Basic studies on gas solubility in natural rubber–cellulose composites

This work reports sorption processes of oxygen, carbon dioxide, methane, ethylene, and propylene in films of both vulcanized natural rubber and vulcanized rubber–regenerated cellulose composites. The curves representing the pressure dependence of the concentration of carbon dioxide in the composites clearly exhibit a slight concavity with respect to the abscissa axis as a result of adsorption processes taking place in Langmuir sites located in the glassy cellulose component. Adsorption processes are also detected in the sorption curves of ethylene at low pressures. The concavity with respect to the ordinate axis of the curve concentration of propylene versus pressure at high pressure is pretty well described by the Flory‐Huggins formalism. The solubilities of the other gases mainly obey Henry's behavior, adsorption processes in the glassy component being in most cases negligible. Values of the interaction χ parameter for gas–natural rubber and gas–natural rubber composites are obtained from the comparison of the experimental solubility coefficients with those predicted by the Flory‐Huggins theory. The theory suggests that Henry's constant is a linear function of the boiling temperature of the gases. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2131–2140, 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     

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     

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     

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     

Sorption of light gases in glassy poly(ethyl methacrylate)

Although gas sorption in glassy polymers is a well‐studied phenomenon, no general microscopical model is developed which is able to describe the gas sorption in a wide temperature range using only characteristics of polymer and gas molecule. In this work, sorption isotherms and desorption kinetics of O₂, Ar, and N₂ for glassy poly(ethyl methacrylate) have been measured in the temperature range from 160 to 308 K. To describe both the phenomena, the model is developed which postulates that, in the frozen structure of glassy polymer, any cavities between macromolecules are the sorption sites for small molecules. The cavities of small size can expand elastically to accommodate a gas molecule. The sorption sites are considered to be the potential wells and their depths are distributed according to Gaussian law. The concentration of sorption sites, their mean depth and depths dispersion, and the frequency of molecules oscillations in the sorption sites are the only parameters which determine both the gas transport and sorption. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 288–296     

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.     

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     

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     

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.     

Investigation of thermodynamic properties of hyperbranched poly(ester amide) by inverse gas chromatography

Thermodynamic properties of the hyperbranched poly (ester amide) (Hybrane® 1200) were investigated by inverse gas chromatography (IGC) using 19 different solvents as the probes at infinite dilution. Retention data of probes were used for an extensive characterization of the polymer, which includes the determination of the Flory‐Huggins interaction parameter, the weight fraction activity coefficient, the total, partial, and additive solubility parameters. The analysis of the results indicated that the additive value of the solubility parameter is lower than the value obtained from a standard procedure. Furthermore, the solubility parameter decreases with increase of temperature. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2166–2172, 2008     

Gas sorption and diffusion processes in polymer matrices at high pressures

A theoretical approach has been developed to describe the processes of gases diffusion and sorption in rubbery and glassy polymers. Various models (Flory-Huggins, dual-mode sorption, gas-polymer-matrix) used for interpreting the sorption-diffusion experiments are discussed within this approach framework. Experimental data on carbon dioxide sorption in glassy and rubbery polymers have been considered using the proposed approach. The comparison of the experimental and theoretical data has permitted to make the conclusion on the developed concepts adequacy. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1339–1348, 1997     

Thermodynamic characterization of poly(2,2,3,3,3‐pentafluoropropyl methacrylate)

The thermodynamic characterization of a fluorinated methacrylic homopolymer was conducted by means of inverse gas chromatography (IGC), at infinite dilution. The homopolymer under study, poly(2,2,3,3,3‐pentafluoropropyl methacrylate) (PPFPMA), was synthesized via a free radical polymerization reaction and was characterized by the employment of Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and size exclusion chromatography (SEC) techniques. The specific retention volume of 15 solvents, used as probes, was used for the assessment of the Flory–Huggins interaction parameter, the weight fraction activity coefficient, the molar heat, energy and entropy of sorption, the partial heat of mixing of the probes, as well as the solubility parameter of the polymer. The results demonstrate that PPFPMA is insoluble in most organic solvents even at increased temperatures, with the exception of solvents like 2‐Butanone. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1826–1833, 2010     

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S‐shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S‐shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999     

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.     

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     

Thermodynamic model of gas permeability in polymer membranes

A new molecular thermodynamic model is developed of the gas permeability in polymer membranes on the basis of configurational entropy and Flory‐Huggins theory to predict permeability dependence on the concentration of penetrant. Three kinds of configurational entropy are taken into account by this model; that is, the disorientation entropy of polymer, the mixing entropy, and specific interaction entropy of polymer/gas. The validity of the mathematical model is examined against experimental gas permeability for polymer membranes. Agreement between experimental and predicted permeability is satisfactory. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 661–665, 2007     

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.     

A Self-Consistent Model for Sorption and Transport in Polyimide-Derived Carbon Molecular Sieve Gas Separation Membranes

Demand for energy-efficient gas separations exists across many industrial processes, and membranes can aid in meeting this demand. Carbon molecular sieve (CMS) membranes show exceptional separation performance and scalable processing attributes attractive for important, similar-sized gas pairs. Herein, we outline a mathematical and physical framework to understand these attributes. This framework shares features with dual-mode transport theory for glassy polymers; however, physical connections to CMS model parameters differ from glassy polymer cases. We present evidence in CMS membranes for a large volume fraction of microporous domains characterized by Langmuir sorption in local equilibrium with a minority continuous phase described by Henry's law sorption. Using this framework, expressions are provided to relate measurable parameters for sorption and transport in CMS materials. We also outline a mechanism for formation of these environments and suggest future model refinements.