Sorption and diffusion of water in poly(vinylpyrrolidone)

The effect of molecular mass, thermal prehistory, physical state, and three-dimensional chemical crosslinked structure of a polymer on dissolution and diffusion in the PVP-water system has been studied. The kinetic dependences of sorption that correspond to the Fickian or pseudonormal type have been measured. In a certain concentration range, sorption is accompanied by transition of the system to the rubbery state. In the glassy state, the negative concentration dependence of the diffusion coefficient related to the nonequilibrium state of the polymer sorbent is observed. Sorption isotherms are described by S-shaped curves. It has been shown that the thermal prehistory of the polymer sorbent has the most pronounced effect on its sorption behavior. The effect of molecular mass is insignificant, while three-dimensional chemical crosslinks in PVP manifest themselves only in the region of the rubbery state. In accordance with the double sorption model, the experimental isotherms are represented as the superposition of two isotherms described by the Langmuir and Flory-Huggins equations. For the glassy state of the polymer sorbent, the degree of the nonequilibrium state has been estimated. With due regard for the excess free volume, the detailed thermodynamic analysis of isotherms has been performed; namely, the pair interaction parameters and the free energy of mixing have been calculated. The state of water in the polymer has been examined within the framework of hydrate contributions and clusterization theory.     

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     

Partial molar volume of small molecules in glassy polymers

The sorption of atoms or molecules in glassy polymers is assumed to occur within a variety of sites belonging to the intermolecular volume and providing different space for the dissolved molecules. If the size of the small molecule is larger than the size of the site, the glassy polymer is elastically distorted during sorption of the solute molecules. Minimizing the total free energy yields the result that large sites are occupied first, giving rise to small volume changes only. By increasing the solute concentration, smaller sites have to be occupied as well and the corresponding volume changes are larger. Thus the molecules can be considered to act as probes for the intermolecular space. A quantitative analysis and comparison with experimental results provides information on the intermolecular space in a glassy polymer. Compared to the dual-sorption model, the model of this study is able to explain the nonlinear relationship between volume change of the polymer and the partial pressure of the solute. At large solute concentrations, swelling of the glassy polymer or its transformation into the rubbery state occurs, which gives rise to structural changes after desorption. © 1993 John Wiley & Sons, Inc.     

Effect of penetrant-induced isothermal glass transition on sorption,dilation, and diffusion behavior of polybenzylmethacrylate/CO2

The effect of a penetrant-induced isothermal glass transition on sorption, dilation, and diffusion behavior was studied in a single experimental run for CO₂ in cast polybenzylmethacrylate films. The dual-mode type sorption isotherms below the glass transition temperature of the polymer changed to linear ones above a certain concentration. Meanwhile, partial molar volume of CO₂ determined from the dilation of the films above the concentration gave a value very close to the one reported for rubbery polymers, and diffusion coefficients became less concentration-dependent. The results were conformable to the concept of unrelaxed volume in glassy polymers. © 1996 John Wiley & Sons, Inc.     

Interval kinetic gravimetric sorption of acetone in random copolymers of poly(ethylene terephthalate) and poly(ethylene 2,6-naphthalate)

Interval sorption kinetics of acetone in solvent cast films of random poly(ethylene terephthalate)-co-(ethylene 2,6-naphthalate) (PET-co-PEN) are reported at 35°C and at acetone pressures ranging from 0 to 7.3 cm Hg. Polymer composition is varied systematically from 0% to 50% poly(ethylene 2,6-naphthalate). Equilibrium sorption is well described by the dual-mode sorption model. Interval sorption kinetics are described using a two-stage model that incorporates both Fickian diffusion and protracted polymer structural relaxation. The incorporation of low levels of PEN into PET significantly reduces the excess free volume associated with the glassy state and, for these interval acetone sorption experiments in ∼ 5 μm-thick films, decreases the fraction of acetone uptake controlled by penetrant-induced polymer structural relaxation. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2973–2984, 1999     

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     

Effect of water sorption on oxygen‐barrier properties of aromatic polyamides

Aromatic polyamides based on poly(m‐xylylene adipamide) (MXD‐based polyamides) and poly(hexamethylene isophthalamide) (HMD‐based polyamides) were examined. Insight into the excellent gas‐barrier properties was obtained by the characterization of the effect of water sorption on the thermal transitions, density, refractive index, free‐volume hole size, and oxygen‐transport properties. Reversing the carbonyl position with respect to the amide nitrogen substantially lowered the oxygen permeability of MXD‐based polyamides in comparison with that of HMD‐based polyamides by facilitating hydrogen‐bond formation. The resulting restriction of conformational changes and segmental motions reduced diffusivity. The primary effect of water sorption was a decrease in the glass‐transition temperature (T_g) attributed to plasticization by bound water. No evidence was found to support the idea that sorbed water filled holes of free volume. When the polymer was in the glassy state, the drop in T_g accounted for hydration‐dependent changes in the density, refractive index, and free‐volume hole size. The correlation of the oxygen solubility with T_g and density confirmed the concept of oxygen sorption as filling holes of excess free volume. In some cases, water sorption produced a glass‐to‐rubber transition. The onset of rubbery behavior was associated with a minimum in the oxygen permeability. The glass‐to‐rubber transition also facilitated the crystallization of MXD‐based polymers, which complicated the interpretation of oxygen‐transport behavior at higher relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1365–1381, 2005     

Gas permeability and hydrocarbon solubility of poly[1‐phenyl‐2‐[p‐(triisopropylsilyl)phenyl]acetylene]

The effects of film thickness, physical aging, and methanol conditioning on the solubility and transport properties of glassy poly[1‐phenyl‐2‐[p‐(triisopropylsilyl) phenyl]acetylene] are reported at 35 °C. In general, the gas permeability coefficients are very high, and this polymer is more permeable to larger hydrocarbons (e.g., C₃H₈ and C₄H₁₀) than to light gases such as H₂. The gas permeability and solubility coefficients are higher in as‐cast, unaged films than in as‐cast films aged at ambient conditions and increase to a maximum in both unaged and aged as‐cast films after methanol conditioning. For example, the oxygen permeability of a 20‐μm‐thick as‐cast film is initially 100 barrer and decreases to 40 barrer after aging for 1 week at ambient conditions. After methanol treatment, the oxygen permeabilities of unaged and aged films increase to 430 and 460 barrer, respectively. Thicker as‐cast films have higher gas permeabilities than thinner as‐cast films. Propane and n‐butane sorption isotherms suggest significant changes in the nonequilibrium excess free volume in these glassy polymer films due to processing history. For example, the nonequilibrium excess free volume estimated from the sorption data is similar for as‐cast, unaged samples and methanol‐conditioned samples; it is 100% higher in methanol‐conditioned films than in aged, as‐cast films. The sensitivity of permeability to processing history may be due in large measure to the influence of processing history on nonequilibrium excess free volume and free volume distribution. The propane and n‐butane diffusion coefficients are also sensitive to film processing history, presumably because of the dependence of diffusivity on free volume and free volume distribution. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1474–1484, 2000     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

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     

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.     

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     

Thermodynamics of Swelling of Poly(N-vinylpyrrolidone)-Poly(ethylene glycol) Complex Due to Water Sorption

The deformation of sorbent caused by the sorption is new method of quantitative investigation “in situ” of interaction in system host-quest. The deformation of PVP-PEG complex, ϕ_PEG=0.36 and ϕ_PEG=0.20 due to water sorption has been studied by the measuring of the relative elongation of the polymer samples and the isotherms of water sorption simultaneously. The investigation of the sorption deformation gives the possibility of direct estimation of polymer sample free volume and it's variation during sorption, also the variation of Gibbs energy of system due to sorption according to the vacancy solution theory. The glassy-plastic state transition of polymer during water sorption has been observed.     

Pure hydrocarbon sorption properties of poly(1-trimethylsilyl-1-propyne) (PTMSP), poly(1-phenyl-1-propyne) (PPP), and PTMSP/PPP blends

Propane and n-butane sorption in blends of poly(1-trimethylsilyl-1-propyne) (PTMSP) and poly(1-phenyl-1-propyne) (PPP) have been determined. Solubilities of propane and n-butane increased as the PTMSP content in the blends increased. This result is consistent with the higher free volume of PTMSP-rich blends and the better thermodynamic compatibility between PTMSP and these hydrocarbons. Propane and n-butane sorption isotherms were well described by the dual-mode model for sorption in glassy polymers. PTMSP/PPP blends are strongly phase-separated, heterogeneous materials. A noninteracting domain model developed for sorption in phase-separated glassy polymer blends suggests that sorption in the Henry's law regions (i.e., the equilibrium, dense phase of the blends) is consistent with the model. However, Langmuir capacity parameters in the blends are lower than predicted from the domain model, suggesting that the amount of nonequilibrium excess free volume associated with the Langmuir sites depends on blend composition. © 1996 John Wiley & Sons, Inc.     

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.     

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.     

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.     

Pressure–volume–temperature properties and free volume parameters of PEO/PMMA blends

Melt-miscible polymer blends of poly(ethylene oxide)/atactic poly(methyl methacrylate (PEO/a-PMMA)) were prepared by melt-mixing and characterized by pressure–volume–temperature (PVT) dilatometry in the pressure and temperature range of 0 to 200 MPa and 20 to 200°C, respectively. The PVT data were analyzed in terms of two equations of state (EOS). The empirical Tait EOS was applied in the glassy, semicrystalline, and equilibrium melt state, and the Simha-Somcynsky EOS theory was applied in the equilibrium melt and glassy state. The Simha-Somcynsky EOS theory contains a free volume function. The temperature, pressure, and composition dependence of the free volume fraction h calculated from the Simha-Somcynsky EOS theory was studied. As a function of blend composition we observe that the free volume fraction, thermal expansivity, and compressibility all deviate mainly positively from linearity while the specific volume deviates mainly negatively from linearity. These findings are reconciled with composition-dependent free volume parameters, the free volume and cell volume as well as with self- and cross-interaction parameters derived from the Simha-Somcynsky EOS theory as applied to polymer mixtures. Moreover, the pressure dependence of glass and melting transitions as well as crystallization kinetics have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1061–1080, 1998     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Sorption of binary liquid mixtures on polymer networks Part I. Determination of surface excess isotherms and free energy functions

Two groups of polymer networks (polymer resins) are investigated by selective liquid sorption fromn-propanol-water mixtures. Group 1 consists of gel polymerized polar (hydrophilic) ion exchangers which swell in the binary liquid mixture. Group 2 consists of non-polar, non-swelling, macroporous resins. The free energy isotherms accompanying the sorption processes are calculated from the excess isotherms and the bulk activities. The adsorption excess free energies reveal the differences in polarity of the polymer network.