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     

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     

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     

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     

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     

Simulation of experimentally observed dilation phenomena during integral gas sorption in glassy polymers

A molecular modeling investigation of dilation effects induced by sorbed gas molecules in two glassy polymers is presented. As experimental reference, integral sorption of CO₂ and CH₄ was measured for polysulfone (PSU) and a polyimide (6FDA‐TrMPD, PI4) at 308 K and a pressure of 10 bar. Simultaneously, the gas induced swelling effect was measured with a dilatometer based on a capacitive distance sensor recorded. The experimental evidence of the (on the observed time scale and concentration levels) elastic nature of the gas induced dilation is supported by the dilation and contraction behavior observed in molecular dynamics (MD) simulations of respective detailed atomistic packing models. These models were constructed in accordance with gas concentration levels obtained from the experimental sorption results. Quantitative deviations between simulated and measured dilations are discussed as a consequence of an anelastic response of the polymer matrix which is too fast to be resolved in the experiments whose kinetics is dominated by diffusional processes. In the simulation, the initial insertion of penetrant molecules into equilibrated packing models “circumvents” the slow diffusional process of the experiment and allows a reasonable representation of the dilation process as well as a closer investigation. Our simulation approach reveals a different behavior for PSU and PI4 on the corresponding time scale. Most likely, the different chain mobility of the two polymers is responsible for the respective response to the inserted amount of gas molecules which is discussed in terms of the different chain mobilities of the two polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 59–71, 2008     

In situ preparation of powder and the sorption behaviors of molecularly imprinted polymers through the complexation between polymer ion of methyl methacrylate/acrylic acid and Ca ion

Molecularly imprinted polymer (MIP) powders were prepared using a simple complexation strategy between the polymer carboxylate groups and template molecule followed by metal cation cross-linking of residual polymer carboxylates. Polymer powders were formed in situ by templating carboxylic acid containing polymers with 4-ethylaniline (4-EA), followed by addition of an aqueous CaCl₂ solution. The solution remained homogeneous. The powders were prepared by precipitation by slowly adding a non-solvent, H₂O, to the mixture. The resulting particles were very porous with uptake capacity that approached the theoretical value. We suggest two types of complexes are formed between the template, 4-EA, and polymer. The isolated entry type forms well defined cavities for the template with high specific selectivity, while the adjacent entry type forms wider binding sites without specific sorption for isomeric molecules. To evaluate conditions for forming materials with high affinity and selectivity, three MIPs were prepared containing 0.5, 1.0, and 1.5 equivalents of template to the base polymer. The MIP containing 0.5 eq showed higher specific selectivity to 4-EA, but the MIP containing 1.5 eq had noticeably lower selectivity. The lower selectivity is attributed to poorly formed binding sites with little selective sorption to any isomer when the higher ratio of template was used. However at the lower ratio of template the isolated entry is preferably formed to produce well defined binding cavities with higher selectivity to template.     

Glassy polymer‐sorption phenomena measured with a quartz crystal microbalance technique

The quartz crystal microbalance (QCM) method is applied to the measurement of CO₂ sorption in glassy poly(ethylene terephthalate) (PET), poly(methyl methacrylate), and polysulfone. Polymer thin films in the thickness range of 350–550 nm are prepared by spin‐casting onto the quartz crystal devices. Sorption isotherms at temperatures below the glass transition are analyzed with the dual‐mode sorption model. As‐cast, quenched, and slow‐cooled thermal‐conditioning protocols yield consistent trends in the sorption level, namely, as‐cast > quenched > slow‐cooled. The sorption levels and model results for the quenched‐conditioned samples measured with QCM compare favorably with those reported from the pressure‐decay and gravimetric methods on thick films. With extended analysis of PET, the QCM technique is also useful for the exploration of the temperature dependence associated with gas sorption in glassy polymer systems. Measured heats of sorption and the collapse of the Langmuir component near the PET glass‐transition temperature agree with those reported previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2109–2118, 2003     

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.     

Hydration mechanism of polysaccharides: A comparative study

Water sorption was studied at 20 °C on films composed of different natural polymers. Three polysaccharides were investigated: chitosan, cellulose, and alginate. The major differences between these polymers, from a structural point of view, lay in the substitution of an OH group by an NH₂ function for chitosan and by an ionic COO^?Na⁺ group for alginate. An analysis of the experimental water sorption isotherms, expressed as the number of water molecules sorbed per repeating unit in the amorphous phase, associated with an analysis of the enthalpy profile related to the water sorption allowed us to propose a water sorption mechanism in two steps for all the polymers: water sorption on polymer‐specific sites in the first step and water clustering around the first sorbed water molecules in the second step. It was determined that two water molecules interacted with the polymer chains for cellulose and chitosan, whereas four water molecules were bonded to alginate chains. The specific sorption sites were identified as OH groups for cellulose, OH and NH₂ groups for chitosan, and ionic and OH groups for alginate. A systematic reduction of the half‐sorption time was observed in the activity range corresponding to this first sorption step, and it was explained by a water plasticization effect. On the other hand, an increase in the half‐sorption time was observed in the second sorption step, at a high activity (>0.8), for chitosan and alginate. A modelization associating the Guggenheim–Anderson–de Boer model and the clustering theory, applied to our systems, allowed us to relate the occurrence of this last phenomenon to the formation of water clusters containing more than two water molecules. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 48–58, 2005     

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.     

Sorption of oxygen by glassy poly(ethyl methacrylate) at low temperatures

The solubility of molecular oxygen in glassy poly(ethyl methacrylate) at 160–308 K and a gas pressure from 50 kPa to 1.7 MPa is studied. The kinetics of desorption of O₂ molecules from films in vacuum at 175 K is investigated at various initial gas concentrations in the glass. It is shown that the dependences of concentration of the dissolved oxygen on temperature and pressure may be described if the intermolecular cavities in the glass are regarded as sorption sites and if the presence of distributions over the energies of insertion of the molecules into these sites are assumed. The same values of sorption-site concentrations and insertionenergy dispersions make it possible to describe both the solubility of the gas and the dependence of the desorption kinetics of oxygen on its initial concentration in the glass. The concentration of sites does not change with temperature throughout the studied temperature range and amounts to ~3.5×10²⁷ m^–3. The function of the distribution over energies is likewise independent of temperature and the concentration of oxygen in the glass up to ~6.5×10²⁶ m^–3 (at 160 K). The dispersion of energies is ~3.9 kJ/mol. The temperature independence of the concentration of sites is explained by the fact that the sizes of cavities in the glass change very weakly at temperatures below the glass-transition temperature.     

Competitive permeation of gas and water vapour in high free volume polymeric membranes

Highly permeable glassy polymeric membranes based on poly (1‐trimethylsilyl‐1‐propyne) (PTMSP) and a polymer of intrinsic porosity (PIM‐1) were investigated for water sorption, water permeability and the separation of CO₂ from N₂ under humid mixed gas conditions. The water sorption isotherms for both materials followed behavior indicative of multilayer adsorption within the microvoids, with PIM‐1 registering a significant water uptake at very high water activities. Analysis of the sorption isotherms using a modified dual sorption model which accounts for such multilayer effects gave Langmuir affinity constants more consistent with lighter gases than the use of the standard dual mode approach. The water permeability through PTMSP and PIM‐1 was comparable over the water activities studied, and could be successfully model ed through a dual mode sorption model with a concentration dependent diffusivity. The water permeability through both membranes as a function of temperature was also measured, and found to be at a minimum at 80 ° C for PTMSP and 70 °C for PIM‐1. This temperature dependence is a function of reducing water solubility in both membranes with increasing temperature countered by increasing water diffusivity. The CO₂ ‐ N₂ mixed gas permeabilities through PTMSP and PIM‐1 were also measured and model ed through dual mode sorption theory. Introducing water vapour further reduced both the CO₂ and N₂ permeabilities. The plasticization potential of water in PTMSP was determined and indicated water swelled the membrane increasing CO₂ and N₂ diffusivity, while for PIM‐1 a negative potential implied that water filling of the microvoids hampered CO₂ and N₂ diffusion through the membrane. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 719–728     

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     

Structure and properties of the mesophase of syndiotactic polystyrene—III. Selective sorption of the mesophase of syndiotactic polystyrene

Syndiotactic polystyrene (sPS) has various crystalline forms such as α, β, γ, and δ forms, and a mesophase depending on the preparation method. In this study, we focused on the mesophase with the molecular cavity of sPS, which is obtained by step‐wise extraction of the guest molecules from the sPS δ form. To prepare the mesophase containing different shapes and sizes of the cavity, two kinds of the sPS δ form membrane cast from either toluene or chloroform solution were first prepared and then the guest molecules were removed by a step‐wise extraction method using acetone and methanol. We could succeed in the preparation of two kinds of mesophase with different shapes and sizes of the molecular cavity. Either toluene or chloroform vapor sorption to the sPS mesophase membranes was examined at 25 °C. Sorption analysis indicates that the mesophase with large molecular cavities can mainly sorb large molecules; on the other hand, the mesophase with small cavities can sorb only the small molecules, and is unable to sorb a large amount of large molecule because the cavity was too small to sorb the large molecules. Therefore, the sPS mesophase membrane has sorption selectivity based on the size of the molecular cavity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 238–245, 2004     

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     

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     

Pressure and temperature dependence of the gas‐transport properties of dense poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] membranes

The gas‐transport properties of poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] (6FDA‐2,6‐DAT) have been investigated. The sorption behavior of dense 6FDA‐2,6‐DAT membranes is well described by the dual‐mode sorption model and has certain relationships with the critical temperatures of the penetrants. The solubility coefficient decreases with an increase in either the pressure or temperature. The temperature dependence of the diffusivity coefficient increases with an increase in the penetrant size, as the order of the activation energy for the diffusion jump is CH₄ > N₂ > O₂ > CO₂. Also, the average diffusion coefficient increases with increasing pressure for all the gases tested. As a combined contribution from sorption and diffusion, permeability decreases with increases in the pressure and the kinetic diameter of the penetrant molecules. Even up to 32.7 atm, no plasticization phenomenon can be observed on flat dense 6FDA‐2,6‐DAT membranes from their permeability–pressure curves. However, just as for other gases, the absolute value of the heat of sorption of CO₂ decreases with increasing pressure at a low‐pressure range, but the trend changes when the feed pressure is greater than 10 atm. This implies that CO₂‐induced plasticization may occur and reduce the positive enthalpy required to create a site into which a penetrant can be sorbed. Therefore, a better diagnosis of the inherent threshold pressure for the plasticization of a glassy polymer membrane may involve examining the absolute value of the heat of sorption as a function of pressure and identifying the turning point at which the gradient of the absolute value of the heat of sorption against pressure turns from a negative value to a positive one. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 354–364, 2004     

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