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     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

A predictive approach based on the Simha–Somcynsky free‐volume theory for the effect of dissolved gas on viscosity and glass transition temperature of polymeric mixtures

The gas concentration and pressure effects on the shear viscosity of molten polymers were modeled by using a unified approach based on a free volume theory. A concentration and pressure dependent “shift factor,” which accounts for free volume changes associated with polymer‐gas mixing and with variation of absolute pressure as well as for dilution effects, has been herein used to scale the pure polymer viscosity, as evaluated at the same temperature and atmospheric pressure. The expression of the free volume of the polymer/gas mixture was obtained by using the Simha and Somcynsky equation of state for multicomponent fluids. Experimental shear viscosity data, obtained for poly(ε‐caprolactone) with nitrogen and carbon dioxide were successfully predicted by using this approach. Good agreement with predictions was also found in the case of viscosity data reported in the literature for polystyrene and poly(dimethylsiloxane) with carbon dioxide. Free volume arguments have also been used to predict the T_g depression for polystyrene/carbon dioxide and for poly(methyl methacrylate)/carbon dioxide mixtures, based on calculations performed, again, with the Simha and Somcynsky theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1863–1873, 2006     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

Sorption and diffusion of carbon dioxide in wood‐fiber/polystyrene composites

In this study, sorption and diffusion of carbon dioxide (CO₂) in wood‐fiber/polystyrene composites were investigated. The effects of gas pressure and fiber content on the solubility and diffusion coefficients were evaluated. A statistical analysis indicated that pressure is more important than fiber content in determining the solubility and diffusivity of CO₂. An increase in saturation pressure causes an increase in the solubility and diffusion coefficients, whereas inclusion of the fibers decreases both of these properties. Models were developed to predict the uptake and diffusion coefficients of CO₂ in the composite samples as functions of pressure and fiber content. A theoretical model based on Henry's law and the Langmuir equation compared favorably to the experimental data for CO₂ solubility. This dual mode model also described both the transient sorption and desorption data, but only if the concentration‐dependent value of diffusivity was treated as a history‐dependent parameter. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 723–735, 2002     

Solubility and partial molar volume of carbon dioxide and ethane in crosslinked poly(ethylene oxide) copolymer

Experimental solubility and sorptive dilation data are reported for carbon dioxide and ethane in a crosslinked poly(ethylene oxide) (XLPEO) rubbery copolymer. Five different temperatures (253 ≤ T(K) ≤ 308) were considered, with a maximum gas pressure of 2.09 MPa (20.6 atm). The polymer was prepared by photopolymerization of a solution containing 70 wt % poly(ethylene glycol) methyl ether acrylate (PEGMEA) and 30 wt % poly(ethylene glycol) diacrylate (PEGDA). Sorption isotherms were described by the Flory‐Huggins model. For each gas, the Flory‐Huggins interaction parameter was a decreasing function of temperature and did not show a composition dependence. Dilation and sorption data were combined to calculate the partial molar volume (PMV) of the gases in the polymer, which was an increasing function of temperature. Based on a comparison with literature data for a XLPEO homopolymer prepared from pure PEGDA over the same range of operating conditions, an effect of the network composition on both gas solubility and PMV was found. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 456–468, 2010     

Dilation and plasticization of polystyrene by carbon dioxide

We have used an optical interference technique to measure the dilation of polystyrene films in the presence of carbon dioxide or helium at pressures up to 20 atm. Dilation isotherms (plots of dilation versus gas pressure at constant temperature) were obtained for three samples of polystyrene which had widely differing molecular weights. The dilation isotherms have the same general shape as sorption isotherms, which means that all of the sorbed gas molecules contribute to volume dilation and non can be thought of as occupying molecular-sized voids in the polymer. Using sorption results from the literature we show that the partial molar volume of CO₂ at 35°C is about 39 cm³ mol^?1 and appears to be independent of polystyrene molecular weight. For a polystyrene sample with M_n = 3600, the partial molar volume of sorbed CO₂ increases to 44 and 50 cm³ mol^?1 at 45 and 55°C, respectively. The sorption of CO₂ in polystyrene is shown to depress the glass transition temperature of the mixture, consistent with theoretical predictions. The shape of the dilation and sorption isotherms are consistent with the depression of the glass transition temperature.     

On the crystallinity effect on the gas sorption in semicrystalline linear low density polyethylene (LLDPE)

This article describes the solubility of carbon dioxide, ethylene and propane in 1‐octene based polyethylene of 0.94, 0.92, 0.904, and 0.87 densities. The isotherms obtained in the gas sorption experimental device display a sorption behavior similar to that of glassy polymers. We apply the dual model to semicrystalline polymers assuming that Henry's sites are related to the amorphous phase, which decreases when the crystallinity percentage increases, whereas the surface of the crystalline phase acts as a Langmuir site with higher gas‐polymer affinity than glassy polymers. The good concordance of the calculated k_D values, using the Flory‐Huggins theory of polymer diluent mixtures, with the experimental results suggest that Henry's gas sorption fulfills this theory and, therefore, it may be a suitable way to estimate polymer‐gas enthalpic interactions. Particularly, the variation of k_D with the crystallinity fraction is exponential and the proportionality of the total sorption with the amorphous content seems only apparent. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1798–1807, 2007     

Carbon dioxide–poly(vinylidene fluoride) interactions at high pressure

The article reports on the behaviour of poly(vinylidene fluoride) in carbon dioxide at 42°C and 80°C and in a pressure range of 0.1–30 MPa. Experimental techniques for the measurement of gas mass uptake and polymer dilatation are described and the corresponding data are reported as mass sorption and dilatation isotherms, respectively. The mass uptake experiment was also used to follow the evolution of the coefficient of diffusion of carbon dioxide into the polymer as a function of pressure or concentration. An analysis for the calculation of the partial molar volume of carbon dioxide as a function of pressure is also given, which shows that the ‘apparent’ partial molar volume of the carbon dioxide decreases with pressure to very low values, at high pressure. The computed values are significantly less than those for either the liquid or the solid phases of pure carbon dioxide, and also lower than some data previously reported for silicone elastomers. A consideration of the origins of this apparent anomaly is given in the conclusions. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2435–2447, 1998     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures

The sorption of carbon dioxide in poly(lactic acid) (PLA) was studied by quartz crystal microbalance at high pressures. To address the effect of the D isomer present in the polymer on the gas sorption, measurements were performed in PLA with two different L:D contents, 80:20 and 98:2. New data for the solubility of carbon dioxide in PLA 80:20 and PLA 98:2 over a temperature range from 303.2 to 323.2 K and up to 5 MPa are presented. The results obtained were correlated with the dual‐mode sorption model and the Flory‐Huggins equation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1010–1019, 2006     

Sorption and partial molar volumes of C2 and C3 hydrocarbons in polypropylene copolymers

The sorption of C₂ and C₃ hydrocarbons in two ethylene–propylene copolymers and a propylene homopolymer and the simultaneous dilation of the polymers were measured at temperatures of 287–363 K and pressures up to 4 MPa. The sorption isotherms were well described by the Flory–Huggins theory of dissolution. Dilation isotherms in the form of elongation versus pressure were similar in shape to the corresponding sorption isotherms. Solubility coefficients, partial molar volumes, and Flory–Huggins interaction parameters were determined from these isotherms. The thermal expansivities of the hydrocarbons dissolved in the polymers were 0.002–0.005 K^?1, and the Flory–Huggins interaction parameters depended not only on temperature but also on concentration. At 323 K, the calculated solubilities of propylene in the ethylene–propylene‐rubber regions of the copolymers were 1.8 times higher than in the amorphous regions of the propylene homopolymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1255–1262, 2001     

Raman spectroscopic investigation of the phase behavior and phase transitions in a poly(methyl methacrylate)‐carbon dioxide system

Laser Raman spectroscopy, in conjunction with an optical high‐pressure cell, was used to investigate the poly(methyl methacrylate)‐carbon dioxide system. The Raman shifts associated with carbon dioxide molecules in the gas phase and those dissolved in the polymer were used to derive sorption kinetics of carbon dioxide and the carbon dioxide‐induced phase changes in the polymer. Measurements were made in the temperature and pressure ranges in which this system is known to exhibit retrograde vitrification behavior. The Raman results on the sorption kinetics and on the onset of plasticization were in agreement with those obtained by gravimetric and calorimetric techniques, respectively. This technique provides a versatile and rapid way of characterizing polymer‐gas systems and information that so far has been obtainable only through painstaking and time‐consuming techniques. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2214–2217, 2003     

Swelling and sorption in polymer–CO2 mixtures at elevated pressures

Experimental data on gas sorption and polymer swelling in glassy polymer—gas systems at elevated pressures are presented for CO₂ with polycarbonate, poly(methyl methacrylate), and polystyrene over a range of temperatures from 33 to 65°C and pressures up to 100 atm. The swelling and sorption behavior were found to depend on the occurrence of a glass transition for the polymer induced by the sorption of CO₂. Two distinct types of swelling and sorption isotherms were measured. One isotherm is characterized by swelling and sorption that reach limiting values at elevated pressures. The other isotherm is characterized by swelling and sorption that continue to increase with pressure and a pressure effect on swelling that is somewhat greater than the effect of pressure on sorption. Glass transition pressures estimated from the experimental results for polystyrene with CO₂ are used to obtain the relationship between CO₂ solubility and the glass transition temperature for the polymer. This relationship is in very good agreement with a theoretical corresponding-states correlation for glass transition temperatures of polystyrene-liquid diluent mixtures.     

Analysis of gas sorption in glassy polymers with the GAB model: An alternative to the dual mode sorption model

The suitability of the Guggenheim–Anderson–De Boer (GAB) model for the parameterization of gas sorption isotherms and their dependences on temperature is explored. The GAB model implies that molecules adsorb on inner surfaces of the polymer in multilayers, which contrasts with the assumptions of the classical Dual Mode Sorption (DMS) model which implies the simultaneous occurrence of Henry‐like dissolution and Langmuir's case I adsorption. The GAB model shows similar efficacy of the parameterization of the gas sorption isotherms in polymers as the DMS model. The isosteric heat of adsorption shows clear dependence on relative surface coverage for carbon dioxide sorption in cellulose acetate, polyethylene terephthalate, and the first polymer of intrinsic microporosity (PIM‐1), thus allowing for the occurrence of adsorption multilayers. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1490–1495     

Neutron reflectivity study of glassy polymer brushes in density fluctuating supercritical carbon dioxide

By using in situ neutron reflectivity, we measured the swelling behavior of two types of polymer brushes, deuterated polystyrene with a trichlorosilane end group and deuterated polystyrene-block-poly(4-vinylpyridine) block copolymer, in supercritical carbon dioxide (scCO₂). The measurements were conducted in the pressure range of 0.1–20 MPa at 36 °C. The pressure dependence of the brush height clearly showed an anomalous peak at the density fluctuation ridge (pressure = 8.2 MPa) that defined the maximum long-range density fluctuation amplitude in the pressure–temperature phase diagram of carbon dioxide (CO₂). The density profile of the brush, which could be approximated by a simple step function, and the magnitude of the brush height both indicated that the solvent quality of scCO₂ for the deuterated polystyrene brushes was still poor even at the density fluctuation ridge. In addition, atomic force microscopy images for the frozen polystyrene brush prepared by the rapid drying of CO₂ showed a phase-separated structure, as predicted from the numerical calculations of Grest and Murat, as a function of the variable Nσ, where N is the polymerization index and σ is the grafting density. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3282–3289, 2004     

Sorption of methanol/MTBE and diffusion of methanol in 6FDA–ODA polyimide

This article discusses the diffusion and solubility behavior of methanol/methyl tert‐butyl ether (MTBE) in glassy 6FDA–ODA polyimide prepared from hexafluoroisopropylidene 2,2‐bis(phthalic anhydride) (6FDA) and oxydianiline (ODA). The diffusion coefficients and sorption isotherm of methanol vapor in 6FDA–ODA polyimide at various pressures and film thicknesses were obtained with a McBain‐type vapor sorption apparatus. Methanol/MTBE mixed‐liquid sorption isotherms were obtained by head‐space chromatography and compared with a pure methanol sorption isotherm obtained with a quartz spring balance. Methanol sorption isotherms obtained with the two methods were almost identical. Both methanol sorption isotherms obeyed the dual‐mode model at a lower activity, which is typical for glassy polymer behavior. The MTBE was readily sorbed into the polymer in the presence of methanol, but the MTBE sorption isotherm exhibited a highly nonideal behavior. The MTBE sorption levels were a strong function of the methanol sorption level. Methanol diffusion in the polymer was analyzed in terms of the partial immobilization model with model parameters obtained from average diffusion coefficients and the dual‐mode sorption parameters. Simple average diffusion coefficients were obtained from sorption kinetics experiments, whereas the dual‐mode sorption parameters were obtained from equilibrium methanol sorption experiments. An analysis of the mobility and solubility data for methanol indicated that methanol tends to form clusters at higher sorption levels. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2254–2267, 2000     

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.     

Sorption and pervaporation properties of sulfonyl‐containing polyimide membrane to aromatic/non‐aromatic hydrocarbon mixtures

Sorption of single‐component vapors of benzene (Bz), n‐hexane (Hx), and cyclohexane (Cx), and of binary liquid mixtures of Bz/Hx and Bz/Cx in a polyimide from 3,3′,4,4′‐diphenylsulfone‐tetracarboxylic dianhydride (DSDA) and 2,8(6)‐dimethyl‐3,7‐diaminobenzothiophene‐5,5‐dioxide (DDBT) were investigated in detail at 333 K. Sorption and desorption of vapors followed the non‐Fickian kinetics and the sorption isotherms were concave to the vapor activity. For the binary liquids, the sorption isotherms of the Bz component were concave to the Bz composition in feed, whereas those of Hx and Cx were convex because of competitive sorption. As a result, the solubility selectivity was much larger than the sorption ratio of pure liquids. The concentration‐averaged diffusion coefficients of Bz (D̄_Bz) and Hx (D̄_Hx) were evaluated using the sorption and pervaporation data of the polyimide membrane toward the binary mixtures. A kind of coupling effect of the coexisting component on D̄ was observed. That is, D̄ of penetrant with smaller molecular size (Hx and Bz for Bz/Hx and Bz/Cx systems, respectively) was reduced by the presence of penetrant with larger molecular size (Bz and Cx, respectively) and vice versa. D̄_Bz was similar to D̄_Hx, but much larger than D̄_Cx. The difference in PV behavior between Bz/Hx and Bz/Cx systems for glassy polymer membranes was understood based on the aforementioned features of sorption and diffusion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2954–2964, 2000     

High‐pressure sorption of carbon dioxide and methane in all‐aromatic poly(etherimide)‐based membranes

The sorption of compressed carbon dioxide and methane in a series of all‐aromatic poly(etherimide) (PEI) thin films is presented. The polymer films are derived from the reactions between an arylether diamine (P1) and four different dianhydrides [3,3′,4,4′‐oxydiphthalic dianhydride (ODPA), 3,3′,4,4′ biphenyltetra‐carboxylic dianhydride (BPDA), 3,3′,4,4′‐benzo‐phenonetetracarboxylic dianhydride (BTDA), and pyromellitic dianhydride (PMDA)] that have been selected to systematically change the flexibility of the polymer backbone, the segmental mobility, and the nonequilibrium excess free volume (EFV) of the polymer. The EFV, gas sorption capacities, and sorption‐ and temperature‐induced dynamic changes in film thickness and refractive index have been investigated by spectroscopic ellipsometry. The sorption capacity depends to a great extent on the PEI backbone composition. PMDA‐P1 shows the highest carbon dioxide sorption, combined with the lowest sorption selectivity because of the predominant sorption of methane in the EFV. For ODPA‐P1, the highest sorption selectivity is obtained, while it shows little long‐term relaxations at carbon dioxide pressures up to 25 bar. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 986–993     

Sorption and swelling of poly(DL‐lactic acid) and poly(lactic‐co‐glycolic acid) in supercritical CO2: An experimental and modeling study

Tissue engineering scaffolds require a controlled pore size and structure to host tissue formation from cell populations. Supercritical carbon dioxide (scCO₂) processing can be used to form porous scaffolds in which the escape of CO₂ from a plasticized polymer melt generates gas bubbles that shape the pores. The process is difficult to control with respect to changes in final pore size, porosity, and interconnectivity, while the solubility of CO₂ in the polymers strongly affects the foaming process. An in‐depth understanding of polymer CO₂ interaction will enable a successful scaffold processing. Amorphous poly(DL ‐lactic acid) (P_DL LA) and poly(lactic acid‐co‐glycolic acid) (PLGA) polymers are attractive candidates for fabricating scaffolds. In this study, CO₂ sorption and swelling isotherms at 35 °C and up to 200 bar on a variety of homo‐ and copolymers of lactic acid and glycolic acids are presented. Sorption is measured through a gravimetric technique using a suspension microbalance and swelling by visualization. The obtained results are modeled using the Sanchez‐Lacombe equation of state. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 483–496, 2008