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).     

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     

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.     

The effect of lattice compressibility on the thermodynamics of gas sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration-dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory-Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.     

Sorption and 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     

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.     

The effect of morphology on sorption and transport of carbon dioxide in poly(4,4'-oxydiphenylene pyromellitimide)

Sorption and transport of carbon dioxide were investigated for poly(4,4'-oxydiphenylene-pyromellitimide) films (PI-1, PI-2, and PI-3) imidized at 160, 200, and 400°C, respectively, as well as for a chemically identical commercial polyimide film, Kapton-H. The solubility, permeability, and diffusion coefficients (S, P, and \[ \overline D \] , respectively) at 80°C and 20 atm in PI-3 were 67, 25, and 37%, respectively, as large as those in PI-2. These significant reductions are attributed to a higher degree of segmental aggregation in PI-3 caused by a 1.7% increase in the density (d) as compared with PI-2. The differences in S, P, \[ \overline D \] , and d between PI-3 and Kapton-H were rather small as compared with those between PI-3 and PI-2, suggesting that the in-plane orientation has a minor effect on the sorption and transport in Kapton-H as compared with the aggregation. Influence of the morphology on the dual-mode sorption and transport parameters was also investigated. With increasing density, the Langmuir capacity constant and the diffusion coefficients for the Henry's law and Langmuir populations decreased by higher rates than the Henry's law solubility constant, being contrary to the results reported for a typical semicrystalline glassy polymer, polyethylene terephthalate. This may suggest that the nonaggregated or less-aggregated regions taking an important part in the sorption and transport are denser for the sample having a higher overall density.     

Gas sorption in poly(vinyl benzoate)

High-pressure sorption (up to 50 atm) for CO₂, N₂, and Ar in poly(vinyl benzoate) (PVB) was studied at temperatures from 25 to 70°C by a gravimetric method utilizing an electromicrobalance. The results are described by Henry's law above the glass transition temperature T_g for all gases. The dual-mode sorption model, Henry's law plus a Langmuir isotherm, applies to the sorption isotherms of N₂ and Ar in the glassy state, and the dual-mode parameters are given. For CO₂, a new type of sorption isotherm is observed below T_g. The isotherm is concave to the pressure axis in the low-pressure region and turns into a straight line with increasing CO₂ pressure which can be extrapolated back to the coordinate origin. The linear part of the isotherm is characteristic of the rubbery state, while the nonlinear part stems from glassystate behavior. The “glass transition solubility” of CO₂, at which PVB film changes from the glassy to the rubbery state, decrease as the temperature increases. The disappearance of microvoids, that is, the decrease of the Langmuir capacity, may be due to a large plasticizing effect of sorbed CO₂. The difference between the N₂ and Ar isotherms and the CO₂ isotherm is discussed from this standpoint.     

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.     

Role and effect of dopant ion on sorption-induced motion of polypyrrole films

The sorption-induced bending and recovery motion of PPy films containing different dopant ions have been investigated, and the interaction between water vapor and PPy was studied from sorption isotherms and kinetics. It was found that the PPy/BF₄ film exhibited the most rapid motion, and the initial speeds of bending and recovery motion were 7.9 and 5.9 mm s⁻¹, respectively. The linear expansion coefficient of the film increased in order of PPy/DBS, PPy/TsO, PPy/ClO₄, and PPy/BF₄, which is consistent with the packing density of the PPy chains (ϕ_PPy). The dual-mode sorption model applied to the isothermal sorption of water vapor to the PPy demonstrated that the Langmuir's capacity constant increased in the same order with the ϕ_PPy, while the Henry's law constant was nearly constant. The sorption kinetics obeyed Fickian despite the dimensional change of the films, and the PPy/BF₄ film had the largest diffusion coefficient of 3.13 × 10⁻⁸ cm² s⁻¹. The experimental results indicated that the kind of dopant ion was crucial to the thermodynamics and kinetics of sorption, and the quick and intensive bending motion of PPy/BF₄ films was attributed to the fast diffusion of water vapor, which caused the large dimensional change of the film.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2635–2642, 1998     

Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory

Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient D_eff, which depends on the details of the microstructure. D_eff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.     

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.     

Effect of partially immobilizing sorption on permeability and the diffusion time lag

The gas permeability and diffusion time lag may exhibit varying degrees of pressure dependence for glassy polymers. The sorption isotherm appears to consist of contributions from both Langmuir and Henry's law terms in such systems. This “dual sorption” theory advanced in the literature pictures gas held by the Langmuir mode as being completely immobilized. In the present paper, this model is extended to accommodate different degrees of partial immobilization of gas sorbed by this mode using two different formulations. One uses a transport expression based on concentration gradients while the other is based on chemical potential gradients. The predictions are that: (1) total immobilization results in a constant permeability with a time lag which strongly decreases with pressure; (2) no immobilization results in a constant time lag with a permeability which decreases strongly with pressure; and (3) incomplete immobilization results in both the permeability and time lag decreasing with pressure but neither as strongly as in the other limiting cases. The differences which may arise by the two formulations of the model are discussed.     

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.     

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     

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.     

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.     

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.     

Transport of water and gases through EVA copolymer films,EVA70/PVC,and EVA70/PVC/gluten blends

The transport of water vapor and gases (oxygen or carbon dioxide) through poly(ethylene‐co‐vinyl acetate) (EVA) films of different VA contents and through EVA₇₀/PVC and EVA₇₀/PVC/gluten blend films, was analysed by permeation measurements. In the case of water, a plasticization effect on the material is observed for EVA films with more than 33percnt; wt. of VA content and also for the EVA₇₀/PVC blend. For EVA of 19 wt.percnt; VA, there is no plasticization, while for LDPE (low density polyethylene) and EVA of 4.5 wt.percnt; VA, the water diffusion coefficient decreases with increasing the water content. A negative plasticization effect was accounted for by an empirical model and attributed to the formation of water clusters in the non polar polymers. The increase in water sorption extent with the VA content leads to a steady increase in the water permeability in the EVA copolymers while for the EVA₇₀/PVC blend, the reduced water permeability is explained by the interaction between chlorinated units and polar groups. In the case of gas permeation, both for O₂ and CO₂ and whatever the VA content of the copolymer used, the experimental curves are characterized by a constant diffusion coefficient. This result is not surprising as it is generally admitted that, gases sorb into rubbery polymers according to Henry's law. By mixing PVC with the EVA of 70percnt; wt. VA, the diffusion coefficients of CO₂ and O₂ are greatly reduced (6 times).     

Gas transport in polymers based on bisphenol-A

Permeation measurements for CO₂, CH₄, O₂, N₂, and He were made with three polymers based on bisphenol-A, namely a polyhydroxyether, a polyetherimide, and a polyarylate. Measurements were also made for CO₂ and CH₄ in polysulfone. The data for CO₂, CH₄, and N₂ plus previous data for these gases in polycarbonate and polysulfone were combined with equilibrium gas sorption data and analyzed with the dual mode/partial immobilization model and the more recent gas-polymer-matrix model. A comparison of the two models was done on the basis of physical interpretations of the resulting parameters. The diffusion coefficient for the Henry's law population was related to the kinetic diameter of the gas. The infinite dilution, Henry's law, and Langmuir diffusion coefficients were related to the free volume of the polymer. The work suggests a means for order-of-magnitude estimation of diffusion coefficients from polymer density and molecular structure.