Effects of substituent groups of polyimides on sorption and diffusion of gases

Sorption rate curves of CO₂, N₂, and He gases below 1 atm were measured for polyimide films prepared from benzophenone tetracarboxylic dianhydride (BTDA) with 3,5-diaminotoluene trifluoride (DATF), 2,4-diaminotoluene (DAT), m-phenylenediamine (MPD), and diaminobenzoic acid (DABA). The molecular structures of these four polyimides differ only in the substituent groups of the diamine structure. These polyimides exhibit dualmode type sorption isotherms for carbon dioxide that are concave to the pressure axis, typical of glassy polymer/gas system. The apparent diffusion coefficients below 1 atm pressure of carbon dioxide for this series of compounds decrease in the order: BTDA-DATF > BTDA-DAT > BTDA-MPD > BTDA-DABA. A linear relation between the logarithm of the apparent diffusion coefficient and the reciprocal of free volume, calculated by the method of Bondi using density data, is found for these polyimides. However, this tendency is not observed for the other two gases. The activation energies of the apparent diffusion coefficients at 20 cmHg pressure of carbon dioxide increase with increasing cohesive energy density of the polyimides. The energy per mole of free volume elements in a liquidlike structure in each cohesive energy density may be equated to the activation energy and used to calculate the free volume. The values from the activation energy are almost the same as those from Bondi's method.     

Effects of carbon filler on sorption and diffusion of gases through rubbery materials

Effects of carbon filler on the sorption and diffusion of carbon dioxide in natural rubber and in styrene-butadiene rubber have been studied. Sorption isotherms conform to Henry's law in unfilled rubber and to Langmuir's law in carbon black. The isotherms in filled rubber exhibit a combination of the two sorption modes. The Henry's law solubility parameter k_D increases with carbon filler content; the Langmuir saturation constant C′_A initially is constant with filler level, but then decreases abruptly when carbon particles begin to aggregate. The diffusion coefficient decreases with increasing filler content, presumably owing to geometric effects and to polymer chain immobilization in the interfacial regions.     

羧化聚苯醚与聚苯乙烯共混体系相分离初期分子量影响的光散射研究

 本文用激光光散射方法研究了具有特殊相行为[(低临界溶解温度(LCST),高临界溶解温度(UCST)共存]共混体系羧化聚苯醚和聚苯乙烯在UCST域内的不稳相分离初期分子量对动力学参数的影响。结果表明:相分离初期动力学过程与Cahn理论吻合;随着分子量增加,表现扩散系数D_app明显减小;该体系的表现扩散系数为10^-14 cm²s^-1数量级。deGennes管子模型可很好地描述不稳相分离初期大分子扩散行为。     

Pressure dependence of the viscosity of dilute polystyrene solutions in toluene

The effect of pressure on the viscosity of dilute solutions of anionically polymerized polystyrene (M?_w = 209,000; M_w/M_n = 1.12) in toluene has been studied at different temperatures and concentrations using a falling-body viscometer. Measurements were performed in the concentration range from 0.0025 to 0.02 g/mL and at temperatures from 25 to 45°C under pressure up to 1057 bars. The viscosity coefficient η increases exponentially with pressure at a given temperature and concentration, while the apparent volume of activation V^? decreases with increasing temperature. The hypothesis that the pressure dependence of η is given by the pressure dependence of the activation energy holds true under the prevailing thermodynamic conditions. Log η increases linearly with increasing concentration at a given pressure. Intrinsic viscosity increases with increasing pressure, whereas the Huggins constant decreases.     

Diffusion of 137Cs in compacted bentonite: Effect of pH and concentration

The effect of pH and concentration on the diffusion of ¹³⁷Cs in the compacted bentonite is studied with capillary method at the ionic strength of 0.1M NaClO₄. The apparent diffusion coefficient increases with increasing concentrations if the sorption of radionuclides is largely dependent on the radionuclide concentrations. The apparent diffusion coefficient decreases with increasing pH because most of the radionuclide sorption on the bentonite increases with increasing pH. The interlaminary space contributes significantly to the radionuclide diffusion and sorption in compacted bentonite. The relationship of the apparent diffusion coefficient and the effective diffusion coefficient of ¹³⁷Cs is also discussed.     

Nonstationary diffusion of polystyrenes through a cellophane membrane

Diffusion of five polystyrene fractions at various concentrations in toluene through cellophane membranes has been observed. The results have been used to calculate friction coefficients between solvent and solute, and between solute and membrane. The calculation requires measurement of the diffusion coefficient and the reflection coefficient of the solute, of the permeability for the solvent, of the pore volume of the membrane, and of the partition coefficient of the solute between membrane and solvent. By comparing the friction coefficient between solvent and solute in the membrane with this coefficient in free solution, the tortuosity factor and the pore diameter of the membrane can be estimated. The dependence of the friction coefficients on molecular weight M₂ of the solute is determined. For large values of M₂, the friction between solute and solvent is the determining factor. The friction coefficient between solute and solvent increases more strongly with M₂ in the membrane than in free solution owing to an entrance effect for the permeating solute at the interface.     

Transient and steady-state permeation in poly(ethylene terephthlate) above and below the glass transition

Transient and steady-state permeation data are reported for CO₂ in semicrystalline poly(ethylene terephthalate) for temperatures ranging from 25 to 115°C over the pressure range from 1 to 20 atm. The pressure dependency of the time lag and permeability disappears completely above the glass transition of the polymer, and Fick's law with a concentration-independent diffusion coefficient applies. In the glassy state, a concentration-dependent diffusion coefficient is necessary to describe the data. The form of this concentration dependence is described well by the partial immobilization transport model that attributes a different mobility to each of the two populations of sorbed gas which exist in local equilibrium with each other in glassy polymers. The importance of reporting the pressure used in transport experiments involving glassy polymers is emphasized by comparing the difference in the activation energy of the apparent diffusivity calculated from the measured time lag at 1 and 20 atm. Also, the magnitude of the observed slope discontinuity at T_g in Arrhenius plots of these apparent diffusities is shown to be a function of the upstream pressure used in the experiment. The independently measured time lags are compared with the predicated values calculated from various transport models and found to be described best by the partial immobilization model.     

Polymerization initiated by an electron donor–acceptor complex. Part IV. Kinetic study of polymerization of methyl methacrylate initiated by the charge-transfer complex consisting of poly-2-vinylpyridine and liquid sulfur dioxide

A kinetic study has been made of the polymerization of methyl methacrylate (MMA) initiated by a charge-transfer complex of poly-2-vinylpyridine (electron donor) and liquid sulfur dioxide (acceptor) in the presence of carbon tetrachloride. It is concluded that the polymerization proceeds through free-radical intermediates, as with the pyridine-liquid sulfur dioxide complex system. The association constants K of acceptor and polymer electron donors which range widely in their molecular weight were determined spectrophotometrically, and it has been found that both K and overall rate of polymerization R_p of MMA decrease with increasing molecular weight of polymer donor; contrary to this, molecular weight of PMMA formed increases with increasing molecular weight of the polymer donor. Other kinetic behaviors was essentially the same as in the pyridine–liquid sulfur dioxide system, i.e., R_p is proportional to the square root of the concentration of the complex and to the 3/2-order of the monomer concentration; R_p is clearly sensitive to the carbon tetrachloride concentration at low concentration of carbon tetrachloride, but for a higher concentration it is practically independent of the carbon tetrachloride concentration. It has been deduced from a kinetic mechanism for the initiation that a primary radical may be produced from the reduction of carbon tetrachloride by an associated complex consisting of liquid sulfur dioxide–polymer donor and the monomer.     

Dilation and plasticization of polystyrene by carbon dioxide

We have used an optical interference technique to measure the dilation of polystyrene films in the presence of carbon dioxide or helium at pressures up to 20 atm. Dilation isotherms (plots of dilation versus gas pressure at constant temperature) were obtained for three samples of polystyrene which had widely differing molecular weights. The dilation isotherms have the same general shape as sorption isotherms, which means that all of the sorbed gas molecules contribute to volume dilation and non can be thought of as occupying molecular-sized voids in the polymer. Using sorption results from the literature we show that the partial molar volume of CO₂ at 35°C is about 39 cm³ mol^?1 and appears to be independent of polystyrene molecular weight. For a polystyrene sample with M_n = 3600, the partial molar volume of sorbed CO₂ increases to 44 and 50 cm³ mol^?1 at 45 and 55°C, respectively. The sorption of CO₂ in polystyrene is shown to depress the glass transition temperature of the mixture, consistent with theoretical predictions. The shape of the dilation and sorption isotherms are consistent with the depression of the glass transition temperature.     

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     

Diffusion through rubbery and glassy polymer membranes

Mass transport of a number of organic vapors through polydimethylsiloxane films (PDMS) and carbon dioxide through a variety of polyimides based on a hexafluorotetracarboxylic acid unit (6FDA) were investigated. Vapor diffusion through PDMS films strongly depends on the concentration of the penetrant molecules in the network. For chloroform, increasing diffusivity at lower upstream activities occurs due to network plasticization, while a decreasing diffusion coefficient at larger concentration is supposed to stem from penetrant molecule clustering. The diffusion of carbon dioxide in 6FDA-based polyimides was modelled on a molecular basis. An exponential relation was found between Δc_p and the diffusion coefficient and the permeability, respectively. This relation holds also for on-chain modifications.     

Kinetics and equilibria of sulfur dioxide sorption in kapton polyimide

The kinetics and equilibria of SO₂ sorption in Kapton polyimide film have been measured at 25°C for pressures up to 58 cm Hg using a quartz spring balance. The observed equilibria are described well by the dual-mode model for sorption of penetrants in glassy polymers. Observed hysteresis in sorption-desorption cycling indicates that the diffusivity of SO₂ increases markedly with increasing local penetrant concentration in the polymer. The concentration dependence of the effective average diffusion coefficient is described well by an expression from dual-mode theory. The Langmuir component of the sorption population has an extremely low mobility compared to that of the Henry's law component; in fact, the so-called “total immobilization” limiting case, which assigns a zero diffusion coefficient to this component, appears to be satisfactory under the conditions studied. These results, coupled with published results for other penetrants, suggest that the degree of immobilization of the Langmuir population depends to a great extent on the condensability and/or the molecular size of the penetrant. Predictions of the SO₂ diffusion time lag and permeability in Kapton as functions of the upstream SO₂ pressure are presented and discussed in terms of the dual-mode theory.     

Review of polystyrene diffusion studies in latex particles by small‐angle neutron scattering

This paper reviews small‐angle neutron scattering (SANS) and some results from direct nonradiative energy transfer (DET), for the observation of the diffusion coefficients of polystyrene chains at latex interfaces. To compare SANS with DET, doubly labeled polystyrene with deuterium and fluorescence groups were synthesized, showing that while SANS and DET produce comparable data in terms of diffusion coefficients, both results differ in detail, each having their own advantages. Chain confinement, ionic end groups, and short branch effects on interdiffusion were studied. Large polymer chains confined in small particles have non‐Gaussian shapes that store rubber elastic energy. Rapid, non‐diffusion relaxation is inhibited because the density would be required to become less than normal. Hence confinement effects on the diffusion rate are not significant. Using the DET method, ionic end‐groups were found to increase the early‐time apparent interdiffusion coefficients during film formation. The early‐time apparent diffusion coefficients of polystyrene with varying end‐groups were found to increase as follows: The higher apparent diffusion coefficients of the chains with ionic groups are presumably due to a surface segregation of the end‐groups caused by the polar, aqueous environment during latex synthesis. The interdiffusion behavior of sulfite‐ended polystyrene (M_n ? 300 000 g/mol) with H‐ends, one sulfite end, and two sulfite ends were compared via SANS and DET. The diffusion coefficients of polystyrene with one or two sulfite end groups were five times and ten times lower than that of polystyrene, respectively. The ionic end group effects on the reduced diffusion coefficients are interpreted as the competition between enhancement by the surface segregation of end groups and reduction by end group aggregation. Noting that sulfate end groups diffused faster, while sulfite end groups diffused slower, the effect is complex, and not yet fully resolved. Diffusion coefficients of polystyrene with branches were studied by DET. Short branches work to decrease the T_g and hence increase the diffusion coefficients. However, after the experimental temperature, T, is converted to a normalized temperature, T‐T_g, the diffusion coefficients are found to be almost independent upon the number of branches and the length of branches. The branch length ranged from one‐carbon to 40 carbons. Side chains of entanglement molecular weight or longer may be required to significantly reduce the diffusion coefficient. Copyright © 2002 John Wiley & Sons, Ltd.     

Chromatography with Supercritical Fluids

Chromatography with supercritical fluids unites the features of both gas chromatography and liquid chromatography, yet retains special characteristics of its own. The diffusion coefficient and particularly the viscosity of fluid phases may approach values for low-pressure gases, while the solvent power may be similar to that of liquids. However, with supercritical fluids it is possible to control chromatographic separations very effectively by pressure programming, since the solubility increases with increasing density. Temperature programming, on the other hand, can have the opposite effect to that in gas- or liquid-chromatography since the density decreases with increasing temperature at a given pressure. Supercritical fluid chromatography is primarily of interest for the separation of higher molecular weight compounds. The efficiency of this method of separation is demonstrated on several homologous series. Thus, a styrene oligomer with nominal M_w=2200 can be resolved by a pressure and temperature program into 40 species.     

Carbon dioxide sorption and transport in polycarbonate

The solubility, permeability, and diffusion time lag for carbon dioxide in polycarbonate are reported at 35°C for pressures ranging from 1 atm to 23 atm. The solubility data are very well described by the dual sorption mechanism model, Henry's law plus Langmuir adsorption, proposed for glassy polymers. Both the permeability and time lag decrease with increased CO₂ pressure. These observations are not consistent with the proposal that CO₂ sorbed by the Langmuir contribution is totally immobilized; however, all of the results are entirely consistent with an extension of this proposal which considers partial immobilization. The data have been quantitatively analyzed in terms of this partial immobilization model, and the results suggest for polycarbonate at 35°C that the CC₂ sorbed by the Langmuir portion of the isotherm behaves as if it has only about 10% of the mobility of the gas sorbed by the Henry's law part of the isotherm. The results have also been interpreted in terms of a concentration-dependent diffusion coefficient which is shown to be mathematically equivalent to the partial immobilization model. The latter model was also formulated in thermodynamic terms, whereby fugacity was used rather than pressure, and diffusion coefficients were defined in terms of chemical potential gradients rather than concentration, but the consequences of these changes proved to be minor and no better. The significance of these observations and their interpretation is discussed.     

Investigation on extremely dilute solution of PEO by PFG-NMR

The technique of pulsed-field gradient nuclear magnetic resonance (PFG-NMR) was applied to study the solution properties of a series of low molecular weight poly(ethylene oxide). The self-diffusion coefficients of solutions from semi-concentrated to extremely diluted were measured, leading to a critical concentration. When the concentration of solution is higher than the value of critical concentration, the diffusion coefficient of the solute decreases as the concentration increases and remains the same when the concentration is lower than it. This critical concentration agrees well with the definition of dynamic contact concentration (C _s) and confirms indirectly the Flory's scaling law between the molecular weight and D ₀. In addition, the influences of molecular weight and terminal groups on C _s were discussed. All the diffusion coefficients determined at extremely dilute condition were equivalent to the diffusion coefficients at infinite concentration (D ₀), from which the polymer coil size was estimated.     

Characterization of thermal diffusion in polymer solutions by thermal field-flow fractionation: Dependence on polymer and solvent parameters

The thermal diffusion coefficient D_T has been obtained for 17 polymer-solvent combinations, each of them spanning a range of polymer molecular weights, using thermal field-flow fractionation. The polymers examined include polystyrene, poly(alpha-methyl)styrene, polymethylmethacrylate, and polysioprene. The solvents include benzene, toluene, ethylbenzene, tetrahydrofuran, methylethylketone, ethylacetate, and cyclohexane. Although D_T was confirmed as essentially independent of polymer molecular weight, it was found to vary substantially with the chemical composition of polymer and solvent. The results were used to evaluate several thermal diffusion theories; the agreement with theory was generally found to be unsatisfactory. Attempts were then made to correlate the measured thermal diffusion coefficients with various physicochemical parameters of the polymers and solvent. A good correlation was found in which D_T increases with the thermal conductivity difference of the polymer and solvent and varies inversely with the activation energy of viscous flow of the solvent.     

Permeation,diffusion, and solution of cyclopropane in silicone rubber

Permeability, solubility, and diffusion coefficients have been determined for cyclopropane (c-C₃H₆) in silicone rubber at temperatures between ?8 and 70°C at relative pressures from 0.04 to 0.30. The permeability coefficients, , are of the order of 10^?6 cm³ (STP) · cm/(s · cm² · cmHg). increases slightly with increasing penetrant pressure and decreases with increasing temperature, the energy of activation for permeation being ?1.27 kcal/gmol at zero pressure. The solubility of cyclopropane in silicone rubber can be represented over the experimental concentration range by the Flory-Huggins equation. The solubility decreases with increasing temperature and the partial molar heat of solution is ?4.95 kcal/gmol. The solubility coefficient in the Henry's law limit, S(0), for cyclopropane and many other gases and vapors can be correlated with (T_c/T)², where T and T_c are the experimental and critical temperatures, respectively. The mutual diffusion coefficients, D, increase with increasing concentration and temperature, the energy of activation for diffusion being 3.68 kcal/gmol. The pressure dependence of &\[\bar P\] is described satisfactorily by a free-volume model proposed by Fujita and extended by Stern, Frisch, and coworkers. The permeability, diffusion, and solubility behavior of cyclopropane in silicone rubber is similar to that of propane (C₃H₈).     

Characterization of thermal diffusion of polystyrene in binary mixtures of THF/dioxane and THF/cyclohexane

The thermal diffusion coefficient (D_τ) was determined for three polystyrene standards of different molecular masses in binary mixtures of tetrahydrofuran/dioxane and tetrahydrofuran/cyclohexane of various compositions. The D_τ values were obtained by combining retention data from thermal field-flow fractionation measurements with diffusion data from dynamic light scattering experiments. In agreement with earlier work of Schimpf and Giddings, the thermal diffusion coefficient was found to be virtually independent of the molecular mass of the polymers. In the binary mixtures of tetrahydrofuran and dioxane, both good solvents for polystyrene, the D_τ value was approximately equal to the average of the D_τ values in the pure solvents, weighted according to the mole fractions of the solvents in the mixture. However, for polystyrene in binary mixtures of tetrahydrofuran and cyclohexane this linear behavior of the thermal diffusion phenomenon was not observed. The addition of cyclohexane to tetrahydrofuran has initially only a minor effect on the molecular and thermal diffusion coefficients of the polystyrene standards. Because cyclohexane is a theta solvent for polystyrene, the preferential solvation of polystyrene by tetrahydrofuran could be an explanation for these results. © 1996 John Wiley & Sons, Inc.     

Effects of temperature and anion species on CO2 permeability and CO2/N2 separation coefficient through ionic liquid membranes

The permeability of carbon dioxide (CO₂) through imidazolium-based ionic liquid membranes was measured by a sweep gas method. Six species of ionic liquids were studied in this work as follows: [emim][BF₄], [bmim][BF₄], [bmim][PF₆], [bmim][Tf₂N], [bmim][OTf], and [bmim][dca]. The ionic liquids were supported with a polyvinylidene fluoride porous membrane. The measurements were performed at T = (303.15 to 343.15) K. The partial pressure difference between feed and permeate sides was 0.121 MPa. The permeability of the CO₂ increases with temperature for the all ionic liquid species. Base on solution diffusion theory, it can be explained that the diffusion coefficient of CO₂ in an ionic liquid affects the temperature dependence more strongly than the solubility coefficient. The greatest permeability was obtained with the [bmim][Tf₂N] membrane. The membrane of [bmim][PF₆] presents the lowest permeability.The separation coefficient between CO₂ and N₂ through the ionic liquid membranes was also investigated at the volume fraction of CO₂ at feed side 0.10. The separation coefficient decreases with the increase of temperature for the all ionic liquid species. The membrane of [emim][BF₄] and [bmim][BF₄] gives the highest separation coefficient at constant temperature. The lowest separation coefficient was obtained from [bmim][Tf₂N] membrane which presents the highest permeability of CO₂.