Effect of antiplasticization on gas sorption and transport. II. Poly(phenylene oxide)

The propensity for various diluents to cause antiplasticization of poly(phenylene oxide) was examined and compared with similar responses for polysufone. Of the diluents used, none resulted in significant stiffening of poly(phenylene oxide) at 35°C relative to what was observed for polysulfone in an earlier paper. However, these diluents did cause substantial reduction in gas sorption levels and permeability coefficients. The latter is consequently a more sensitive indicator of changes in molecular motions of glassy polymers caused by diluents. The permeability response of adding low molecular weight diluents is compared with that of adding a high molecular weight polymer, polystyrene, to poly(phenylene oxide). The data were analyzed and interpreted along lines used in the companion paper for polysulfone.     

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.     

Effect of antiplasticization on gas sorption and transport. III. Free volume interpretation

Previous papers have shown that antiplasticization of polysulfone and poly(phenylene oxide) by low molecular weight diluents is accompanied by substantial reductions in permeability to gases like helium, carbon dioxide, and methane because of reduced mobility in the glass. These effects are not explained even qualitatively by the extent of volume contraction on mixing for these mixtures. However, as shown here, a simple free volume treatment provides an excellent correlation of these effects. Free volume was computed from measured specific volume and an estimate of the volume at the absolute zero of temperature of the material from a group contribution method. Application of this approach to the mechanical stiffening associated with antiplasticization is suggested. The basis and limitations of this analysis are discussed.     

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.     

Influence of the organic compounds addition in the polymer free volume,gas sorption and diffusion

Three low molecular compounds were added to a glassy polymer, poly(amino-ether) resin, in order to change its free volume and to study the subsequent effect in transport properties. Free volume characterization was carried out using the positron annihilation lifetime spectroscopy technique. Two electrobalances were used to obtain carbon dioxide sorption kinetic. Diffusion coefficient variation is in good agreement with the additive antiplasticizer character, i.e. the reduction of the free volume fraction. However, solubility is affected by other variables too, as the balance of the interactions between penetrant, additive and polymer as well as the effect of coming closer the sorption temperature to the glass transition temperature in the sorption mode.     

Gas sorption and transport in polysulfone

The sorption and transport of CO₂, CH₄, Ar, and N₂ were measured in a melt-extruded film of polysulfone at 35°C. The results are interpreted in terms of the dual sorption and mobility models and compared to the structurally similar glassy polycarbonate. In addition, sorption measurements were made on specimens with various processing and treatment histories including porous membranes prepared by water coagulation of concentrated polysulfone solutions in DMF and THF. The sorption capacity for CO₂ varied considerably with the history of the specimen.     

Recent theories of gas sorption in polymers

Theories and models are presented for gas sorption in polymers above and below the glass transition temperature. With the exception of predictive theories that do not represent the data well, the models are fit to data for the carbon dioxide/silicone rubber and carbon dioxide/polycarbonate systems for the purposes of comparison. During the past decade, a number of new models and theories have been proposed specifically for gas sorption in glassy polymers. Each new model attempts to incorporate aspects of the gas sorption process that are unique to polymers below the glass transition temperature. This review discusses these recent advances, the assumptions used in their development and their advantages and disadvantages.     

Reversible isopentane-induced depression of carbon dioxide permeation through polycarbonate

Permeability data are reported for carbon dioxide in Lexan polycarbonate at 35°C. Measurements were made for both pure carbon dioxide and for a mixed feed consisting of carbon dioxide with a 117.8-torr (0.155-atm) Partial pressure of isopentane. The effects of varying upstream CO₂ driving pressure from 1 up to 20 atm were studied. The permeability to CO₂ is reduced significantly in the presence of isopentane; however, the fractional depression of the CO₂ permeability due to the isopentane at low driving pressures is much more significant than at high CO₂ driving pressures. The well-known pressure dependence of carbon dioxide permeabilities in glassy polymers, therefore, is largely diminished by introducing isopentane to the pure carbon dioxide feed. These observations are consistent with a model for transport in glassy polymers which explains the observed trends in terms of competition between the two penetrants for microvoid sorption sites existing in the non-equilibrium glassy polymer. Exclusion of carbon dioxide from microvoid sorption sites by the more condensable isopentane preempts transport through the microvoid regions, resulting in the observed depression of the CO₂ permeability.     

Glassy polymer‐sorption phenomena measured with a quartz crystal microbalance technique

The quartz crystal microbalance (QCM) method is applied to the measurement of CO₂ sorption in glassy poly(ethylene terephthalate) (PET), poly(methyl methacrylate), and polysulfone. Polymer thin films in the thickness range of 350–550 nm are prepared by spin‐casting onto the quartz crystal devices. Sorption isotherms at temperatures below the glass transition are analyzed with the dual‐mode sorption model. As‐cast, quenched, and slow‐cooled thermal‐conditioning protocols yield consistent trends in the sorption level, namely, as‐cast > quenched > slow‐cooled. The sorption levels and model results for the quenched‐conditioned samples measured with QCM compare favorably with those reported from the pressure‐decay and gravimetric methods on thick films. With extended analysis of PET, the QCM technique is also useful for the exploration of the temperature dependence associated with gas sorption in glassy polymer systems. Measured heats of sorption and the collapse of the Langmuir component near the PET glass‐transition temperature agree with those reported previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2109–2118, 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.     

A quantitative model for the specific volume of polymer–diluent mixtures in the glassy state

A mathematical model to describe the specific volume of glassy mixtures of a polymer and a low molecular weight diluent or additive is presented. The model is based on understandable physical assumptions and relies on parameters that can be determined experimentally or estimated from methods available in the literature. The predictions of the model show good agreement with the experimental data for mixtures of four polymers with diluents that in the pure state are liquid, glassy, or crystalline. The observed negative departure from volume additivity, as defined by simple additivity of the specific volume of the pure glassy polymer and the pure amorphous diluent, is the result of the relaxation of the excess volume of the glassy mixture relative to the equilibrium state caused by mixing two components with different glass transition temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1037–1050, 1998     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Dynamic mechanical properties of plasticized polystyrene-based ionomers. I. Glassy to rubbery zones

The plasticizing effect of a nonpolar and a polar diluent in ionomers was studied by dynamic mechanical methods in the glassy to rubbery regions. Specifically, a carboxylate and a sulfonate polystyrene-based ionomer were investigated with variation of diethylbenzene content and of glycerol content. It was found that the nonpolar diluent plasticizes the transition by formation of ionic aggregates as well as lowering the glass transition temperature. However, the ionic regions of the carboxylate ionomer are plasticized more than those of the sulfonate ionomer. This corroborates the results of other studies which had found that the sulfonate groups in ionomers interact more strongly than the carboxylate groups. The polar diluent causes the ionic transition to disappear; this is probably due to solvation of the ions by the diluent.     

Mechanism of diffusion and sorption of carbon dioxide in poly(vinyl acetate) above and below the glass transition temperature

The pressure dependence below 1 atm of the apparent diffusion and permeation coefficients were observed by using the permeation time lag method for carbon dioxide in poly(vinyl acetate), which has a glass transition near room temperature, at temperatures ranging from 8 to 50°C. Above the glass transition temperature, pressure dependence of the diffusion and permeation coefficient has not been observed; hence, Fick's law with a concentration independent diffusion coefficient applies. On the other hand, in the glassy state, the apparent diffusion coefficient shows pressure dependence. Moreover, the behavior of the pressure dependence does not show a clear curve in the ranges between 30°C to 17°C. Above 17°C, the apparent diffusion coefficients show discontinuities, but below 17°C increase with pressure is regular. Using the theoretical prediction of Paul, a computer was used in the numerical calculation to determine the true diffusion coefficient and other dual sorption parameters. p]The compensated diffusion coefficients controlled only by Henry's law dissolution was described by three straight lines with two intersection in the form of Arrhenius plots, which give good agreement with both our results for He and Ar and those of Meares. It is assumed that beside the dual sorption mechanism, another effect, for instance some relaxation effect may also contribute to the diffusion for carbon dioxide in poly(vinyl acetate) near the glass transition temperature region.     

Permeation of carbon dioxide through homogeneous and asymmetric polysulfone membranes

To confirm the validity of the working assumption that a thin dense skin layer in an asymmetric membrane can be essentially replaced by a thick homogeneous dense membrane, both homogeneous and asymmetric polysulfone membranes were prepared by solvent casting, and the permeation behavior of carbon dioxide through these two types of membranes was investigated. The pressure dependence of the mean permeability coefficient through an asymmetric polysulfone membrane is apparently very similar to that through a homogeneous dense membrane, following the dual mode mobility model driven by gradients of chemical potential. The dense skin layer in the asymmetric membrane can be simulated approximately by a homogeneous dense membrane from the point of view of gas sorption and diffusion.     

Modeling of penetrant diffusion in glassy polymers with an integral sorption deborah number

A mathematical model was developed to explain the anomalous penetrant diffusion behavior in glassy polymers. The model equations were derived by using the linear irreversible thermodynamics theory and the kinematic relations in continuum mechanics, showing the coupling between the polymer mechanical behavior and penetrant transport. The Maxwell model was used as the stress–strain constitutive equation, from which the polymer relaxation time was defined. An integral sorption Deborah number was proposed as the ratio of the characteristic relaxation time in the glassy region to the characteristic diffusion time in the swollen region. With this definition, an integral sorption process was characterized by a single Deborah number and the controlling mechanism was identified in terms of the value of the Deborah number. The model equations were two coupled nonlinear differential equations. A finite difference method was developed for solving the model equations. Numerical simulation of integral sorption of penetrants in glassy polymers was performed. The simulation results show that (1) the present model can predict Case II transport behavior as well as the transition from Case II to Fickian diffusion and (2) the integral sorption Deborah number is a major parameter affecting the transition. © 1993 John Wiley & Sons, Inc.     

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

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

Transport of hexane vapor in polystyrene at 25°C I. Analysis of integral sorption data

A series of measurements of integral n-hexane vapor sorption at 25°C and moderate activity, in polystyrene microspheres of varying radii, exhibits typical non-Fickian behavior: nonoverlap of curves of fractional uptake versus (square root of time)/radius. The data are examined in light of a sorption isotherm indicating hexane solubility in excess of that predicted by the Flory–Huggins equation, up to the hexane activity at which the glass transition apparently occurs. A transport analysis is developed based on the assumption that below the transition temperature T_g the rate of sorption is limited by the rate of polymer chain relaxations induced by the penetrant, which facilitate hexane entry into, and immobilization in, glassy microvoids.     

Effect of water sorption on oxygen‐barrier properties of aromatic polyamides

Aromatic polyamides based on poly(m‐xylylene adipamide) (MXD‐based polyamides) and poly(hexamethylene isophthalamide) (HMD‐based polyamides) were examined. Insight into the excellent gas‐barrier properties was obtained by the characterization of the effect of water sorption on the thermal transitions, density, refractive index, free‐volume hole size, and oxygen‐transport properties. Reversing the carbonyl position with respect to the amide nitrogen substantially lowered the oxygen permeability of MXD‐based polyamides in comparison with that of HMD‐based polyamides by facilitating hydrogen‐bond formation. The resulting restriction of conformational changes and segmental motions reduced diffusivity. The primary effect of water sorption was a decrease in the glass‐transition temperature (T_g) attributed to plasticization by bound water. No evidence was found to support the idea that sorbed water filled holes of free volume. When the polymer was in the glassy state, the drop in T_g accounted for hydration‐dependent changes in the density, refractive index, and free‐volume hole size. The correlation of the oxygen solubility with T_g and density confirmed the concept of oxygen sorption as filling holes of excess free volume. In some cases, water sorption produced a glass‐to‐rubber transition. The onset of rubbery behavior was associated with a minimum in the oxygen permeability. The glass‐to‐rubber transition also facilitated the crystallization of MXD‐based polymers, which complicated the interpretation of oxygen‐transport behavior at higher relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1365–1381, 2005     

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