Pressure–volume–temperature properties and free volume parameters of PEO/PMMA blends

Melt-miscible polymer blends of poly(ethylene oxide)/atactic poly(methyl methacrylate (PEO/a-PMMA)) were prepared by melt-mixing and characterized by pressure–volume–temperature (PVT) dilatometry in the pressure and temperature range of 0 to 200 MPa and 20 to 200°C, respectively. The PVT data were analyzed in terms of two equations of state (EOS). The empirical Tait EOS was applied in the glassy, semicrystalline, and equilibrium melt state, and the Simha-Somcynsky EOS theory was applied in the equilibrium melt and glassy state. The Simha-Somcynsky EOS theory contains a free volume function. The temperature, pressure, and composition dependence of the free volume fraction h calculated from the Simha-Somcynsky EOS theory was studied. As a function of blend composition we observe that the free volume fraction, thermal expansivity, and compressibility all deviate mainly positively from linearity while the specific volume deviates mainly negatively from linearity. These findings are reconciled with composition-dependent free volume parameters, the free volume and cell volume as well as with self- and cross-interaction parameters derived from the Simha-Somcynsky EOS theory as applied to polymer mixtures. Moreover, the pressure dependence of glass and melting transitions as well as crystallization kinetics have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1061–1080, 1998     

Chromatographic investigation of the effect of dissolved carbon dioxide on the glass transition temperature of a polymer and the solubility of a third component (additive)

The effect of dissolved carbon dioxide on the glass transition temperature of a polymer, PMMA, has been investigated using molecular probe chromatography. The probe solute was iso-octane, and the specific retention volumes of this solute in pure PMMA and mixtures of PMMA with CO₂ were measured over a temperature range of 0 to 180°C and CO₂ pressures from 1 to 75 atm. The amount of CO₂ dissolved in the polymer was calculated from a model fit to previously published solubility data determined chromatographically. Classical van't Hoff-type plots were used to determine the glass transition temperature of CO₂-impregnated PMMA from low pressure up to 46 atm of CO₂. Solvent-induced plasticization was observed with the glass transition temperature decreasing by about 40°C. At some pressures, glass transitions at low temperatures could not be determined from the van't Hoff plots because of the proximity of the polymer glass transition temperature to the gas–liquid transition temperature for CO₂. For these pressures, a new method was developed to determine the glass transition composition. The glass transition pressure was then calculated from the measured composition and temperature using an isotherm model. In every case, the glass transition temperature decreased linearly with increasing concentration of CO₂ in the polymer. However, at higher compositions, the glass transition pressure decreased with increasing composition and decreasing temperature. The observed retention volume of iso-octane with PMMA in a glassy state was correlated with an adsorption model developed from a theory for liquid–solid chromatography derived by Martire. This model accurately described the observed decrease in retention of iso-octane by adsorption on the surface of glassy PMMA with increasing concentration of CO₂ dissolved in the polymer. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2537–2549, 1998     

Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

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     

Understanding the effect of skin formation on the removal of solvents from semicrystalline polymers

The effect of glassy skin formation on the drying of semicrystalline polymers was investigated with a comprehensive mathematical model developed for multicomponent systems. Polymers with high glass‐transition temperatures can become rubbery at room temperature under the influence of solvents. As the solvents are removed from the polymer, a glassy skin can form and continue to develop. The model takes into account the effects of diffusion‐induced polymer crystallization as well as glassy–rubbery transitions on the overall solvent content and polymer crystallinity. A Vrentas–Duda free‐volume‐based diffusion scheme and crystallization kinetics were used in our model. The polymer–solvent system chosen was a poly(vinyl alcohol) (PVA)–water–methanol system. The drying kinetics of PVA films were obtained by gravimetric methods with swollen films with known water/methanol concentrations. The overall drying behaviors of the polymer system determined by our model and experimental methods were compared and found to match well. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3191–3204, 2005     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Interval kinetic gravimetric sorption of acetone in random copolymers of poly(ethylene terephthalate) and poly(ethylene 2,6-naphthalate)

Interval sorption kinetics of acetone in solvent cast films of random poly(ethylene terephthalate)-co-(ethylene 2,6-naphthalate) (PET-co-PEN) are reported at 35°C and at acetone pressures ranging from 0 to 7.3 cm Hg. Polymer composition is varied systematically from 0% to 50% poly(ethylene 2,6-naphthalate). Equilibrium sorption is well described by the dual-mode sorption model. Interval sorption kinetics are described using a two-stage model that incorporates both Fickian diffusion and protracted polymer structural relaxation. The incorporation of low levels of PEN into PET significantly reduces the excess free volume associated with the glassy state and, for these interval acetone sorption experiments in ∼ 5 μm-thick films, decreases the fraction of acetone uptake controlled by penetrant-induced polymer structural relaxation. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2973–2984, 1999     

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     

Transport of organic vapors through poly(1-trimethylsilyl-1-propyne)

Poly(1-trimethylsilyl-1-propyne) [PTMSP], a high-free-volume glassy polymer, has the highest gas permeability of any known synthetic polymer. In contrast to conventional, low-free-volume, glassy polymers, PTMSP is more permeable to large, condensable organic vapors than to permanent gases. The organic-vapor/permanent-gas selectivity of PTMSP based on pure gas measurements is low. In organic-vapor/permanent-gas mixtures, however, the selectivity of PTMSP is much higher because the permeability of the permanent gas is reduced dramatically by the presence of the organic vapor. For example, in n-butane/methane mixtures, as little as 2 mol% n-butane (relative n-butane pressure 0.16) lowers the methane permeability 10-fold from the pure methane permeability. The result is that PTMSP shows a mixed-gas n-butane/methane selectivity of 30. This selectivity is the highest ever observed for this mixture and is completely unexpected for a glassy polymer. In addition, the gas mixture n-butane permeability of PTMSP is considerably higher than that of any known polymer, including polydimethylsiloxane, the most vapor-permeable rubber known. PTMSP also shows high mixed-gas selectivities and vapor permeabilities for the separation of chlorofluorocarbons from nitrogen. The unusual vapor permeation properties of PTMSP result from its very high free volume - more than 20% of the total volume of the material. The free volume elements appear to be connected, forming the equivalent of a finely microporous material. The large amount of condensable organic vapor sorbed into this finely porous structure causes partial blocking of the small free-volume elements, reducing the permeabilities of the noncondensable permanent gases from their pure gas values.     

Oxygen transport as a solid‐state structure probe for polymeric materials: A review

In the quest to elucidate the solid‐state structures of polymers, insight into the amorphous phase is particularly elusive. Although the permeability of small molecules is often measured as an important performance property, numerous researchers have found that a deeper analysis of the transport characteristics provides insight into polymer morphology, especially if used in combination with more usual characterization techniques. The transport of small gas molecules senses the permeable amorphous structure and probes the nature of the free volume. In recent years, our interest in the gas barrier of polyesters has resulted in an unusual opportunity to investigate the nature of the free volume in the polymer glassy state. This effort has been aided by access to aromatic polyesters with designed variations in their chemical structure. This review focuses on oxygen transport, supplemented with other methods of physical analysis, as a probe of the excess‐hole free volume. The review addresses the profound effects of orientation and crystallization on the free volume of the glassy state. The discussion also presents a simple odel for the gas permeability of the isotropic glass based on lattice concepts and tests more sophisticated models for the gas permeability of semicrystalline polymers. The final section addresses other opportunities for fruitful applications of oxygen transport as a solid‐state structure probe. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1047–1063, 2005     

Solution and Diffusion Behavior of Pure Gases and Gas Mixtures in Glassy Polymer Membranes

A general model for the solution and diffusion behavior in pure gas-polymer membrane systems and gas mixture-polymer membrane systems has been developed. Proved by experiments on different glassy and rubbery polymer membranes at various temperatures and pressures, this model can achieve the prediction of permeation behavior of pure gases and gas mixtures in polymer membranes only using the model parameters obtained from experiments on pure gases. The calculated results are in good agreement with experimental.     

Photopolymerization of nematic liquid crystal monomers for structural applications: Linear viscoelastic behavior and cure effects

This article is concerned with molecular orientation in liquid crystal (LC) monomers and the retention of orientation in crosslinked network polymers formed from them by photopolymerization. This is of importance because anisotropic mechanical and physical properties can be beneficial in certain structural applications. To this end, linear viscoelastic behavior of liquid crystal photo-monomers was investigated with dynamic mechanical analysis, and molecular order was studied by infrared dichroism measured with Fourier transform infrared spectroscopy. Although the order parameter of the monomer could vary from 0.45 to 0.70, depending on temperature, the order parameters of the polymer samples varied only from 0.50 to 0.62 and depended on polymerization temperature and extent of cure. The mechanical anisotropy was found to be a complicated phenomenon that depended not only on the molecular order, but also on other factors such as free volume and network structure. The difference in the elastic modulus parallel and perpendicular to the alignment direction was as high as a factor of two in the glassy state, and a factor of three above T_g. In addition, different amounts of mechanical anisotropy could be induced by varying the cure conditions. Finally, different postcuring schemes could cause variations in mechanical behavior by advancing cure or by inducing secondary reactions. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1081–1089, 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     

Permeation and separation of benzene/cyclohexane mixtures through liquid-crystalline polymer membranes

The side-chain liquid-crystalline polymer (LCP) was synthesized by the addition of the mesogenic monomer to poly(methylsiloxane) with Pt catalyst. When the benzene/cyclohexane mixtures were permeated through the LCP membranes by pervaporation at various temperatures, the permeation rate increased with increasing benzene concentration in the feed solution and permeation temperature. Though the LCP membranes exhibited a benzene permselectivity, a mechanism of the permeation and separation for the benzene/cyclohexane mixtures was different in the glassy, liquid-crystalline and isotropic state of the LCP membranes. These results suggested that the permselectivity was fairly influenced by the change of the LCP membrane structure, that is, a state transformation. It was found that a balance of the orientation of mesogenic groups and flexibility of siloxane chains is very important for the permeability and selectivity. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 699–707, 1997     

Sensing the glass transition in thin and ultrathin polymer films via fluorescence probes and labels

Fluorescence was used to characterize the glass transition in thin and ultrathin supported polymer films with common chromophores. The temperature dependence of the fluorescence intensity exhibits a transition or break upon cooling from the rubbery state to the glassy state, and this is identified as the glass transition. A variety of chromophores are investigated including pyrene, anthracene, and phenanthrene either as dopants, covalently attached to the polymer as a label, or both. The particular choice of the chromophore as well as the nature of the attachment, in the case of labels, have significant impact on the success of this method. Problematic cases include those in which the excited‐state chromophore undergoes significant photochemistry in addition to fluorescence or those in which the particular attachment of the chromophore as a label may allow for conformational interactions that affect the fluorescence quantum yield in a nontrivial way. Polymers that have an intrinsic fluorescence unit, for example, polystyrene, may allow for the fluorescence sensing of the glass transition without added dopants or labels. Finally, it is demonstrated that this technique holds promise for the study of the glass transition in polymer blends and within specific locations in multilayer films. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2745–2758, 2002     

Diffusion in gas separation membrane materials: A comparison and analysis of experimental characterization techniques

Typically, materials with high-performance transport properties such as zeolites, carbon molecular sieves, or hyper rigid polymers are inherently difficult or impossible to characterize by steady-state membrane permeation experiments used for conventional polymers. Diffusion coefficients determined by transient sorption, a measurement easily performed on brittle media, are analyzed here and compared to those determined by steady-state permeation/sorption and transient permeation for a glassy polymer and a carbon molecular sieve. Average and local diffusion coefficients are extrapolated to zero upstream partial pressure to eliminate effects caused by concentration dependence. Good agreement between the techniques was observed for the glassy polymer. On the other hand, carbon molecular sieves, possessing a more complex morphology, exhibit a greater difference in diffusion coefficients determined by the various techniques. Nevertheless, comparison of the analysis techniques is shown to provide potentially valuable insights into the morphological features of such carbon molecular sieves. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1747–1755, 1998     

PVT properties of dodecane/polystyrene systems

The PVT properties of crosslinked polystyrene samples containing various amounts of dodecane were measured. The Tait equation was used to describe the PVT behavior of each system in both the glassy and rubbery regions. The glass transition temperature was determined from the abrupt change of the thermal expansion coefficient. Increase in the dodecane content in the samples resulted in a significant decrease of the difference between the expansion coefficients in the glassy and rubbery regions. Addition of dodecane lowered the glass transition temperature linearly. However, the dependence of the glass transition temperature on pressure was not affected by the presence of dodecane in the polymer samples. Above the glass transition temperature, the volume of the swollen polymer, V_m, could be determined by simple addition of the volumes of the pure components at the appropriate temperature and pressure; the volume change of mixing, δV_m, was independent of temperature and pressure. Below the glass transition temperature, volume additivity of the two components was also applicable after appropriate adjustment of the glass transition temperature of the polymer to that of the dodecane/polymer samples. © 1994 John Wiley & Sons, Inc.     

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     

Multiple glass transitions and local composition effects on polymer solvent mixtures

Recent differential scanning calorimetry (DSC) results on polystyrene–solvent mixtures show two distinct glass transitions whose positions and widths vary with composition. Parallel work on the dynamic response in polymer blends has focused on how segmental mobilities are controlled by local composition variations within a “cooperative volume” containing the segment. Such variations arise from both chain connectivity and composition fluctuations. We account for both using a lattice model for polymer–solvent mixtures that yields the composition distribution around polymer and solvent segments. Insights from our lattice model lead us to simplified calculations of the mean and variance of local composition, both in good agreement with lattice results. Applying our model to compute DSC traces leads to an estimate of the cooperative volume, since a larger cooperative volume both reduces the biasing effect of connectivity, and narrows the composition distribution. Comparing our results to data, we are able to account for the composition-dependent broadening with a cooperative length scale of about 2.5 nm. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3528–3545, 2006     

Gas solubility and permeability in MFA

An experimental analysis has been performed in this work, aimed to the characterization of thermodynamic and mass transport properties of a semicrystalline fluoro polymer (MFA) obtained from the copolymerization of tetrafluoroethylene (TFE) and perfluoromethylvinylether. Sorption and permeation experiments for two alkanes and corresponding perfluorinated compounds in MFA were performed at two different temperatures and solubility coefficients, as well as diffusivity and permeability, were determined. Experimental data were analyzed through different thermodynamic models to draw general conclusions about properties of MFA polymeric phases. Special attention was devoted to the glassy nature of MFA polymeric mixtures around room temperature. Indeed, analysis of experimental sorption data was performed through the use of specific models for glassy polymeric phases as well as by means of classical equilibrium models for fluid mixtures. Conclusions have been drawn from the aforementioned analysis, which significantly contributes to the discussion of correct location of glass‐transition temperature for PTFE and its copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1637–1652, 2007