Estimation of diffusion and permeability coefficients of CO2 in polymeric membranes by FTIR method

Infrared spectra of CO₂ sorbed in rubbery and glassy polymeric membranes were measured to examine the relationships between the spectroscopic data and the physical properties of the membranes. The two peaks observed in the spectra of CO₂ were attributed to the R branch and P branch of CO₂ sorbed in the membranes based on the consideration that both peaks were observed at a temperature above the glass transition temperature of the membranes. Apparent diffusion coefficients of CO₂ in the membranes were measured from the desorption kinetics of CO₂ detected by FTIR spectroscopy. The solubility coefficients of CO₂ were also estimated from absorbance spectra of CO₂ sorbed in the membranes using Lambert-Beer's rule. The permeability, solubility, and diffusion coefficients estimated by the FTIR method were found to correlate well with the coefficients obtained by conventional methods such as vacuum-pressure or sorption isotherm methods. © 1996 John Wiley & Sons, Inc.     

Transient and steady-state permeation in poly(ethylene terephthlate) above and below the glass transition

Transient and steady-state permeation data are reported for CO₂ in semicrystalline poly(ethylene terephthalate) for temperatures ranging from 25 to 115°C over the pressure range from 1 to 20 atm. The pressure dependency of the time lag and permeability disappears completely above the glass transition of the polymer, and Fick's law with a concentration-independent diffusion coefficient applies. In the glassy state, a concentration-dependent diffusion coefficient is necessary to describe the data. The form of this concentration dependence is described well by the partial immobilization transport model that attributes a different mobility to each of the two populations of sorbed gas which exist in local equilibrium with each other in glassy polymers. The importance of reporting the pressure used in transport experiments involving glassy polymers is emphasized by comparing the difference in the activation energy of the apparent diffusivity calculated from the measured time lag at 1 and 20 atm. Also, the magnitude of the observed slope discontinuity at T_g in Arrhenius plots of these apparent diffusities is shown to be a function of the upstream pressure used in the experiment. The independently measured time lags are compared with the predicated values calculated from various transport models and found to be described best by the partial immobilization model.     

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.     

Diffusion with discontinuous swelling. V. Type II diffusion into sheets and spheres

Type II diffusion into uniform spheres (radius R) and sheets (thickness 2l) is calculated under the assumption that the glass-gel boundary proceeds at a constant velocity v from the surface towards the interior of the sample, that the diffusion coefficient D_g in the glass is constant and that the diffusion coefficient D_r of the rubbery gel is so much higher than vR or vl that practically no sorbate gradient is needed for the transport through the gel of the sorbate. The diffusion process is completed when this boundary reaches the center of the sample. The concentration profile of the sorbate in the glassy matrix in front of the boundary varies with time and velocity v. It does not, however, influence the boundary propagation velocity. Hence the often observed increase of the rate of the weight gain just at the end of the diffusion process is not considered at all. The relative weight gain of the sample W(t)/W_∞ as a function of time is the only quantity usually measured. From the ordinate intercept A and the initial slope B of the plot of W(t)/t^1/2W_∞ vs. t^1/2, one can calculate the characteristic transport properties, i.e., the diffusion coefficient D_g of the glass and the velocity v of the glass–gel boundary.     

Sorption of carbon dioxide in fluorinated poyimides

Sorption isotherms of CO₂ for ten fluorinated polyimides measured at 35°C and up to about 25 atm are analyzed according to the dual-mode sorption model. Sorption properties for these polyimides are compared with those for other glassy Polymers including unfluorinated polyimides. The glassy polymers with higher glass transition temperatures T_g tend to show greater CO₂ sorption. Introduction of a ? C (CF₃)₂? linkage into the repeat unit of the main chain increases the sorption by 20–80%. For glassy polymers, including the fluorinated and unfluorinated polyimides, the Langmuir affinity constant b and Henry's law solubility constant k_D are correlated with the content of functional (carbonyl or sulfonyl) groups [FG], and composite parameter reflecting the magnitude of both [FG] and free-space fraction V_F, respectively, with some exceptions. The Langmuir capacity constant C′_H is correlated with T_g, but there are two correlation lines; one for unfluorinated polyimides and a different one for other glassy polymers including fluorinated polyimides. The slope of the former group is smaller probably because of smaller differences in thermal probably because of smaller differences in thermal expansion coefficients in rubbery and glassy states. Most fluorinated polyimides show greater solubility of CO₂ than unfluorinated polyimides and other glassy polymers, because of their larger C′_H and k_D. © 1993 John Wiley & Sons, Inc.     

Gas sorption in poly(vinyl benzoate)

High-pressure sorption (up to 50 atm) for CO₂, N₂, and Ar in poly(vinyl benzoate) (PVB) was studied at temperatures from 25 to 70°C by a gravimetric method utilizing an electromicrobalance. The results are described by Henry's law above the glass transition temperature T_g for all gases. The dual-mode sorption model, Henry's law plus a Langmuir isotherm, applies to the sorption isotherms of N₂ and Ar in the glassy state, and the dual-mode parameters are given. For CO₂, a new type of sorption isotherm is observed below T_g. The isotherm is concave to the pressure axis in the low-pressure region and turns into a straight line with increasing CO₂ pressure which can be extrapolated back to the coordinate origin. The linear part of the isotherm is characteristic of the rubbery state, while the nonlinear part stems from glassystate behavior. The “glass transition solubility” of CO₂, at which PVB film changes from the glassy to the rubbery state, decrease as the temperature increases. The disappearance of microvoids, that is, the decrease of the Langmuir capacity, may be due to a large plasticizing effect of sorbed CO₂. The difference between the N₂ and Ar isotherms and the CO₂ isotherm is discussed from this standpoint.     

Conductance and relaxations in the glassy and rubber states of aqueous poly( vinyl pyrrolidone): A cryofixation medium

The dielectric permittivity and loss of poly(vinyl pyrrolidone), molecular weight 40,000, containing 40% (by weight) water have been measured over the temperature range 77–325 K and frequency range 12 Hz to 0.1 MHz. A prominent relaxation due to rotational diffusion of water molecules in a hydrogen-bonded structure occurs at T < T_g (237 K). The half-width of the dipolar relaxation spectra is 2.27 decades and is temperature independent, which is strikingly different from the corresponding features of pure polymers. It is concluded that H-bonded amorphous solid water persists in the glassy polymer matrix and that the H-bonded structure contains the pyrrolidone side groups of the randomly oriented chain. The relaxation peak at T near T_g is masked by a large dc conductivity which, when expressed in terms of electric modulus, has a spectrum of half-width 1.37 instead of 1.14 decades expected for dc conductivity alone. The contribution from dipolar reorientation in the glass-rubber range of the PVP-H₂O solution is smaller than that in its sub-T_g relaxation.     

Water sorption in poly(ammonium sulfopropylbetaines). I. Differential scanning calorimetry

The hydration of four amorphous acrylic and methacrylic poly(zwitterions) bearing the ammonium sulfopropylbetaine function as a side-groups () was studied by differential scanning calorimetry over broad ranges of temperature (150-400 K) and water content (weight fraction W₁ < 0.5). Analyses were made of the first-order transitions and heat capacity of sorbed water, glass transition temperature (T_g) measurements. Nonfreezable bound water, about 7.7 ± 0.9 mol/monomeric unit, behaves as a single phase: Its mobility, fairly similar to that of bulk liquid water in viscoelastic systems at T > 250 K, decreases with temperature in the glassy systems, but never disappears, even at 185 K. The depression of the glass transition temperature of the hydrated polymers obeys Couchman's equation: T_g = Σ_i W_i ΔC_pi T_gi / Σ_gi W_iΔC_pi. Freezable bound water, about 6.7 ± 0.9 mole/monomeric unit, shows multipeak melting endotherms in the range 242–272 K. Because of their charged sites, the hydration process of the poly(zwitterions) appears more similar to that of poly(electrolytes) than to that of uncharged hydrophilic polymers. © 1992 John Wiley & Sons, Inc.     

An application of an homogenization method to a model of diffusion in glassy polymers

The sorption of gases in polymers below their glass-transition temperature T_g is known in many cases to be described by the “dual sorption” theory, according to which the gas is held in accordance with both the Langmuir and Henry's laws. Based on this theory, expressions for the “effective diffusion coefficient” in the glassy polymers have been obtained by investigators in the past, notably by Paul and Koros.² The present analysis regards the glassy polymers as inhomogeneous with regions on which the gas sorption follows the Langmuir law. Assuming that the linear dimensions of these regions, which are often referred to as “microvoids” (although they are not space filled by vacuum), are small compared to the macroscopic length of interest but large compared to the mean free path of the penetrant gas molecules, we derive a rigorous relation between the average flux and the concentration gradient in the polymer and show that this relation can be expressed in terms of an “effective diffusion coefficient” D_eff which depends on the details of the microstructure, i.e., the size, shape and spatial distribution of the “microvoids.” This expression for D_eff is shown to reduce to that of Paul and Koros² in two situations: (1) when the “voids” consist of slabs running parallel to the concentration gradient, and (2) when the “voids” are spherical and the temperature of the polymer is not too different from T_g. The results of the present study lead to an alternative procedure for interpreting the experimental data on sorption and permeation which may have some advantages over the procedure currently employed. Finally, the analysis presented here is also applicable to polymers containing adsorptive fillers.     

Thickness dependence of structural relaxation in spin‐cast polynorbornene films with high glass transition temperatures (>613 K)

The isothermal structural relaxation (densification) of a family of glassy polynorbornene films with high glass transition temperatures (T_g > 613 K) is assessed via spectroscopic ellipsometry. Three polymers were examined: poly(butylnorbornene) (BuNB), poly(hydroxyhexafluoroisopropyl norbornene) (HFANB), and their random copolymer, BuNB‐r‐HFANB. The effective aging rate, β(T), of thick (∼1.2 μm) spun cast films of BuNB‐r‐HFANB is approximately 10⁻³ over a wide temperature window (0.49 < T/T_g < 0.68). At higher temperatures, these polymers undergo reactions that more dramatically decrease the film thickness, which prohibits erasing the process history by annealing above T_g. The aging rate for thick BuNB‐r‐HFANB films is independent of the casting solvent, which infers that rapid aging is not associated with residual solvent. β (at 373 K) decreases for films thinner than ∼500 nm. However, the isothermal structural relaxation of thin films of BuNB‐r‐HFANB exhibits nonmonotonic temporal evolution in thickness for films thinner than 115 nm film. The thickness after 18 h of aging at 373 K can be greater than the initial thickness. The rapid aging of these polynorbornene films is attributed to the unusual rapid local dynamics of this class of polymers and demonstrates the potential for unexpected structural relaxations in membranes and thin films of high‐T_g polymers that could impact their performance. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 53–61     

Diffusion Kinetics at Liquid‐Glassy Polymer Interphases

Summary: We explored the diffusion mechanisms in a series of liquid/glassy polymer interphases. The diffusion experiments were performed in a unique way: the temperature range studied encompassed the glass transition temperature (T_g) of the glassy matrices. We observed that the diffusion behavior of the liquid polymer was remarkably continuous when passing through the matrix T_g, and that the diffusion modes at the liquid/glassy interphases were very similar to those observed in liquid/liquid polymer diffusion.

Diffusion profiles of liquid PS in glassy PPO obtained by confocal Raman spectroscopy. The sample was held at 160 °C for the times indicated in the plot.     

Gravimetric study of high-pressure sorption of gases in polymers

A gravimetric method for determining precisely the solubility of gases in polymers at high pressure is described. The solubilities of N₂ and CO₂ in low-density polyethylene (LDPE); CO₂ in polycarbonate (PC); and N₂, CH₄, C₂H₆, and CO₂ in polysulfone (PSUL) have been measured as a function of pressure up to 50 atm. Most of the measured sorption isotherms agreed closely with published data, but reproducible and time-dependent hysteresis in the sorption of CO₂, C₂H₆, and CH₄ in glassy polymers, PC, and PSUL, was observed in this study for the first time. Like the well known conditioning effect of high-pressure CO₂ on the sorption capacity of glassy polymers, these hysteresis phenomena are believed to be due to the plasticizing effect of sorbed gases. On the basis of the current data, the dual-mode sorption model including the plasticization by sorbed gas is discussed and a primitive equation for the concentration of sorbed gases in a quasiequilibrium state of sorption or desorption is proposed.     

Sorption of water vapor by poly(vinyl acetate)

Summary The sorption property of water vapor by poly(vinyl acetate) (PVAc) of relatively low glass transition temperature (T _g) was studied at temperatures nearT _g.Tc_g of humidity-controlled samples of various moisture contents was measured and its variation with the moisture content was determined.T _g of the dry sample was estimated by dilatometry and DSC methods, and to confirm the value, the temperature dependence of mutual diffusion coefficient of the system of water vapor + PVAc was determined. A difference between the sorption mechanisms of water vapor by PVAc at 20 and 30 °C was observed: two sorption mechanisms are involved at 30 °C, while three mechanisms at 20 °C are involved which include the above two and another intermediate one. In earlier stage of sorption, at both 20 and 30 °C, water molecules sorbed by PVAc showed a tendency towards aggregation, while a mixing effect was found at higher stage of the sorption.

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Zusammenfassung In der Arbeit werden Wasserdampfsorptionseigenschaften von Polyvinylacetat mit relativ niedriger Glastemperatur (T _g) in der Nähe vonT _g untersucht. Es wurden Plastizitätseinflüsse und Veränderungen vonT _g mit dem Wassergehalt studiert. Es wurde gefunden, daß bei 30 °C ein 2-Stufen-Sorptionsmechanismus, bei 20 °C ein 3-Stufen-Mechanismus existiert.

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With 7 figures     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Effect of temperature and membrane preparation parameters on gas permeation properties of polymethacrylates

Permeabilities of N₂, Ar, O₂, CO₂, and H₂ gases in PEMA (Polyethylmethacrylate) membranes have been measured above and below glass transition in the temperature range of 25–70 °C. The permeabilities of the gases were observed increasing with temperature. Arrhenius plot of permeability versus temperature data showed that there is a slope discontinuity at near to T_g of PEMA. In addition, the effects of membrane preparation parameters by solvent casting method (percentage of polymer in solvent, annealing temperature, annealing time, evaporation temperature, and evaporation time) have been investigated by using homogenous dense membranes of PEMA. It is observed that membrane preparation parameters strongly affect the membrane performance and the reproducibility of the permeability measurements. On the other hand, the effect of polymer structure on membrane performance has been investigated. Comparison of the permeabilities of N₂, Ar, O₂, CO₂, and H₂ gases in PEMA and PMMA membranes shows that PMMA membranes have smaller permeabilities and higher selectivities than PEMA membranes because of their higher glass transition temperature, T_g. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3025–3033, 2007     

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.     

Transport of water in polyvinyl alcohol films: Effect of thermal treatment and chemical crosslinking

Data on sorption and transport of water in polyvinyl alcohol films, modified by thermal treatment above T_g, or by chemical crosslinking with glutaraldehyde at different crosslinking degrees, are presented. Equilibrium swelling is constrained by both treatments, except for low degrees of crosslinking where the said reduction is counterbalanced by the partial loss of crystallinity. Analysis of the resulting water uptake kinetics indicates that viscous relaxation effects are, at least partly, responsible for the observed non-Fickian kinetic behavior. Thermodynamic diffusion coefficients of water, D_W, and relaxation frequencies of the swelling polymer, β_W, are determined by application of a theoretical model accounting for relaxation-dependent sorption kinetics in glassy polymers. The results indicate that the effect of both heat-treatment and chemical crosslinking is more intense on the macromolecular relaxation process than on the diffusion coefficient of water. Comparison of the release kinetics of a model drug from as-prepared, non-crosslinked and from crosslinked matrices indicate that the retardation of macromolecular relaxations process induced by crosslinking results in a more uniform release rate.     

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.     

A relationship between macroradical decay kinetics and α-segmental dynamics in glassy amorphous polymers

For a series of five amorphous polymers with a broad range of T_g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T_tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T₀ of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for α-segmental dynamics. This parameter represents the onset of α-segmental mobility in glassy state below T_g. A nontraditional way of the estimation of T₀ values for α-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested. © 1996 John Wiley & Sons, Inc.     

Mechanism of thermal decolorization of benzospirans in some amorphous polymeric matrices

The photochromic effect has been investigated for three compounds of the benzospiran group dissolved in amorphous polymers: poly(methyl methacrylate), poly(n-butyl methacrylate), poly(vinyl acetate), and poly(vinyl n-butyrate). The kinetics of the thermal bleaching reaction above T_g of the matrix follow a first-order equation due to the averaging of free volume distribution related to the diffusion of segments in viscoelastic state. A more complex mechanism of decolorization below T_g has been considered from the point of view of unequal, discrete distribution of environments in which the photochromic molecules exist in the glassy matrix. A change of the activation energy and the mechanism of color decay on passing through T_g is not a rule (PVB), which shows, that for a polymer having long, flexible chains, secondary glass transition phenomena play a decisive role. In the case of glassy polymers (PMMA), the photochromic effect of benzospirans may be employed to determine T_β. It seems, that in addition to steric restrictions for trans–cis isomerization in the decolorization process one must consider the interactions of photochromic molecules with the matrix as well as their chemical nature.