Sorption of methanol/MTBE and diffusion of methanol in 6FDA–ODA polyimide

This article discusses the diffusion and solubility behavior of methanol/methyl tert‐butyl ether (MTBE) in glassy 6FDA–ODA polyimide prepared from hexafluoroisopropylidene 2,2‐bis(phthalic anhydride) (6FDA) and oxydianiline (ODA). The diffusion coefficients and sorption isotherm of methanol vapor in 6FDA–ODA polyimide at various pressures and film thicknesses were obtained with a McBain‐type vapor sorption apparatus. Methanol/MTBE mixed‐liquid sorption isotherms were obtained by head‐space chromatography and compared with a pure methanol sorption isotherm obtained with a quartz spring balance. Methanol sorption isotherms obtained with the two methods were almost identical. Both methanol sorption isotherms obeyed the dual‐mode model at a lower activity, which is typical for glassy polymer behavior. The MTBE was readily sorbed into the polymer in the presence of methanol, but the MTBE sorption isotherm exhibited a highly nonideal behavior. The MTBE sorption levels were a strong function of the methanol sorption level. Methanol diffusion in the polymer was analyzed in terms of the partial immobilization model with model parameters obtained from average diffusion coefficients and the dual‐mode sorption parameters. Simple average diffusion coefficients were obtained from sorption kinetics experiments, whereas the dual‐mode sorption parameters were obtained from equilibrium methanol sorption experiments. An analysis of the mobility and solubility data for methanol indicated that methanol tends to form clusters at higher sorption levels. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2254–2267, 2000     

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     

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     

Water transport properties of thermoplastic polyurethane films

Two linear segmented polyurethanes, based on poly(oxyethylene) (POE) as a soft segment and 4,4′‐diphenylmethane diisocyanate and 1,4‐butanediol as hard segments and differing in their soft segment length, have been studied from a water vapor transport point of view. For both polyurethanes, the water sorption is governed by a Fickian process, and the thermoplastic polyurethane with the longer POE segments displays the higher water diffusion rate. The water sorption isotherms are Brunauer Emmet Teller (BET) type III for both thermoplastic polyurethanes, and the water uptakes are directly related to the polymer POE content. The Flory–Huggins theory cannot correctly describe the sorption isotherms. More sophisticated approaches (Koningsveld–Kleinjtens or Guggenheim‐Anderson‐de Boer (GAB) models) are needed to fit the experimental water uptakes. The positive deviation from Henry's law and the decrease in the apparent diffusion coefficient observed at a high activity have been particularly studied. In this activity range, an isotherm analysis based on the cluster integral of Zimm and Lundberg suggests some clustering phenomenon, which seems consistent with the diffusion coefficient variation. In agreement with the sorption results, the water permeability coefficients are small at low activities, and they increase greatly with the relative pressure of water. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 473–492, 2004     

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     

Study of Sorption of 2,4‐D on Outer Peristaltic Part of Waste Tire Rubber Granules

From this study it was evident that outer peristaltic parts of waste tire granules gave the highest removal. Film and pore diffusions are the major factors controlling rates of sorption from solution by porous adsorbents. For sorption of 2,4‐D on waste tire rubber granules, the sorption rate coefficient of second‐order kinetic equation was utilized indirectly to determine the rate‐limiting step. The diffusion coefficient lies in the scale of 10^?8 cm²/s, and the pore diffusion coefficient is in the range of 10^?9–10^?10 cm²/s. So both film and pore diffusion are rate limiting. Considering external mass transfer from fluid to particle, using the effect of initial concentration, and using the effect of adsorbent size, no conclusion was reached regarding rate‐controlling steps. It is apparent from the study that external mass transfer (film diffusion) as well as intra‐particle diffusion (pore diffusion) play significant roles in the sorption process for 2,4‐D removal from water onto rubber granules.     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

Polyimide-epoxy alloys prepared via micro-modification: Water sorption and diffusion

A novel polyimide-epoxy or PI-EP alloys are prepared by the modification of polyamic acid in the concentration range of 1.54×10⁻⁶ to 1.54×10⁻² mol/L. The methanol sorption for these alloys at 24 hrs and at equilibrium conditions are determined and the residual solvent in fully cyclized polyimides were calculated. The presence of the residual solvent is visualized in fully imidized polymer and a structure containing partly imidized amic acid moiety is proposed and their concentration (in percentage) is calculated. The water sorption for these alloys at 24 hrs and at equilibrium conditions and the values of the water diffusion coefficient are determined from absorption isotherms. The PI-EP alloys have shown comparatively lower water sorption and higher diffusion coefficient than the unmodified polyimide. The mechanistic aspects of water sorption and diffusion are discussed.     

Water sorption by poly(tetrahydrofurfuryl methacrylate‐co‐2‐hydroxyethyl methacrylate). I. A mass‐uptake study

Cylindrical samples (≈5 mm × 20 mm) of poly(2‐hydroxyethyl methacrylate) and copolymers of 2‐hydroxyethyl methacrylate and furfuryl methacrylate were prepared, and the sorption of water into these cylinders was studied by the mass‐uptake method and by the measurement of the volume change at equilibrium. The equilibrium water content and volume change for the cylinders both varied systematically with the copolymer composition. The diffusion of water into the cylinders followed Fickian behavior, with the diffusion coefficients, dependent on the copolymer composition, varying from 2.00 × 10⁻¹¹ m²s⁻¹ for poly(2‐hydroxyethyl methacrylate) to 5.00 × 10⁻¹² m²s⁻¹ for poly(2‐hydroxyethyl methacrylate‐co‐tetrahydrofurfuryl methacrylate) with a 1 : 4 composition. The polymers that were rich in 2‐hydroxyethyl methacrylate were characterized by a water‐sorption overshoot, which was attributed to a slow reorientation of the polymer chains in the swollen rubbery regions formed after water sorption. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1939–1946, 2000     

Probing the molecular interactions in the diffusion of water through epoxy and epoxy–bismaleimide networks

Fourier transform infrared spectroscopy in the near‐infrared (NIR) frequency range was used to investigate the molecular interactions occurring between absorbed water molecules and networks based on a tetrafunctional epoxy resin. One of these networks was a typical formulation containing 4,4′‐diamino diphenylsulfone as a hardener, and the other was a modified resin containing 4,4′‐bismaleimide‐diphenylmethane (BMI) as a coreactive monomer. Molecular spectroscopy analysis confirmed the existence of mobile water localized into network defects (microvoids) that did not interact with the networks and water molecules bound to the networks through hydrogen‐bonding interactions. In the BMI‐containing system, the fraction of bound water decreased significantly with respect to the unmodified epoxy resin. This was a relevant result because the bound water was primarily responsible for the plasticization of the network and for the consequent worsening of mechanical performance. Water diffusion was investigated with gravimetric sorption measurements and time‐resolved Fourier transform NIR spectroscopy measurements. These showed that the presence of BMI decreased the water uptake at equilibrium, enhanced the diffusivity, and reduced the activation energy for diffusion. A dual‐mode model for diffusion was found to be suitable for accurately describing the mass‐transport process in both investigated systems. The results of the model simulations allowed us to estimate the ratio of free and bound water, which was in good agreement with that obtained from the spectroscopic analysis. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 922–938, 2002     

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     

Viscoelastic diffusion

A constitutive equation is proposed for the viscoelastic diffusion flux, and this equation is used to calculate sorption curves for differential step‐change sorption experiments. The predictions of the theory are shown to be consistent with eight experimental observations that report a wide range of diffusional behaviors for polymer–solvent systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1529–1547, 2001     

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     

Water‐sorption behaviors of poly(3,4′‐oxydiphenylene pyromellitimide) films depending on the thickness variation

The effect of film thickness on the water‐sorption behaviors of poly(3,4′‐oxydiphenylene pyromellitimide) (PMDA‐3,4′ODA) films was gravimetrically investigated and interpreted with a Fickian diffusion model in films. The diffusion coefficient increased with increasing film thickness, whereas the water uptake and the activation energy decreased. Overall, the water‐sorption behaviors of PMDA‐3,4′ODA films are strongly dependent on the changes in morphological structure, which originated from the variation in the film thickness. As the film thickness increased, the molecular in‐plane orientation decreased, consequently leading to the increased diffusion coefficient and decreased activation energy. In contrast, the water uptake decreased with increasing film thickness because of the increase in the out‐of‐plane packing order. The diffusion coefficient and activation energy were strongly dependent on the in‐plane orientation in the films. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 669–676, 2001     

Glassy polymer‐sorption phenomena measured with a quartz crystal microbalance technique

The quartz crystal microbalance (QCM) method is applied to the measurement of CO₂ sorption in glassy poly(ethylene terephthalate) (PET), poly(methyl methacrylate), and polysulfone. Polymer thin films in the thickness range of 350–550 nm are prepared by spin‐casting onto the quartz crystal devices. Sorption isotherms at temperatures below the glass transition are analyzed with the dual‐mode sorption model. As‐cast, quenched, and slow‐cooled thermal‐conditioning protocols yield consistent trends in the sorption level, namely, as‐cast > quenched > slow‐cooled. The sorption levels and model results for the quenched‐conditioned samples measured with QCM compare favorably with those reported from the pressure‐decay and gravimetric methods on thick films. With extended analysis of PET, the QCM technique is also useful for the exploration of the temperature dependence associated with gas sorption in glassy polymer systems. Measured heats of sorption and the collapse of the Langmuir component near the PET glass‐transition temperature agree with those reported previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2109–2118, 2003     

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

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

Transport behavior of carbon disulfide into poly aryl ether ether ketone

The sorption/desorption of carbon disulfide into/from PEEK as a function of crystallinity and temperature was investigated. The sorption curves of carbon disulfide into PEEK show only two major regions: (a) an increase of penetrant weight with time, and (b) a limiting equilibrium value (solubility). This is in contrast to the sorption of toluene into PEEK which shows three regions. The solubility of carbon disulfide decreases with increasing crystallinity, but temperature has little effect on the solubility in the temperature range of 25–40°C. An acceleration in penetration rate at the later stage of diffusion is observed for PEEK films whose crystallinity is greater than 13.4%, suggesting Supercase II diffusion. Carbon disulfide can be desorbed completely from PEEK in contrast to other fluids, such as toluene or methylene chloride, which are difficult to desorb. The normalized weight loss of carbon disulfide during desorption is an exponential function of square-root time. Solvent-induced crystallization was observed. Crystallinity was estimated from both the measured density and microhardness of the desorbed polymer and polymer which had undergone a sorption/desorption/resorption/desorption cycle. © 1996 John Wiley & Sons, Inc.     

Evaluation of gas sorption parameters and prediction of sorption isotherms in glassy polymers

A model of continuous‐site distribution for gas sorption in glassy polymers is examined with sorption data of CO₂ and Ar in polycarbonate. A procedure is presented for determining from a measured isotherm the number of sorption sites in a polymer, an important parameter that previously had to be assumed. With this parameter value and solubility data obtained at zero pressure, the model can reasonably predict sorption isotherms of CO₂ in glassy polycarbonate for a wide temperature range. The number of sorption sites and the average site volume evaluated from CO₂ sorption isotherms are employed for the prediction of Ar sorption isotherms with zero‐pressure solubility data and the independently measured partial molar volume of Ar. A reasonable fit to the measured isotherms of Ar is achieved. With the proposed procedure, the continuous‐site model shows several advantages over the conventional dual‐mode sorption model. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 883–888, 2000     

Decoupling Study of Melt Polycondensation of Polycarbonate: Experimental and Modeling of Reaction Kinetics and Mass Transfer in Thin Films Polycondensation Process

During the melt polycondensation process of polycarbonate, reaction and mass transfer are deeply coupled owing to relatively high melt viscosity. In this work, the polycondensation reaction kinetics and mass transfer behavior of volatile phenol are decoupling studied in detail by using thin‐film experiments with 250–280 °C, 10–1000 Pa and 0.085–0.68 mm film thickness. A realistic apparent rate model coupled the reaction kinetics with thermodynamic equilibrium and diffusion behavior is developed to describe the polycondensation process, while the diffusion characteristic of small molecule (phenol) is further obtained based on penetration theory. The obtained polycondensation equilibrium constant ranges from 0.3 to 0.55, while the activation energy and pre‐exponential factor of temperature‐dependent diffusion coefficients of phenol are 87.9 kJ mol⁻¹ and 5.08 × 10² m² s⁻¹, respectively. It is also observed that the overall apparent rate of polycarbonate (PC) polycondensation process increases with higher temperature, lower pressure, and thinner film thickness. Coupling the reaction kinetics with mass transfer, the predictions of the realistic apparent rate model are in quite satisfactory agreement with experimental data.     

Transport and mechanical properties of blends of poly(ϵ‐caprolactone) and a modified montmorillonite‐ poly(ϵ‐caprolactone) nanocomposite

The structural characterization and transport properties of blends of a commercial high molecular weight poly(?‐caprolactone) with different amounts of a montmorillonite‐poly(?‐caprolactone) nanocomposite containing 30 wt % clay were studied. Two different vapors were used for the sorption and diffusion analysis—water as a hydrophilic permeant and dichloromethane as anorganic permeant—in the range of vapor activity between 0.2 and 0.8. The blends showed improved mechanical properties in terms of flexibility and drawability as compared with the starting nanocomposites. The permeability (P), calculated as the product of the sorption (S) and the zero‐concentration diffusion coefficient (D₀), showed a strong dependence on the clay content in the blends. It greatly decreased on increasing the montmorillonite content for both vapors. This behavior was largely dominated by the diffusion parameters. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1118–1124, 2002