Sorption and diffusion of alcohols in amorphous polymers

The effects of polymer composition and penetrant molecular size on the solubility and diffusivity of alcohol vapors in a series of well characterized isoprene-methyl methacrylate copolymers and their corresponding homopolymers has been investigated at room temperature. The rate of sorption behavior changes progressively from Fickian to non-Fickian, to Case II to “Super Case II” transport with increasing methyl methacrylate (MMA) content in the polymers. The equilibrium solubility of the alcohols increases linearly with increasing penetrant molecular size for polymers which are above their glass transition temperature and decreases for polymers which are below their T_g. The solubility also initially increases as an approximately linear function of MMA content in the copolymers. At about 55 mole percent MMA, the sorbed concentration either levels off or passes through a maximum depending on the size of the penetrant. The apparent “diffusion coefficients” (D) decrease with increasing molecular volume of the penetrants. An exponential dependence was found between these two variables for PMMA. These “diffusion coefficients” also decrease exponentially with increasing MMA content in these polymers. However, at 55 mole percent MMA the copolymer undergoes a rubber to glass transition at the temperature of the experiments. On this basis, it is suggested that the hindered chain segmental motion contributes to the sorption process in addition to strictly thermodynamic considerations. Free volume theory can be used to explain the mechanism of diffusion through the rubbery polymers while the “hole” theory can be applied to explain the transport of the penetrants through the glassy polymers.     

Effect of sorption behavior on transport properties of gases in polymeric membranes

The purpose of this work was to study the relationships between the gas sorption and transport properties in polymeric membranes. The intrinsic gas transport properties: permeation, diffusion, and sorption in a series of dense membranes with various carbonyl group densities were investigated. The poly(methyl methacrylate) (PMMA), polycarbonate (PC), and cyclic olefin copolymer (COC) membranes have similar helium permeability, but the helium permeability of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) membrane was very high. The variation of permeability for these four membranes consists with their fraction free volume. In this study, a direct relationship was found between the carbonyl group density and Langmuir affinity constant. Furthermore, dependence of the fractional free volume on the membrane Langmuir capacity constant was observed.     

Energetics of gas sorption in glassy polymers

The molar enthalpy for gas sorption in glassy polymers at a fixed concentration, often called the isosteric enthalpy of sorption, exhibits a clearly discernable minimum when plotted as a function of penetrant concentration. This unexpected behaviour has been observed in several glassy polymer systems including poly(ethylene terephthalate), polyacrylonitrile and polycarbonate. The behaviour can be modelled by analysing the temperature dependence of the various equilibrium parameters comprising the so-called dual mode sorption model for gas sorption in glassy polymers. The fundamental significance of the various enthalpies describing the temperature dependence of the Henry's law solubility constant, the Langmuir affinity constant and the Langmuir capacity constant are included in the discussion. Provision is made for non-ideal vapours and gases by introduction of the compressibility factor in the expression for the isosteric enthalpy. Application of relationships for calculating both the isosteric and the isothermal enthalpies of sorption is made to the case of CO₂ in poly(ethylene terephthalate) in the temperature range 35° to 115°C. These results and analyses complement the wealth of equilibrium and transport data which are consistent with the dual mode sorption model for penetrant sorption in glassy polymers.     

Gas sorption and transport in poly(phenylene oxide) and comparisons with other glassy polymers

The sorption and transport of several gases in poly(phenylene oxide) were measured at 35°C, and the results have been analyzed in terms of the dual sorption/mobility models which have been successfully employed for this purpose for other glassy polymers. Both the extent of sorption and rate of permeation of gases are quite large for poly(phenylene oxide) compared to other glassy polymers with rigid chain backbones. It is shown that the high extent of sorption is owing to the high glass transition temperature of this polymer, but this is not a significant factor in its high permeability to gases. The latter stems from large diffusion coefficients. It is shown that the capacity of the Langmuir mode of sorption inherent to glassy polymers is related to the value of the glass transition temperature in a general way for a wide variety of polymers. Observations about the diffusion coefficients for numerous gas–polymer pairs are discussed.     

Transport phenomena in gas permeation through glassy polymer membranes with concentration-dependent sorption and diffusion parameters

The modified dual-mode mobility model for permeation of a gas in glassy polymer membranes was combined with the extended dual-mode sorption model to take account of the plasticization effect of sorbed gas molecules on both sorption and diffusion processes. The combined model was further simplified by the introduction of a concentration of the mobile gas species. However, the observed pressure dependence of mean permeability coefficients of carbon dioxide in methylmethacrylate-n-butyl acrylate copolymer and polymethylmethacrylate films at 30°c and also that of oxygen in a polycarbonate film at 50°C and 60°C showed that a plasticization action of sorbed gas species has an influence on the diffusion process rather than on the sorption process, that is, were simulated by the modified dual-mode mobility model combined with the conventional dual-mode sorption model.     

Transport of styrene monomer through natural rubber

The diffusion and transport of inhibitor-free styrene through crosslinked natural rubber (NR) have been studied at various temperatures. NR has been vulcanized by conventional, efficient, peroxide and mixed vulcanization techniques. The dependence of diffusion coefficient on the crosslinking system has been studied for all the systems. The influence of temperature on the sorption and the activation energies of sorption have been calculated. The interaction parameter, permeability, sorption coefficient and molecular weight between crosslinks have been evaluated using the diffusion data. The effect of degree of crosslinking on the sorption characteristics of styrene through NR has also been investigated for the different crosslinking systems. The peroxide system showed lowest uptake and the conventional system showed highest uptake.     

Sorption and permeation properties of water and ethanol vapors in poly[bis(trifluoroethoxy)phosphazene] (PTFEP) membranes

The permeability and solubility for water and ethanol in PTFEP membranes were determined experimentally, and the data were analyzed by the solution-diffusion model. The permeability for water and ethanol ranged from several hundreds to several thousands Barrers, and they increased exponentially with the vapor activity and increased with temperature. At the same temperature and vapor activity, the permeability ratio between water and ethanol ranged from 5.7 to 2.3, and it decreased as the vapor activity increased. The sorption isotherms for water and ethanol were fitted by the Henry’s law relationship. The solubility decreased as the temperature increased so that the heat of sorption for both water and ethanol was negative. The solubility for water was more than twice the solubility for ethanol. The solubility seems to be inversely proportional to the molecular size of the penetrants in such a system. The solubility ratio between water and ethanol is smaller than their molecular volume ratio possibly due to the slightly stronger nonpolar interaction and the higher degree of plasticization in the ethanol-polymer system. The diffusivity for water and ethanol ranged from 10⁻⁸ to 10⁻⁷ cm²/s, and the values for water were larger than those for ethanol at the same temperature and vapor activity. The diffusivity for water and ethanol also increased exponentially with the vapor activity. The diffusivities for water and ethanol increased with temperature and their activation energies of diffusion were very similar possibly due to the same energy characteristic of polymer main chain movement.     

Sorption and diffusion of hydrocarbon vapors in glassy polymers

Sorption isotherms in the region of low relative pressures have been determined at several temperatures for methane, propane, and chlorodifluoromethane in polystyrene and for propane in bisphenol-A polycarbonate and poly(vinylacetate). The results are well represented by the isotherm equation of Dual Sorption Theory as applied to glassy polymers. The temperature dependence of the isotherm parameters is examined and discussed; the Langmuir component to sorption decreases as the glass transition temperature is approached and measurements with poly(vinylacetate) confirm that this component is absent above the transition. Average diffusion coefficients were obtained from sorption (desorption) rate curves at constant pressure for propane in polystyrene and polycarbonate and a procedure developed for their analysis to yield the diffusion coefficients of the two sorbed species of penetrant. For the polycarbonate there is evidence of mobility in that fraction of the penetrant: population exhibiting Langmuir-type sorption.     

A model to predict the solubility and permeability of gaseous penetrant in the glassy polymeric membrane at high pressure

In this work, the transport properties of gaseous penetrant through several dense glassy polymeric membranes are studied. The nonequilibrium lattice fluid (NELF) in conjunction with the modified Fick's law and dual mode sorption model was used to simulate the gas transport in glassy polymeric membranes. The approach is based on the sorption, diffusion, in which solubility is calculated based on the NELF model, and diffusion coefficient is obtained from the product thermodynamic coefficient and molecular mobility. The governing equation is solved by the finite element method using COMSOL multi-physics software. The developed model for gas permeability of glassy polymeric membrane can be applied in a wide range of pressure and temperature. The comparison of the calculated permeability and solubility of gasses with the experimental data represented the ability of the developed model. Increasing feed gas temperature increases the gas permeability, while this variation leads to lower gas solubility in the glassy polymeric membranes. The effect of feed temperature and pressure on permeability and solubility is investigated, and the experimental data from literature are described by the developed model. A good prediction of the experimental data can be observed over the considered condition.     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

Sorption and transport of aqueous salt solutions of acetates, acetic and monochloroacetic acids in polyurethane

Sorption, diffusion and permeation of aqueous salt solutions of acetates of sodium, calcium and nickel in addition to acetic and monochloroacetic acid solutions have been investigated in the temperature interval of 25–60°C in a commercial polyurethane. An immersion/weight-gain experiment was used to study sorption and diffusion of 0.15, 0.5 and 1.0 M solutions of acids and salts. Permeability coefficients were estimated from sorption and diffusivity coefficients. From the temperature dependence of transport coefficients, the Arrhenius activation parameters have been estimated and the results were used in the discussion of transport mechanisms. The diffusivity of monochloroacetic acid solution was smaller but its solubility was higher than all the solutions used in this research. For comparative purposes, the transport of water was also studied.     

Sorption and diffusion of water vapor in poly(ethylene terephthalate) film

The sorption and diffusion of water vapor in poly(ethylene terephthalate) (PET) film were measured by applying a thermogravimetric analyzer (TG‐DTA), which customarily has been used to detect the weight loss of a sample with the increase of temperature under a given atmosphere. In this case, we detected the weight gain of PET film by sorption of water vapor under a given humidity at a constant temperature. Sorption‐rate curves were successfully obtained in spite of the low solubility of PET film and the presence of Fickian‐type curves. The solubility was better described according to the dual‐mode sorption model. The diffusion coefficients were determined in their initial slopes by the short‐time method. We found that the diffusion coefficient depended on vapor pressure. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 67–74, 2000     

Solubility and diffusion coefficient of supercritical-CO2 in polycarbonate and CO2 induced crystallization of polycarbonate

The solubility and diffusion coefficient of supercritical CO₂ in polycarbonate (PC) were measured using a magnetic suspension balance at sorption temperatures that ranged from 75 to 175 °C and at sorption pressures as high as 20 MPa. Above certain threshold pressures, the solubility of CO₂ decreased with time after showing a maximum value at a constant sorption temperature and pressure. This phenomenon indicated the crystallization of PC due to the plasticization effect of dissolved CO₂. A thorough investigation into the dependence of sorption temperature and pressure on the crystallinity of PC showed that the crystallization of PC occurred when the difference between the sorption temperature and the depressed glass transition temperature exceeded 40 °C (T − T_g ≥ 40 °C). Furthermore, the crystallization rate of PC was determined according to Avrami's equation. The crystallization rate increased with the sorption pressure and was at its maximum at a certain temperature under a constant pressure.     

Diffusion of mineral oil in styrene‐butadiene polymer films

Mineral oil diffusion in styrene‐butadiene polymer films was investigated with a simple gravimetric sorption method. Over the selected range of temperatures and film thicknesses for which sorption tests were performed, the diffusion process is described in terms of Fick's third law. Polymer dissolution was found to compete with the diffusion process especially at high temperature. Possible interference due to dissolution on data generated using a gravimetric method, resulted in an estimation of apparent activation energy using diffusion coefficient set calculated with Crank's half‐time relationship. The mineral oil diffusion activation energy was found to be relatively high compared with those of hydrocarbons diffusing in natural and synthesized rubbers or crosslinked polybutadiene as reported in the literature. The influence of polymer T_g, crosslinking density, and polarity on mineral oil ability to penetrate polymer film was evaluated in terms of percent weight increase over time. Maximum absorption after 60‐min sorption time linearly correlates with mineral oil absorption rate for polymers prepared with different structures. This linear relationship suggests that diffusion of solvent in styrene‐butadiene polymers reveals the macroscopic composition and structural polymer modification rather than local changes. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Permeability of polyimides derived from non-coplanar diamines and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride

A series of polyimides including a non-coplanar moiety were synthesized in order to investigate the effect on gas permeability and selectivity. The gas permeation properties of He, H₂, O₂, N₂, CH₄ and CO₂ were measured using a constant-volume method. Only 6FDA-terphenyl consisting of laterally attached phenyl groups shows a substantial increase because its terphenyl moiety is a rigid structure with a high aspect ratio. The order of permeability increase from 6FDA-phenyl to 6FDA-terphenyl is consistent with the calculated fraction free volume and measured permittivity. It is observed that the most gain in permeability for 6FDA-terphenyl polyimide arises from the enhancement in apparent diffusion coefficient, while the permeability increase for 6FDA-biphenyl is mainly due to the increase in solubility. A relationship of diffusivity vs. gas penetrant size as well as gas solubility vs. critical temperature of gas penetrant was also investigated.     

Diffusion and sorption of nitroplasticizers in vinyl copolymer elastomer and its composites

To study the aging behavior of cured vinyl copolymer elastomer (VCE) under thermal and nitroplasticizer (NP) environment, we investigated the sorption and diffusion of NP in VCE and its composites. The sorption kinetics of NP into VCE and its composites with respect to filler concentration (0–80%) and temperature (18–70°C) were investigated by conventional gravimetric method. The NP sorption process is endothermic. Kinetic studies show that Fickian diffusion can describe the NP sorption in the VCE polymer. The samples with a high filler concentration show more complicated behavior at low temperature than that at high temperature. The present article discusses the dependences of diffusion coefficient and other related parameters on the polymer concentration and morphological structures of the samples. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40729.     

Desorption of water vapor in hydrogen-bonded polymer blends

Successive desorption experiments of water vapor in poly(methyl methacrylate) (PMMA) were performed at temperatures from 31.0 to 45.0°C. The solubility of water in PMMA was found to be independent of temperature in agreement with literature findings. But the results for diffusion showed stronger dependence on water concentration than those in literature. The diffusion coefficients of water in PMMA became almost independent of temperature at high water concentrations. However, at lower water concentrations, the temperature effect on diffusion was more pronounced. The observed weak temperature dependence of diffusivity at high concentrations is likely due to a high degree of clustering of water molecules found in the PMMA we prepared. Two modified polystyrenes containing 5 and 15 mol %, respectively, 4-hydroxystyrene as comonomer units were blended with PMMA to form hydrogen-bonded polymer blends. Successive desorption experiments of water vapor in the hydrogen-bonded polymer blends were carried out at 31.0°C. The solubility of water in both blends was found to increase with increasing composition of PMMA. The diffusion coefficients for PMMA and its blends increased with increasing concentration of water first, reached a maximum, then decreased with water concentration. When the desorption results were plotted with the previous study of absorption, hysteresis phenomenon of sorption existed in all blend compositions for our experimental time span. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 39–45, 1998     

Analysis of the solvent diffusion in glassy polymer films using a set inversion method

Within the framework of solvent diffusion in glassy polymers, this paper concerns an experimental study of toluene sorption and desorption in P(MMA/nBMA) copolymer films. Gravimetric experiments (quartz microbalance) are performed in a pressure and temperature controlled chamber. Coupling between solvent diffusion and viscoelastic relaxation is taken into account through the time-dependent solubility model, based on the Fick diffusion equation inside the film and a time variable boundary condition at the film/vapor interface. Viscoelastic relaxation is described by a first order model or by a stretched exponential. In the present paper, a special focus is given on the set inversion method used to analyze the data and to derive well-defined uncertainty intervals upon each determined quantity, taking all the uncertainties on the weight measurements into account. We find that the mutual diffusion coefficient strongly decreases in the glassy state, of about two orders of magnitude for a 0.05 decrease in the solvent weight fraction.     

Gas permeation related to the moisture sorption in films of glassy hydrophilic polymers

The purpose of this article is to elucidate the effect of integral sorption of moisture on gas permeation in glassy hydrophilic polymers. The oxygen and the simultaneous moisture sorption into various hydroxypropyl methylcellulose (HPMC) films were measured under a wide range of relative humidities using sorption analyzer equipment. Correspondingly, the oxygen permeability at different ambient conditions was measured using an oxygen detector. The solubility of oxygen in the HPMC film was found to be affected by the amount of water and therefore by the water state. At low moisture content, the water molecules are present as bound water, which promotes the sorption of oxygen in the HPMC films. At moisture content higher than 5%, water clusters are rapidly formed, which increase the affinity of HPMC polymer towards water rather than towards oxygen molecules, resulting in a decrease of oxygen solubility in the polymer. This was found to be the governing factor for the reduction in the oxygen permeability in glassy HPMC films at high water activity. This proposes a specific interaction between moisture sorption and oxygen transport in coating films like HPMC, which is of important aspect in the coating design and formulation. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Sorption, diffusion, and permeation of light olefins in poly(ether block amide) membranes

Sorption, diffusion, and permeation of three olefins (i.e., C₂H₄, C₃H₆, and C₄H₈) in poly(ether block amide) (PEBA 2533) membranes at different temperatures and pressures were investigated. This is pertinent to olefin recovery from resin off gas in polyolefin manufacturing. The relative contribution of solubility and diffusivity to the preferential permeability of olefins over nitrogen was elucidated. It was revealed that the favorable olefin/nitrogen permselectivity was primarily attributed to the solubility selectivity, whereas the diffusivity selectivity may affect the permselectivity negatively or positively, depending on the operating temperature and pressure. The olefin permeability is in the order of C₄H₈>C₃H₆>C₂H₄, the same order as their solubility in the membrane. In general, a low temperature favors both the permeability and selectivity. With an increase in pressure and/or a decrease in temperature, the sorption uptake of the olefin in the membrane increases progressively, and the diffusivity and hence the permeability are also enhanced because of the increased membrane plasticization/swelling caused by the penetrant sorbed in the membrane. At a given temperature, the pressure dependence of solubility and permeability could be described empirically by an exponential function. The limiting solubility at infinite dilution was correlated with the reduced temperature, and the hypothetical diffusivity at zero pressure was related to temperature by the Arrhenius equation.