Ethylbenzene solubility,diffusivity, and permeability in poly(dimethylsiloxane)

The pure‐gas sorption, diffusion, and permeation properties of ethylbenzene in poly(dimethylsiloxane) (PDMS) are reported at 35, 45, and 55 °C and at pressures ranging from 0 to 4.4 cmHg. Additionally, mixed‐gas ethylbenzene/N₂ permeability properties at 35 °C, a total feed pressure of 10 atm, and a permeate pressure of 1 atm are reported. Ethylbenzene solubility increases with increasing penetrant relative pressure and can be described by the Flory–Rehner model with an interaction parameter of 0.24 ± 0.02. At a fixed relative pressure, ethylbenzene solubility decreases with increasing temperature, and the enthalpy of sorption is −41.4 ± 0.3 kJ/mol, which is independent of ethylbenzene concentration and essentially equal to the enthalpy of condensation of pure ethylbenzene. Ethylbenzene diffusion coefficients decrease with increasing concentration at 35 °C. The activation energy of ethylbenzene diffusion in PDMS at infinite dilution is 49 ± 6 kJ/mol. The ethylbenzene activation energies of permeation decrease from near 0 to −34 ± 7 kJ/mol as concentration increases, whereas the activation energy of permeation for pure N₂ is 8 ± 2 kJ/mol. At 35 °C, ethylbenzene and N₂ permeability coefficients determined from pure‐gas permeation experiments are similar to those obtained from mixed‐gas permeation experiments, and ethylbenzene/N₂ selectivity values as high as 800 were observed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1461–1473, 2000     

Permeation of CO2 and N2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions

Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time-dependent permeation of N₂ and CO₂ through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.     

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     

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     

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     

Gas‐transport properties of indan‐containing polyimides

A series of indan‐containing polyimides were synthesized, and their gas‐permeation behavior was characterized. The four polyimides used in this study were synthesized from an indan‐containing diamine [5,7‐diamino‐1,1,4,6‐tetramethylindan (DAI)] with four dianhydrides [3,3′4,4′‐benzophenone tetracarboxylic dianhydride (BTDA), 3,3′4,4′‐oxydiphthalic dianhydride (ODPA), (3,3′4,4′‐biphenyl tetracarboxylic dianhydride (BPDA), and 2,2′‐bis(3,4′‐dicarboxyphenyl) hexafluoropropane dianhydride (6FDA)]. The gas‐permeability coefficients of these four polyimides changed in the following order: DAI–BTDA < DAI–ODPA < DAI–BPDA < DAI–6FDA. This was consistent with the increasing order of the fraction of free volume (FFV). Moreover, the gas‐permeability coefficients were almost doubled from DAI–ODPA to DAI–BPDA and from DAI–BPDA to DAI–6FDA, although the FFV differences between the two polyimides were very small. The gas permeability and diffusivity of these indan‐containing polyimides increased with temperature, whereas the permselectivity and diffusion selectivity decreased. The activation energies for the permeation and diffusion of O₂, N₂, CH₄, and CO₂ were estimated. In comparison with the gas‐permeation behavior of other indan‐containing polymers, for these polyimides, very good gas‐permeation performance was found, that is, high gas‐permeability coefficients and reasonably high permselectivity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2769–2779, 2004     

Hydrogen uptake mechanism of a silicone‐rubber DEB getter mixture

The kinetics of the hydrogen getter 1,4‐bis(phenylethynyl)benzene (DEB) blended with carbon‐supported Pd (DEB‐Pd/C) dispersed uniformly in silicone [DEB‐Pd/C‐poly(dimethyl siloxane)] were studied with a thermogravimetric method as a function of the hydrogen pressure and temperature. A diffusion‐controlled reaction model was developed to explain the experimental results. The diffusion coefficient, solubility coefficient, and permeability of hydrogen through silicone rubber were determined. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 425–431, 2001     

Dual mode model for mixed gas permeation of CO2, H2, and N2 through a dry chitosan membrane

Dry chitosan is an excellent candidate for facilitated transport membranes that can be utilized in industrial applications, such as fuel cell operations and other purification processes. This article is the first to report temperature effects on transport properties of CO₂, H₂, and N₂ in a gas mixture typical of such applications. At a feed pressure of 1.5 atm, CO₂ permeabilities increased (0.381–26.1 barrers) at temperatures of 20–150 °C with decreasing CO₂/N₂ (19.7–4.55) and CO₂/H₂ (3.14–1.71) separation factors. The pressure effect on solubilities and permeabilities were fitted to the extended dual mode model and its corresponding mixed gas permeation model. The dual mode and transport parameters, the sorption heats and the activation energies of Henry's and Langmuir's regimes and their pre‐exponential parameters were determined. The Langmuir's capacity constants were utilized to estimate chitosan's glass transition temperature (CO₂: 172 °C, N₂: 175 °C, and H₂: 171 °C). The activation energies of diffusion in the Henry's law and Langmuir regimes were dependent on the collision diameter of the gases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2620–2631, 2007     

Gas permeation of fullerene‐dispersed poly(1‐trimethylsilyl‐1‐propyne) membranes

Homogeneously fullerene‐dispersed membranes were prepared under the conditions in which a 10 wt % poly(1‐trimethylsilyl‐1‐propyne) solution containing 0.5 wt % fullerene was dried under a reduced pressure of 50 cmHg at 100 °C. UV‐vis spectra and microscopic observations of the fullerene membranes indicated that the fullerene was homogeneously dispersed in the membranes. The permeability coefficients of 1‐butene were found to be higher than those of n‐butane in the fullerene membranes, although the permeability coefficients of olefin gases were nearly equal to those of paraffin gases having the same number of carbon in poly(1‐trimethylsilyl‐1‐propyne) membranes containing no fullerene. Pressure dependence of permeability coefficients was clearly observed for the permeation of carbon dioxide, ethylene, ethane, 1‐butene, and n‐butane through the fullerene membranes, while no significant dependence was found for poly(1‐trimethylsilyl‐1‐propyne) membranes except for the permeation of 1‐butene and n‐butane. The pressure dependence of the permeability was explained by the dual‐mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1749–1755, 2000     

Sorption,diffusion, and permeation of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne)

The solubility, diffusivity, and permeability of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) at 35, 45 and 55 °C were determined using kinetic gravimetric sorption and pure gas permeation methods. Ethylbenzene solubility in PTMSP was well described by the generalized dual‐mode model with χ = 0.39 ± 0.02, b = 15 ± 1, and C^′_H = 45 ± 4 cm³ (STP)/cm³ PTMSP at 35 °C. Ethylbenzene solubility increased with decreasing temperature; the enthalpy of sorption at infinite dilution was −40 ± 7 kJ/mol and was essentially equal to the enthalpy change upon condensation of pure ethylbenzene. The diffusion coefficient of ethylbenzene in PTMSP decreased with increasing concentration and decreasing temperature. Activation energies of diffusion were very low at infinite dilution and increased with increasing concentration to a maximum value of 50 ± 10 kJ/mol at the highest concentration explored. PTMSP permeability to ethylbenzene decreased with increasing concentration. The permeability estimated from solubility and diffusivity data obtained by kinetic gravimetric sorption was in good agreement with permeability determined from direct permeation experiments. Permeability after exposure to a high ethylbenzene partial pressure was significantly higher than that observed before the sample was exposed to a higher partial pressure of ethylbenzene. Nitrogen permeability coefficients were also determined from pure gas experiments. Nitrogen and ethylbenzene permeability coefficients increased with decreasing temperature, and infinite dilution activation energies of permeation for N₂ and ethylbenzene were −5.5 ± 0.5 kJ/mol and −74 ± 11 kJ/mol, respectively. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1078–1089, 2000     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

Kinetics of solvent absorption and permeation through a highly swellable elastomeric network

To model a polymer gel or an elastomer undergoing a large change in volume under the action of a solvent diffusing in or out of it, a theoretical approach based on an elastohydrodynamic point of view is proposed. Drawing a parallel between the polymer network/solvent system of interest and a liquid flowing through a porous medium, the friction between the polymer and the solvent is described phenomenologically. An equation that couples the large elastic deformations undergone by the polymer network and the diffusion process is derived and then solved numerically in various cases. Special emphasis is placed on the influence of the shear elasticity during the diffusion process. During the swelling process, a nonzero shear modulus induces a nonisotropic swelling at the surface that is responsible for the “sigmoidal” shape of the mass uptake of solvent with the square root of time, as well as for the presence of a “front” in the concentration profile when the solvent advances inside the network. In a permeation process, the solvent flux deviates from its linear behavior as soon as a nonnegligible deformation of the membrane is present. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 166–182, 2003     

An advanced gas/vapor permeation system for barrier materials: Design and applications to poly(ethylene terephthalate)

A new gas/vapor mixture permeation system is described to investigate the effect of organic molecules on oxygen (O₂) and carbon dioxide (CO₂) transport in barrier materials. Methanol vapor was considered as a flavor simulant mainly because of its conveniently high diffusion coefficient, which makes the experimental time accessible. A highly accurate syringe pump was used to introduce a desired activity level of vapor into gas feed stream. Adsorption of methanol on high energy surfaces is carefully characterized to prevent underestimation of methanol permeability. A special permeation cell was also developed to study the effect of interacting vapors on O₂ and CO₂ transport in barrier materials. Systematic permeation measurements were conducted for binary and ternary gas/vapor permeation measurements (e.g., MeOH/O₂ and O₂/CO₂/MeOH) to verify the feasibility of our new vapor/gas permeation system. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Molecular model for solubility of gases in flexible polymers

We propose a model for a priori prediction of the solubility of gases in flexible polymers. The model is based on the concept of ideal solubility of gases in liquids. According to this concept, the mole fraction of gases in liquids is given by Raoult's law with the total pressure and the vapor pressure of the gas, where the latter may have to be extrapolated. However, instead of considering each polymer molecule as a rigid structure, we estimate the effective number of degrees of freedom from an equivalent freely jointed bead‐rod model for the flexible polymer. In this model, we associate the length of the rods with the molecular weight corresponding to a Kuhn step. The model provides a tool for crude estimation of the gas solubility on the basis of only the monomer unit of the polymer and properties of the gas. A comparison with the solubility data for several gases in poly(dimethylsiloxane) reveals agreement between the data and the model predictions within a factor of 7 and that better model results are achieved for temperatures below the critical temperature of the gas. The model predicts a decreasing solubility with increasing temperature (because of the increasing vapor pressure) and that smaller gas molecules exhibit a lower solubility than larger ones (e.g., CH₄ has a smaller solubility than CO₂), which agrees with the experimental data. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 701–706, 2003     

Water sorption and permeation in chitosan films: Relation between gas permeability and relative humidity

The water sorption of chitosan has been studied at 20 °C. Water transport is governed by a Fickian process for relative humidities lower than 0.4, and in that range of partial pressures, the diffusion coefficient is concentration‐dependent. At a higher activity, anomalous diffusion is observed. The sorption isotherm is well described by the Guggenheim‐Anderson‐de Boer (GAB) model, and the clustering phenomenon observed at high relative pressures can be studied with the parameters of this model. The water permeability coefficient greatly increases with the relative pressure, and the water plasticization effect leads to a loss of the gas barrier properties under wet conditions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3114–3127, 2001     

Permeation of a solvent mixture through an elastomeric membrane—The case of pervaporation

This article presents a model for the permeation of solvent mixtures through an elastomer in the particular case of pervaporation. An analytical expression for each solvent permeation rate is derived, in the limited case of a membrane that undergoes small swelling, without making any assumptions on the solvent diffusion coefficients and their dependence on solvent concentrations. Applying this analytical expression to different situations, we fitted most of the curves previously published on pervaporation experiments. In particular, we correlated the synergy developed by a mixture of two solvents in the permeation process with the sign of their Flory–Huggins interaction parameter χ_AB. This explains why, in most cases (χ_AB > 0), a molecule permeating easily through a membrane is mixed with a molecule permeating much less easily; the latter can see its permeation flux increase by a factor 10 or 100 because the swelling of the polymer induced by the more permeable molecule “opens the meshes of the network” allowing the less permeable molecule to pass through more easily. Within our analysis, the efficiency of the pervaporation process, expressed through the separation factor, is derived very simply as a function of the interaction coefficients and the viscosities of solvents and exhibits an exponential dependence on the volume fraction of either component as seen in most experiments. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 183–193, 2003     

Method of determining the absolute molecular weight from gel permeation chromatograms for star‐shaped styrenic block copolymers

A gel permeation chromatography (GPC) calculation method has been developed to determine the absolute molecular weight of a star‐shaped styrenic block copolymer with GPC–ultraviolet/refractive index calibrated with linear polystyrene standards. To illustrate the simplicity of this method, we have synthesized nearly monodisperse, multiple‐arm model polymers either by linking living polymeric arms with multifunctional silicon halide or by oligomerizing the p‐chloromethylstyrene‐terminated polystyrene macromonomers. The good agreement between the absolute molecular weight determined with this calculation method and that actually measured with a multi‐angle laser light scattering device has corroborated the validity of the calculation method. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 976–983, 2003     

Effect of supercritical carbon dioxide on the diffusion coefficient of phenol in poly(bisphenol A carbonate)

For some polymers, the rate of solid‐state polymerization (SSP) is higher with supercritical carbon dioxide (scCO₂) as the sweep gas than with atmospheric N₂. One explanation for this higher rate is that the diffusion coefficient of the condensate molecule is higher in the CO₂‐swollen polymer. To investigate this hypothesis, we measured the diffusion coefficient of phenol in poly(bisphenol A carbonate) (BPA‐PC) by carrying out SSP of this polymer under diffusion‐limited conditions. Under these conditions, the diffusion coefficient of the condensate molecule could be calculated from the profile of the molecular weight versus time. The phenol diffusivity was determined between 135 and 180 °C in the presence of N₂ at about 1 bar and in the presence of scCO₂ at about 138, 207, and 345 bar. The diffusion coefficient of phenol was up to 200% higher in scCO₂ than in N₂, depending on the temperature and CO₂ pressure. With both N₂ and scCO₂, the activation energy for phenol diffusion in BPA‐PC was larger than the activation energy for the reaction between hydroxyl and phenyl end groups that occurred during SSP of BPA‐PC. As a result, the overall SSP reaction shifted from diffusion control at low temperatures toward chemical‐reaction control at high temperatures. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1143–1156, 2003     

Gas permeation of poly(amide-6-b-ethylene oxide) copolymer

Block copolymers exhibit a different gas permeation behavior from that of homopolymers. In the diffusion process, the fraction of impermeable regions in the block copolymer decreases the diffusivity and the permeability. As the amount of impermeable regions in the block copolymer increases, the flow paths for the gas diffusion are restricted. Poly(amide-6-b-ethylene oxide) (PEBAX^®) copolymer consists of a regular linear chain of rigid polyamide for hard segment interspaced with flexible polyether for soft segment. PEBAX^® copolymer shows a typical permeation behavior of rubbery polymers. The permeability of CO₂ increases with the pressure originating from the increment of the sorbed CO₂ amounts. PEBAX^® copolymer shows the high permeability and the high selectivity for polarizable/nonpolar gas pairs. Particularly, the selectivity of CO₂ over N₂ is 61 and that of SO₂ over N₂ is 500. For small and nonpolar gases (i.e. He, H₂, O₂ and N₂), the permeability decreases with increasing the molecular size or volume of gases. On the other hand, for polarizable and larger gases (i.e. CO₂ and SO₂), it shows the high permeability. The high permeability and permselectivity of PEBAX^® copolymer are attributed of polarizable gases to polyether segment in PEBAX^®.     

Measuring the diffusion of noble gases through a porous medium using prompt gamma activation analysis

Detection of anthropogenic noble gas isotopes in the atmosphere is an important indication that a below ground nuclear-test has taken place. Diffusion plays a critical role in the transport of these gases through the geological media to the surface where they can be detected. Better techniques are need with which to study the diffusion of noble gases through porous systems. Here we demonstrate the suitability of using prompt gamma activation analysis to measure the time dependent concentration of argon as a result of its diffusion through a porous medium that is saturated with nitrogen at atmospheric pressure. The experiments were conducted in a 1 m long tube, 10 cm diameter, and packed with fine SiO₂ sand. Prompt gamma activation analysis was used to measure the concentration of argon within the experimental system as a function of time.