Permeation and sorption for oxygen and nitrogen into polyimide membranes

The permeation rate curves and sorption rate curves of oxygen and nitrogen below 1.3 atm were measured for seven polyimides of which chemical structures were systematically changed. These rate curves were applied Fickian model curves. The Fick's law was found to hold from the pressure independencies of diffusion coefficients for both the experiments. The solubility was better described according to dual-mode sorption model rather than Henry-s law from the sorption experiments. The diffusivities of both the gases were correlated with packing density (reciprocal of specific free volume) of the polymer, except two polyimides. The packing density of these two polymers could not be successfully calculated from Bondi's method. However, all the diffusion coefficients decreased linearly with an increase in the cohesive energy density (CED), which was calculated by the group contribution method of van Krevelen. These results suggest that the gas diffusions in polyimides better correlate with CED than with the packing density. Therefore, the cohesive energy density may be considered as a more reliable indication of the efficient gas separation. © 1995 John Wiley & Sons, Inc.     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

Gas transport in vulcanized natural rubber‐cellulose. II. Composites

This work reports the transport of carbon dioxide, oxygen, and nitrogen in amorphous membranes of vulcanized natural rubber reinforced with regenerated cellulose. The values of the permeability coefficient of carbon dioxide, oxygen, and nitrogen in the composites with 25% of cellulose, measured at 25 °C and 15 cmHg of pressure, are roughly one‐third of those measured in the same conditions for these gases in natural rubber. The isotherms representing the variation of both the permeability and diffusion coefficients of the gases with pressure present a relatively sharp increase in the region of low pressures, attributed to changes in the free volume. The analysis of the permeability characteristics of the membranes in terms of the free‐volume theory suggests that gas transport is severely hindered in both the cellulose phase and the cellulose–rubber interphase of the composites. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 393–402, 2000     

Structure/permeability relationships of polyimides with branched or extended diamine moieties

Mean permeability coefficients for CO₂, O₂, N₂, and CH₄ in seven types of 6FDA polyimides with branched or extended diamine moieties were determined at 35.0°C (95.0°F) and at pressures up to 10.5 atm (155 psia). In addition, solubility coefficients for CO₂, O₂, N₂, and CH₄ in six of these polyimides were determined at 35.0°C and at 6.8 atm (100 psia). Mean diffusion coefficients for the six gas/polyimide systems were calculated from the permeability and solubility data. The relationships between the chemical structure of the polyimides, some of their physical properties (glass transition temperature, mean interchain spacing, specific free volume), and their gas permeability, diffusivity, and solubility behavior are discussed. The 6FDA polyimides studied here exhibit a considerably lower selectivity for the CO₂/CH₄ and O₂/N₂ gas pairs than 6FDA polyimides with short and stiff aromatic diamines with comparable CO₂ and O₂ permeabilities. © 1993 John Wiley & Sons, Inc.     

Effect of methyl substituents on permeability and permselectivity of gases in polyimides prepared from methyl-substituted phenylenediamines

Permeability and solubility coefficients for H₂, CO₂, O₂, CO, N₂, and CH₄ in polyimides prepared from 6FDA and methyl-substituted phenylenediamines were measured to investigate effects of the substituents on gas permeability and permselectivity. The methyl substituents restrict internal rotation around the bonds between the phenyl rings and the imide rings. The rigidity and nonplanar structure of the polymer chain, and the bulkiness of methyl groups make chain packing inefficient, resulting in increases in both diffusion and solubility coefficients of the gases. Polyimides from tetramethyl-p-phenylenediamine and trimethyl-m-phenylenediamine display very high permeability coefficients and very low permselectivity due to very high diffusion coefficients and very low diffusivity selectivity, as compared with the other polyimides having a similar fraction of free space. This suggests that these polyimides have high fractions of large-size free spaces.     

Sorption and diffusion of oxygen in plasticized ethyl cellulose films of varying degrees of substitution

Plasticized films cast from ethyl cellulose were examined to evaluate the effect of the degree of substitution, DS, and the plasticizer content on the sorption and diffusion of oxygen. Sorption and permeation measurements were performed over a temperature range of 25–65°C on three different types of ethyl cellulose in the DS range 1.7–2.5 that had been plasticized with organic esters of comparatively low molecular weight. Sorption coefficients were determined by the pressure decay method, and permeability coefficients were measured independently according to ASTM D-1434-66. The diffusion coefficients were calculated assuming Fickian transport, and were compared to the values directly obtained from the evaluation of the sorption kinetics. The permeability coefficient indicates that there is a significant improvement of the barrier properties of the materials when the DS is reduced and when the plasticizer content is at the absolute minimum required. It was found that the variation in the magnitude of the permeability coefficient is related to the value of the diffusion coefficient, which is governed by the chemical composition of the mixtures. In contrast, the solubility of oxygen was determined by the physical state of the polymer matrix and increased rapidly at temperatures significantly below the glass transition temperature. Using an ergodic model, the diffusion coefficients obtained were related to the size distribution of microvoids in the materials and relative values for the diffusion coefficient were computed as a function of DS and temperature. The model calculates the concentration (number per volume) of voids that are large enough to be occupied by a penetrant molecule. It was assumed that the unoccupied volume fraction as a function of the cohesive energy density follows a Boltzmann distribution. The cohesive energy density and the unoccupied volume fraction of the polymer-plasticizer mixtures were calculated by fitting the Simha-Somcynsky equation of state to pressure-volume-temperature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 639–653, 1997     

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

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

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     

The solubility of Carbon Dioxide and Methane in polyimides at elevated pressures

The solubility of CO₂ and CH₄ in five polyimides was measured at 35.0°C and at pressures up to 10 atm (147 psia). The concentration of the penetrant gases dissolved in the polymers can be represented satisfactorily as a function of penetrant pressure by the “dual-mode sorption” model. The solubility coefficients for CO₂ and CH₄, S(CO₂) and S(CH₄), increase in the polyimide order: The magnitude of the solubility coefficients appears to depend primarily on the intermolecular forces between the penetrant gases and the polymers. The values of these coefficients are greater for the polyimides with larger mean interchain spacings, but no one-to-one correspondence appears to exist in this respect. The lower solubility of CO₂ in PMDA-4,4'-m-APPS compared with that in the 6FDA polyimides may be due to the lower “excess” free volume of the former polymer. The ratio S (CO₂)/S (CH₄) varies relatively little for a variety of PMDA and 6FDA polyimides.     

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     

Gas permeation through hydrogels : I. Gel cellophane membranes

Permeabilities and diffusion coefficients of various gases, Ar, N₂, O₂, CO₂, CH₄, C₂H₄, C₃H₈ and C₄H₁₀, were measured for Water-swollen gel cellophane membranes. No dependence of permeabilities on gas pressure below 1 atm was found. It was observed that the permeability coefficients were not related linearly to the coefficients in bulk water. For the two states of water in the membrane, an analytical method is presented to estimate the diffusion coefficients and the solubilities in free water and non-freezing water. It was found that the diffusion coefficients in non-freezing water were lower than those in free water, and the solubilities in non-freezing water were higher than in free water for all gases studied except CO₂ and C₂H₄, which gave reverse results.     

Chemical structure-transport behavior relationship for polyimides and copolyimides based on rigid and flexible dianhydrides

Gas-separation membrane characteristics of a number of new polyimides containing common dianhydride and diamine moieties, including two copolymers of the regular structure, have been investigated. The densities of polymer films have been measured, and the permeability and diffusion coefficients of H₂, CO, CO₂, and CH₄ gases have been estimated. The values of free volume, solubility coefficients of these gases, and selectivities of gas separation have been determined. The transport parameters of polyimides depend on the combination of rigid and flexible dianhydride and diamine fragments. The combination of rigid dianhydride fragments with rigid diamine moieties and of flexible dianhydride fragments with symmetric flexible diamine moieties is the most promising for membrane applications.     

Gas transport properties of soluble poly(amide imide)s

The influence of the molecular structure of five soluble poly(amide imide)s (PAI)s on their gas transport properties for carbon dioxide, oxygen, nitrogen, and methane has been studied. Permeabilities, diffusivities, and solubilities were determined by time lag measurements and correlated to chain packing and mobility as well as to polymer gas interaction. The PAIs were characterized by small‐ and wide‐angle X‐ray scattering. Molar masses and polymerization degrees were measured by light scattering. Additionally, glass transition temperatures, densities, and persistence lengths were determined. Pressure‐ and temperature‐dependent gas transport measurements have been done. It was found that the permeability is increasing with the diffusion coefficient which can be related to the fractional free volume. PAIs containing cardo diamines show higher diffusivities and permeabilities than poly(amide imide)s containing linear aromatic diamines due to higher fractional free volumes. The solubilities for PAIs containing the same imide compound correlate with the molar cohesive energy density. The exchange of hydrogen to fluorine atoms at one aromatic ring of the diamine increases the fractional free volume and cohesive energy density and, in consequence, the diffusion and solubility coefficient. Arrhenius behavior was observed for temperature dependence and decreasing permeability with increasing pressure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2183–2193, 1999     

Control of phase separation behavior of PC/PMMA blends and their application to the gas separation membranes

Gas transport and thermodynamic properties for the blends of polycarbonate (PC) and polymethylmethacrylate (PMMA) were studied. To explore glass transition temperatures of blends and their phase separation temperatures due to a lower critical solution temperature, LCST, a type of phase boundary, transparent blend films that are miscible and do not contain solvent-induced PC crystals were prepared by controlling molecular weights of each component. The average value of interaction energy densities between PC and PMMA obtained from the phase boundaries and the equation of a state theory based on the lattice fluid model was 0.04 cal/cm³. This result confirmed that miscibility of PC and PMMA blends at equilibrium depends upon the molecular weights of components. Gas transport properties of miscible blends and immiscible blends having the same chemical components and composition but a difference in morphology were examined at 35°C and 1 atm for the gases N₂ and O₂. Permeability and apparent diffusion coefficients were ranked in the order of the immiscible blend having a domain–matrix structure > the immiscible blend having an interconnected structure > the miscible blend. These results might be related to the differences in the local chain motions that depend on the intermolecular mixing level. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2950–2959, 1999     

BARRIER PROPERTIES OF VINYLIDENE CHLORIDE COPOLYMERS

The permeability coefficients of a series of copolymers of vinylidene chloride (VDC)with methyl acrylate (MA), butyl acrylate (BA) or vinyl chloride (VC) (as comonomer)to oxygen and carbon dioxide have been measured at 1.0 MPa and 30℃, while those towater vapor have been measured at 30℃ and 100% relative humidity All the copolymersare semicrystalline. VDC/MA copolymers have lower melting temperature compared withVDC/BA copolymers, while that melting temperature of VDC/VC copolymer is higherthan that of VDC/acrylate copolymers with the same VDC content. The barrier propertyof the copolymers is predominantly controlled by crystallite, free volume fraction, andcohesive energy The permeability coefficients of VDC/MA copolymers to oxygen, carbondioxide, and water vapor were successfully correlated with the ratio of free volume tocohesive energy.     

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     

Solubility and diffusion of CO2 and H2S in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate

The solubility and diffusion coefficient were determined for carbon dioxide and hydrogen sulfide gases in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtSO₄]) at temperatures ranging from (303.15 to 353.15) K and pressures up to 1.6 MPa. The Krichevsky–Kasarnovsky equation was used to correlate solubility data and Henry’s law constants at different temperatures were obtained. The partial molar thermodynamic functions of solution such as Gibbs free energy, enthalpy, and entropy were calculated using the solubility data. A semi-infinite volume approach is used to obtain the diffusion coefficients for CO₂ and H₂S and a correlation equation with temperature is presented for each gas. Comparison showed that H₂S is more soluble than CO₂ and its diffusion coefficient is about two orders of magnitude as that of CO₂ in the ionic liquid studied in this work.     

Direct measurement of gas solubility and diffusivity in poly(vinylidene fluoride) with a high-pressure microbalance

We present solubility and diffusion data for the gases methane and carbon dioxide in the polymer poly(vinylidene fluoride). The polymer was cut from extruded piping intended for use in offshore oil and gas applications. Measurements were carried out using a purpose-built high-pressure microbalance. These properties were determined in the temperature range 80-120 °C and in the pressure range 50-150 bar for methane and 20-40 bar for carbon dioxide. In general, good agreement was obtained for similar measurements reported in the literature. Solubility follows a Henry’s law (linear) dependence with pressure. Diffusion coefficients for each of the gases in the polymer were also measured using the balance. Activation energies for diffusion and heats of solution for the two gases in the polymer were also determined.     

Molecular modeling study on surface,thermal, mechanical and gas diffusion properties of chitosan

The motivation of this work is to provide reliable and accurate modeling studies of the physical (surface, thermal, mechanical and gas diffusion) properties of chitosan (CS) polymer. Our computational efforts have been devoted to make a comparison of the structural bulk properties of CS with similar type of polymers such as chitin and cellulose through cohesive energy density, solubility parameter, hydrogen bonding, and free volume distribution calculations. Atomistic modeling on CS polymer using molecular mechanics (MM) and molecular dynamics (MD) simulations has been carried out in three dimensionally periodic and effective two dimensionally periodic condensed phases. From the equilibrated structures, surface energies were computed. The equilibrium structure of the films shows an interior region of mass density close to the value in the bulk state. Various components of energetic interactions have been examined in detail to acquire a better insight into the interactions between bulk structure and the film surface. MD simulation (NPT ensemble) has also been used to obtain polymer specific volume as a function of temperature. It is demonstrated that these V–T curves can be used to locate the volumetric glass transition temperature (T_g) reliably. The mechanical properties of CS have been obtained using the strain deformation method. Diffusion coefficients of O₂, N₂, and CO₂ gas molecules at 300 K in CS have been estimated. The calculated properties of CS are comparable with the experimental values reported in the literature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1260–1270, 2007     

The effect of drawing on the transport of gases through polyethylene

A study has been made of the gas transport properties of polyethylene films of two different grades, Hizex 7000F and Rigidex 002-55, one-way drawn at 115°C to draw ratios in the range 1–20. Measurements of the permeability and diffusion coefficients of helium, oxygen, carbon dioxide and nitrogen have been made with a dynamic flow rate technique, utilizing a mass spectrometer detection system, and of oxygen using a commercial OXTRAN system. The samples were characterized by the measurement of density, birefringence and modulus and by wide-angle x-ray diffraction and differential scanning calorimetry. There is a large decrease in both the permeability and diffusion coefficients for all gases with increasing polymer draw ratio, with up to an 80-fold decrease in permeability for the larger permeants compared with the 10-fold decrease observed for helium. The solubilities of all the gases decrease only by a factor of ～ 2. The diffusion results are discussed in terms of geometric impedance and chain immobilization factors. The solubilities, on the other hand, appear to relate primarily to the amorphous volume fraction of the polymer. © 1993 John Wiley & Sons, Inc.