Synergistic effects of PEG and MWCNTs on crystallization behavior of PLLA

This work reported the crystallization behaviors of poly(L ‐lactide) (PLLA) with the presence of polyethylene glycol (PEG) and/or functionalized multiwalled carbon nanotubes (FMWCNTs). The crystallization behaviors occurred in the different conditions, including nonisothermal, isothermal and during the annealing process, were analyzed comparatively using differential scanning calorimetry, wide angle X‐ray diffraction, and polarized optical microscope. The results show that PEG as an efficient plasticizer of PLLA enhances the mobility of PLLA chain segments, which leads to the decrease of glass transition temperature and the enhancement of crystallization ability of PLLA. FMWCNTs as a nucleating agent of PLLA crystallization promote the crystallization of PLLA apparently. With the presence of PEG and FMWCNTs, the crystallization of PLLA is well improved in all conditions, indicating the synergistic effects of PEG and FMWCNTs on PLLA crystallization. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 520–528, 2010     

光学纯度对聚左旋乳酸结晶与熔融行为的影响

通过示差扫描量热仪(DSC)和广角X射线衍射仪(WAXD)研究了聚左旋乳酸(PLLA)的光学纯度(91.6%、93.3%、94.0%、97.0%、98.4%)对聚乳酸结晶和熔融行为的影响。 在非等温结晶过程中,随着光学纯度的提高,聚乳酸的结晶峰值温度、熔点、熔融焓均提高。 在等温结晶过程中,PLLA的半结晶时间(t_1/2)随着光学纯度的增加而减少,在结晶温度100~110 ℃区间内半结晶时间均达到最小值;含有不同光学纯度PLLA的Avrami指数n≈3,表明光学纯度的变化不能改变聚乳酸以三维球晶生长的异相成核机理。 随着光学纯度的增加,聚乳酸δ-晶型转变为α-晶型的临界温度升高。 聚乳酸的结晶和熔融行为对光学纯度具有依赖性。     

Rheology and crystallization behavior of asymmetric PLLA/PDLA blends based on linear PLLA and PDLA with different structures

In this study, several asymmetric poly(L‐lactide)/poly(D‐lactide) (PLLA/PDLA) blends were prepared by adding small amounts of PDLA with different structures into linear PLLA matrix. The effect of PDLA on rheological behavior, crystallization behavior, nucleation efficiency and spherulite growth of PLLA was investigated. Rheological results indicated that PLLA/PDLA blends showed solid‐like viscoelastic behavior at low temperature (<200°C), and the cross‐linking density of PLLA/PDLA melt at 180°C followed the order: PLLA/6PDLA > PLLA/L‐PDLA > PLLA/3PDLA > PLLA/4PDLA. No‐isotherm and isotherm crystallization results indicated that the crystallization capacity of PLLA/PDLA blends was strongly related to the PDLA structure, crystallization temperature and thermal treatment temperature. Furthermore, the dimension of crystal growth during isotherm crystallization presented the obvious dependent on the PDLA structure. The nucleation efficiency of sc‐crystallites in the blends and spherulite density during isothermal crystallization were also studied. Nucleation efficiency of sc‐crystallites in the PLLA/S‐PDLA blends showed the obvious dependent on thermal treatment temperature with respect to PLLA/L‐PDLA, and nucleation efficiency sc‐crystallites in the PLLA/S‐PDLA blends first decreased and then increased as the thermal treatment temperature increased. Spherulite density of PLLA/PDLA blends was also related to thermal treatment temperature and the PDLA structure. This study has discussed the temperature dependence of the stereocomplex networks between PLLA and PDLA with different structure, and then its consequential influence on rheology and crystallization capacity of PLLA, which would provide the theoretical direction for PLA processing. Copyright © 2016 John Wiley & Sons, Ltd.     

左旋聚乳酸/聚(ε-己内酯)共混物在取向聚乙烯基底上的附生结晶行为

利用电子显微镜结合电子衍射研究了左旋聚乳酸/聚(ε-己内酯)(PLLA/PCL)共混物在取向聚乙烯(PE)基底上的结晶行为.纯PLLA在取向PE基底上能够附生结晶,主要形成分子链相互垂直的片晶结构.PCL在PE基质上也能发生附生结晶,导致两者分子链平行.PLLA/PCL共混物在取向PE基底上结晶的形态结构依赖于共混组成.在PLLA含量大于95 wt%时,PCL不影响PLLA与PE的附生结晶行为.当PCL含量增加至10 wt%时,PLLA在PE上的附生结晶行为受到了一定程度的影响.当PCL含量超过40 wt%时,PLLA在PE上的附生结晶被抑制,取而代之是PCL在PE取向基质上附生结晶,产生两者分子链平行的取向片晶.另外,在PLLA含量在50 wt%~30 wt%之间时,体系产生明显的微相分离,微相分离并不影响PCL与PE的附生结晶,在PCL的富集区仍然发生平行链附生结晶,而PLLA的富集区结构变得模糊.当PLLA含量少于20 wt%时,微相分离不明显,少量PLLA应该分散在PCL片晶间的非晶区.     

Transient and athermal effects in the crystallization of polymers. I. Isothermal crystallization

The isothermal crystallization of poly(propylene) and poly(ethylene terephthalate) was investigated with differential scanning calorimetry and optical microscopy. It was found that the induction time depends on the cooling rate to a constant temperature. The isothermal crystallization of the investigated polymers is a complex process and cannot be adequately described by the simple Avrami equation with time‐independent parameters. The results indicate that crystallization is composed of several nucleation mechanisms. The homogeneous nucleation occurring from thermal fluctuations is preceded by the nucleation on not completely melted crystalline residues that can become stable by an athermal mechanism as well as nucleation on heterogeneities. The nucleation rate depends on time, with the maximum shortly after the start of crystallization attributed to nucleation on crystalline residues (possible athermal nucleation) and on heterogeneities. However, the spherulitic growth rate and the exponent n do not change with the time of crystallization. The time dependence of the crystallization rate corresponds to the changes in the nucleation rate with time. The steady‐state crystallization rate in thermal nucleation is lower than the rate determined in a classical way from the half‐time of crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1835–1849, 2002     

Effects of thermal stability on the crystallization behavior of poly(vinylidene chloride)

Thermal analysis based on TGA (thermal gravimetric analysis) and DSC (differential scanning calorimeter) shows no significant degradation for PVDC which has been annealed at 210°C for less than 2 min. And the following recrystallization behavior at lower temperature (120°C) is also independent of the thermal treatment and is not affected by the difference of molecular weight. The degradation which includes dehydrochlorination at lower temperature and intramolecular cyclization or intermolecular crosslinking of the polyenes at higher temperature starts when the melting time at 210°C is more than 2 min, which also causes weight loss and heat exchange in the TGA and DSC thermograms. The recrystallization behavior of the degraded PVDC (staying at 210°C for more than 2 min) shows a strong dependence on the molecular weight. The crystallinity is decreased with the melting time at 210°C due to the increase of the degree of crosslinking. However, the POM (polarized optical microscopy) pictures and IR spectra show a favorable nucleation effect is present due to the formation of trichlorobenzene from the cyclization of the polyenes as nuclei. The crystallinity of the PVDC recrystallized at 120°C after staying at 210°C for more than 2 min is actually dependent on the molecular weight, melting time at 210°C, and cyclized or crosslinking types of degradation. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3269–3276, 1999     

Enhancing crystallization behavior for optimized performances of poly(TMC‐b‐(LLA‐ran‐GA)) by PDLA/PLLA stereocomplex crystallization

The blends of poly(1,3‐trimethylene carbonate‐b‐(l ‐lactide‐ran‐glycolide)) (PTLG) with poly(d ‐lactide) (PDLA) were prepared via solution‐casting method using CH₂Cl₂ as solvent. The poly(l ‐lactide) (PLLA) segments of PTLG with PDLA chain constructed as stereocomplex structures and growth stereocomplex crystals of PLA (sc‐PLA). The effects of sc‐PLA crystals on thermal behavior, mechanical properties, thermal decomposition of the PTLG/PDLA blends were investigated, respectively. The differential scanning calorimetry (DSC) and wide‐angle X‐ray diffraction (WAXD) results showed that the total crystallinity of the PTLG/PDLA blends was increased with the PDLA content increasing. Heterogeneous nucleation of sc‐PLA crystals induced crystallization of the PLLA segments in PTLG. The crystallization temperature of samples shifted to 107.5°C for the PTLG/PDLA‐20 blends compared with that of the PTLG matrix, and decreased the half‐time of crystallization. The mechanical measurement results indicated that the tensile strength of the PTLG/PDLA blends was improved from 21.1 MPa of the PTLG matrix to 39.5 MPa of PTLG/PDLA‐20 blends. The results of kinetics of thermal decomposition of the PTLG/PDLA blends by TGA showed that the apparent activation energy of the PTLG/PDLA blends was increased from 59.1 to 72.1 kJ/mol with the increasing of the PDLA content from 3 wt% to 20 wt%, which indicated the enhancement of thermal stability of the PTLG/PDLA blends by addition of PDLA. Furthermore, the biocompatibility of the PTLG/PDLA blends cultured with human adipose‐derived stem cells was evaluated by CCK‐8 and live/dead staining. The experiment results proved the PTLG/PDLA blends were a kind of biomaterial with excellent physical performances with very low cytotoxicity.     

Cooperative effects of nucleation agent and plasticizer on crystallization properties of stereocomplex‐type poly(lactide acid)

An investigation of the cooperative effects of plasticizer (PEG) and nucleation agent (TMC‐306) on stereocomplex‐type poly(lactide acid) formation and crystallization behaviors between poly(L‐lactide acid) (PLLA) and poly(D‐lactide acid) (PDLA) was conducted. Wide‐angle X‐ray diffraction (WAXD) and differential scanning calorimetry (DSC) analysis indicated that exclusive stereocomplex‐type poly(lactide acid) (sc‐PLA) crystallites without any homocrystallites poly(lactide acid) (hc‐PLA) did form by incorporation of PEG, TMC‐306, or both at a processing temperature higher than the melting temperature of sc‐PLA (around 230°C). The non‐isothermal and isothermal crystallization kinetics showed that PEG and TMC‐306 could independently accelerate the crystallization rate of sc‐PLA. The crystallization peak temperature and crystallization rate of sc‐PLA were significantly improved by the presence of PEG and TMC‐306. The influence of PEG and TMC‐306 on the morphologies of sc‐PLA was also investigated using polarized optical microscopy (POM). Copyright © 2016 John Wiley & Sons, Ltd.     

Toughening modification of PLLA with PCL in the presence of PCL‐b‐PLLA diblock copolymers as compatibilizer

To obtain an effective compatibilizer for the blends of poly(L‐lactide) (PLLA) and poly(ε‐caprolactone) (PCL), the diblock copolymers PCL‐b‐PLLA with different ratios of PCL/PLLA (CL/LA) and different molecular weights (M_n) were synthesized by ring‐opening polymerization (ROP) of L‐lactide with monohydric poly(ε‐caprolactone) (PCL‐OH) as a macro‐initiator. These copolymers were melt blended with PLLA/PCL (80/20) blend at contents between 3.0 and 20 phr (parts per hundred resin), and the effects of added PCL‐b‐PLLA on the mechanical, morphological, rheological, and thermodynamic properties of the PLLA/PCL/PCL‐b‐PLLA blends were investigated. The compatibility between PLLA matrix and PCL phase was enhanced with decreasing in CL/LA ratios or increasing in M_n for the added PCL‐b‐PLLA. Moreover, the crystallinity of PLLA matrix increased because of the added compatibilizers. The PCL‐b‐PLLA with the ratio of CL/LA (50/50) and M_n ≥ 39.0 kg/mol were effective compatibilizers for PLLA/PCL blends. When the content of PCL‐b‐PLLA is greater than or equal to 5 phr, the elongations at break of the PLLA/PCL/PCL‐b‐PLLA blends all reached approximately 180%, about 25 times more than the pristine PLLA/PCL(80/20) blend.     

Compatibilization of polypropylene/poly (ethylene oxide) blends and crystallization behavior of the blends

The compatibilization of incompatible polypropylene (PP)/poly(ethylene oxide) (PEO) blends was studied. The experimental results showed that the graft copolymer [(PP-MA)-g-PEO] of maleated PP(PP-MA) and mono-hydroxyl PEO (PEO-OH) was a good compatibilizer for the PP/PEO blends in which PP-MA also had some compatibilization. The crystallization of the blends was affected by the compatibility between PP and PEO. The interfacial behavior of the compatibilizers had an important effect on crystallization behavior of the PP/PEO blends. PEO showed fractionated crystallization in the PP/PEO blends. This behavior was studied from the view point of the theory of fractionated crystallization. © 1994 John Wiley & Sons, Inc.     

Effect of molecular weight and temperature on the isothermal crystallization of poly(oxetane)

Poly(oxetane) fractions ranging in number-average molecular weights from 7800 to 157000 have been isothermally crystallized in the temperature range from –50 to 19 C, using dilatometric and calorimetric techniques. In both cases, reproducible isotherms were obtained with an Avrami exponent equal to three. The crystallization rate against crystallization temperature presents a maximum at –30 C. The level of crystallinity changes with molecular weight and the influence of this parameter on the rate of crystallization is pronounced. The crystallization temperature coefficient was studied using nucleation theory and it was found an slight increase in the basal interfacial free energy for the lowest molecular weight fraction. For the analysis of the temperature coefficient at the higher undercoolings, different approximations for the free energy of fusion and the transport term have been considered. The conclusion of this analysis is that, independently of these approximations, the obtained temperature coefficients are the same.     

静电纺丝法制备PLLA/g-HNTs复合纳米纤维膜及其性能研究

以辛酸亚锡为催化剂,利用HNTs表面的羟基引发L-LA开环聚合,合成了表面接枝聚(L-乳酸)(PLLA)链段的埃洛石纳米管(g-HNTs),通过红外、热失重和透射电镜对改性前后HNTs的组成与形貌进行了观察;然后采用静电纺丝技术制备了PLLA纳米纤维膜以及不同组成的PLLA/HNTs和PLLA/g-HNTs复合纳米纤维膜,探讨了纺丝条件对纳米纤维膜形貌的影响,并对复合膜的组成、形貌、力学性能和细胞相容性进行了研究.结果表明,当HNTs与L-LA的摩尔投料比为1∶10时,g-HNTs表面PLLA链段的接枝率为14.22％,HNTs纳米管的形态在接枝后变化不大,易于在无水乙醇中分散.电压强度和进样速率对纤维膜的形貌有一定影响,当电压强度为15 kV、进样速率为1 mL/h时,电纺纤维的直径较为均匀.复合纤维膜中g-HNTs在基体PLLA中的分散性以及与基体的界面相容性要优于相应的HNTs,当g-HNTs含量高达40％时,复合纳米纤维膜中的纤维形态仍然保持较好,可以得到连续、粗细较均匀的纤维;随着HNTs和g-HNTs含量增加,复合纳米纤维膜的拉伸强度和模量先增大后下降,当HNTs和g-HNTs的含量为5％时,两种复合纳米纤维膜的拉伸强度和模量均达到最大值,但PLLA/g-HNTs组复合纳米纤维膜的拉伸强度始终大于相应的PLLA/HNTs组.体外3T3细胞培养结果显示,PLLA/g-HNTs复合纳米纤维膜具有良好的细胞相容性,且优于相应的PLLA和PLLA/HNTs纳米纤维膜.     

The role of cold crystallization of homochiral crystallites in the superb heat resistant poly(lactic acid)

The superb heat resistance poly(lactic acid) (PLA) were prepared by blending PLA and poly(d ‐lactic acid) (PDLA) with various molecular weight (M_n). Formation of the stereocomplex in the blends was confirmed by differential scanning calorimetry and wide‐angle X‐ray diffraction. The results of the heat resistance implied it is possible that elevating the Vicat penetration temperature of PLA up to 150°C by blending with PDLA. The cold crystallization of homochiral crystallites is proven to be the critical factor affecting the heat resistance of PLA. While the PLA or PLA/PDLA blends were heated to cold crystallization temperature of samples, both the crystal content and the rigid amorphous region content are increased due to the cold crystallization and tethering effect, and the stiffness and heat resistance of the sample are improved. The cold crystallization homochiral crystallites kinetics of PLA and PLA/PDLA blends was also studied. The results showed the activation energy (?E) of cold crystallization increased from 120.30 kJ/mol to 144.66 kJ/mol with the increasing of PDLA content from 2% to 10%.     

On the macro- and microphase separation of compatibilizers in immiscible polymer blends

Macro- and microphase separation of compatibilizing graft copolymers in melt-mixed polystyrene/polyamide-6 blends was studied by transmission electron microscopy and thermal analysis. Three different graft copolymers with main chains of polystyrene and side chains of poly(ethylene oxide) were used as additives at various concentrations. The polyamide-6 domain sizes decreased with increasing amounts of compatibilizing graft copolymers in the blends up to a saturation concentration, after which no further reduction was noted. Macrophase separation of the graft copolymers into discrete macrodomains 20–200 nm in size occurred at concentrations equal to or slightly lower than the saturation concentration. The macrodomains of the graft copolymers were microphase separated, and the sizes and shapes of the microdomains were found to largely depend on the graft copolymer structure and composition. As a consequence of microphase separation, poly(ethylene oxide) crystallinity was noted in blends with sufficiently high macrophase contents. Observations of a graft copolymer interphase between the polystyrene matrix and the polyamide-6 domains confirmed that the graft copolymer was present at the blend interfaces in some of the compatibilized blends. © 1996 John Wiley & Sons, Inc.     

Trifluoperazine effects on anionic and zwitterionic micelles: a study by small angle X-ray scattering

In this work small angle X-ray scattering (SAXS) studies on the interaction of the phenothiazine trifluoperazine (TFP, 2-10 mM), a cationic drug, with micelles of the zwitterionic surfactant 3-(N-hexadecyl-N,N-dimethylammonium) propane sulfonate (HPS, 30 mM) and the anionic surfactant sodium dodecyl sulfate (SDS, 40 mM) at pH 4.0, 7.0, and 9.0 are reported. The data were analyzed through the modeling of the micellar form factor and interference function, as well as by means of the distance distribution function p(r). For anionic micelles (SDS), the results evidence a micellar shape transformation from prolate ellipsoid to cylinder accompanied by micellar growth and surface charge screening as the molar ratio TFP:SDS increases in the complex for all values of pH. Small ellipsoids with axial ratio nu=1.5+/-0.1 (long dimension of 60 A) grow and reassemble into cylinder-like aggregates upon 5 mM drug incorporation (1 TFP:8 SDS monomers) with a decrease of the micelle surface charge. At 10 mM TFP:40 mM SDS cylindrical micelles are totally screened with an axial ratio nu approximately 4 (long dimension approximately 140 A at pH 7.0 and 9.0). However, at pH 4.0, where the drug is partially diprotonated, 10 mM TFP incorporation gives rise to a huge increase in micellar size, resulting in micelles at least 400 A long, without altering the intramicellar core. For zwitterionic micelles (HPS), the results have shown that the aggregates also resemble small prolate ellipsoids with averaged axial ratio approximately nu=1.6+/-0.1. Under TFP addition, both the paraffinic radius and the micellar size show a slight decrease, giving evidence that the micellar hydrophobic core may be affected by phenothiazine incorporation rather than that observed for the SDS/TFP comicelle. Therefore, our results demonstrate that the axial ratio and shape evolution of the surfactant:TFP complex are both dependent on surfactant surface-charge and drug:surfactant molar ratio. The results are compared with those recently obtained for another phenothiazine drug, chlorpromazine (CPZ), in SDS and HPS micelles (Caetano, Gelamo, Tabak, and Itri, J. Colloid Interface Science 248 (2002) 149).     

Interfacial effect on confined crystallization of poly(ethylene oxide)/silica composites

The impact of nanoconfinement introduced by nanoparticles on polymer crystallization has attracted extensive attention because it plays an important role in the ultimate properties of polymer nanocomposites. In this study, interfacial and spatial confinement effects of silica (SiO₂) nanoparticles on the crystallization behaviors of poly(ethylene oxide) (PEO)/SiO₂ composites were systematically investigated by changing the size and concentration of SiO₂ in PEO matrix. The composites with high silica loadings exhibit two crystallization peaks of PEO as determined by differential scanning calorimetry. The first peak at 7–43 °C is related to the bulk PEO, while the second peak at ?20 to ?30 °C is attributed to the restricted PEO segments. Three‐layer (amorphous, interfacial, and bulk) model is proposed to interpret the confined crystallization of PEO/SiO₂ composites, which is supported by the results of thermogravimetric analysis and solid‐state ¹H nuclear magnetic resonance. In amorphous layer, most PEO segments are directly adsorbed on SiO₂ surface via hydrogen bonding. The interfacial PEO layer, which is nonuniform, is composed of crystallizable loops and tails extending from amorphous layer. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 414–423     

Effect of wood flour as nucleating agent on the isothermal crystallization of poly(lactic acid)

The effect of wood flour (WF) as an efficient nucleating agent on the isothermal melt crystallization and isothermal cold crystallization behavior of poly(lactic acid) (PLA) was investigated by differential scanning calorimeter and polarized optical microscopy. It was found that the incorporation of 4 wt% WF promoted the crystallization of PLA about 4.2%. Polarized optical microscopy results showed the Maltese cross of the samples. The presence of the 4 wt% WF may increase the nucleation density, leading to the increase of the spherulites; however, the size of the spherulites decreased, and the structure became incomplete. The Avrami model was applied to analyze the isothermal crystallization kinetics. It is concluded that the addition of WF modified the crystallization process of PLA (the value of Avrami exponent changed). Various parameters, such as the crystallization half time and crystallization rate constant, reflect that 4 wt% WF significantly improves the crystallization process. The observations in this article indicate that WF is an efficient nucleating agent of PLA. Copyright © 2016 John Wiley & Sons, Ltd.     

Self‐decelerated crystallization in blends of polyhydroxyether of bisphenol A and poly(ethylene oxide) upon isothermal crystallization

The growth of spherulites of poly(ethylene oxide) in blends with poly(hydroxyether of bisphenol A) was investigated. In a very narrow range of crystallization temperatures, the spherulite growth deviates from the usual constant growth rate regime in a systematic manner in which the growth rate decreases with time. This is explained by local and overall changes in the composition with the proceeding crystallization that are due to the competition between the crystallization and diffusional chain displacement rates, respectively. These kinetic phenomena and processes can quantitatively be described by a suitable analysis of the experimental findings. Deceleration is predominantly caused by a slowing of the chain motion by the glass‐transition temperature being approached (i.e., vitrification) and, to a lesser extent, by dilution. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1250–1257, 2000     

Reactive compatibilization of blends of PET and PP modified by GMA grafting

The melt radical grafting of glycidyl methacrylate (GMA) onto isotactic polypropylene (PP) was carried out in Brabender internal mixer and the influence of reaction procedure, radical initiator concentration and addition of co-monomer (styrene) on the grafting efficiency was examined. The viscosity, the thermal behaviour and melt rheology of PP-g-GMA samples was then analysed as a function of grafted GMA content. Blends of poly(ethylene terephthalate) (PET) with PP and PP-g-GMA (5.2 wt% GMA), prepared in internal mixer, were characterised by SEM, DSC and melt viscosimetry. The morphological analysis of PET/PP-g-GMA blends (80/20, 50/50 w/w) pointed out a marked improvement of phase dispersion (with particle size of about 0.6 μm for 80/20 blend) and interfacial adhesion, as compared to non-compatibilized PET/PP blend. The results of mixing torque and thermal analysis supported the occurrence of in-situ compatibilization reaction between epoxy groups of GMA modified PP and carboxyl end-groups of PET in the melt.     

Observations of crystallization and melting in poly(ethylene oxide)/poly(methyl methacrylate) blends by hot-stage atomic-force microscopy

The binary blend of poly(ethylene oxide)/atactic poly(methyl methacrylate) is examined using hot-stage atomic-force microscopy (AFM) in conjunction with differential scanning calorimetry and optical microscopy. It was found possible to follow in real time the melting process, which reveals itself to be nonuniform. This effect is ascribed to the presence of lamellae having different thicknesses. The crystallization process of poly(ethylene oxide) from the miscible melt is also followed in real time by AFM, affording detailed images of the impingement of adjacent spherulites and direct observation of lamellar growth and subsequent polymer solidification in the interlamellar space.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2643–2651, 1998