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     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

Gas sorption and diffusion processes in polymer matrices at high pressures

A theoretical approach has been developed to describe the processes of gases diffusion and sorption in rubbery and glassy polymers. Various models (Flory-Huggins, dual-mode sorption, gas-polymer-matrix) used for interpreting the sorption-diffusion experiments are discussed within this approach framework. Experimental data on carbon dioxide sorption in glassy and rubbery polymers have been considered using the proposed approach. The comparison of the experimental and theoretical data has permitted to make the conclusion on the developed concepts adequacy. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1339–1348, 1997     

Permeation of CO2 and N2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions

Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time-dependent permeation of N₂ and CO₂ through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.     

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 of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

Comparison of permeability coefficients of organic vapors through non-porous polymer membranes by two different experimental techniques

The permeability coefficients of saturated and non-saturated vapors of benzene, hexane and cyclohexane through flat polymer membranes (low density polyethylene BRALEN FB2-30 and polyether-block-amide PEBA 4033-PE) by two different experimental techniques at 298.15 K are reported. The permeation data have been obtained using the differential flow permeameter and sorption ones by glass sorption apparatus with McBain’s spiral balance. The so-called stationary (steady) diffusion theory has been applied for evaluating the permeability coefficients from sorption (equilibrium) data and obtained values have been compared with the permeability coefficients from permeation (steady-state) measurements. In the case of relative lower vapors sorption in polymers (hexane and cyclohexane) good agreement between permeability coefficients from sorption and permeation is obtained. Hence, this paper proves the possibility to estimate the permeability coefficients of organic vapors from sorption data without need of performing the permeation experiments.     

Impact of average free‐volume element size on transport in stereoisomers of polynorbornene. I. Properties at 35 °C

This article demonstrates that transport of gases through glassy polymers is significantly influenced not only by the absolute amount but also by the distribution of free volume. Two stereoisomers of polynorbornene with nearly equivalent total free volume, but markedly different average free‐volume sizes, were evaluated. The free‐volume element size was probed with positron annihilation lifetime spectroscopy, wide‐angle X‐ray scattering, gas sorption, and molecular modeling. The permeation, sorption, and diffusion of light gases were measured in each stereoisomer at 35 °C. All analytical techniques indicated that one isomer (labeled as Architecture II) had a larger average free‐volume element size but fewer elements. This isomer also had a very slightly higher bulk density (1.000 vs 0.992 g/cm³ for the other stereoisomer). Architecture II also had gas sorption and diffusion coefficients that were two to three times those of the less dense counterpart. These differences have been attributed to differences in the free‐volume element size available within the polymer matrix. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2185–2199, 2003     

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     

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     

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     

The effect of lattice compressibility on the thermodynamics of gas sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration-dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory-Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.     

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

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

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

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     

Characterization of water vapor transport in glassy polyacrylonitrile by combined permeation and sorption techniques

Diffusion time lags, steady state permeabilities and sorption/desorption kinetics are reported for water vapor in biaxially oriented, solvent cast polyacrylonitrile (PAN) films. A wide range of vapor activities was studied at 15°C, 30°C, and 45°C. The transient and steady state permeation behavior at low and intermediate upstream vapor activities suggests that Fickian transport occurs under most of the conditions studied. Specifically, time lags predicted by Fick's law using the concentration-dependent diffusion coefficient derived from steady state permeation measurements agree reasonably well with experimentally measured values in most cases. p]Integral sorption/desorption kinetics at low and intermediate vapor activities also appear to be Fickian with a concentration-dependent diffusion coefficient. The form of the concentration dependency, evaluated from the “long time” solution of the diffusion equation for sorption experiments, is consistent with the form established for the diffusion coefficient from the steady-state permeation data. The diffusion coefficient exhibits a maximum near the concentration at which clustering is initiated. Presumably, the effective diffusion coefficient of water increases initially due to plasticizing or dual mode sorption effects associated with gap filling in the glassy matrix. As clustering becomes significant, the effective mobility of water is substantially reduced; therefore, the diffusion coefficient decreases at higher activities as clustering becomes the dominant mode of sorption. p]A tendency of the “early time” sorption/desorption kinetic data to exhibit concavity to the square root time axis at high activities suggests that time-dependent reductions in the diffusion coefficient may be occurring. Such reductions could be related to the kinetics of cluster formation at the higher vapor activities during sorption and to slow polymer consolidation during desorption. Any such non-Fickian effects, related to chain segment relaxations occurring over time scales similar to those of a diffusional jump, appear to be of importance only at short times. The short time nature of any such processes is suggested by the fact that diffusion coefficients evaluated from the “long time” solution to the diffusion equation for sorption are consistent with coefficients evaluated from steady state permeation data, in which case all time-dependent relaxation phenomena should be absent.     

Gas sorption in polymer membranes containing adsorptive fillers

The equilibrium and kinetics of gas sorption by a silicone rubber filled with highly adsorptive molecular sieves was studied. Sorption in this system is by two mechanisms: gas is simply dissolved in the polymer matrix according to Henry's law, while it is adsorbed by the dispersed sieve phase in accordance with a Langmuir's isotherm. The latter effectively immobilizes the gas molecules preventing their further diffusion. All equilibrium parameters were determined experimentally. Immobilization greatly affects sorption kinetics and renders conventional analyses invalid. A theory to account for this process was adapted from a previous analysis by Vieth and Sladek which assumes that the kinetics of adsorption is very fast compared to diffusion. For this situation the kinetics always assume a Fickean form. The experimental data agreed very well with the predictions of this theory in a comparison where all parameters were defined by independent experiments. It was found that a single effective diffusion coefficient describes sorption kinetics, steady-state permeation, and time-lag results once the effects of immobilization are properly accounted for.     

Permeation of water through polar and nonpolar polymers and copolymers: Determination of the concentration‐dependent diffusion coefficient

The diffusion and permeation properties of liquid water through different polar and nonpolar polymers and copolymers were studied with a highly sensitive permeameter. The transient permeation fluxes through the polar polymer films could be fitted well only with an exponential equation for the diffusivity concentration dependence; this empirical exponential equation represented the diffusion plasticization effect of water on the materials. For the hydrophobic polyolefins, this exponential equation was no longer valid, and another form of the equation was empirically found to account for the reduction of the water diffusivity with the extent of the permeation. Such a negative plasticization effect might be attributed to the formation of water clusters in the polyolefins. The values of the diffusion coefficient of water in the dry polar polymers were smaller than those in dry polyolefins, but the opposite behavior was found for the permeability because it was much more favorable for water sorption in the polar polymers than in the hydrophobic polyolefins. For the ethylene–vinylacetate copolymers, the plasticization effect of water on its own diffusion was negative for the sample with a low vinyl acetate (VA) content; it became nil at 19 wt % VA and positive at higher VA contents. This increase in the extent of the water sorption with the increase in the VA content led to a steady increase in the water permeability in the poly(ethylene‐co‐vinylacetate) copolymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1998–2008, 2000     

Pure and mixed gas acetone/nitrogen permeation properties of polydimethylsiloxane [PDMS]

The permeability of polydimethylsiloxane [PDMS] to acetone, nitrogen, and acetone/nitrogen mixtures has been determined at 28°C. In pure gas experiments, the permeability of PDMS to nitrogen was 245 × 10⁻¹⁰ cm³(STP) · cm/cm² · s · cmHg and was independent of pressure. The permeability of PDMS to acetone vapor increased exponentially with increasing acetone pressure. PDMS is much more permeable to acetone than to nitrogen; acetone/nitrogen selectivity increases from 85 to 185 as acetone partial pressure in the feed increases from 0 to 67% of saturation. In mixed gas permeation experiments, the nitrogen permeability coefficient is independent of acetone relative pressure and is equal to the pure gas permeability coefficient. The acetone permeability coefficient has the same value in both mixed gas and pure acetone permeation experiments. Average acetone diffusivity in PDMS, determined as the ratio of permeability to solubility, decreases with increasing acetone concentration due to mild clustering of acetone in the polymer (because acetone is a poor solvent for PDMS) and changes in the polymer–penetrant thermodynamic interactions which influence diffusion coefficients. A Zimm–Lundberg analysis of the acetone sorption isotherm is also consistent with acetone clustering in PDMS. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 289–301, 1998     

Transport of sulphur dioxide in polymers

Summary Studies were made of the permeation, solution, and diffusion of sulphur dioxide in polyethylene, polyamide (Nylon 11), and polycarbonate at 25 °C and at pressures up to one atmosphere. The steady-state permeability coefficients of sulphur dioxide in all three polymers were pressure-dependent, and the effect of pressure on the solution and diffusion processes, which together govern the overall permeation process, account for the observed relations. Solution and diffusion in the two glassy polymers, polyamide and polycarbonate, were strongly pressure-dependent whereas in polyethylene diffusion was pressure-dependent but solution obeyed Henrys law. The vapour pressure isotherms of the glassy polymers obeyed a modified Langmuir expression suggesting that two concurrent sorption mechanisms were operative, the filling of microvoids within the polymer structures and ordinary Henrys law solution. Kinetic sorption-desorption studies showed that diffusion was “Fickian” in polyethylene and polyamide over the entire pressure range. It was also “Fickian” in polycarbonate at pressures up to approximately 25 cm Hg, but “non-Fickian” at higher levels. For each polymer, diffusion coefficients were determined by steady-state permeation and transient sorption-desorption methods, and the separate methods gave similar values.

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Zusammenfassung Permeation, L?sung und Diffusion von Schwefeldioxid in Poly?thylen, Polyamid (Nylon 11) und Polycarbonat wurden bei 25 °C und Drucken bis zu einer Atmosph?re untersucht. Die station?ren Permeationskoeffizienten von Schwefeldioxid waren in allen drei Polymeren druckabh?ngig, und es erwies sich der Einflu? des Druckes auf die den Permeationsvorgang bestimmenden L?sungs- und Diffusionsvorg?nge als verantwortlich für die beobachteten Beziehungen. L?sung und Diffusion in den beiden glasigen Polymeren, Polyamid und Polycarbonat zeigen eine starke Druckabh?ngigkeit, w?hrend die Diffusion im Poly?thylen zwar druckabh?ngig war, der L?sungsvorgang jedoch dem Henryschen Gesetz gehorcht. Die Dampfdruckisothermen der glasigen Polymeren gehorchen einem modifizierten Langmuirschen Ausdruck, womit sie andeuten, da? zwei Sorptionsmechanismen gleichzeitig wirksam sind: die Auffüllung der Mikrohohlr?ume im Inneren des Polymergefüges und eine normale Henrysche L?sung. Kinetische Sorptions-Desorptionsuntersuchungen haben gezeigt, da? es sich bei Poly?thylen und Polyamid im ganzen Druckbereich um eine Ficksche Diffusion handelt. Das gleiche gilt für Polycarbonat bei Drucken bis zu etwa 25 cm Hg, jedoch nicht für h?here Drucke. Für jedes Polymer wurden die Diffusionskoeffizienten mit Hilfe von station?ren Permeationsund nichtstation?ren Sorptions- und Desorptionsverfahren ermittelt, wobei die Verfahren ?hnliche Werte ergaben.