New insights into the multiple melting behaviors of the semicrystalline ethylene‐hexene copolymer: Origins of quintuple melting peaks

A semicrystalline ethylene‐hexene copolymer (PEH) was subjected to a simple thermal treatment procedure as follows: the sample was isothermally crystallized at a certain isothermal crystallization temperature from melt, and then was quenched in liquid nitrogen. Quintuple melting peaks could be observed in heating scan of the sample by using differential scanning calorimeter (DSC). Particularly, an intriguing endothermic peak (termed as Peak 0) was found to locate at about 45 °C. The multiple melting behaviors for this semicrystalline ethylene‐hexene copolymer were investigated in details by using DSC. Wide‐angle X‐ray diffraction (WAXD) technique was applied to examine the crystal forms to provide complementary information for interpreting the multiple melting behaviors. Convincing results indicated that Peak 0 was due to the melting of crystals formed at room temperature from the much highly branched ethylene sequences. Direct heating scans from isothermal crystallization temperature (T_c, 104–118 °C) were examined for comparison, which indicated that the multiple melting behaviors depended on isothermal crystallization temperature and time. A triple melting behavior could be observed after a relatively short isothermal crystallization time at a low T_c (104–112 °C), which could be attributed to a combination of melting of two coexistent lamellar stack populations with different lamellar thicknesses and the melting‐recrystallization‐remelting (mrr) event. A dual melting behavior could be observed for isothermal crystallization with both a long enough time at a low T_c and a short or long time at an intermediate T_c (114 °C), which was ascribed to two different crystal populations. At a high T_c (116–118 °C), crystallizable ethylene sequences were so few that only one single broad melting peak could be observed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2100–2115, 2008     

Ethylene‐Norbornene Terpolymerization with 5‐Vinyl‐2‐norbornene Using Single‐Site Catalysts

The incorporation of 5‐vinyl‐2‐norbornene (VNB) into ethylene‐norbornene copolymer was investigated with catalysts [Ph₂C(Fluo)(Cp)]ZrCl₂ ( 1 ), rac‐[Et(Ind)₂]ZrCl₂ ( 2 ), and [Me₂Si(Me₄Cp)^tBuN]TiCl₂ ( 3 ) in the presence of MAO by terpolymerizing different amounts of 5‐vinyl‐2‐norbornene with constant amounts of ethylene and norbornene at 60°C. The highest cycloolefin incorporations and highest activity in terpolymerizations were achieved with 1 . The distribution of the monomers in the terpolymer chain was determined by NMR spectroscopy. As confirmed by XRD and DSC analysis, catalysts 1 and 3 produced amorphous terpolymer, whereas 2 yielded terpolymer with crystalline fragments of long ethylene sequences. When compared with poly‐(ethylene‐co‐norbornene), VNB increased both the glass transition temperatures and molar masses of terpolymers produced with the constrained geometry catalyst whereas decreased those for the metallocenes.     

High-temperature aging of Halar film. II. Analysis of melting behavior

Melting behavior of an experimental Halar film, a predominantly alternating 1:1 copolymer of ethylene (E) and chlorotrifluoroethylene (CTFE), has been studied. Differential scanning calorimetry (DSC) reveals single or double melting peaks, depending upon the thermal history. The lower-temperature melting peak T_m1 is produced only by the thermal treatment and shows a strong dependence on annealing time and temperature. On the basis of the DSC and x-ray data it can be suggested that T_m1 represents the melting of relatively small crystallites formed upon annealing. The higher-temperature melting peak T_m2 is always shown at 238°C. (Note: the specification for commercial Halar product is 240°C. The slightly lower melting temperature reported in this study is probably due to the fact that we are dealing with an experimental melt-processed material.) On the basis of the heating rate study we propose that Halar crystallizes with stable crystals (T_m2 = 238°C) regardless of the crystallization conditions, i.e., quenching, slow cooling, or even annealing. Crystals of Halar have a heat of fusion of approximately 35 cal/g or 146 kJ/kg. Detailed analysis of the melting behavior of Halar is presented.     

Synthesis of novel cyclic olefin polymers with excellent transparency and high glass‐transition temperature via gradient copolymerization of bulky cyclic olefin and cis‐cyclooctene

Novel cyclic olefin polymers (COPs) with excellent transparency and high glass‐transition temperature (T_g) synthesized from bulky norbornene derivative, exo‐1,4,4a,9,9a,10‐hexahydro‐9,10(1',2')‐benzeno‐l,4‐methanoanthracene (HBMN), and cis‐cyclooctene (COE) by ring‐opening metathesis copolymerization utilizing the “first‐generation Grubbs” catalyst, RuCl₂(PCy₃)₂(CHPh), and subsequent hydrogenation was reported herein. To get amorphous copolymers, it was of great importance to control the feed ratios and the polymerization time for gradient copolymerization. All these copolymers showed very high T_gs (141.1–201.2 °C), which varied with the content of HBMN. The films of the gradient copolymers with only one T_g were highly transparent. On the contrary, all the block copolymers synthesized through sequential addition showed two thermal transition temperatures, T_g and melt temperature (T_m), and the films of these block copolymers were opaque. The mechanical performances of the COPs were also investigated. It is the first report that transparent COP could be prepared from bulky norbornene derivative and monocyclic olefin. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3240–3249     

Melting behavior of a poly(ether‐block‐amide) copolymer melt‐crystallized under quiescent,isothermal conditions

Segmented poly(ether‐block‐amide) copolymers are typically known as polyamide‐based thermoplastic elastomers consisting of hard, crystallizable polyamide block and flexible, amorphous polyether block. The melting characteristics of a poly(ether‐block‐amide) copolymer melt‐crystallized under various quiescent, isothermal conditions were calorimetrically investigated using differential scanning calorimetry (DSC). For such crystallized copolymer samples, their crystalline structures under ambient condition and the structural evolutions upon heating from ambient to complete melting were characterized using ambient and variable‐temperature wide‐angle X‐ray diffractometry (WAXD), respectively. It was observed that dependent of specific crystallization conditions, the copolymer samples exhibited one, two, or three melting endotherms. The ambient WAXD results indicated that all melt‐crystallized copolymer samples only exhibited γ‐form crystals associated with the hexagonal habits of the polyamide homopolymer, whereas variable‐temperature WAXD data suggested that upon heating from ambient, a melt‐crystallized copolymer might exhibit so‐called Brill transition before complete melting. Based on various DSC and variable‐temperature WAXD experimental results obtained in this study, the applicability of different melting mechanisms that might be responsible for multiple melting characteristics of various crystallized PEBA copolymer samples were discussed. It was postulated that the low (T _m1) endotherm was primarily because of the disruption of less thermally stable, short‐range ordered structure of amorphous polyamide segments of the copolymer, which was only formed after the completion of primary crystallization via so‐called annealing effects. The intermediate (T_m2) and high (T_m3) endotherms were attributed to the melting of primary crystals within polyamide crystalline microdomains of the copolymer. The appearance of these two melting endotherms might be somehow complicated by thermally induced Brill transition. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2035–2046, 2008     

Influence of mixed aluminoxane systems on ethylenenorbornene copolymerization catalyzed by metallocene

The norbornene/ethylene copolymerization was investigated using Me₂SiCp₂MCl₂ (M = Zr, Ti)/EBAO and MAO as catalyst systems (EBAO: mixed ethyl-isobutylaluminoxane, MAO: methylaluminoxane). The copolymers were characterized by DSC and ¹³C NMR. Copolymers with high content of norbornene and high T_g were obtained with the mixed EBAO. It is suggested that the copolymerization is greatly influenced by the state of the ion pair of the metallocene catalyst. The effect of aluminoxane on the composition and the microstructure of copolymer is discussed.     

Synthesis and characterization of materials prepared via the copolymerization of ethylene with 1‐octadecene and norbornene using a [(π‐cyano‐nacnac)Cp] zirconium complex

[3‐Cyano‐2‐(2,6‐diisopropylphenyl)aminopent‐2‐en‐4‐(phenylimine)tris (pentafluorophenyl)borate](η⁵‐C₅H₅)ZrCl₂, [(B(C₆F₅)₃‐ NC‐nacnac)CpZrCl₂], precatalyst ( 2 ) can be treated with low concentrations of methylaluminoxane (MAO) to generate active sites capable of copolymerizing ethylene with 1‐octadecene or norbornene under mild conditions. A series of poly(ethylene‐co‐octadecene) and poly(ethylene‐co‐norbornene) copolymers were prepared, and their properties were characterized by NMR, differential scanning calorimetry, and mechanical analysis. The results show that this system produced poly(ethylene‐co‐octadecene) copolymers with a branching content of about 8 mol %. However, upon increasing the comonomer concentration, a drastic reduction in the M_n of the product is observed concomitant with an increase in comonomer incorporation. This leads to a gradual decrease in Young's modulus and stress at break, indicating an increase in the “softness” of the copolymer. In the case of copolymerizations of ethylene and norbornene, the catalytic system ( 2 /MAO) shows a substantial decrease in reactivity in the presence of norbornene and generates copolymer chains in which 5–10 mol % norbornene is in blocks. We also observe that ethylene norbornene copolymers exhibit a high degree of alternating insertions (close to 50%), as determined by NMR spectroscopy. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

RING OPENING COPOLYMERIZATION OF SUCCINIC ANHYDRIDE-ETHYLENE OXIDE BY Al(Ⅲ) ORGANOMETALLIC CATALYSTS

Ring opening copolymerization of succinic anhydride (SA) with ethylene oxide (EO)was successfully carried out by using a series of aluminum-based catalyst in 1,4-dioxane at62±2℃. The results showed that in-situ AlR_3-H_2O (R=ethyl, iso-butyl) catalysts gavehigher molecular weight (M_w～10~4), while Al(OR)_3 catalysts gave the higher alternatingcopolymer structure with slightly lower molecular weight. The in-situ AlR_3-H_2O systemshave been evaluated in more detail for the reaction which showed the optimum H_2O/Almolar ratio to be 0.5. The copolymers with different composition (F_(SA)/F_(EO)= 36/64to 45/55 mol/mol) were synthesized by using different monomer feed ratio. The melt-ing point (T_m), glass transition temperature (T_g) and enthalpy of fusion (ΔH_f) of thesecopolymers are depended on the copolymer composition and in the range of 87～102℃,-12～-18℃, and 37～66J/g, respectively. The second heating scan of DSC also in-dicated that the higher alternating copolymer was more easily recrystallized. The onsetdecomposition temperature was more than 300℃ under nitrogen and influenced by thecopolymer composition.     

Crystallization of poly(ethylene terephthalate–co–isophthalate)

Melt crystallization behaviors of poly(ethylene terephthalate) (PET) and poly(ethylene terephthalate‐co‐isophthalate) (PETI) containing 2 and 12 mol % of noncrystallizable isophthalate components were investigated. Differential scanning calorimetry (DSC) isothermal results revealed that the introduction of 2 mol % isophthalate into PET caused a change of the crystal growth process from a two‐dimensional to a three‐dimensional spherulitic growth. The addition of more isophthalate up to 12 mol % into the PET structure induced a change in the crystal growth from a three‐dimensional to a two‐dimensional crystal growth. DSC heating scans after completion of isothermal crystallization at various T_c's showed three melting endotherms for PET and four melting endotherms for PETI‐2 and PETI‐12. The presence of an additional melting endotherm is attributed to the melting of copolyester crystallite composed of ethylene glycol, tere‐phthalate, and isophthalate (IPA) or the melting of molecular chains near IPA formed by melting the secondary crystallite T_m (I) and then recrystallizing during heating. Analyses of both Avrami and Lauritzen‐Hoffman equations revealed that PETI containing 2 mol % of isophthalate had the highest Avrami exponent n, growth rate constant G_o, and product of lateral and end surface free energies σσ_e. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2515–2524, 2000     

Ethylene–propylene copolymerization behavior of ansa‐dimethylsilylene(fluorenyl)(amido)dimethyltitanium complex: Application to ethylene–propylene–diene or ethylene–propylene–norbornene terpolymers

Copolymerization behavior of ethylene (E) and propylene (P) using ansa‐dimethylsilylene(fluorenyl)(amido)dimethyltitanium complex was investigated. P was more reactive than E regardless of the chain‐end monomer unit, which was very unusual in the coordination polymerization system. The terpolymerizations of E, P and norbornene (NB) or 5‐ethylidene‐2‐norbornene (5E2N) were also performed. The each content in the E/P/NB terpolymer was independently controlled by the initial concentration of NB and E/P feed ratio. Glass transition temperature (T_g) of the terpolymer was raised in proportion to the NB content and close to that of the corresponding NB/E random copolymer with the same NB content. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 685–691     

Characterization,crystallization kinetics,and melting behavior of poly(ethylene succinate) copolyester containing 10 mol % butylene succinate

Copolyester was synthesized and characterized as having 89.9 mol % ethylene succinate units and 10.1 mol % butylene succinate units in a random sequence, as revealed by NMR. Isothermal crystallization kinetics was studied in the temperature range (T_c) from 30 to 73 °C using differential scanning calorimetry (DSC). The melting behavior after isothermal crystallization was investigated using DSC by varying the T_c, the heating rate and the crystallization time. DSC curves showed triple melting peaks. The melting behavior indicates that the upper melting peaks are associated primarily with the melting of lamellar crystals with various stabilities. As the T_c increases, the contribution of recrystallization slowly decreases and finally disappears. A Hoffman‐Weeks linear plot gives an equilibrium melting temperature of 107.0 °C. The spherulite growth of this copolyester from 80 to 20 °C at a cooling rate of 2 or 4 °C/min was monitored and recorded using an optical microscope equipped with a CCD camera. Continuous growth rates between melting and glass transition temperatures can be obtained after curve‐fitting procedures. These data fit well with those data points measured in the isothermal experiments. These data were analyzed with the Hoffman and Lauritzen theory. A regime II → III transition was detected at around 52 °C. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2431–2442, 2008     

Preparation of novel cyclic olefin copolymer with high glass transition temperature

A series of novel cyclic olefin copolymers (COCs), including ethylene/tricyclo[4.3.0.1^2,5]deca‐3‐ene (TDE), ethylene/tricyclo[4.4.0.1^2,5]undec‐3‐ene (TUE), and ethylene/tricyclo[6.4.0.1^9,12]tridec‐10‐ene (TTE) copolymers, have been synthesized via effective copolymerizations of ethylene with bulk cyclic olefin comonomers using bis(β‐enaminoketonato) titanium catalysts ( 1a [PhN?C(CH₃)CHC(CF₃)O]₂TiCl₂; 1b : [PhN?C(CF₃)CHC(Ph)O]₂TiCl₂). With modified methylaluminoxane as a cocatalyst, both catalysts exhibit high catalytic activities, producing high molecular weight copolymers with high comonomer incorporations and unimodal molecular weight distributions. The microstructures of obtained ethylene/COCs are established by combination of ¹H, ¹³C NMR, ¹³C DEPT, HSQC ¹H? ¹³C, and ¹H? ¹H COSY NMR spectra. DSC analyses indicate that the glass transition temperature (T_g) increases with the enhancement of comonomer volume (TDE < TUE < TTE). High T_g value up to 180 °C is easily attained in ethylene/TTE copolymer with the low content of 35.8 mol %. TGA analyses reveal that these copolymers all possess high thermal stability with degradation temperatures (T_d) higher than 370 °C in N₂ and air. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3144–3152     

Appreciable norbornene incorporation in the copolymerization of ethylene/norbornene using titanium catalysts containing trianionic N[CH2CH(Ph)O]33− ligands

The newly synthesized 1‐TiCl (C₃ symmetric) and 2‐TiCl (C_s symmetric) precatalysts in combination with MAO polymerized ethylene, cyclic olefins, and copolymerized ethylene/norbornene in good yields. The catalyst with C₃ symmetry exhibits moderate catalytic activity and efficient norbornene incorporation for E/NBE copolymerization in the presence of MAO [activity = 360 kg polymer/(mol Ti h), ethylene 1 atm, NBE 5 mmol/mL, 10 min], affording poly(ethylene‐co‐NBE)s with high norbornene contents (42.0%) and the C_s symmetric catalyst showed an activity of 420 kg polymer/(mol Ti h), ethylene 1 atm, NBE 5 mmol/mL affording poly(ethylene‐co‐NBE)s with 33.0% norbornene content. The effect of monomer concentration at ambient temperature and constant Al/Ti ratio for the homo and copolymerization was studied in a detailed manner. We found that apart from the electronic environment around the metal center the steric environment provided by the symmetry of the catalyst systems has a considerable influence on the percentage of norbornene content of the copolymer obtained. We also found that with a given catalyst a variable clearly influencing the copolymer microstructure, hence also the copolymer properties, is the monomer concentration at a given feed ratio. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 444–452, 2008     

Mechanism of polymorph selection during crystallization of random butene-1/ethylene copolymer

Starting from an initial sample of butene-1/ethylene copolymer with stable form I’, we examined the nucleation of different crystalline polymorphs (here metastable form II and stable form I’) at different isothermal crystallization temperatures after being melted at different melt temperature (T _melt). When T _melt was just above the melting temperature (T _m) of the crystallites, self-seeding took place. There, residue crystallites served as nuclei leading to the crystallization of the same crystalline phase. When T _melt was a few degrees above the T _m, self-seeding was disabled due to complete melting of the initial crystals. Upon crystallization, the selection of the different polymorphs in this random copolymer was found to depend on an interplay between the domain size of segregated long crystallizable sequences and the size and energy barrier of the critical nucleus of the respective crystalline forms. Our results provide a clear understanding of the polymorphs selection during crystallization of a random copolymer as well as homo-polymers under confinement.     

Copolymerization of ethylene and non-conjugated diene using homogenous catalyst

Ethylene and different amounts of 1,7-octadiene were copolymerized using the metallocene catalyst system ethylidene-bis(fluorenyl) zirconium dichloride and methylaluminoxane (MAO) at both 50 and 90 °C. The catalyst activity has slightly increased with the addition of low amounts of the diene in relation to the homopolymerization of ethylene. The obtained polymers were characterized according to their melting temperature (T_m) and crystallinity degree (x_c) by differential scanning calorimetry (DSC). Weight-average molecular weight (M_w) and polydispersity were determined by gel permeation chromatography (GPC). Diene contents in the copolymer were obtained through the FTIR spectroscopy. The results indicated that at polymerization temperature of 90 °C, crosslinking bonds in the obtained copolymers were low, differently from what was observed at 50 °C. The diene content in the copolymer achieved more than 3 mol% and the comonomer conversion was around 15%. Moreover, the obtained copolymers have M_w around 100,000 and large polydispersity.     

The equilibrium melting points of random ethylene‐octene copolymers: A test of the Flory and Sanchez–Eby theories

Ethylene/l‐octene copolymers produced with metallocene catalysts are believed to have a homogeneous comonomer content with respect to molecular weight. Two series of copolymers of different molecular weights with a 1‐octene content ranging from 0 to 39 branches per 1000 carbon atoms were studied. The influence of branch content on structure and melting behavior as well as on isothermal and nonisothermal bulk crystallization was studied. In this article, the equilibrium melting temperatures of ethylene/l‐octene random copolymers is the focus. The principal techniques used were thermal analysis and small‐angle X‐ray scattering. The use of Hoffman–Weeks plots to obtain the equilibrium melting temperatures of ethylene/l‐octene random copolymers resulted in nonsensical high values of the equilibrium melting point or showed behavior parallel to the T_m = T_c line, resulting in no intercept and, hence, an infinite equilibrium melting point. The equilibrium melting temperatures of linear polyethylenes and homogeneous ethylene/l‐octene random copolymers were determined as a function of molecular weight and branch content via Thompson–Gibbs plots involving lamellar thickness data obtained from small‐angle X‐ray scattering. This systematic study made possible the evaluation of two equilibrium melting temperature depression equations for olefin‐type random copolymers, the Flory equation and the Sanchez–Eby equation, as a function of defect content and molecular weight. The range over which the two equations could be applied depended on the defect content after correction for the effect of molecular weight on the equilibrium melting temperature. The equilibrium melting temperature, T(n, p_B), of the ethylene/l‐octene random copolymers was a function of the molecular weight and defect content for low defect contents (p_B ≤ 1.0%). T(n, p_B) was a weak function of molecular weight and a strong function of the defect content at a high defect content (p_B ≥ 1.0%). The Flory copolymer equation could predict T(n, p_B) at p_B ≤ 1.0% when corrections for the effect of molecular weight were made. The Sanchez–Eby uniform inclusion model could predict T(n, p_B) at a high defect content (1.6% ≤ p_B ≤ 2.0%). We conclude that some defects were included in the crystalline phase and that the excess free energies (18–37 kJ/mol) estimated in this study were within the theoretical range. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 154–170, 2000     

Synthesis and properties of poly(ethylene oxide)‐grafted polyethylene copolymer and terpolymer

A series of graft copolymers were synthesized based on ethylene‐co‐m,p‐methylstyrene (EMS) (backbone copolymer), ethylene‐1‐hexene‐m,p‐methylstyrene (EHMS) (backbone terpolymer), and polyethylene glycol monomethyl ethers (PEGM) (grafts) in this study. The PEGMs with molecular weights of 750 and 2000 were used. The chemical composition of the graft copolymers was analyzed by NMR and DSC measurements. The graft copolymers exhibited a phase‐separated morphology with the backbone and the methoxy polyethylene glycol (MPEG) grafts forming separate crystalline phases. The MPEG phase had a melting temperature lower than the corresponding MPEG homopolymer, as determined by DSC. The melting point of the crystalline phase formed by the EMS and EHMS main chains was lower than that of pure polymer backbone. Copyright © 2009 John Wiley & Sons, Ltd.     

Ethylene/Norbornene Copolymerization with iPr(Cp)(Flu)ZrCl2 Catalyst: Effect of MAO Cocatalyst and 3rd Monomer

The copolymerization of ethylene and norbornene (N) was carried out with iPr(Cp)(Flu)ZrCl₂ catalyst and modified methylaluminoxane (MMAO) cocatalyst. The catalytic activity was dependent on the structure of MMAO, i.e., MMAO-4 exhibited higher catalyst activity than MMAO-3A containing more i-butyl groups. The glass transition temperature (T_g) and the composition of the produced copolymer were not affected by MMAO type. With styrene derivatives as 3^rd monomer, T_g of copolymer increased while the catalytic activity decreased. With the addition of 3^rd monomer, not only the content of 3^rd monomer but also the content of N increased.     

On the origin of the multiple melting behavior in poly(ethylene naphthalene‐2,6‐dicarboxylate): Microstructural study as revealed by differential scanning calorimetry and X‐ray scattering

In this article a study on the melting behavior and microstructure of semicrystalline poly(ethylene naphthalene‐2,6‐dicarboxylate) (PEN) prepared by crystallization from the glass under different annealing conditions is presented. The influence of the annealing temperature (T_a), annealing time (t_a), and the heating rate (R_h) at which T_a is reached on the endothermic behavior of the samples was investigated by means of differential scanning calorimetry (DSC). A dual melting behavior appeared for low R_h values (2 deg · min⁻¹) within the range of 145 °C < T_a < 250 °C and 1 min ≤ t_a. ≤ 16 h. Samples subjected to fast heating rates (R_h = 200 deg · min⁻¹) to reach a T_a ≥ 230 °C showed DSC traces in which a transition is observed from three peaks to a single melting peak when t_a increases in the 30–240 min range. On the basis of the DSC results, PEN samples were prepared displaying single or dual endothermic behavior. The microstructure of these samples was studied by wide (WAXS) and small‐angle X‐Ray scattering (SAXS) techniques. The SAXS data were analyzed using the correlation function and interface distribution function formalisms, respectively. In samples with a single melting behavior, microstructural parameters such as the long spacing, the amorphous and the crystalline phase thicknesses are consistent with a lamellar stacking model in which the thickness distributions of both phases are almost the same. For samples exhibiting two melting endotherms, a dual lamellar model, which is in agreement with the experimental results is proposed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1167–1182, 2000