Impact of average free‐volume element size on transport in stereoisomers of polynorbornene. I. Properties at 35 °C

This article demonstrates that transport of gases through glassy polymers is significantly influenced not only by the absolute amount but also by the distribution of free volume. Two stereoisomers of polynorbornene with nearly equivalent total free volume, but markedly different average free‐volume sizes, were evaluated. The free‐volume element size was probed with positron annihilation lifetime spectroscopy, wide‐angle X‐ray scattering, gas sorption, and molecular modeling. The permeation, sorption, and diffusion of light gases were measured in each stereoisomer at 35 °C. All analytical techniques indicated that one isomer (labeled as Architecture II) had a larger average free‐volume element size but fewer elements. This isomer also had a very slightly higher bulk density (1.000 vs 0.992 g/cm³ for the other stereoisomer). Architecture II also had gas sorption and diffusion coefficients that were two to three times those of the less dense counterpart. These differences have been attributed to differences in the free‐volume element size available within the polymer matrix. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2185–2199, 2003     

Structural and free‐volume analysis for alkyl‐substituted palladium‐catalyzed poly(norbornene): A combined experimental and Monte Carlo investigation

Increasing the length of an alkyl side chain on a rigid polynorbornene (PNB) backbone is shown to decrease the glass‐transition temperature of the resultant polymer, decrease the density of the bulk polymer, decrease the number and average free‐volume element size present, and decrease the permeability of gases through the polymer. Methyl‐, butyl‐, and hexyl‐substituted PNBs were investigated. Experimental results were compared with predictions based on molecular modeling. By using models that provided good agreement between the experimental and simulated wide‐angle diffraction patterns, the distributions of free‐volume elements were predicted. These predictions clearly indicate that the number of large free‐volume elements decreases as the length of the side chain increases, suggesting that the flexible aliphatic side chains can be largely accommodated within the free volume between the rigid PNB backbones. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 215–233, 2006     

Prediction and estimation of solvent diffusivities in polyacrylate and polymethacrylates

The relationship between polymer side‐chain length and the hole free volume that is effective for solvent diffusion was investigated for polyacrylates and polymethacrylates on the basis of free‐volume theory. Measurements of a polymer's viscoelasticity and solvent diffusivity provided experimental evidence for polymer segment mobility, and the results indicated that hole free volume in a linear polymer increases with hydrocarbon side‐chain length. Because the molecular mechanisms of polymer viscoelasticity and diffusivity are identical, the free‐volume parameters obtained for polyacrylates and polymethacrylates by measuring the polymer viscoelastic‐temperature dependence can reliably be used in predicting the solvent diffusion coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1393–1400, 2003     

Solubility and diffusivity of methylmethacrylate and butylacrylate monomers in a MMA–BA copolymer

Mutual diffusion coefficients and sorption isotherms of methyl methacrylate (MMA) and butyl acrylate (BA) monomers in methyl methacrylate‐butyl acrylate copolymer (MMA‐BA) have been measured by gravimetric sorption. MMA is found to have higher solubility and diffusion rates in the copolymer than BA. Sorption data for MMA were interpreted using classical Flory‐Huggins thermodynamic theory with a constant interaction parameter (χ). A modified version of this theory has been applied to correlate the sorption data of BA, which exhibit a temperature and concentration‐dependent χ parameter. For MMA, the isotherm data reveal enhanced polymer‐solvent interactions with increasing temperature, while for BA the data indicate a drive toward phase separation with increasing temperature. Despite the difference in thermodynamic behavior, both monomers are found to exhibit Fickian diffusion and the diffusivity data are correlated reasonably well with the Vrentas‐Duda free volume theory. Some deviation between the free‐volume correlation and the experimental data is observed at the lowest temperature and BA concentration examined. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1996–2006, 2007     

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     

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

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

Experimental and theoretical investigation of anomalous sorption kinetics in the methanol vapor–poly(methyl methacrylate) system at 35 °C

Non‐Fickian sorption kinetics of methanol vapor in a poly(methyl methacrylate) film of 8 μm, at 35 °C, are presented. The behavior of the system was studied in series of interval absorption runs. The relevant diffusion and viscous relaxation processes were studied by kinetic analysis of the sorption kinetic curves, using the relaxation‐dependent solubility model. The sorption isotherm concaves upward at high activities, typical to Florry–Huggins behavior, while it exhibits a convex‐upward curvature at low methanol vapor activities, indicating sorption in the excess free volume of the polymer matrix. Thermodynamic diffusivity presents a complex functional dependence on the concentration, while relaxation rate is found to be a function of concentration as well as of concentration interval. Relaxation rate becomes increasingly concentration‐dependent as the effective glass transition of the system is approached. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3173–3184, 2006     

Stereoselective synthesis and polymerization of Exo‐5‐trimethylsilylnorbornene

Herein the stereoselective two‐step synthesis of pure exo‐5‐trimethylsilylnorbornene is reported. The monomer proved to be highly reactive in both metathesis and addition polymerization. ROMP polymerization was catalyzed by the first‐generation Grubbs catalyst. High‐molecular‐weight saturated addition polymers were prepared using nickel or palladium complexes as precatalysts and Na⁺[B(3,5‐(CF₃)₂C₆H₃)₄]⁻ and/or MAO as cocatalysts. The obtained addition polynorbornenes are highly gas permeable and microporous materials possessing large free volume and BET surface area (up to 540 m²/g). The influence of the substituent orientation (exo‐ vs. exo‐/endo‐mixture) on polymer properties was established. The metathesis polymer based on exo‐isomer exhibits 1.5‐ to 2‐fold increase of permeability coefficients for all gases in comparison to the similar polymer based on the mixture of exo‐ and endo‐isomers. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1234–1248     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Positron annihilation and free volume studies in polymer glasses

In this article, the interconnections between the ortho-positronium (the bound state of the positron and electron having parallel orientation of spins, ^TPs) pick-off annihilation characteristics and concentration and effective size of elementary free volumes in polymer structures are discussed. Free volume parameters are responsible for many important properties of polymers such as permeability to gases, selectivity, ageing mechanical strength, etc. However, the ways of quantitative estimations of size distributions of the free volume elements on the bases of experimental data are sometime not obvious. Various approaches to this problem are analyzed in this review mostly on examples of glassy polymer membrane materials. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2485–2503, 2008     

Light olefins/paraffins sorption in poly(lactic acid) films

The sorption behavior of small molecules like ethane and ethylene in poly (lactic acid) (PLA) was studied in the temperature interval from 283 to 313 K using a Quartz Crystal Microbalance (QCM). The effect of the polymer structure on the solubility selectivity of PLA films with respect to these two gases was studied using polymer with two different L:D ratios (98:2 and 80:20). Furthermore, the polymer films were submitted to different thermal treatments to address the influence of crystallinity and morphology of the noncrystalline fraction on the sorption behavior. The sorption results obtained indicate that ethylene solubility coefficient in annealed PLA 98:2 is about 26% higher than that of ethane and 41% higher in PLA 98:2 melted. The dual‐mode sorption model describes well the sorption isotherms behavior, which is concave concerning the pressure axis. The fully amorphous PLA presents the better selectivity for the studied gases, since the crystallinity seems to produce a negative effect on the selectivity. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1312–1319, 2008     

Effect of CO2 exposure on free volumes in polystyrene studied by positron annihilation spectroscopy

Free‐volume properties, size and distribution, in amorphous polystyrene exposed to CO₂ gases have been measured as a function of pressure to 800 psi (5.5 MPa), of time, and of temperature using positron annihilation lifetime spectroscopy. The free volume increases significantly and its distribution broadens as a function of pressure. The free volume relaxes as a function of time with a characteristic time of 15 h, and 5.7 h for 400, and 800 psi, respectively, after depressurizing under vacuum. A portion of free volume created by CO₂ exposure remains permanently in the polymer after CO₂ exposure. The glass transition temperature decreases significantly as a function of CO₂ pressure from the free‐volume data and is compared with the differential scanning calorimeter results. The observed free‐volume variations as a function of pressure, time, and temperature are discussed in terms of hole expansion, creation, free‐volume relaxation, plasticization, and hole filling in amorphous polymers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 388–405, 2008     

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     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003     

Permeation measurements in ethylene‐1‐hexene,ethylene‐1‐octene,and ethylene‐1‐dodecene copolymers synthesized with metallocene catalysts

The permeation behavior of different ethylene‐1‐hexene, ethylene‐1‐octene, and ethylene‐1‐dodecene copolymers synthesized with metallocene catalysts has been analyzed. These copolymers cover a wide range of comonomer contents, so their crystallinities display rather considerable variations. The results for the permeability to oxygen of the different ethylene copolymers show that the main factor influencing the permeability is the noncrystalline fraction, although some influence of the kind of comonomer may also be present, which may be explained by the fact that when the alkyl branch of the α‐olefin is longer, there is an increase in the free volume in the amorphous and interfacial regions, causing slightly higher values of the permeability coefficient. From the results with different gases, it follows that, in general, an increase in the size of the penetrant (as expressed by its kinetic diameter or critical molar volume) leads to an increase in the solubility and a decrease in the diffusion coefficient. A wide range of permeability values is covered by these ethylene copolymers, depending basically on the crystallinity of the sample, but the permselectivity of CO₂ with respect to oxygen (and probably between other pairs of gases) does not differ very much among the different copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2174–2184, 2003     

Pressure and temperature dependence of the gas‐transport properties of dense poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] membranes

The gas‐transport properties of poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] (6FDA‐2,6‐DAT) have been investigated. The sorption behavior of dense 6FDA‐2,6‐DAT membranes is well described by the dual‐mode sorption model and has certain relationships with the critical temperatures of the penetrants. The solubility coefficient decreases with an increase in either the pressure or temperature. The temperature dependence of the diffusivity coefficient increases with an increase in the penetrant size, as the order of the activation energy for the diffusion jump is CH₄ > N₂ > O₂ > CO₂. Also, the average diffusion coefficient increases with increasing pressure for all the gases tested. As a combined contribution from sorption and diffusion, permeability decreases with increases in the pressure and the kinetic diameter of the penetrant molecules. Even up to 32.7 atm, no plasticization phenomenon can be observed on flat dense 6FDA‐2,6‐DAT membranes from their permeability–pressure curves. However, just as for other gases, the absolute value of the heat of sorption of CO₂ decreases with increasing pressure at a low‐pressure range, but the trend changes when the feed pressure is greater than 10 atm. This implies that CO₂‐induced plasticization may occur and reduce the positive enthalpy required to create a site into which a penetrant can be sorbed. Therefore, a better diagnosis of the inherent threshold pressure for the plasticization of a glassy polymer membrane may involve examining the absolute value of the heat of sorption as a function of pressure and identifying the turning point at which the gradient of the absolute value of the heat of sorption against pressure turns from a negative value to a positive one. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 354–364, 2004     

Poly(methyl acrylate)/poly(hydroxyethyl acrylate) sequential interpenetrating polymer networks. Miscibility and water sorption behavior

Sequential poly(methyl acrylate)/poly(hydroxyethyl acrylate) interpenetrating polymer networks with different poly(hydroxyethyl acrylate) contents were prepared by free radical polymerization of hydroxyethyl acrylate inside the previously polymerized poly(methyl acrylate) network. Differential scanning calorimetry on dry samples shows that the interpenetrating polymer networks exhibit phase separation, and no differences are found between the glass transition temperatures of the two phases present in the interpenetrating polymer network and those of the pure components. Thermally stimulated depolarization current experiments were used to study the influence of water sorption on the mobility of the different molecular groups in the poly(hydroxyethyl acrylate) phase of the interpenetrating polymer network. Isothermal water sorption of the interpenetrating polymer networks and pure poly(methyl acrylate) and poly(hydroxyethyl acrylate) networks is analyzed with different theories to compare the behavior of the poly(hydroxyethyl acrylate) phase in the interpenetrating polymer networks with that of the pure poly(hydroxyethyl acrylate) network. Diffusion coefficients of water in the interpenetrating polymer networks are obtained by means of dynamic sorption experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1587–1599, 1999     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006