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     

High‐pressure sorption of carbon dioxide and methane in all‐aromatic poly(etherimide)‐based membranes

The sorption of compressed carbon dioxide and methane in a series of all‐aromatic poly(etherimide) (PEI) thin films is presented. The polymer films are derived from the reactions between an arylether diamine (P1) and four different dianhydrides [3,3′,4,4′‐oxydiphthalic dianhydride (ODPA), 3,3′,4,4′ biphenyltetra‐carboxylic dianhydride (BPDA), 3,3′,4,4′‐benzo‐phenonetetracarboxylic dianhydride (BTDA), and pyromellitic dianhydride (PMDA)] that have been selected to systematically change the flexibility of the polymer backbone, the segmental mobility, and the nonequilibrium excess free volume (EFV) of the polymer. The EFV, gas sorption capacities, and sorption‐ and temperature‐induced dynamic changes in film thickness and refractive index have been investigated by spectroscopic ellipsometry. The sorption capacity depends to a great extent on the PEI backbone composition. PMDA‐P1 shows the highest carbon dioxide sorption, combined with the lowest sorption selectivity because of the predominant sorption of methane in the EFV. For ODPA‐P1, the highest sorption selectivity is obtained, while it shows little long‐term relaxations at carbon dioxide pressures up to 25 bar. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 986–993     

Sorption,diffusion, and permeation of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne)

The solubility, diffusivity, and permeability of ethylbenzene in poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) at 35, 45 and 55 °C were determined using kinetic gravimetric sorption and pure gas permeation methods. Ethylbenzene solubility in PTMSP was well described by the generalized dual‐mode model with χ = 0.39 ± 0.02, b = 15 ± 1, and C^′_H = 45 ± 4 cm³ (STP)/cm³ PTMSP at 35 °C. Ethylbenzene solubility increased with decreasing temperature; the enthalpy of sorption at infinite dilution was −40 ± 7 kJ/mol and was essentially equal to the enthalpy change upon condensation of pure ethylbenzene. The diffusion coefficient of ethylbenzene in PTMSP decreased with increasing concentration and decreasing temperature. Activation energies of diffusion were very low at infinite dilution and increased with increasing concentration to a maximum value of 50 ± 10 kJ/mol at the highest concentration explored. PTMSP permeability to ethylbenzene decreased with increasing concentration. The permeability estimated from solubility and diffusivity data obtained by kinetic gravimetric sorption was in good agreement with permeability determined from direct permeation experiments. Permeability after exposure to a high ethylbenzene partial pressure was significantly higher than that observed before the sample was exposed to a higher partial pressure of ethylbenzene. Nitrogen permeability coefficients were also determined from pure gas experiments. Nitrogen and ethylbenzene permeability coefficients increased with decreasing temperature, and infinite dilution activation energies of permeation for N₂ and ethylbenzene were −5.5 ± 0.5 kJ/mol and −74 ± 11 kJ/mol, respectively. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1078–1089, 2000     

Gas permeability and n‐butane solubility of poly(1‐trimethylgermyl‐1‐propyne)

The gas permeability and n‐butane solubility in glassy poly(1‐trimethylgermyl‐1‐propyne) (PTMGP) are reported. As synthesized, the PTMGP product contains two fractions: (1) one that is insoluble in toluene and soluble only in carbon disulfide (the toluene‐insoluble polymer) and (2) one that is soluble in both toluene and carbon disulfide (the toluene‐soluble polymer). In as‐cast films, the gas permeability and n‐butane solubility are higher in films prepared from the toluene‐soluble polymer (particularly in those films cast from toluene) than in films prepared from the toluene‐insoluble polymer and increase to a maximum in both fractions after methanol conditioning. For example, in as‐cast films prepared from carbon disulfide, the oxygen permeability at 35 °C is 330 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 73 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. After these films are conditioned in methanol, the oxygen permeability increases to 5200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 6200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. The rankings of the fractional free volume and nonequilibrium excess free volume in the various PTMGP films are consistent with the measured gas permeability and n‐butane solubility values. Methanol conditioning increases gas permeability and n‐butane solubility of as‐cast PTMGP films, regardless of the polymer fraction type and casting solvent used, and minimizes the permeability and solubility differences between the various films (i.e., the permeability and solubility values of all conditioned PTMGP films are similar). © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2228–2236, 2002     

Gas transport behavior of mixed-matrix membranes composed of silica nanoparticles in a polymer of intrinsic microporosity (PIM-1)

Recently, high-free volume, glassy ladder-type polymers, referred to as polymers of intrinsic microporosity (PIM), have been developed and their reported gas transport performance exceeded the Robeson upper bound trade-off for O₂/N₂ and CO₂/CH₄. The present work reports the gas transport behavior of PIM-1/silica nanocomposite membranes. The changes in free volume, as well as the presence and volume of the void cavities, were investigated by analyzing the density, thermal stability, and nano-structural morphology. The enhancement in gas permeability (e.g., He, H₂, O₂, N₂, and CO₂) with increasing filler content shows that the trend is related to the true silica volume and void volume fraction.     

Ethylbenzene solubility,diffusivity, and permeability in poly(dimethylsiloxane)

The pure‐gas sorption, diffusion, and permeation properties of ethylbenzene in poly(dimethylsiloxane) (PDMS) are reported at 35, 45, and 55 °C and at pressures ranging from 0 to 4.4 cmHg. Additionally, mixed‐gas ethylbenzene/N₂ permeability properties at 35 °C, a total feed pressure of 10 atm, and a permeate pressure of 1 atm are reported. Ethylbenzene solubility increases with increasing penetrant relative pressure and can be described by the Flory–Rehner model with an interaction parameter of 0.24 ± 0.02. At a fixed relative pressure, ethylbenzene solubility decreases with increasing temperature, and the enthalpy of sorption is −41.4 ± 0.3 kJ/mol, which is independent of ethylbenzene concentration and essentially equal to the enthalpy of condensation of pure ethylbenzene. Ethylbenzene diffusion coefficients decrease with increasing concentration at 35 °C. The activation energy of ethylbenzene diffusion in PDMS at infinite dilution is 49 ± 6 kJ/mol. The ethylbenzene activation energies of permeation decrease from near 0 to −34 ± 7 kJ/mol as concentration increases, whereas the activation energy of permeation for pure N₂ is 8 ± 2 kJ/mol. At 35 °C, ethylbenzene and N₂ permeability coefficients determined from pure‐gas permeation experiments are similar to those obtained from mixed‐gas permeation experiments, and ethylbenzene/N₂ selectivity values as high as 800 were observed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1461–1473, 2000     

Gas permeation parameters and other physicochemical properties of a polymer of intrinsic microporosity: Polybenzodioxane PIM-1

A detailed study of gas permeation, thermodynamic properties and free volume was performed for a novel polymer of intrinsic microporosity (PIM-1). Gas permeability was measured using both gas chromatographic and barometric methods. Sorption of vapors was studied by means of inverse gas chromatography (IGC). In addition, positron annihilation lifetime spectroscopy (PALS) was employed for investigation of free volume in this polymer. An unusual property of PIM-1 is a very strong sensitivity of gas permeability and free volume to the film casting protocol. Contact with water in the process of film preparation resulted in relatively low gas permeability (P(O₂) = 120 Barrer), while soaking with methanol led to a strong increase in gas permeability (P(O₂) = 1600 Barrer) with virtually no evidence of fast aging (decrease in permeability) that is typical for highly permeable polymers. For various gas pairs (O₂/N₂, CO₂/CH₄, CO₂/N₂) the data points on the Robeson diagrams are located above the upper bound lines. Hence, a very attractive combination of permeability and selectivity is observed. IGC indicated that this polymer is distinguished by the largest solubility coefficients among all the polymers so far studied. Free volume of PIM-1 includes relatively large microcavities (R = 5 Å), and the results of the PALS and IGC methods are in reasonable agreement.     

Gas sorption and characterization of poly(ether‐b‐amide) segmented block copolymers

The solubilities of He, H₂, N₂, O₂, CO₂, CH₄, C₂H₆, C₃H₈, and n‐C₄H₁₀ were determined at 35°C and pressures up to 27 atmospheres in a systematic series of phase separated polyether–polyamide segmented block copolymers containing either poly(ethylene oxide) [PEO] or poly(tetramethylene oxide) [PTMEO] as the rubbery polyether phase and nylon 6 [PA6] or nylon 12 [PA12] as the hard polyamide phase. Sorption isotherms are linear for the least soluble gases (He, H₂, N₂, O₂, and CH₄), convex to the pressure axis for more soluble penetrants (CO₂, C₃H₈, and n‐C₄H₁₀) and slightly concave to the pressure axis for ethane. These polymers exhibit high CO₂/N₂ and CO₂/H₂ solubility selectivity. This property appears to derive mainly from high carbon dioxide solubility, which is ascribed to the strong affinity of the polar ether linkages for CO₂. As the amount of the polyether phase in the copolymers increases, gas solubility increases. The solubility of all gases is higher in polymers with less polar constituents, PTMEO and PA12, than in polymers with more polar PEO and PA6 units. CO₂/N₂ and CO₂/H₂ solubility selectivity, however, are higher in polymers with higher concentrations of polar repeat units. The sorption data are complemented with physical characterization (differential scanning calorimetry, elemental analysis, and wide angle X‐ray diffraction) of the various block copolymers. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2463–2475, 1999     

CO2 sorption in poly(butylene terephthalate)

The Sorption of CO₂ in poly(butylene terephthalate) (PBT) has been examined according to the equilibrium-sorption method in the pressure range of 1–30 bar at temperatures of 298–338 K. In the temperature range 298–328 K it does not respond to Henry's law. At about 20 K above the glass-transition temperature Langmuir adsorption takes place.Dedicated to Professor Dr. G. Kanig on his 70th birthday.     

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.     

Iron(II) and Nickel(II) Complexes of N‐Alkylimidazoles and 1‐Methyl‐1H‐1, 2, 4‐Triazole: X‐ray Studies,Magnetic Characterization,and DFT Calculations

Using the ligands N‐methylimidazole ( MeIm ), N‐ethylimidazole ( EtIm ), N‐propylimidazole ( PrIm ), and 1‐methyl‐1H‐1, 2, 4‐triazole ( MeTz ) three series with a total of 13 iron(II) complexes were isolated. The series comprise of the following complexes: (a) [Fe( MeIm )₆](ClO₄)₂ ( 1 ), [Fe( EtIm )₆](ClO₄)₂ ( 2 ), [Fe( PrIm )₆](ClO₄)₂( 3 ), [Fe( MeTz )₆](ClO₄)₂ ( 4 ), [Fe( MeIm )₆](MeSO₃)₂ ( 5 ), [Fe( EtIm )₆](MeSO₃)₂ ( 6 ), and [Fe( MeTz )₆](BF₄)₂ ( 10 ); (b) [Fe( MeIm )₄(MeSO₃)₂]( 7 ), [Fe( EtIm )₄(MeSO₃)₂] ( 8 ), and [Fe( PrIm )₄(MeSO₃)₂] ( 9 ); (c) [Fe( MeIm )₄(NCS)₂] ( 15 ), [Fe( EtIm )₄(NCS)₂] ( 16 ), and [Fe( MeTz )₄(NCS)₂] ( 17 ). Single crystal X‐ray diffraction studies were performed on 7 – 10 and 15 – 17 . Temperature dependent magnetic susceptibility measurements were performed on selective examples of all series, and confirmed them to be in the HS state over the range 6–300 K. DFT calculations were performed at BP86/def‐SV(P) and TPSSh/def2‐TZVPP level on all [Fe L ₆]²⁺ complex cations and the neutral complexes 7 – 9 and 15 – 17 . Additionally the four homoleptic nickel(II) complexes [Ni L ₆](ClO₄)₂ ( 11 : L = MeIm ; 12 : L = EtIm ; 13 : L = PrIm ; 14 : L = MeTz ) were synthesized and compounds 11 – 13 structurally characterized. UV/Vis/NIR spectroscopic measurements were carried out on all homoleptic iron(II) and nickel(II) complexes. The 10Dq values were determined to be in the range of 11547–11574 and 10471–10834 cm^–1 for the iron(II) and nickel(II) complexes, respectively.     

Surface characterization and sorption efficacy of tire‐obtained carbon: experimental and semiempirical study of rhodamine B adsorption

This work focuses on the surface characterization and sorption activity of carbon derived from waste tires. The carbon was prepared by thermal treatment of waste rubber tires, followed by exposure to nitric acid and hydrogen peroxide. The tired‐obtained activated carbon (AC) was evaluated using a variety of techniques. Fourier transform infrared spectroscope and Raman spectra reveal existence of hydroxyl and carboxylic groups on AC surface. Scanning electron microscope and Brunauer–Emmett–Teller revealed the porosity of AC is well developed with mesopore structure (mesopore volume of 0.96 cm³/g). AC was tested for Rhodamine B sorption, and the adsorption kinetics well fitted using a pseudo second‐order kinetic model. The adsorption isotherm data could be well described by the Langmuir model. Semiempirical calculations using Austin Model 1 were performed to explain the adsorption at molecular level. Binding enthalpies in the range of 0.5–4 kcal/mol of four possible scenarios were computed. We believe the combination between experimental work and semiempirical calculations allows for a better understanding of Rhodamine B molecules adsorption on the AC surface. Copyright © 2015 John Wiley & Sons, Ltd.     

Diiodobis(2‐hydroxymethyl‐1‐methyl‐1‐imidazole‐N3)cadmium(II)

The Cd atom in Cd(Hmmi)₂I₂ is five‐coordinate with a trigonal bipyramidal geometry in which the apical sites are occupied by I and O atoms. Copyright © 2005 John Wiley & Sons, Ltd.     

Influence of poly(N‐isopropylacrylamide) and poly(N,N′‐diethyl acrylamide) coatings on polysulfone/polyacrylonitrile‐based membranes for protein separation

Herein we describe the design and the assembly of temperature sensitive polysulfone (PS)/polyacrylonitrile (PAN) blend membranes using supercritical fluid technology. Blended membranes were prepared using the CO₂‐assisted phase inversion method, and their pores were coated with two thermoresponsive hydrogels‐poly(N‐isopropylacrylamide) (PNIPAAm) and poly(N,N′‐diethylacrylamide) (PDEAAm). Permeation experiments of bovine serum albumin (BSA) and lysozyme (LYS) solutions were used to evaluate the performance and temperature‐responsive behavior of coated membranes. While membranes coated with PNIPAAm presented similar protein permeation profiles at temperatures below and above its lower critical solution temperature, PDEAAm coating imparted a temperature‐responsive behavior to PS/PAN (90:10) membranes and selective permeation of proteins with different sizes. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthesis,characterization, and gas permeation properties of adamantane‐containing polymers of intrinsic microporosity

A new bis(catechol) monomer, namely, 4,4′‐((1r,3r)‐adamantane‐2,2‐diyl)bis(benzene‐1,2diol) (THADM) was synthesized by condensation of 2‐adamantanone with veratrole followed by demethylation of the formed (1r,3r)‐2,2‐bis(3,4 dimethoxyphenyl)adamantane. Polycondensation of THADM and various compositions of THADM and 5,5,6′,6′‐tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was performed with 2,3,5,6‐tetrafluoroterephthalonitrile (TFTPN) to obtain the homopolymer and copolymers. These polymers demonstrated good solubility in common organic solvents such as dichloromethane, chloroform, and tetrahydrofuran and could be cast into tough films from their chloroform solutions. GPC analysis revealed that number average molecular weights of polymers were in the range 48,100–61,700 g mol⁻¹, suggesting the formation of reasonably high molecular weight polymers. They possessed intrinsic microporosity with Brunauer‐Emmett‐Teller (BET) surface area in the range 703–741 m² g⁻¹. Thermogravimetric analysis of polymers indicated that 10% weight loss temperature was in the range 513–518 °C demonstrating their excellent thermal stability. THADM‐based polymer of intrinsic microporosity (PIM) showed P(CO₂) = 1080, P(O₂) = 232 and appreciable selectivity [α(CO₂/CH₄) = 22.6, α(CO₂/N₂) = 26.7, and α(O₂/N₂)= 5.7]. The gas permeability measurements revealed that with increase in the content of adamantane units in PIMs, selectivity increased and permeability decreased, following the trade‐off relationship. The gas separation properties of PIMs containing adamantane units were located close to 2008 Robeson upper bound for gas pairs such as CO₂/CH₄, CO₂/N₂, H₂/N₂, and O₂/N₂. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 16–24     

Mechanically Strong and Flexible Hydrolyzed Polymers of Intrinsic Microporosity (PIM‐1) Membranes

A systematic strategy to molecularly design flexible tough hydrolyzed polymers of intrinsic microporosity (hPIM‐1) films from the PIM‐1 polymer is explored in this study. Flexible films can be fabricated from N‐methyl‐2‐pyrrolidone (NMP) by appropriate hydrolysis conditions. The optimal weight ratio of NaOH/H₂O/EtOH in the base‐catalyzed reaction is 0.5/2/2. Because of the highly polar carboxylic acid groups, the resultant hPIM‐1 has a lower water contact angle. The hPIM‐1 has one‐half fractional free volume compared to PIM‐1 which is in good agreement with permeability. Moreover, hPIM‐1 follows as the same dual‐mode sorption model as PIM‐1. To the best of our knowledge, this is the first ever reported flexible hPIM‐1 film in the literature. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 344–354     

The Stereospecific Substitution of the Xenon Atom in cis‐Perfluoroalk‐1‐enylxenon(II) Salts by Hydrogen,Halogens, and the Phenyl Group

The substitution of the xenon atom in reactions of [cis‐C_nF_2n+1CF=CFXe][Y] salts with benzene, iodide, and bromide anions in propionitrile solution by the phenyl group, or iodine, and bromine atoms, respectively, occurred stereospecifically. When a propionitrile solution of [cis‐C₂F₅CF=CFXe][AsF₆] was kept at —40 °C without an additional reactant, the fluoroalkene cis‐C₂F₅CF=CFH was the only isomer obtained.     

Kinetics,polymer molecular weights,and microstructure in zirconocene‐catalyzed 1‐hexene polymerization

1‐Hexene was polymerized by rac‐(dimethylsilyl)bis(4,5,6,7‐tetrahydro‐1‐indenyl)zirconium dichloride catalyst and methylaluminoxane cocatalyst over the temperature range 0–100 °C. The polymerization rate, polymer molecular weight, and polymer microstructure (stereospecificity and regiospecificity) were studied as a function of the temperature and the concentrations of monomer, catalyst, and cocatalyst. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3802–3811, 2000     

Sorption and diffusion of normal alkanes through poly(ethylene‐co‐vinyl acetate) membranes

The transport behavior of uncrosslinked and crosslinked poly(ethylene‐co‐vinyl acetate) membranes has been investigated using normal alkanes as probe molecules, in the temperature range of 30–60 °C. Benzoyl peroxide was used for crosslinking the matrix. It has been observed that, a critical concentration of crosslinker is necessary for maximum solvent uptake, followed by a decrease at higher concentration. The effect of free volume on liquid transport was investigated by positron annihilation lifetime spectroscopy. The mechanism of transport has been found to deviate from the regular Fickian behavior. The dependence of the transport coefficients on crosslink density, nature of penetrants, and temperature was studied. The polymer–solvent interaction parameter, enthalpy, and entropy of sorption have also been estimated from the transport data. The affine and phantom models for chemical crosslinks were used to predict the nature of crosslinks. Finally, the experimental sorption data were compared with theoretical predictions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2470–2480, 2007     

Water sorption and diffusion coefficients of protons and water in PVDF-g-PSSA polymer electrolyte membranes

Water sorption properties, proton NMR spectra, and diffusion of water and protons in poly(vinylidene fluoride)-graft-polystyrene sulfonic acid (PVDF-g-PSSA) polymer electrolyte membranes were studied. Sorption curves for the membranes with different degrees of grafting in protonated and Na⁺ form were measured by equilibrating the membranes over saturated salt solutions. The membrane water content was found to be sensitive to changes in relative humidity (RH). The water/sulfonic acid ratio λ for the protonated samples was around 2 at 20% RH and increased to λ ∼ 30 at 100%. Proton NMR, pulsed field gradient proton NMR (PFG-NMR), and impedance measurements were made on membranes with different λ. In the proton NMR spectra only one peak was found, originating from the water in the membrane. The chemical shift of the peak was found to be dependent on the counterion and the water content. The water self-diffusion coefficients D_H2O, measured by PFG-NMR, increased with degree of grafting and water content of the membranes. The proton conductivity and the calculated proton mobility decreased more steeply than the D_H2O with decreasing water content. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2893–2900, 1999