Diffusion of methyl ethyl ketone in polyisobutylene: Comparison of spectroscopic and gravimetric techniques

In this study, vapor sorption FTIR–ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy was combined with a conventional gravimetric sorption balance to examine diffusion in polymers. Mutual diffusion coefficients of methyl ethyl ketone in polyisobutylene were measured using both methods at various penetrant activities and temperatures in the range 40–60°C. Actual penetrant concentrations were determined from the sorption balance. The diffusion coefficients from the two techniques agree very well with each other. In addition, the diffusivity data from both techniques could be correlated successfully as a function of temperature and concentration with the Vrentas and Duda free-volume model. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1261–1267, 1997     

Multicomponent diffusion of methyl ethyl ketone and toluene in polyisobutylene from vapor sorption FTIR-ATR spectroscopy

In this study, diffusion coefficients of toluene/methyl ethyl ketone (MEK) mixtures in polyisobutylene were measured at 50°C using vapor sorption FTIR-ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy. For three mixture compositions, the diffusion coefficients were determined using a diffusion framework for ternary systems. The “crossterm” diffusion coefficient for MEK was found to be very small under the experimental conditions studied here, while that for toluene was found to increase with increasing MEK concentration. On the basis of this finding, a binary diffusion model was used to determine diffusion coefficients for MEK over a wide range of mixture compositions and the results compared well with those determined from pure MEK transport data. Relative transport rates during integral sorption experiments with mixtures were used to explain the results. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 337–344, 1998     

Water sorption and transport in blends of poly(vinyl pyrrolidone) and polysulfone

Water sorption and transport properties for a series of miscible blends of hydrophobic bisphenol A polysulfone and hydrophilic poly(vinyl pyrrolidone) are reported. Study was restricted to blends that remained homogeneous after exposure to liquid water. The solubility of water in the blend films increased with increasing hydrophilic polymer content. Equilibrium sorption isotherms show dual-mode behavior at low activities and swelling behavior at high activities. The sorption kinetics are generally Fickian for blends containing 20% poly(vinyl pyrrolidone) or less, but exhibit two-stage behavior in blends containing 40% poly(vinyl pyrrolidone). Diffusion coefficients extrapolated to zero concentration decrease with increasing poly(vinyl pyrrolidone) content, owing to a decrease in the fractional free volume. However, the diffusion coefficient becomes a greater function of activity as the composition of hydrophilic polymer in the blend is increased, due to plasticization of the material by large levels of sorbed water. Permeability coefficients generally decrease with increasing poly(vinyl pyrrolidone) content for blends containing 20% poly(vinyl pyrrolidone) or less because the decrease in the diffusion coefficient is greater than the increase in the solubility coefficient. Blends containing 40% poly(vinyl pyrrolidone) have permeability coefficients greater than those of polysulfone due to high water solubility. The permeability coefficients depend on water concentration in approximately the same way for all blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 655–674, 1997     

Sorption and transport of linear alkane hydrocarbons in biaxially oriented polyethylene terephthalate

Equilibrium sorption and uptake kinetics of n‐butane and n‐pentane in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were examined at 35 °C and for pressures ranging from 0 to approximately 76 cmHg. Sorption isotherms were well described by the dual‐mode sorption model. Sorption kinetics were described either by Fickian diffusion or a two‐stage model incorporating Fickian diffusion at short times and protracted polymer structural relaxation at long times. Diffusion coefficients increased with increasing penetrant concentration. n‐Butane solubility was lower than that of n‐pentane, consistent with the more condensable nature of n‐pentane. However, n‐butane diffusion coefficients were higher than those of n‐pentane. Infinite‐dilution, estimated amorphous phase diffusion and solubility coefficients were well correlated with penetrant critical volume and critical temperature, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1160–1172, 2001     

Water sorption and transport in blends of polyethyloxazoline and polyethersulfone

Water sorption and transport properties for a series of homogeneous blends of hydrophobic polyethersulfone and hydrophilic polyethyloxazoline are reported. Only blends that remained homogeneous after exposure to liquid water were studied in detail. Equilibrium solubility of water in the blend films increases with increasing hydrophilic polymer content. For all materials, equilibrium sorption isotherms show dual-mode behavior at low water vapor activities and swelling behavior at high activities. The sorption/desorption kinetics for PES are generally Fickian, but two-stage behavior is evident in blends containing 10 and 20% polyethyloxazoline. Diffusion coefficients decrease with increasing polyethyloxazoline content, owing to a decrease in the fractional free volume. For all materials, the diffusion coefficient shows a positive dependence on water vapor activity or concentration due to plasticization of the material by high levels of sorbed water, but it becomes a greater function of activity as the composition of hydrophilic polymer in the blend is increased. Since the decrease in the diffusion coefficient is greater than the increase in the solubility coefficient, the permeability coefficient decreases with increasing hydrophilic polymer content. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 993–1007, 1997     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Permeation of carbon dioxide through homogeneous dense and asymmetric cellulose acetate membranes

Sorption isotherms for carbon dioxide in a homogeneous dense cellulose acetate membrane were measured by the pressure decay method at three temperatures between 20 and 40°C and gas pressures up to 1.7 MPa. Steady-state permeation rates for the same system at three temperatures between 24 and 40°C and gas pressures up to 2.2 MPa were measured by the variable volume method. The equilibrium sorption was described well in terms of the dual-mode sorption model. The pressure dependence of the mean permeability coefficient was interpreted by the total immobilization model, i.e., a limiting case of the dual-mode mobility model, where the diffusion coefficient for the Henry's law mode is not assumed to be constant but depends upon gas pressure via a modified free-volume theory. The observed pressure dependence of the mean permeability coefficient through an asymmetric cellulose acetate membrane was very similar to that through a homogeneous dense membrane. The thin skin layer in the asymmetric membrane can be simulated by a homogeneous dense membrane from the point of view of gas sorption and diffusion.     

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     

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     

Finite concentration inverse gas chromatography: Diffusion and partition measurements

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate–toluene, and polystyrene–toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas–Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1279–1290, 1997     

Gas solubility and permeability in MFA

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

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.     

Transport of toluene/methyl ethyl ketone mixtures in polyisobutylene

In this study, the diffusion behavior of methyl ethyl ketone (MEK)/toluene mixtures, with MEK molar fractions (x₁) in the liquid source lower than 0.2, in polyisobutylene (PIB) was investigated with vapor‐sorption Fourier transform infrared attenuated total reflectance (FTIR‐ATR) spectroscopy. FTIR‐ATR Fickian diffusion models for both binary and ternary systems were used to determine diffusion coefficients. Obtained diffusion coefficients for MEK from the binary diffusion model did not agree with those determined previously for the diffusion of MEK/toluene mixtures, with x₁ > 0.2, in PIB. When the ternary diffusion model was used, the main‐term and cross‐term diffusion coefficients of MEK were comparable. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 908–914, 2001     

Effect of ultraviolet light irradiation on gas permeability in polyimide membranes. 1. Irradiation with low pressure mercury lamp on photosensitive and nonphotosensitive membranes

Two types of polyimide membranes; one crosslinkable and the other noncrosslinkable using ultraviolet light irradiation (UV irradiation), were prepared and investigated concerning the effect of UV irradiation on their gas permeabilities and selectivities. Permeability and diffusion coefficients for O₂, N₂, H₂, and CO₂ were determined using the vacuum pressure and time lag method. Sorption properties for carbon dioxide were carried out to evaluate the changes in the free volume in the membranes due to the irradiation. In both membranes, permeability coefficients for all gases used in this study decreased and permselectivity, particularly for H₂ over N₂, increased with increasing UV irradiation time without a significant decrease in the flux of H₂. The coefficients depended on the membrane thickness, suggesting asymmetrical changes in both membranes due to UV irradiation. It was suggested by an attenuated total reflection (ATR) FTIR method and analysis of the gas sorption properties of the membranes that the physical changes due to UV irradiation at the irradiated side in both membranes significantly affected their gas permeation properties compared with the chemical changes, especially the crosslinking in the crosslinkable type. © 1997 John Wiley & Sons, Inc. J. Polym Sci B: Polym Phys 35: 2259–2269, 1997     

Sorption of methanol,dimethyl carbonate,methyl acetate,and acetone vapors in CTA and PTMSP: General findings from the GAB Analysis

Sorption of vapors of four organic compounds in two glassy polymers, cellulose triacetate (CTA) and poly[(trimethylsilyl)propyne] (PTMSP), has been reported and analyzed in terms of Guggenheim‐Anderson‐De Boer (GAB) model. These two structurally and physicochemically different glassy polymers both independently showed that one sorption site was formed by about three monomeric units. This finding held true for vapors of all characterized compounds; that is, for methanol, for its derivatives dimethyl carbonate and methyl acetate, and for acetone. The “rule of three” might thus also be applicable to other sorbates and glassy polymers. Further, an original modification of the GAB model for the sorption of alcohols in PTMSP was derived and successfully tested. Overall, the analyses of the sorption isotherms, heats of sorption and diffusion coefficients supported the view that the sorption of vapors in glassy polymers has adsorptive nature. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 561–569     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

Sorption and diffusion of methanol and water in PVDF‐g‐PSSA and Nafion® 117 polymer electrolyte membranes

Sorption and diffusion properties of poly(vinylidene fluoride)‐graft‐poly(styrene sulfonic acid) (PVDF‐g‐PSSA) and Nafion® 117 polymer electrolyte membranes were studied in water/methanol mixtures. The two types of membranes were found to have different sorption properties. The Nafion 117 membrane was found to have a maximum in‐solvent uptake around 0.4 to 0.6 mole fraction of methanol, while the PVDF‐g‐PSSA membranes took up less solvent with increasing methanol concentration. The proton NMR spectra were recorded for membranes immersed in deuterated water/methanol mixtures. The spectra showed that the hydroxyl protons inside the membrane exhibit resonance lines different from the resonance lines of hydroxyl protons in the external solvent. The spectral features of the lines of these internal hydroxyl groups in the membranes were different in the Nafion membrane compared with the PVDF‐g‐PSSA membranes. Diffusion measurements with the pulsed field gradient NMR (PFG‐NMR) method showed that the diffusion coefficient of the internal hydroxyl groups in the solvent immersed Nafion membrane mirrors the changes in the diffusion coefficients of hydroxyl and methyl protons in the external solvent. For the PVDF‐g‐PSSA membranes, a decrease in the diffusion coefficient of the internal hydroxyl protons was seen with increasing methanol concentration. These results indicate that the morphology and chemical structure of the membranes have an effect on their solvent sorption and diffusion characteristics. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3277–3284, 2000     

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     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Permeation,sorption, and diffusion of water in ethyl cellulose

The permeability of ethyl cellulose to water vapor and liquid water was measured as a function of temperature. A change of slope was found in the Arrhenius plots at about 50°C., close to the glass transition. The sorption isotherms showed essentially zero heat of mixing in agreement with other workers. The diffusion constants were measured in four ways, viz., sorption, desorption, time lag, and by dividing the permeability constants by the equilibrium solubility coefficients. The time lag method gave diffusion constants which were independent of concentration, whereas the other three methods led to diffusion constants which steadily decreased with concentration. All the methods, however, extrapolated to about the same value at zero concentration. The decreasing diffusivities are believed to be due to the clustering of water molecules in the polymer. However, no clustering appeared to take place under the conditions of the time lag measurements.