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 and transport of carbon dioxide in a polyimide from 3,3′4,4′-biphenyltetracarboxylic dianhydride and 4,4′-diaminodiphenyl sulfone

CO₂ sorption and transport were investigated for the polyimide prepared from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-diaminodiphenyl sulfone (DDS). The morphology of films did not change on annealing above the glass transition temperature and remained amorphous unlike the polyimide prepared from BPDA and 4,4′-oxydianilline (ODA). This seems to be due to the strong hindrance to rotation of the sulfonyl linkage. Sorption and transport data were analyzed according to the dual-mode model. Solubility, diffusion, and permeability coefficients at 20 atm and 80°C for BPDA-DDS polyimide were substantially equal between as-cast and annealed films and were 1.7, 2.2, and 3.7 times greater, respectively, than for the as-cast films of the BPDA-ODA polyimide. The higher solubility was due to larger values of the Henry's law solubility constant k_D, Langmuir capacity constant C, and the Langmuir affinity constant b. The sorption and transport properties were compared with those for amorphous glassy aromatic polymers including other polyimides. The relation of k, C, b, and the diffusion coefficients in the Henry's law population and the Langmuir population (D_D and D_H) with other properties of the polymers were discussed. Values D_D and D_H for BPDA-DDS polyimide were much larger than expected from the estimated free-volume fraction.     

On the crystallinity effect on the gas sorption in semicrystalline linear low density polyethylene (LLDPE)

This article describes the solubility of carbon dioxide, ethylene and propane in 1‐octene based polyethylene of 0.94, 0.92, 0.904, and 0.87 densities. The isotherms obtained in the gas sorption experimental device display a sorption behavior similar to that of glassy polymers. We apply the dual model to semicrystalline polymers assuming that Henry's sites are related to the amorphous phase, which decreases when the crystallinity percentage increases, whereas the surface of the crystalline phase acts as a Langmuir site with higher gas‐polymer affinity than glassy polymers. The good concordance of the calculated k_D values, using the Flory‐Huggins theory of polymer diluent mixtures, with the experimental results suggest that Henry's gas sorption fulfills this theory and, therefore, it may be a suitable way to estimate polymer‐gas enthalpic interactions. Particularly, the variation of k_D with the crystallinity fraction is exponential and the proportionality of the total sorption with the amorphous content seems only apparent. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1798–1807, 2007     

Structure/permeability relationships of polyimides with branched or extended diamine moieties

Mean permeability coefficients for CO₂, O₂, N₂, and CH₄ in seven types of 6FDA polyimides with branched or extended diamine moieties were determined at 35.0°C (95.0°F) and at pressures up to 10.5 atm (155 psia). In addition, solubility coefficients for CO₂, O₂, N₂, and CH₄ in six of these polyimides were determined at 35.0°C and at 6.8 atm (100 psia). Mean diffusion coefficients for the six gas/polyimide systems were calculated from the permeability and solubility data. The relationships between the chemical structure of the polyimides, some of their physical properties (glass transition temperature, mean interchain spacing, specific free volume), and their gas permeability, diffusivity, and solubility behavior are discussed. The 6FDA polyimides studied here exhibit a considerably lower selectivity for the CO₂/CH₄ and O₂/N₂ gas pairs than 6FDA polyimides with short and stiff aromatic diamines with comparable CO₂ and O₂ permeabilities. © 1993 John Wiley & Sons, Inc.     

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.     

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

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

Effect of methyl substituents on permeability and permselectivity of gases in polyimides prepared from methyl-substituted phenylenediamines

Permeability and solubility coefficients for H₂, CO₂, O₂, CO, N₂, and CH₄ in polyimides prepared from 6FDA and methyl-substituted phenylenediamines were measured to investigate effects of the substituents on gas permeability and permselectivity. The methyl substituents restrict internal rotation around the bonds between the phenyl rings and the imide rings. The rigidity and nonplanar structure of the polymer chain, and the bulkiness of methyl groups make chain packing inefficient, resulting in increases in both diffusion and solubility coefficients of the gases. Polyimides from tetramethyl-p-phenylenediamine and trimethyl-m-phenylenediamine display very high permeability coefficients and very low permselectivity due to very high diffusion coefficients and very low diffusivity selectivity, as compared with the other polyimides having a similar fraction of free space. This suggests that these polyimides have high fractions of large-size free spaces.     

Synthesis and characterization of organosoluble polyimides with trifluoromethyl‐substituted benzene in the side chain

New aromatic diamines substituted with a trifluoromethyl group in the side chain, 2,4‐diamino‐3′‐trifluoromethylazobenzene, 2,4‐diamino‐1‐[(4′‐trifluoromethylphenoxy) phenyl] aniline, and 3,5‐diamino‐1‐[(4′‐trifluoromethyl phenoxy) phenyl] benzamide were synthesized and characterized and used to prepare polyimides by a one‐step high‐temperature polycondensation method. Experimental results indicated that the prepared polyimides possess good solubility in strong organic solvents such as N‐methyl‐2‐pyrrolidinone, N,N′‐dimethylformamide, and N,N′‐dimethylacetamide. Homogeneous solutions with solid contents as high as 15–20% can be prepared, which are stable for storing longer than 2 weeks at room temperature. The polyimides exhibited glass‐transition temperatures of 249–292 °C and good thermal stability. The PI‐I_c and PI‐III_c films prepared by casting the fully imidized polymer solutions showed good transparency with cutoff wavelengths at 320–330 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1572–1582, 2002     

Synthesis and Characterization of Fluorinated Polyimide Derived from 3,3′‐Diisopropyl‐4,4′‐diaminodiphenyl‐3′′,4′′‐difluorophenylmethane

A novel aromatic diamine monomer, 3,3′‐diisopropyl‐4,4′‐diaminodiphenyl‐3′′,4′′‐difluorophenylmethane (PAFM), was successfully synthesized by coupling of 2‐isopropylaniline and 3,4‐difluorobenzaldehyde. The aromatic diamine was adopted to synthesize a series of fluorinated polyimides by polycondensation with various dianhydrides: pyromellitic dianhydride (PMDA), 3,3′,4,4′‐biphenyltetracarboxylic dianhydride (BPDA), 4,4′‐oxydiphthalic anhydride (ODPA) and 3,3′,4,4′‐benzophenone tetracarboxylic dianhydride (BTDA) via the conventional one‐step method. These polyimides presented excellent solubility in common organic solvents, such as N,N‐dimethylformamide (DMF), N,N‐dimethyl acetamide (DMAc), dimethyl sulfoxide (DMSO), N‐methyl‐2‐pyrrolidone (NMP), chloroform (CHCl₃), tetrahydrofuran (THF) and so on. The glass transition temperatures (T_g) of fluorinated polyimides were in the range of 260–306°C and the temperature at 10% weight loss in the range of 474–502°C. Their films showed the cut‐off wavelengths of 330–361 nm and higher than 80% transparency in a wavelength range of 385–463 nm. Moreover, polymer films exhibited low dielectric properties in the range of 2.76–2.96 at 1 MHz, as well as prominent mechanical properties with tensile strengths of 66.7–97.4 MPa, a tensile modulus of 1.7–2.1 GPa and elongation at break of 7.2%–12.9%. The polymer films also showed outstanding hydrophobicity with the contact angle in the range of 91.2°–97.9°.     

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     

CO2 sorption in poly(ethylene terephthalate) above and below the glass transition

High-pressure CO₂ sorption data in semicrystalline poly(ethylene terephthalate) (PET) are presented for temperatures ranging from 25 to 115°C. The results are described by Henry's law above the glass-transition temperature of PET, while a dual-mode sorption model comprised of a Henry's law and a Langmuir isotherm applies in the glassy state. The disappearance of the Langmuir capacity of the polymer above T_g presumably results from the elimination of regions of localized lower density which are frozen into the glass upon quenching from the rubbery state. Exposure of PET to a high CO₂ pressure produced a systematic variation in the apparent sorption equilibria. Correlation of the Langmuir capacity of PET with the dilatometric parameters of the polymer provides a useful framework for understanding the origin of the Langmuir sorption mode and for interpreting annealing and conditioning effects in glassy polymers.     

On pressure dependence of the parameters of the dual-mode sorption model

Sensitivity of the parameters of the dual-mode sorption (DMS) model on the pressure range, in which sorption of gases in polymers have been studied, was analyzed. Different “gas-polymer” systems were considered but the most detailed analysis was performed for sorption of argon and nitrogen in poly[5,5-difluoro-6,6-bis(trifluoromethyl)] norbornene and polysulfone. It was shown that the model parameters depend upon the range of gas pressure studied. Expanding of the pressure range (0-p_i) results in an increase in the Langmuir adsorption capacity C′_H and in reduction of Henry's law solubility coefficient k_D and Langmuir affinity parameter b. These behaviors does not depend on a choice of an experimental apparatus or software and procedure of nonlinear least squares treatment of the data. As statistical analysis indicated, a systematic error of the measurement cannot call forth the observed dependencies of the model parameters. Different physical reasons of these behaviors were considered, among them: the pressure dependence of the affinity parameter, and the dilation of a polymer. The results obtained showed that although the DMS model, as a rule, gives an excellent fit of the experimental curves, and, hence, can be used as a form of compact storage of information on gas sorption in polymers, one should be careful in using it outside the pressure range in which its parameters have been determined. © 1996 John Wiley & Sons, Inc.     

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.     

Model for sorption of mixed gases in glassy polymers

A model is presented for analysis of the sorption of mixed gases in glassy polymers at concentrations below which significant plasticization occurs. The well-known dual-mode sorption model comprised of a Henry's law term and a Langmuir isotherm term, which has been used extensively for interpretation of single-component gas sorption data, forms the basis for the analysis of binary mixtures discussed here. Measurements using pure gases provide dual mode parameters which can then be used to predict the resultant sorption isotherms for binary mixtures of any of the pure gases. The proposed analysis is based upon recognition that the Langmuir component of the overall sorption concentration should be governed by competition between the two penetrants for the fixed unrelaxed volume in the polymer, which is believed to be the locus of the Langmuir capacity. This effect may result in a significant depression of the measured sorption of similar penetrants competing for the limited Langmuir capacity. A numerical example is considered which illustrates the range of behavior expected for CO₂ and CH₄ in polycarbonate. Deviations from the theoretical predictions of the simple dual-mode model for binary systems are discussed in terms of plasticizing effects on the Henry's law constant and the Langmuir affinity constant. The analyses proposed here are of direct and critical interest to the applied problems of migration of trace contaminants in glassy polymers and analysis of barrier packaging for foods since all of these applied problems involve mixed-penetrant sorption. Specifically, it is predicted that the presence of residual monomers or solvents in glassy polymers can produce both anomolously low Langmuir sorption affinity constants and sorption enthalpies compared with the residual-free case.     

Synthesis and characterization of soluble polyimides derived from [1,1′;4′,1″]terphenyl‐2′,5′‐diol and biphenyl‐2,5‐diol

Two series of polyimides based on laterally attached p‐terphenyl and biphenyl groups were synthesized. The solubility and thermal properties were studied using DSC, thermogravimetric analysis, and the solubility test. These polymers exhibited good thermal stability and excellent solubility. The high solubility for both polymer series was attributed to the non‐coplanarity of diamine monomers and the use of fluorinated dianhydride, whereas the slightly better solubility for polymers based on p‐terphenyl was attributed to further weakening of interchain interaction of the polymers. Both polymer series exhibited glass‐transition temperatures (T_g's) in the range of 244–272 °C. The T_g's of polymers containing laterally attached p‐terphenyls were higher than those of their counterparts containing biphenyls by 5–17 °C. This was attributed to the formation of an interdigitated structure that hinders the segmental movement of polymer chains. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2998–3007, 2001     

Infrared spectroscopic studies of CO2 sorbed in glassy and rubbery polymeric membranes

Infrared spectra of CO₂ sorbed in rubbery and glassy polymers were measured to examine the relationships between the spectroscopic data and physical properties of the polymeric membranes. The “V-shape” tendency in the plot of W₁ [i.e., half-width of CO₂ peak sorbed in the membranes] vs glass-transition temperature (T_g) is observed, and has exactly the same tendency that is widely known from the plot of log D (diffusion coefficient) vs T_g. It is suggested that the membranes having a wider W₁ give a faster diffusion coefficient, since W₁ is inversely related to the moment of inertia of CO₂ in the membranes. Two distinct peaks of CO₂ were not observed in the infrared spectra of CO₂ sorbed in the glassy polymers. This suggests that the states of CO₂ in the Henry mode and Langmuir mode in the glassy polymers are similar in the spectroscopic measurements. © 1994 John Wiley & Sons, Inc.     

Dilation kinetics of glassy,aromatic polyimides induced by carbon dioxide sorption

Over the past years, the equilibrium sorption of gases in polymers has been intensively studied. Mostly, glassy polymers were investigated because of their excellent selective mass transport properties. This work does not focus on the equilibrium sorption but on the kinetics to reach the equilibrium. We developed a new experimental method measuring the sorption-induced dilation kinetics of a polymer film. Carbon dioxide and glassy, aromatic polyimides were chosen as model systems. Low-pressure experiments demonstrate that the measured dilation kinetics represent the sorption kinetics. A significant delay between the sorption and dilation kinetics is based on the fact that dilation kinetics occurs simultaneously with the concentration increase in the center of the polymer film. High-pressure experiments reveal significant differences in dilation kinetics compared to low-pressure experiments. Generally, three regimes can be distinguished in the dilation kinetics: a first, fast volume increase followed by two much slower regimes of volume increase. The magnitude of fast and slow dilation kinetics strongly depends on the swelling history of the polymer sample. The results of the experiments are analyzed in the light of a model relating the fast dilation kinetics to a reversible “Fickian” dilation and the slower dilation kinetics to an irreversible, relaxational dilation. © 1995 John Wiley & Sons, Inc.     

The solubility of Carbon Dioxide and Methane in polyimides at elevated pressures

The solubility of CO₂ and CH₄ in five polyimides was measured at 35.0°C and at pressures up to 10 atm (147 psia). The concentration of the penetrant gases dissolved in the polymers can be represented satisfactorily as a function of penetrant pressure by the “dual-mode sorption” model. The solubility coefficients for CO₂ and CH₄, S(CO₂) and S(CH₄), increase in the polyimide order: The magnitude of the solubility coefficients appears to depend primarily on the intermolecular forces between the penetrant gases and the polymers. The values of these coefficients are greater for the polyimides with larger mean interchain spacings, but no one-to-one correspondence appears to exist in this respect. The lower solubility of CO₂ in PMDA-4,4'-m-APPS compared with that in the 6FDA polyimides may be due to the lower “excess” free volume of the former polymer. The ratio S (CO₂)/S (CH₄) varies relatively little for a variety of PMDA and 6FDA polyimides.     

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