Controlled synthesis and evaluation of cyanate ester/epoxy copolymer system for high temperature molding compounds

Epoxy molding compounds (EMCs) have become an integral component for high power electronics to work under harsh environment nowadays. For high temperature operation, polymer networks with high glass transition temperature (T_g) are required to ensure device stability. In this work, high T_g polymers were designed via controlled incorporation of in situ formed and thermally stable triazine structures into epoxy matrix. Reactions involved in the copolymer system of cyanate ester and epoxy (CE/EP) were investigated. Increasing ratio of cyanate ester dramatically promoted T_g of the copolymer up to 275 °C with improved heat resistance. High temperature aging and moisture absorption tests revealed that hydrolysis of polycyanurate network and rearrangement of cyanurate occurred during aging, especially for copolymers with higher than 75% of cyanate ester. Based on thermal properties and aging performance, the composition of CE/EP system was optimized. The formulated bisphenol A cyanate ester and biphenyl epoxy copolymer system has great potential to be applied as high temperature encapsulation materials in electronic packaging. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1337–1345     

Viscoelastic properties and morphology of dicyanate ester/epoxy co-polymers modified with polysiloxane and butadiene–acrylonitrile rubbers

Dynamic mechanical analysis was conducted on specimens prepared from cyanate ester (CE) and epoxy (EP) resins cured together at various mass compositions. Increase of amount of epoxy resin in composition was shown to have a disadvantageous effect on glass transition temperature (T _g). It was shown that post-curing procedure was needed to produce a polymer matrix with a single glass transition relaxation, but increase in post-cure temperature up to 250 °C resulted in slight reduction in T _g for epoxy/cyanate copolymers. TG results proved that the presence of epoxy resin reduces thermal stability of the cyanate/epoxy materials. The neat CE and EP/CE systems containing 30 wt% of epoxy resin were modified using epoxy-terminated butadiene–acrylonitrile rubber (ETBN) and polysiloxane core–shell elastomer (PS). The scanning electron microscopy (SEM) results showed the existence of second phase of ETBN and PS modifiers. Only in the case of EP/CE composition modified with ETBN, well-dispersed second phase domains were observed. Analysis of SEM images for other CE- and EP/CE-modified systems revealed the formation of spherical aggregates.     

Poly(phenylene oxide) modified cyanate resin for self‐healing

Self‐healing cyanate ester resins (CE) were developed by adding low molecular weight poly(phenylene oxide) (PPO) resin, yielding a high performance CE/PPO system via a low‐temperature process. The addition of PPO improved the flexural strength and fracture toughness of the CE matrix without sacrificing thermal properties. CE/PPO formulations with 5, 10, and 15 wt.% PPO showed 43%, 65%, and 105% increase in fracture toughness due to a combination of crack deflection, crack pinning, and matrix cavitation around second‐phase particles. When PPO was introduced into the CE, dielectric properties were either unchanged or declined. During thermal treatment to heal damaged CE, liquid PPO flowed into cracks, and during subsequent cooling, solidified to bond the crack surfaces. The self‐healing efficiency for CE with 15 wt.% PPO after heating to 220°C for 1 h exhibited a recovery of 73% in toughness and 81% in microtensile strength. Copyright © 2014 John Wiley & Sons, Ltd.     

Preparation and characterization of bismaleimide/1,3-dicyanatobenzene modified epoxy intercrosslinked matrices

An intercrosslinked network of cyanate ester (CE)-bismaleimide (BMI) modified epoxy matrix system was made by using epoxy resin, 1,3-dicyanatobenzene and bismaleimide (N,N^′-bismaleimido-4,4^′-diphenyl methane) with diaminodiphenylmethane as curing agent. BMI-CE-epoxy matrices were characterised using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and heat deflection temperature (HDT) analysis. The matrices, in the form of castings, were characterised for their mechanical properties such as tensile strength, flexural strength and unnotched Izod impact test as per ASTM methods. Mechanical studies indicated that the introduction of cyanate ester into epoxy resin improves the toughness and flexural strength with reduction in tensile strength and glass transition temperature, whereas the incorporation of bismaleimide into epoxy resin influences the mechanical and thermal properties according to its percentage content. DSC thermograms of cyanate ester as well as BMI modified epoxy resin show an unimodal reaction exotherm. Electrical properties were studied as per ASTM method and the morphology of the BMI modified epoxy and CE-epoxy systems were studied by scanning electron microscope.     

Flame retardant polycyanurate thermosets from the cyanate esters of triphenylphosphine oxide

Three cyanate esters containing phosphorus are synthesized in good overall yields starting from bromoanisoles. Di‐ and tricyanates with meta configuration are most stable while para is less so. The para dicyanate ester isomer is particularly affected by water from the atmosphere. The meta dicyanate ester 2 has good thermal properties with glass transition at 268 °C and char yield of 65% in air at 600 °C. All three phosphorus‐containing cyanate esters are low flammability in an open flame. They make highly combustible cyanate esters resins less flammable simply by blending. Mixing 10 wt% dicyanate ester 2 into bisphenol A or E dicyanate esters makes them rate V‐0. Published 2018.^† J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1100–1110     

Morphology and properties of cyanate ester/liquid polyurethane/silica nanocomposites

The high‐speed homogeneous shearing method was applied to prepare nanocomposites of cyanate ester (CE) with liquid polyurethane elastomer (PUR) and silica. To investigate the influence of various components on the morphology and properties of the ternary composites, the binary composites of CE/PUR and CE/silica were also involved in this article. The morphology of the cured materials of binary and ternary systems was investigated by transmission electron microscopy (TEM), and the results show that silica nanoparticles were uniformly distributed in the ternary and binary matrix. Phase separation of elastomer in composites was not observed by TEM. FTIR test and dynamic mechanical analysis (DMA) proved that chemical linking was existent between PUR and CE. Scanning electron microscopy examinations and mechanical properties tests were carried out. The results show that ternary composites displayed higher fracture toughness and impact strength compared with most of the binary systems. This suggests that the addition of PUR and nanosilica can synergistically improve the toughness of CE. DMA studies confirmed that the incorporation of silica can increase the storage modulus and T_g for CE and CE/PUR system, since there are a good adhesion and a strong hydrogen bonding between silica and polymers. The thermal property of ternary composites increases with the increase of silica nanoparticle loading. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1243–1251, 2008     

Influence of the type of epoxy hardener on the structure and properties of interpenetrated vinyl ester/epoxy resins

The morphology–toughness relationship of vinyl ester/cycloaliphatic epoxy hybrid resins of interpenetrating network (IPN) structures was studied as a function of the epoxy hardening. The epoxy was crosslinked via polyaddition reactions (with aliphatic and cycloaliphatic diamines), cationic homopolymerization (via a boron trifluoride complex), and maleic anhydride. Maleic anhydride worked as a dual‐phase crosslinking agent by favoring the formation of a grafted IPN structure between the vinyl ester and epoxy. The type of epoxy hardener strongly affected the IPN morphology and toughness. The toughness was assessed by linear elastic fracture mechanics, which determined the fracture toughness and energy. The more compact the IPN structure was, the lower the fracture energy was of the interpenetrated vinyl ester/epoxy formulations. This resulted in the following toughness ranking: aliphatic diamine > cycloaliphatic diamine ≥ boron trifluoride complex > maleic anhydride. For IPN characterization, the width of the entangling bands and the surface roughness parameters were considered. Their values were deduced from atomic force microscopy scans taken on ion‐etched surfaces. More compact, less rough IPN‐structured resins possessed lower toughness parameters than less compact, rougher structured ones. The latter were less compatible according to dynamic mechanical thermal and thermogravimetric analyses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5471–5481, 2004     

Thermal and water absorption properties of cyanate ester resins modified by fluoride‐containing and silicone‐containing components

In order to enhance the moisture resistance of cyanate ester resins, modifiers containing silicon or fluorine moieties were introduced. The curing behaviors of the obtained resins, as well as thermal, water absorption, and dielectric properties of all cured polymers, were investigated in detail. Results show that properties of fillers in polymer have great influence on the thermal property and of polymer. In all cases, modifier exhibited percolation threshold at 5 wt%. Compared with pristine cyanate ester resins (CE), when the methyl phenyl silicone resin B filler was added, the cured polymer exhibited water absorption as low as 0.39% and excellent thermal oxygen stability at 300°C. The introduction of silicon H improved thermal oxidative stability at 400°C without significant compromise in processability or mechanical properties.     

High performance toughened cyanate ester resin with low injection temperature for RTM process

A high‐performance modified cyanate resin system with low injection temperature for fabricating advanced composites via resin transfer molding (RTM) was developed, which was made of bisphenol A dicyanate ester (BADCy) and diallyl phthalate (DAP). The processing characteristics, mechanical, and thermal properties of the resin were studied, and the effect of the content of DAP on the processing and performance parameters was discussed. The results show that the processing properties of the modified cyanate system are dependent on the content of DAP. All the formulations studied in this paper have good processing characteristics; their injection temperatures are between 30 and 40°C and the pot life is about 20 hr at 50°C. The cured resins exhibited good thermal stability, excellent toughness, and good hot–wet resistance, suggesting that the toughened cyanate resin is a potential high‐performance RTM matrix for advanced composites. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigations on the cure chemistry and polymer properties of benzoxazine-cyanate ester blends

Thermosetting polymer blends composed of bisphenol A based benzoxazine (BA-a) and cyanate ester (BACY) were prepared via co-curing of benzoxazine with cyanate ester. DSC results manifested a multiple curing pattern with associated heat of reaction implying a co-reaction between oxazine moiety and cyanate group. The catalysis during the co-curing of blend was ascribed to the cycloaddition reaction between the two groups followed by the ring-opening of benzoxazine and cyclotrimerisation of cyanate ester. The spectral and analytical data supported the possibilities of further polymerization through the insertion of the phenolic OH of polybenzoxazine to cyanate group to form the intermediate iminocarbonate, which further induce curing of cyanate ester to form polycyanurate. A co-reacted network composed of triazine ring as a part of polybenzoxazine matrix is postulated. The co-reaction temperature diminished with increase in cyanate ester content in the blend. A single T_g was observed in DMTA of the cured matrix that implied a linked homogeneous matrix containing both triazine and polybenzoxazine. This was substantiated by the TGA, DTA and SEM behavior of the cured polymer. The modulus of the cured blend was higher than those of the component resins of the blend. The co-reaction with cyanate ester enhanced the high temperature stability of polybenzoxazine.     

Free volume hole size of Cyanate ester resin/Epoxy resin interpenetrating networks and its correlations with physical properties

Cyanate ester (CE) resin was blended with epoxy resin (EP) at different mass ratios (CE/EP: 100/0, 90/10, 70/30, 50/50, 30/70, 10/90, and 0/100). The curing process of the blend system was characterized by Fourier transform infrared spectrometry (FTIR) and differential scanning calorimetry (DSC). Examination of the mechanical properties, thermal stability, and morphology of the blend systems showed that addition of epoxy resin resulted in improved toughness but a little sacrifice in thermal stability when compared with neat CE. The free volume size of the blend system determined by positron annihilation lifetime spectroscopy (PALS) decreased with the epoxy resin content, which is consistent with the chemical structure changes for the copolymerization between CE and EP. The crosslinking units of curing products (oxazoline, oxazolidinone, and polyether network) of the blends are all smaller in size than those of triazine ring structure from neat CE. Therefore, the free volume size of the blends decreases with increase of EP content. The correlations between the free volume properties and other physical properties (thermal stability and mechanical properties) have also been discussed.     

Polycarbonate-modified epoxies. I. Studies on the reactions of epoxy resin/polycarbonate blends prior to cure

An epoxy resin based upon the diglycidyl ether of bisphenol-A was modified with poly(bisphenol A carbonate) (PC). Prior to aromatic amine cure, the possible reactions in the epoxy resin/PC blend were investigated using GPC and FTIR techniques. It was shown that at 150°C, the epoxy resin acted as a plasticizer and promoted the crystallization of PC. In addition, a transesterification between the secondary hydroxyl groups in the epoxy resin with the carbonate groups in PC occurred. This reaction resulted in degraded PC chains with phenolic hydroxyl end groups. There was no evidence of reaction of epoxide groups at 150°C in this blend. At 200°C, the secondary hydroxyl groups acted as a catalyst converting most of the aromatic–aromatic carbonates to the aromaticndash;liphatic and aliphaticndash;aliphatic carbonates through transesterification. At this elevated temperature, the secondary hydroxyl groups were regenerated by the addition reaction between the epoxide groups and the phenolic hydroxyl end groups, either from the transesterification or the hydrolysis of PC. This addition reaction combining the PC chains and epoxy chains eventually resulted in a crosslinked polymer if the extent of reaction was high. Thus, by using a melt blending process at high temperature, e.g., 200°C, a copolymer network structure of PC-modified epoxy could be formed. The fracture toughness should be increased by increasing the capability for plastic deformation due to the incorporation of PC chains into the network; results will be reported in a future study. © 1996 John Wiley & Sons, Inc.     

酚醛型氰酸酯与双酚A型环氧共固化反应的FTIR研究

在恒温固化条件下,通过FTIR跟踪方法,研究了酚醛型氰酸酯与双酚A型环氧共固化反应的路径及其反应机理.共固化体系的反应过程包括在150℃及其以下温度,主要发生的是氰酸酯的三嗪环化固化反应,其中三嗪环化固化反应由于环氧的加入,反应速率被极大地提高了;同时,酚醛型氰酸酯中的氨基甲酸酯类杂质与环氧发生开环聚合反应,引起环氧官能团产生弱而持续的消耗.但在此阶段,酚醛型氰酸酯与环氧之间没有化学反应发生;在180℃及其以上温度,三嗪环和环氧发生反应,异构为异氰脲酸环结构,并进一步反应生成唑啉酮环结构,由于该反应的发生,促进了环氧官能团的消耗速度,在环氧官能团的转化率-时间图中,出现倒S曲线;在三嗪环的转化率图中,出现一个极大值后再降落的曲线.反应温度的提高有利于促进酚醛型氰酸酯与环氧之间的共固化反应,特别是当反应温度为220℃时,氰酸酯官能团和环氧官能团的消耗、三嗪环和唑啉酮环的生成均以较快的速率进行,—OCN生成三嗪环的转化率可以较容易地达到1,而唑啉酮环的转化率不超过0.5.     

Synthesis and properties of a cyanate ester containing dicyclopentadiene(II)

A 2,6‐dimethyl phenol‐dicyclopentadiene novolac (DCPDNO) was synthesized from dicyclopentadiene and 2,6‐dimethyl phenol, and the resultant DCPDNO was reacted with cyanogen bromide into 2,6‐dimethyl phenol‐dicyclopentadiene cyanate ester (DCPDCY). The structures of the novolac and cyanate ester were confirmed with Fourier transform infrared spectroscopy, elemental analysis, mass spectrometry (MS), and nuclear magnetic resonance. For the purpose of increasing the mobility of residual DCPDCY during the final stage of curing and achieving a complete reaction of cyanate groups, a small quantity of a monofunctional cyanate ester, 4‐tert‐butylphenol cyanate ester (4TPCY), was added to DCPDCY to form the cyanate ester copolymer. The synthesized DCPDCY was then cured with 4TPCY at various molar ratios. The thermal properties of the cured cyanate ester resins were studied with dynamic mechanical analysis, dielectric analysis, and thermogravimetric analysis. These data were compared with those of the commercial bisphenol A cyanate ester system. Compared with the bisphenol A cyanate ester system, the cured DCPDCY resins exhibited lower dielectric constants (2.52–2.67 at 1 GHz), dissipation factors (0.0054–0.0087 at 1 GHz), glass‐transition temperatures (261–273 °C), thermal stability (5% degradation temperature at 406–450 °C), thermal expansion coefficients (4.8–5.78 × 10^?5/°C before the glass‐transition temperature), and moisture absorption (0.8–1.1%). © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 671–681, 2005     

Synthesis and characterization of novel epoxy resins‐filled microcapsules with organic/inorganic hybrid shell for the self‐healing of high performance resins

Novel microcapsules (MCs) with organic/inorganic hybrid shell were successfully fabricated using epoxy resin as core material and nano boron nitride (BN) and mesoporous silica (SBA‐15) as inorganic shell materials in aqueous solution containing a water‐compatible epoxy resin curing agent. The morphologies, thermal properties and Young's moduli of MCs were investigated. The results indicated that epoxy resins were encapsulated by BN/SBA‐15/epoxy polymer hybrid layer, the resulting MCs were spherical in shape and the introduction of inorganic particles made MCs had rough surface morphology. The mean modulus value of MCs was from 2.8 to 3.1 GPa. The initial decomposition temperature (T_di) of MCs at 5 wt% weight loss was from 309 to 312°C. MCs showed excellent thermal stability below 260°C. The structures and properties of MCs could be tailored by controlling the weight ratio of inorganic particle. When the weight ratio of BN to SBA‐15 was 0.15:0.10, MCs had the highest T_di and modulus. The resulting MCs were applied to high performance 4,4′‐bismaleimidodiphenylmethane/O,O′‐diallylbisphenol A (BMI/DBA) system to design high performance BMI/DBA/MC systems. Appropriate content of MCs could improve the fracture toughness and maintain the glass transition temperature (T_g) of BMI/DBA system. The core materials released from fractured MCs could bond the fracture surfaces of the BMI/DBA matrix through the polymerization of epoxy resins. When the healing temperature schedule of 100°C/2h+150°C/1h was applied, 15 wt% MCs recovered 98% of the virgin fracture toughness of BMI/DBA. Copyright © 2016 John Wiley & Sons, Ltd.     

Studies on thermal and morphological properties of 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane-epoxy-bismaleimide matrices

A new cyanate ester monomer, 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane has been synthesized and characterized. Epoxy modified with 4, 8 and 12% (by weight) of cyanate ester were made using epoxy resin and 1,1-bis(3-methyl-4-cyanatophenyl)cyclohexane and cured by using diaminodiphenylmethane. The cyanate ester modified epoxy matrix systems were further modified with 4, 8 and 12% (by weight) of bismaleimide (N,N′-bismaleimido-4,4′-diphenylmethane). The formation of oxazolidinone and isocyanurate during cure reaction of epoxy and cyanate ester blend was confirmed by IR spectral studies. Bismaleimide-cyanate ester-epoxy matrices were characterized using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and heat deflection temperature (HDT) analysis. Thermal studies indicate that the introduction of cyanate ester into epoxy resin improves the thermal degradation studies at the expense of glass transition temperature. Whereas the incorporation of bismaleimide into epoxy resin enhances the thermal properties according to its percentage content. However, the introduction of both cyanate ester and bismaleimide influences the thermal properties according to their percentage content. DSC thermogram of cyanate ester modified epoxy and bismaleimide modified epoxy show unimodel reaction exotherms. The thermal degradation temperature and heat distortion temperature of the cured bismaleimide modified epoxy and cyanate ester-epoxy systems increased with increasing bismaleimide content. The morphology of the bismaleimide modified epoxy and cyanate ester-epoxy systems were also studied by scanning electron microscopy. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermal and mechanical properties of a dendritic hydroxyl‐functional hyperbranched polymer and tetrafunctional epoxy resin blends

Blends of a tetrafunctional epoxy resin, tetraglycidyl‐4,4′‐diaminodiphenylmethane (TGDDM), and a hydroxyl‐functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 3,3′‐diaminodiphenyl sulfone (DDS) as curing agent. The phase behavior and morphology of the DDS‐cured epoxy/HBP blends with HBP content up to 30 phr were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The phase behavior and morphology of the DDS‐cured epoxy/HBP blends were observed to be dependent on the blend composition. Blends with HBP content from 10 to 30 phr, show a particulate morphology where discrete HBP‐rich particles are dispersed in the continuous cured epoxy‐rich matrix. The cured blends with 15 and 20 phr exhibit a bimodal particle size distribution whereas the cured blend with 30 phr HBP demonstrates a monomodal particle size distribution. Mechanical measurements show that at a concentration range of 0–30 phr addition, the HBP is able to almost double the fracture toughness of the unmodified TGDDM epoxy resin. FTIR displays the formation of hydrogen bonding between the epoxy network and the HBP modifier. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 417–424, 2010     

Influence of the network chain orientation on the fracture toughness of a mesogenic epoxy resin modified with CTBN

A biphenol‐type epoxy resin, which had a mesogenic group in the backbone moiety, was modified with carboxy‐terminated butadiene acrylonitrile copolymer (CTBN) as a reactive elastomer, and its fracture toughness was measured. With the addition of CTBN, the fracture toughness of the biphenol‐type epoxy resin significantly increased and became significantly higher than that of a bisphenol A‐type epoxy resin modified with CTBN. The network chain orientation in the cured biphenol‐type epoxy resin system was clearly observed during the fracture process with polarized microscopy Fourier transform infrared measurements, although such a phenomenon was not observed in the bisphenol A‐type epoxy resin system. The high toughness of the cured biphenol‐type system was clearly due to the consumption of the mechanical energy by a large deformation of the matrix resin due to the orientation of the network chains during the fracture process. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1198–1209, 2003     

Preparation and characterization of novel cyanate ester/epoxy resin microspheres

A novel kind of cyanate ester (CE)/epoxy resin microspheres have been synthesized using the polymerization technology of cyanate ester and epoxy resin in anhydrous ethanol media; surfactant sodium dodecylbenzene sulfonate was used as an emulsifier, and imidazole was used as catalyst or curing agent. The morphologies, chemical structures, and thermal properties of microspheres were investigated by Fourier transform infrared spectroscopy, scanning electron microscope, laser scanning confocal fluorescence microscopy, optical microscope, differential scanning calorimeter, and thermogravimetric analyzer, respectively. The effects of process parameters such as the amount of imidazole and the weight ratio of epoxy resin to CE on the size and morphology of microsphere were discussed. Results indicate that the reactivity and surface morphology of microsphere can be adjusted by the amount of imidazole and the weight ratio of epoxy resin to CE. The prepared microsphere shows excellent thermal stability and good reactivity.     

Effects of temperature on cure kinetics and mechanical properties of vinyl–ester resins

The relationships among cure temperature, chemical kinetics, microstructure, and mechanical performance have been investigated for vinyl–ester resins. Fourier transform infrared spectroscopy was used to follow the reactions of vinyl–ester and styrene during isothermal curing of Dow Derakane 411‐C‐50 at 30 and 90°C. Reactivity ratios of vinyl–ester and styrene vinyl groups were evaluated using the copolymer composition equation. The results indicate that the ratio of vinyl–ester to styrene double bonds incorporated into the network is greater for 30 than for 90°C cure. Mechanical properties were obtained for systems subjected to isothermal cures at 30 and 90°C and postcured above ultimate T_g. The results show that the initial cure temperature significantly affects the mechanical behavior of vinyl–ester resin systems. In particular, values of strength and fracture toughness for postcured samples initially cured isothermally at 30°C are significantly higher than those obtained for samples cured isothermally at 90°C. Examination of fracture surfaces using atomic force microscopy revealed the existence of a nodular microstructure possessing characteristic nodule dimensions that are affected by the temperature of cure. Such features suggest the existence of phase separation during cure. A binary interaction model in conjunction with chemical kinetic data and estimated solubility parameters was used to evaluate enthalpic interactions between the growing polymer network and monomers of the vinyl–ester system. The results indicate that the interaction energy becomes increasingly endothermic as cure progresses and that this energy is affected by the temperature of cure through differences in copolymerization behavior. Hence, in addition to entropic factors, the changes in enthalpic contribution to the Gibbs free energy suggest that the probability of phase separation increases with extent of cure and that its onset is potentially affected by cure temperature. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 725–744, 1999