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.     

Gas permeation through glassy polymer membranes with relatively low glass-transition temperature

When the glass-transition temperature of the polymer is not so much higher than the experimental temperature, the pressure dependence of the mean permeability coefficient of the poly-mer membrane to a gas is apt to deviate from the prediction by the conventional dual-mode mobility model, and to obey a similar model with concentration-dependent diffusivities because of the plasticization action of sorbed gas in the polymer membrane. In this work, sorption and permeation for oxygen and carbon dioxide in a membrane of polystyrene whose glass-transition temperature is 95°C, were measured to discuss the mechanism of gas diffusion in glassy polymer membranes with relatively low glass-transition temperature at 30, 40 and 50°C respectively.     

Transient sorption of sulfur dioxide in epoxy resin of aliphatic diglycidyl ether

Diffusion of sulfur dioxide in epoxy resin of aliphatic diglycidyl ether was studied performing differential sorption kinetic measurements at temperatures ranging from 1°C to 45°C and activities varying from 0.12 to 0.55. The diffusion of sulfur dioxide appears to be Fickian over the entire temperature range studied. There is a marginal increase in the diffusion coefficient with increase in concentration. The diffusion coefficients evaluated from both “small times” data and “large times” data are in reasonable agreement.     

Sorption and permeation behavior for a gas in glassy polymer membrane near the glass transition temperature

The deviation from the conventional dual-mode sorption and mobility model for a gas in glassy polymer membranes has separately been studied thus far, and to simulate sorption and diffusion behavior, an extended dual-mode sorption model and a modified dual-mode mobility model, respectively, have been proposed independently. However, simultaneous deviation from the conventional dual-mode sorption and mobility model was observed in cases of CO₂in poly-4-methyl-1-pentene membrane at 20°C and in polystyrene membrane at 60 and 70°C. The plasticization effect of sorbed CO₂ on both the sorption and diffusion processes tends to be brought about in glassy polymer membranes near the glass transition temperature. The behavior was simulated based on the concept that only one population of sorbed gas molecules exists. © 1996 John Wiley & Sons, Inc.     

Anomalous sorption kinetics in the methanol vapor–poly(methyl methacrylate) system

The non‐Fickian sorption kinetics of methanol vapor in poly(methyl methacrylate) films 8 and 51 μm thick at 25°C are presented. The behavior of the system was studied in series of interval and integral absorption runs. The relevant diffusion coefficient and viscous relaxation processes were studied separately by kinetic analysis of the first and second stages of sorption kinetic curves. The sorption isotherm concaved upward at high activities, this being typical of Flory–Huggins behavior, whereas it exhibited a convex‐upward curvature at low methanol vapor activities, this indicating sorption in the excess free volume of the polymer matrix. After excess free‐volume fill‐up, the concentration dependence of the diffusion coefficient was found to be well represented by the free‐volume theory of Vrentas and Duda. Relaxation frequencies calculated from the second stage of two‐stage curves exhibited a weak dependence on the concentration. Integral sorption experiments indicated that the system exhibited nearly case II kinetics at high methanol vapor activities. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1184–1195, 2005     

Equilibrium solubility and permeability of sulfur dioxide in epoxy resin of aliphatic diglycidyl ether

Equilibrium sorption isotherms were obtained for the sulfur dioxide-epoxy resin of aliphatic diglycidyl ether system over a temperature range of 1° to 45°C. The sorption isotherms indicated the presence of Langmuir sorption due to specific interaction. This is uncommon for rubbery polymers, though similar behavior was also observed previously. Zimm-Lundberg's clustering analysis indicated a slight tendency for clustering of the penetrant molecules at low temperatures and higher activities. The number of Langmuir sites for sorption was found to be independent of temperature. The mobilities of the molecules sorbed in Henry's law mode and the Langmuir mode were found to be approximately equal. Predictions of the permeability values for this system are presented and compared with other data from the literature. The temperature dependence of different sorption parameters is presented and discussed in detail.     

Sorption and transport of CO2 above and below the glass transition of poly(ethylene terephthalate)

At temperatures at least 30°C above the glass transition (T_g) the sorption and transport of carbon dioxide in poly(ethylene terephthalate) (PET) can be described conveniently using Henry's law and Fick's law with a constant diffusion coefficient. Below T_g Fick's law with a concentration- dependent diffusion coefficient, coupled with a sorption isotherm which is concave toward the pressure axis adequately describes the observed sorption and transport data. Physical interpretations of the quantitative deviations from Henry's law and the form of the concentration dependence of the diffusion coefficient is provided by a model which hypothesizes dual modes of sorption and separate non zero mobilities of two populations of sorbed species in local equilibrium. The implications of the observed temperature variations of the phenomenological model parameters are discussed. Dilatometric parameters for PET, polycarbonate, and poly(acrylonitrile) (PAN) are shown to correlate well with a simple. relationship developed to explain the existence of the “extra” mode of sorption responsible for deviations from Henry's law for CO in glassy polymers. In the temperature range from T_g to + 20°C, deviations from Fickian behavior are also apparent. These effects are consistent with a transition in the nature of the polymer from an elastic solid below T_g to a viscous liquid above T_g In the narrow temperature range slightly above T the time scale for chain rearrangements apparently approaches that for the diffusion process. The polymer's viscoelastic response to the probing molecule, therefore, causes deviations from the classical time lag predictions. These deviations disappear 30°C above T_g.     

Sorption and diffusion of acrylonitrile monomer through crosslinked nitrile rubber

As the first step for the preparation of interpenetrating polymer networks from nitrile rubber and polyacrylonitrile, the sorption and diffusion of acrylonitrile monomer through nitrile rubber crosslinked by three different vulcanization systems—conventional (CV), dicumyl peroxide (DCP), and a mixture consisting of sulfur and peroxide (mixed)—were studied in the temperature interval of 30–70°C. Kinetic curves have been generated for these systems to compute diffusion and sorption coefficients. The equilibrium sorption is found to be maximum for the CV system. The molar mass between crosslinks (M_c) has estimated and compared with affine and phantom models. It was found that the M_c values follow the affine model. The diffusion coefficient values are highest for DCP and lowest for CV. It was observed that the kinetics of liquid sorption followed an anomalous behavior. The temperature dependence of the transport parameters was followed by an Arrhenius relationship, from which the activation energy for diffusion, permeation, and sorption were calculated. It is found that temperature activates diffusion in all cases. The polymer–solvent interaction parameter was determined. The amount of polysulfidic linkages in the rubber network was also estimated. The experimental results were compared with theoretical predictions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 941–952, 2000     

Transport properties of dichloromethane in glassy polymers. II. Amorphous syndiotactic polystyrene films

Sorption and diffusion of dichloromethane vapor were measured in amorphous syndiotactic polystyrene films, obtained with different cooling conditions and after controlled aging times at different temperatures. The diffusional behavior, at the temperature of 25°C, was characterized by three stages, depending on penetrant activity. In the first stage, at low activity, the diffusion coefficient was independent of vapor concentration; the second stage was characterized by concentration-dependent diffusion, whereas in the third stage, at high activity, the strong interaction solvent–polymer increased the mobility, allowing the polymer crystallization. The different cooling conditions neither have an effect on the diffusional behavior nor on the sorption curve. The aging, both at room temperature and at 70°C, did not change the diffusion parameters, but led to the appearance of more and more anomalous sorption behavior. The sorption curve, as a function of vapor activity, did not show any difference for the fresh and the aged-at-room temperature samples, whereas the samples aged at 70°C presented a lower sorption at low activity. The presence of ordered domains, impermeable to the penetrant at low activity, was suggested on the basis of sorption results. The solvent-induced crystallization was investigated for all the samples. Crystallization was induced at an activity of 0.45 for the fresh and the aged-at-room temperature samples; at variance, the samples aged at 70°C crystallize at a slightly higher activity, reaching, nevertheless, a higher level of crystallinity. © 1993 John Wiley & Sons, Inc.     

Determination of sorption kinetic parameters using the relaxation‐dependent solubility model in the methanol vapor—Poly(methyl methacrylate) system

The relaxation‐dependent solubility model was applied to simulate the experimentally observed sorption kinetic behavior of the PMMA–vapor MeOH system at 25°C, to obtain the main transport parameters. Application of the model in series of successive sorption kinetic runs covering small concentration intervals revealed certain trends in the concentration dependence of the diffusion coefficient of the system, not detectable by a previous simpler analysis of the data. Following excess free volume fill up, relaxation frequencies exhibit a weak exponential dependence on concentration. The functional dependence of the thermodynamic diffusivity on the concentration, deduced from the aforementioned simulation procedure, was tested and found to reproduce reasonably well the series of sorption kinetic runs covering considerably larger concentration intervals. In addition, this analysis indicates a strong dependence of the relaxation mechanism on the concentration interval. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2278–2288, 2006     

Sorption and transport of benzene in poly(ethylene terephthalate)

The kinetics and equilibria of benzene sorption in poly(ethylene terephthalate) were measured at 40°C, 50°C, and 60°C, with benzene activities ranging from 0.02 to 0.3. At most experimental conditions, diffusion was found to be Fickian; however, evidence of non-Fickian transport was found at the highest activity levels. Values of the diffusion coefficient of benzene range from 10^-14 cm²/s at 40°C to 10^?12 cm²/s at 60°C in the limit of low concentrations. Nonlinear isotherms observed for benzene sorption were successfully interpreted in terms of the dual mode model for sorption in glassy polymers, whereby the sorbed penetrant exists as two populations: one sorbed according to Henry's law and the other following a Langmuir isotherm. Non-Fickian transport data were correlated with a model that superimposes diffusion of both the Henry's law and Langmuir populations (the “partial immobilization” model) upon first-order relaxation of the polymer matrix.     

Breakthrough and Sulfate Conversion Analysis during Removal of Sulfur Dioxide by Calcium Oxide Sorbents

Sorption of sulfur dioxide (SO₂) was carried out on calcium‐based sorbents under dynamic conditions in a fixed bed. The experimental conditions were reaction temperature (700 to 1000°C), SO₂ concentration (1000‐10 000 ppm), sorbent particles size (1 to 2 mm) and the types of sorbents (hydroxide or carbonate). The sorption process was found to be effective at low concentration levels (less than 10 000 ppm) as the breakthrough time significantly decreased with increase in concentration. The maximum removal of SO₂ was observed at a reaction temperature of 950°C. The hydroxide‐based sorbents of relatively smaller particle size were found to exhibit superior sorption performance in terms of longer breakthrough time and higher sulfate conversion. A mathematical model developed, assuming a porous structure of the sorbent materials, attributed the low sulfation conversion during SO₂ sorption due to a pore diffusion mechanism.     

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.     

Sorption and migration of aliphatic organic esters into VITON® fluoroelastomer membranes

Sorption and migration of six aliphatic esters into four VITON^® fluoroelastomers were studied by a gravimetric sorption method in the temperature interval of 30–60°C. Fick's equation was used to obtain diffusion coefficients. The dependence of fluorine contents and the polymer morphology on the sorption and diffusion characteristics of esters was investigated. The permeability coefficients were obtained from the sorption and diffusion data. Fick's equation was solved to compute the concentration profiles of liquids at various locations within the membrane materials using initial and boundary conditions. These profiles were compared with those obtained from the numerical method based on finite difference technique. Activation parameters for diffusion and sorption were calculated using the Arrhenius relationship. These results were discussed in terms of molecular size and shapes of the esters. For higher esters, namely, n- and iso-amyl acetates, a concentration dependency of the diffusion coefficient was investigated. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1223–1235, 1997     

Sorption and transport of water vapor in glassy poly(acrylonitrile)

Sorption data for H₂O in glassy poly(acrylonitrile)(PAN) are presented for a range of relative vapor pressures at temperatures from 20 to 50°C. Simple dual mode sorption, involving “hole-filling” and molecular solution appears to dominate the low activity region of sorption. Based on the clustering analysis suggested by Zimm and Lundberg, pronounced clustering of penetrant appears to occur above a relative pressure of 0.6. The form of the effective concentration-dependent diffusion coefficient for H₂O in PAN, determined by analysis of steady state permeation data, suggests that water in the microvoids and clusters has a lower mobility than the molecularly dissolved water in the polymer matrix. Time lag measurements at high upstream relative water vapor pressures suggest that the transient state permeation has a non-Fickian character due to relaxations which occur slowly to accommodate the clustering process.     

Water in epoxy resins Part II. Diffusion mechanism

A model is proposed for the diffusion mechanism of water in glassy epoxy resins. The polymer network is assumed to consist of two regions in which water molecules possess different mobilities. By considering the distribution of water molecules among these regions it is possible to describe the concentration dependency of the diffusion coefficient in the sorption and resorption processes. The diffusion coefficient becomes constant when the sorption temperature is close to the effective glass transition temperature of the epoxy-water binary mixture. An explanation of this effect is also provided by the model.     

Humidity regulation by stretched PP and PLA films with dispersed CaCl2

Polymer materials that regulate the relative humidity in their environment are relevant for applications in the packaging and building sectors. By integration of salts in polymer structures, such materials are able to absorb and desorb high amounts of water vapor. In this study, films of polylactic acid and polypropylene with dispersed calcium chloride (2 and 4 wt %) were produced and biaxially stretched to induce the formation of cavities. The resulting cavities in these films account up to 10 vol % and are able to contain emerging calcium chloride solution formed by water vapor absorption. These films absorb reversibly up to 15 wt % water vapor at 75% relative humidity at 23 °C. This absorption behavior is described by effective diffusion and effective sorption coefficients. Using a simple model, the effective water vapor diffusion coefficient of these films can be estimated from the permeation coefficient of the polymer and the sorption coefficient of the absorber. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45713.     

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.     

Messung der Selbstdiffusion im System Polystyrol-Benzol; Temperatur-, Konzentrations- und Molekulargewichtsabhängigkeit

Self-diffusion of benzene and polystyrene in the system benzene-polystyrene is studied by means of spin-echo-technique as function of temperature, concentration and polymer molecular weight. From the dependence of temperature the activation energies are calculated as function of concentration and molecular weight. The concentration dependence is discussed in terms of restricted diffusion and the Fujita Free-Volume-Theory. The computed free volume shows a significant maximum at 50°C. This effect may be attributed to a change in the mobility of the phenyl side groups of polystyrene and is vanishing with decreasing molecular weight. The free-volume-temperature curves are giving references to the glass transition.     

Diffusion and Sorption of Organic Liquids Through Polymer Membranes. IX. Bromobutyl Rubber,Chlorosulfonated Polyethylene,and Epichlorohydrin Versus Substituted Monocyclic Aromatic Liquids

Sorption and diffusion of four monocyclic aromatic liquids—namely, chlorobenzene, o-dichlorobenzene, bromobenzene, and nitrobenzene into bromobutyl rubber, chlorosulfonated polyethylene, and epichlorohydrin—have been investigated in the temperature interval of 25–60°C by using a gravimetric technique. The transport results have been analyzed by using the Fickian model of diffusion. The dependence of transport coefficients on the size and shape of the penetrant molecules has been discussed. Transport coefficients have not shown any systematic variation with the penetrant size, but the results are greatly influenced by the polymer-solvent interactions. The Arrhenius activation parameters have been estimated from a temperature dependence of sorption, diffusion, and permeation coefficients. The first-order kinetic rate constants have been obtained from the time-dependent sorption data. Enthalpy and entropy of sorption for the polymer-solvent systems have been studied. The molar mass between network crosslinks was calculated from the Flory-Rehner theory. Computed parameters and experimental results are used to discuss the transport mechanism in terms of the type and nature of the polymer membranes and solvent molecules. None of the polymer membranes studied have shown any degradative reactions and significant swelling in the presence of the chosen solvents. The present results would have applications in areas such as those including the studies on barrier properties, separation science, and chemical pond lining, etc.