the diffusion jump is CH₄ > N₂ > O₂ > CO₂. Also, the average diffusion coefficient increases with increasing pressure for all the gases tested. As a combined contribution from sorption and diffusion, permeability decreases with increases in the pressure and the kinetic diameter of the penetrant molecules. Even up to 32.7 atm, no plasticization phenomenon can be observed on flat dense 6FDA‐2,6‐DAT membranes from their permeability–pressure curves. However, just as for other gases, the absolute value of the heat of sorption of CO₂ decreases with increasing pressure at a low‐pressure range, but the trend changes when the feed pressure is greater than 10 atm. This implies that CO₂‐induced plasticization may occur and reduce the positive enthalpy required to create a site into which a penetrant can be sorbed. Therefore, a better diagnosis of the inherent threshold pressure for the plasticization of a glassy polymer membrane may involve examining the absolute value of the heat of sorption as a function of pressure and identifying the turning point at which the gradient of the absolute value of the heat of sorption against pressure turns from a negative value to a positive one. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 354–364, 2004     

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 plasticization on the transport of gases in and through glassy polymers

The effects of plasticization on the transport of gases and vapors in and through glassy polymers are examined from the viewpoint of the “dual-mode” sorption model with partial immobilization. The analysis assumes the existence of two penetrant populations with different mobilities in the Henry's law and Langmuir domains of the glassy polymers. These mobilities are characterized by their mutual diffusion coefficients D_D and D_H. The plasticization of the polymer by penetrant gases is reflected in the concentration dependence of D_D and D_H. Expressions for the effective (apparent) diffusion and permeability coefficients are derived assuming that D_D and D_H are exponential functions of the penetrant concentration in the polymers. The results of this study are compared with a similar analysis which assumed the existence of a single mobile penetrant population. The present analysis provides information on the effects of plasticization on the penetrant transport in the Henry's law and Langmuir domains separately. The effects of antiplasticization or clustering of penetrant molecules on the effective diffusion and permeability coefficients are also examined.