Sorption and diffusion of water vapor in polyimide films

Sorption and diffusion of water vapor are investigated gravimetrically for polyimide films. The activity dependence of the solubility and diffusion coefficients, S and D, respectively, is classified under four types: (1) constant S and D type, (2) dual-mode sorption and transport type, (3) dual-mode type followed by a deviation due to a plasticization effect at high vapor activity, and (4) constant S and D type followed by a deviation due to water cluster formation at high activity. For the dual-mode type, the Henry's law component is much larger than the Langmuir component except at low activity, and therefore deviation in behavior from the first type is small. S is larger for polyimides with higher content of polar groups such as carbonyl, carboxyl, and sulfonyl. D is larger for polyimides with a higher fraction of free space, with some exceptions. The polyimide from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and dimethyl-3,7-diaminodibenzothiophene-5, 5-dioxide belongs to the third type and displays both large S and large D. The polyimide from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride and 4,4′-oxydianiline belongs to the fourth type, and has the largest D but rather small S because of the hydrophobic C(CF₃)₂ groups. © 1992 John Wiley & Sons, Inc.     

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     

Sorption and pervaporation properties of sulfonyl‐containing polyimide membrane to aromatic/non‐aromatic hydrocarbon mixtures

Sorption of single‐component vapors of benzene (Bz), n‐hexane (Hx), and cyclohexane (Cx), and of binary liquid mixtures of Bz/Hx and Bz/Cx in a polyimide from 3,3′,4,4′‐diphenylsulfone‐tetracarboxylic dianhydride (DSDA) and 2,8(6)‐dimethyl‐3,7‐diaminobenzothiophene‐5,5‐dioxide (DDBT) were investigated in detail at 333 K. Sorption and desorption of vapors followed the non‐Fickian kinetics and the sorption isotherms were concave to the vapor activity. For the binary liquids, the sorption isotherms of the Bz component were concave to the Bz composition in feed, whereas those of Hx and Cx were convex because of competitive sorption. As a result, the solubility selectivity was much larger than the sorption ratio of pure liquids. The concentration‐averaged diffusion coefficients of Bz (D̄_Bz) and Hx (D̄_Hx) were evaluated using the sorption and pervaporation data of the polyimide membrane toward the binary mixtures. A kind of coupling effect of the coexisting component on D̄ was observed. That is, D̄ of penetrant with smaller molecular size (Hx and Bz for Bz/Hx and Bz/Cx systems, respectively) was reduced by the presence of penetrant with larger molecular size (Bz and Cx, respectively) and vice versa. D̄_Bz was similar to D̄_Hx, but much larger than D̄_Cx. The difference in PV behavior between Bz/Hx and Bz/Cx systems for glassy polymer membranes was understood based on the aforementioned features of sorption and diffusion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2954–2964, 2000     

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S‐shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S‐shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999     

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.     

Sorption and diffusion of water vapour on edible films

Two types of films consisting of sodium salt of carboxymethyl cellulose (NaCMC) and hydroxypropyl cellulose (HPC) as film forming materials and glycerin as plasticizer were prepared, characterized and their water vapour sorption properties were determined. The water sorption isotherms of the films were measured using a magnetic suspension balance. Results show that diffusion of water vapour in NaCMC based film is faster than that in HPC based films, due to the heterogeneous structure and larger pore dimensions of the NaCMC films.     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

Sorption of water and organic solutes in polyimide films and its effects on dielectric properties

The effect of structure on the sorption kinetics of water and of various organic solutes into polyimide (PMDA-ODA) thin films was studied. The major techniques employed include measurements of sorption kinetics, density, and dielectric relaxation. More solute uptake, lower densities and higher diffusivities were observed for films cured at lower temperatures. By measuring both changes of mass and of density, the volume expansion of the polymer due to each solute was obtained; this was found to be proportional to the molar volume of the solute. The two dielectric relaxation peaks (denoted by γ₁ and γ₂) due to water (and other solutes) were studied in detail to obtain the relevant activation energies and the separate dipole moments. While water and methylene chloride appear in both γ₁ and γ₂ configurations, methyl and ethyl alcohol appear mainly as γ₂, while acetic acid is primarily γ₁. It was concluded that the γ₁ configurations are relatively homogeneously distributed throughout the polymer, involving loose bonding to the polymer structure, while the γ₂ configurations involve small clusters, probably chains of molecules. © 1993 John Wiley & Sons, Inc.     

Sorption and diffusion of aliphatic hydrocarbons into crosslinked natural rubber

The sorption and transport of four aliphatic hydrocarbons into natural rubber crosslinked by different vulcanization systems [conventional (CV), efficient (EV), peroxide (DCP) and a mixed system consisting of sulfur and peroxide (mixed)] were investigated in the temperature interval of 28–60°C. Of the four systems, natural rubber vulcanized by DCP exhibited lowest penetrant uptake. It was observed that the kinetics of liquid sorption in every case deviates from the regular Fickian trend, characteristic of sorption of liquids by rubbers. The diffusion coefficient, activation energy of sorption, enthalpy, entropy, and the rubber-solvent interaction parameter were evaluated for the four systems from the swelling data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 725–734, 1997     

Gas diffusion electrodes for polymer electrolyte fuel cell using sulfonated polyimide

Gas diffusion electrodes for high temperature polymer electrolyte fuel cells (PEFCs) have been prepared by using a novel proton conductive sulfonated polyimide (SPI) electrolyte. The catalyst layer was composed of Pt-loaded carbon black (Pt-CB) and SPI ionomer. The polarization properties and the microstructure of the catalyst layer were investigated as a function of the SPI/CB weight ratio. The anodic polarization was found to be negligibly small for all the compositions examined. The highest cathode performance was obtained at SPI/CB = 0.5 (by weight), where the best balance of high catalyst utilization and oxygen gas diffusion rate through the ionomer was obtained.     

Non-fickian diffusion in thin polymer films

Diffusion of penetrants through polymers often does not follow the standard Fickian model. Such anomalous behavior can cause difficulty when designing polymer networks for specific uses. One type of non-Fickian behavior that results is so-called case II diffusion, where Fickian-like fronts initially move like √t with a transition to a non-Fickian concentration profile and front speed for moderate time. A mathematical model is presented that replicates this behavior in thin polymer films, and an analysis is performed that yields relevant dimensionless groups for study. An unusual result is derived: In certain parameter ranges, the concentration profile can change concavity, reflecting Fickian behavior for short times and non-Fickian behavior for moderate times. Asymptotic and numerical results are then obtained to characterize the dependence of such relevant quantities as failure time, front speed, and mass transport on these dimensionless groups. This information can aid in the design of effective polymer protectant films. © 1996 John Wiley & Sons, Inc.     

Sorption of light gases in glassy poly(ethyl methacrylate)

Although gas sorption in glassy polymers is a well‐studied phenomenon, no general microscopical model is developed which is able to describe the gas sorption in a wide temperature range using only characteristics of polymer and gas molecule. In this work, sorption isotherms and desorption kinetics of O₂, Ar, and N₂ for glassy poly(ethyl methacrylate) have been measured in the temperature range from 160 to 308 K. To describe both the phenomena, the model is developed which postulates that, in the frozen structure of glassy polymer, any cavities between macromolecules are the sorption sites for small molecules. The cavities of small size can expand elastically to accommodate a gas molecule. The sorption sites are considered to be the potential wells and their depths are distributed according to Gaussian law. The concentration of sorption sites, their mean depth and depths dispersion, and the frequency of molecules oscillations in the sorption sites are the only parameters which determine both the gas transport and sorption. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 288–296     

Permeation and sorption for oxygen and nitrogen into polyimide membranes

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

Nonlinear viscoelastic diffusion in concentrated polystyrene/ethylbenzene solutions

Nonlinear gradient-driven diffusion was studied in concentrated polystyrene (PS)/ethylbenzene (EB) solutions using vapor sorptions with a finite driving force. The nonlinear sorptions were carried out on thin films (≅2.05, 3.50 μ thick) at conditions where non-Fickian, “viscoelastic” effects appear. These data were modeled with the nonlinear diffusion equation studied by Tang. Four dimensionless material parameters in the model were determined from a limited amount of linear-response, differential sorption data on PS/EB mixtures measured in the same range of experimental conditions as for the nonlinear sorptions. The nonlinear model successfully predicts the observed nonlinear response either above or below the glass transition (T_g). In order to simultaneously capture the nonlinear response both above and below T_g, the abrupt change in the concentration dependence of physical properties at T_g must be accounted for. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2103–2119, 1997     

Temperature effect on solvent diffusion in rigid and semirigid polyimide films

The diffusion of NMP (n-methyl-pyrrolidinone) solvent in a semirigid rod-like PMDA-ODA (pyromellitic dianhydride-4,4′-oxydianiline) film coated on silicon is found to be case I diffusion at temperatures ranging from 30 to 90°C by the use of a bending beam technique. The diffusion constant increases for the 7.4 μm PMDA-ODA film (which was cured at 300°C) from 3.3 to 318 × 10^?11 cm²/s as the diffusion temperature increases from 30 to 90°C. The corresponding hygroscopic stress in the direction parallel to the film decreases with the increase of temperature, possibly due to the softening of the film at elevated temperatures. The diffusion mechanism, however, changes from case II to case I in a rigid rod-like PMDA-PDA (pyromellitic dianhydride-p-phenylenediamine) film when the diffusion temperature increases. The change in the diffusion mechanism occurs at a higher temperature for thinner films, presumably due to higher ordering and/or orientation in the films. The activation energy for NMP diffusion in the PMDA-ODA films markedly decreases from 93 to 59 kJ/mole as the film thickness increases from 2.2 μm to 11.3 μm. This may also be attributed to decreased ordering in thicker films. © 1994 John Wiley & Sons, Inc.     

Sorption and diffusion of carbon dioxide in single-phase polystyrene/poly(vinylmethylether) blends

The sorption and transport properties of CO₂ in miscible PS/PVME blends at 20°C are reported as a function of pressure from 1 to 15 atm. The complex shape of isotherms for glassy blends and the concentration-dependent diffusion coefficient for rubbery blends reveal a plasticization by sorbed CO₂. The significant depression in T_g has to be taken into account in the analysis of the sorption data. Diffusion coefficient for CO₂ passes through a minimum when plotted against the blend composition. Such a behavior can be quantitatively related to the negative volume mixing of the PS/PVME system in the framework of the theories based on unoccupied volume. © 1996 John Wiley & Sons, Inc.     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

Sorption and pervaporation properties of crosslinked membranes of poly(ethylene oxide imide) segmented copolymer to aromatic/nonaromatic hydrocarbon mixtures

Poly(ethylene oxide imide) segmented copolymer (PEO‐PI) membranes were crosslinked by the chemical reaction between ethylene glycol diglycidyl ether and benzylalcohol groups of diamine moieties in polyimide segments at high temperatures. Sorption and diffusion of penetrants took place in poly(ethylene oxide) segment microdomains. Sorption and desorption behavior of pure vapors such as benzene (Bz), cyclohexane (Cx) and n‐hexane (Hx) was classified as the Fickian diffusion. Sorption isotherms of binary liquid mixtures could be represented by the Flory–Rehner model, but the model overpredicted the sorption amounts of Cx and Hx, leading to small predictions of sorption selectivity α_S for Bz/Cx and Bz/Hx systems. UNIFAC‐FV model fairly well predicted the sorption amounts of aromatic hydrocarbons, but significantly overestimated those of nonaromatic ones, leading to too small predictions of α_S. Pervaporation (PV) behavior of PEO‐PI membranes was governed by sorption behavior followed by membrane swelling. Diffusion coefficient weakly depended on the minimum cross section of a penetrant. The diffusivity selectivity α_D hardly depended on the feed composition and was about 1.4 and 0.75 for Bz/Cx and Bz/Hx, respectively. PV selectivity α_PV was larger for Bz/Hx than for Bz/Cx because of larger α_S. PEO‐PI membranes displayed high specific permeation flux Ql and reasonably high α_PV for aromatic/nonaromatic hydrocarbons; for example, Ql = 60 Kg μm/(m² h) and α_PV = 8 for a feed mixture containing Bz, Tol, Hx, n‐Ot and i‐Ot of 20 wt % at 353 K. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1800–1811, 2000     

Sorption and Diffusion of Propylene and Ethylene in Heterophasic Polypropylene Copolymers

Summary: Sorption experiments of ethylene and propylene in different polypropylene powder samples, both homopolymer and heterophasic copolymers with different rubber content, have been carried out in a high-pressure magnetic suspension balance at 10 bars pressure and 70 °C. The gross solubilities measured can be well correlated with the rubber content of the polymer samples. Solubility of ethylene and propylene in the rubber phase differ from solubility in the amorphous fraction of the homopolymer, especially the concentration ratio of propylene to ethylene differs significantly between rubber phase and amorphous fraction of the homopolymer. From the slope of monomer uptake, information on kinetics of mass-transfer can be gained. No significant differences were observed in terms of mass-transfer for ethylene and propylene. With increasing rubber content, effective diffusion coefficients increased slightly. By combined sorption studies with powder samples and compressed films, information about both effective diffusion coefficients and the effective length scale of diffusion could be gained. It could be shown, that the particle radius is not the characteristic length of diffusion in the studied powder samples. Mass transfer of nearly all samples could be described by a constant diffusion length of 120 to 130 µm, independently on particle size. This indicates that the effective scale of diffusion in polymer particles is in between microparticle and macroparticle scale used in classical particle modeling.     

Sorption of rubidium chloride by crown-containing polymer

The kinetics and mechanism of the sorption of rubidium chloride from ethanol by granulated polymer containing immobilized dibenzo-18-crown-6 are studied. The sorption of RbCl is controlled by internal diffusion accompanied by complex formation in the polymer. The equilibrium constants of the sorption and diffusion coefficients of the electrolyte in the sorbent are calculated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1025–1028, June, 1995.