Effect of annealing on the structure and properties of poly(vinylidene fluoride) β‐form films

Oriented poly(vinylidene fluoride) (PVDF) films consisting of β crystals were prepared by the solid‐state coextrusion (SC) of a gel film near the melting temperature (T_m) and by conventional cold tensile drawing (TD) of a melt‐quenched film. These films were annealed over the temperature range of 75–190 °C (below and above the static T_m) while the sample length was kept constant or constant loads were applied. After annealing with the sample length kept constant, the dynamic Young's modulus markedly decreased because of the relaxation of oriented amorphous chains, as shown by infrared spectroscopy. In contrast, annealing under a constant load improved the chain orientation in both the crystalline and amorphous regions, resulting in an increase in the modulus from an initial 10.5 to 14.3 GPa for the SC and from an initial 3.3 to 4.8 GPa for the TD. The SC, annealed at 190 °C with a constant load corresponding to an initial tension of 200 MPa, exhibited an extreme crystalline‐chain orientation of 0.998 and a modulus of 14.3 GPa, among the highest values ever reported for PVDF. Although the remanent polarization (P_r) of the TD increased slightly from the initial 62 to 68 mC/m², P_r of the SC stayed constant at 100 mC/m² independently of the annealing conditions. This suggests that the P_r value of 100 mC/m² approached the equilibrium value for this PVDF sample containing 3.5 mol % structural defects. Therefore, although the modulus and P_r of the TD increased slightly with annealing, the maximum values achieved by annealing were markedly lower than those of the SC and annealed SC. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1701–1712, 2003     

Elastic modulus of poly(isobutylene oxide) crystals parallel to the chain axis

The elastic tensile modulus of the crystalline regions parallel to the chain axis E₁ for poly(isobutylene oxide) (PIBO) was determined by an x-ray diffraction method. The stress-strain (σ—ε) curve calculated from the meridional reflection of (002) shows an inflection point at about 75 MN/m² or an extension of 0.25%. The observed moduli below and above this point are 29 and 47 GN/m², respectively, at room temperature. The initial lower modulus agrees well with the value, 29.7 GN/m², calculated on the basis of the double zigzag structure of PIBO chain determined by Kaji and Sakurada. The higher modulus may be due to an intrachain steric hindrance between the hydrogen atoms of the methylenic group in the main chain and those of the two side methyl groups.     

Ultra‐low modulus polyazomethines and enhanced adhesion strength with copper foils

Polyazomethines (PAzMs) were prepared from dialdehydes containing different lengths of alkylene groups (m = 2–12) and an ether‐containing common aromatic diamine. The main purpose of this work is to achieve an ultra‐low modulus and a considerably high adhesion strength with a smooth surface (S‐side) of electro‐deposited copper foils for applications as novel coating‐type protective layer materials of flexible printed circuit boards. The elongation at break of the PAzM films was drastically enhanced by increasing the annealing temperature (T_a). The results are probably attributed to a chain extension effect accompanied with solid‐state polymerization promoted at elevated temperatures. An increase in the alkylene chain length (m) led to a gradual decrease in the modulus of the PAzM films owing to an increase in the chain flexibility. It also drastically improved the adhesion strength (S‐side); 8.3 N cm^–1 at m = 12 in spite of the absence of anchoring effect. To further decrease the modulus, the PAzM (m = 12) was modified with another diamine comonomer containing a polybutylene oxide block. This approach was very effective for achieving the present target properties; the PAzM copolymer displayed ultra‐low tensile modulus (0.20 GPa) and a very high adhesion strength (9.8 N cm^–1) with the S‐side of copper foils. Copyright © 2015 John Wiley & Sons, Ltd.     

Palladium Nanoparticles Embedded into Graphene Nanosheets: Preparation,Characterization, and Nonenzymatic Electrochemical Detection of H2O2

A novel nonenzymatic H₂O₂ sensor based on a palladium nanoparticles/graphene (Pd‐NPs/GN) hybrid nanostructures composite film modified glassy carbon electrode (GCE) was reported. The composites of graphene (GN) decorated with Pd nanoparticles have been prepared by simultaneously reducing graphite oxide (GO) and K₂PdCl₄ in one pot. The Pd‐NPs were intended to enlarge the interplanar spacing of graphene nanosheets and were well dispersed on the surface or completely embedded into few‐layer GN, which maintain their high surface area and prevent GN from aggregating. XPS analysis indicated that the surface Pd atoms are negatively charged, favoring the reduction process of H₂O₂. Moreover, the Pd‐NPs/GN/GCE could remarkably decrease the overpotential and enhance the electron‐transfer rate due to the good contact between Pd‐NPs and GN sheets, and Pd‐NPs have high catalytical effect for H₂O₂ reduction. Amperometric measurements allow observation of the electrochemical reduction of H₂O₂ at 0.5 V (vs. Ag/AgCl). The H₂O₂ reduction current is linear to its concentration in the range from 1×10^?9 to 2×10^?3 M, and the detection limit was found to be 2×10^?10 M (S/N=3). The as‐prepared nonenzymatic H₂O₂ sensor exhibits excellent repeatability, selectivity and long‐term stability.     

Mechanical Properties of 3-Glycidoxypropyltrimethoxysilane Based Hybrid Organic-Inorganic Materials

Hybrid organic-inorganic materials were synthesized from acid catalysed sols of tetraethyl orthosilicate, 3-glycidoxypropyltrimethoxysilane and titanium or zirconium alkoxides. The mechanical properties of these materials were measured in different conditions of preparation. The elastic modulus E was determined by a resonance method and by Knoop microindentation. After a thermal treatment at 125°C for 120 h, E was around 3–5 and 1–2 GPa for the samples synthesized with titanium butoxide or zirconium butoxide, respectively. An increase in E in the samples cured for longer times was observed. Knoop microhardness also increased with the heating time and was larger in samples synthesized from titanium alkoxides than zirconium alkoxides. The two methods gave results in good agreement when applied to samples treated for shorter times. In the other samples Knoop microindentation gave a larger value of E compared to the resonance vibration method. Hardness to elastic modulus ratio, H/E, was evaluated by Knoop microindentation. The elastic recovery at the longest heat treatment time was similar to that of soda-lime glasses. Fracture toughness was measured by three points flexural test, a _KIc in the range of 0.4–0.5 MPa m^1/2 was evaluated for samples treated during 168 h.     

Annealing effects of phase I poly(vinylidene fluoride)

The effects of annealing temperatures on stretched poly(vinylidene fluoride) film were systematically studied from the “as-received” condition up to the melting range (180°C). X-ray diffraction studies indicate that the annealing process brings about better chain packing and increased crystallite perfection. The elastic modulus and piezoelectric strain and stress constants, d₃, and e₃₁, decrease as the annealing temperature T_a increases up to 160°C, while the remanent polarization P_r remains almost constant. Some of these characteritics may be interpreted in terms of a morphological transformation of microfibrils. The values of P_r, d₃₁, and e₃₁ increase dramatically as T_a increases from 160 to 180°C; P_r increases from 56 to 85 mC/m², d₃₁ from 20.2 to 27.7 pC/N, and e₃₁ from 51.4 to 65.2 mC/m². As a result, the values of P_r and d₃₁ were the largest recorded from any of the samples used in the present study. e₃₁ showed a value close to the largest one; this usually occurs in unannealed samples. Samples annealed in the melting range also exhibit significantly improved ageing characteristics. The large value of P_r and the small relaxation strength of both the dielectric constant and elastic modulus indicates that the largest crystallinity obtained is approximately 70%.     

Molecular orbital studies of polyethylene deformation

Young's modulus E for polyethylene in the chain direction is calculated with molecular orbital theory applied to n-alkanes C₃H₈ through n-C₁₃H₂₈ and analyzed with the cluster-difference method. Semiempirical CNDO, MNDO, and AM1 models and ab initio HF/STO-3G, HF/6-31G, HF/6-31G*, and MP2/6-31G* models are used. Cluster-difference results, when extrapolated to infinite chain length, give E in good agreement with moduli evaluated with molecular cluster or crystal orbital methods, provided minimal basis sets are employed. E decreases from 495 GPa (CNDO) to 336 GPa (MP2/6-31G*) as the level of theory is improved, consistent with established behaviors of the various models. Our calculations do not reproduce earlier molecular cluster or crystal orbital results, which gave E < 330 GPa. The most rigorous MP2/6-31G* model is known to overestimate force constants by ∼ 11%; the scaled modulus E = 299 GPa is in good accord with E = 306 GPa from recent calculations based on experimental vibration frequencies. © 1996 John Wiley & Sons, Inc.     

Instantaneous strain recovery elasticity and endothermic heat change in nylon-6 monofilaments and silicone rubbers

The instantaneous elastic moduli for a nylon-6 monofilament were derived on strain recoveries right after creep, stress relaxation, and rapid elongation,E _c ,E _s andE _e , respectively. It was found that during strain recoveryE _s (>E _e ) andE _e increase monotonically with increasing load,m ₁, on the sample. The extrapolated value of E_s atm ₁=0 g is almost equal to Young's modulus, 4.06 GPa. The value ofE _c also increased with increasingm ₁, and atm ₁=600 g (1.93 t cm^–2) reached about 14 GPa. The endothermic heat change right after creep, stress relaxation or rapid elongation,Q, was negligibly small. For comparison,E _s ,E _c andQ were also investigated for silicone rubber. It was found thatE _s (53.8 M Pa at the draw ratioD=1.2) decreased abruptly atD=1.3. In the range ofD=1.4–1.9,E _s was only 22.6 MPa. In the case of stress relaxation,Q increased with increasingD from 4 J mol^–1 (atD=1.2) to 56 J mol^–1 (atD=1.9). FurthermoreE _c (5.58 MPa atm ₁=133.8 g (429.4 kg cm^–2)) increased gradually with increasing m₁ and attained 16.6 MPa atm ₁=548.4 g (1.76 t cm^–2). In the case of creep,Q was in the range of 0–11.5 J mol^–1 and larger when larger loads,m ₂ were removed during the later stages of creep.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayThe author wishes to thank Mr. Keizi Igarashi and Mr. Tetsuya Yasui for helping in the experiments.     

Compression of Self‐Assembled Nano‐Objects: 2D/3D Transitions in Films of (Perfluoroalkyl)Alkanes—Persistence of an Organized Array of Surface Micelles

Understanding and controlling the molecular organization of amphiphilic molecules at interfaces is essential for materials and biological sciences. When spread on water, the model amphiphiles constituted by C_nF_2n+1C_mH_2m+1 (FnHm) diblocks spontaneously self‐assemble into surface hemimicelles. Therefore, compression of monolayers of FnHm diblocks is actually a compression of nanometric objects. Langmuir films of F8H16, F8H18, F8H20, and F10H16 can actually be compressed far beyond the “collapse” of their monolayers at ～30 Ų. For molecular areas A between 30 and 10 Ų, a partially reversible, 2D/3D transition occurs between a monolayer of surface micelles and a multilayer that coexist on a large plateau. For A<10 Ų, surface pressure increases again, reaching up to ～48 mN m^?1 before the film eventually collapses. Brewster angle microscopy and AFM indicate a several‐fold increase in film thickness when scanning through the 2D/3D coexistence plateau. Compression beyond the plateau leads to a further increase in film thickness and, eventually, to film disruption. Reversibility was assessed by using compression–expansion cycles. AFM of F8H20 films shows that the initial monolayer of micelles is progressively covered by one (and eventually two) bilayers, which leads to a hitherto unknown organized composite arrangement. Compression of films of the more rigid F10H16 results in crystalline‐like inflorescences. For both diblocks, a hexagonal array of surface micelles is consistently seen, even when the 3D structures eventually disrupt, which means that this monolayer persists throughout the compression experiments. Two examples of pressure‐driven transformations of films of self‐assembled objects are thus provided. These observations further illustrate the powerful self‐assembling capacity of perfluoroalkyl chains.     

Properties and morphologies of UV‐cured epoxy acrylate blend films containing hyperbranched polyurethane acrylate/hyperbranched polyester

The properties and morphologies of UV‐cured epoxy acrylate (EB600) blend films containing hyperbranched polyurethane acrylate (HUA)/hyperbranched polyester (HPE) were investigated. A small amount of HUA added to EB600 improved both the tensile strength and elongation at break without damaging its storage modulus (E′). The highest tensile strength of 31.9 MPa and an elongation at break around two times that of cured pure EB600 were obtained for the EB600‐based film blended with 10% HUA. Its log E′ (MPa) value was measured to be 9.48, that is, about 98% of that of the cured EB600 film. The impact strength and critical stress intensity factor (K_1c) of the blends were investigated. A 10 wt % HUA content led to a K_1c value 1.75 times that of the neat EB600 resin, and the impact strength of the EB600/HPE blends increased from 0.84 to 0.95 kJ m^?1 with only 5 wt % HPE addition. The toughening effects of HUA and HPE on EB600 were demonstrated by scanning electron microscopy photographs of the fracture surfaces of films. Moreover, for the toughening mechanism of HPE to EB600, it was suggested that the HPE particles, as a second phase in the cured EB600 film, were deformed in a cold drawing, which was caused by the difference between the elastic moduli of HPE and EB600. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3159–3170, 2005     

Deformation of lamellar structures: Simultaneous small- and wide-angle X-ray scattering studies of polyamide-6

Structural changes during tensile deformation in semicrystalline polymers are studied by the analysis of both small- and wide-angle X-ray scattering data from polyamide-6 fibers. The strain in the lamellar spacing is about the same as or higher than the fiber strain, suggesting that fiber elongation occurs by the deformation of the lamellar stack rather than slippage of the fibrils, especially during initial stages of elongation. The modulus of the lamellar structure is approximately 5 GN/m², and this is close to the fiber modulus, which is only 2–3% of the crystal modulus. Fiber modulus is, therefore, determined by the lamellar structure as much as by the interfibrillar oriented chain segments. The four-point small-angle X-ray scattering pattern in the relaxed fiber transforms reversibly into a two-point pattern under strain. The structures that correspond to these two patterns, the bistable states of the lamellae, coexist until fiber breakage. The structure that gives rise to the two-point pattern determines the ultimate strength of the fiber. Despite the small crystalline strain in the fiber direction, it is possible to follow the almost fully reversible changes in the orientation, size, and unit cell of the lamellar crystals. It is proposed that the appearance of the two-point pattern, the decrease in the lateral crystallite size, and the increase in the stack diameter are due to tilting of the lamellar surface caused by large-scale reversible strain in the interlamellar amorphous regions. This tilt is accomplished by slippage of the hydrogen-bonded sheets along the chain axis. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 691–705, 2002     

Stepwise annealing of poly(butylene terephthalate)

Annealing of poly(butylene terephthalate) (PBT) was studied by differential scanning calorimetry (DSC) and small angle X‐ray scattering (SAXS) measurement. A PBT sample was annealed at a recrystallization temperature where recrystallization occurs with a maximum rate in the heating process of the sample. In the subsequent annealing steps, the annealed sample was annealed repeatedly at the recrystallization temperatures, and the stepwise annealing sample was obtained. Peak melting temperature (T_m) and sharpness of DSC peak of the stepwise annealing sample increased with the annealing step. A high melting‐temperature sample was obtained in a short time, and T_m increased up to 238.5°C which is higher than all the T_m values that appear in the literature. The long period calculated from SAXS curves of the stepwise annealing sample increased with the annealing step. The increase of crystallite size and perfection of the crystal in the stepwise annealing process is suggested. Annealing experiment indicated that T^°_m should be higher than about 235°C. T_m increased linearly with the annealing temperature of the final step in the stepwise annealing (T_a). The equilibrium melting temperature (T^°_m) for PBT was estimated to be 247°C by the application of a Hoffman–Weeks plot to the relation between T_m vs. T_a. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2420–2429, 1999     

Studies on dynamic mechanical and mechanical properties of vinyloxyaminosilane grafted ethylene propylene diene terpolymer/linear low density polyethylene (EPDM-g-VOS/LLDPE) blends

The dynamic mechanical properties of vinyloxyaminosilane grafted ethylene propylene diene terpolymer/linear low density polyethylene (EPDM-g-VOS/LLDPE) blends have been evaluated with special reference to the effect of blend ratio. It has been found that increasing the proportion of LLDPE in the blends decreases the T_g values and increases the storage modulus (E^′) and loss modulus (E^′′) due to increase in crystallinity. A gradual increase in the values of tanδ_max is observed for the blends with increase in EPDM-g-VOS concentration, which indicates that no phase inversion occurs. But however the higher increase in tanδ_max after 50 wt.% of EPDM-g-VOS composition is due to small change in crystallinity and is ascertained by SEM micrographs. Mechanical properties such as tensile strength, Young’s modulus and hardness increase with increases in LLDPE concentration in the blends and with dicumyl peroxide (DCP) concentration whereas the values of elongation at break are decreased with increase in LLDPE and DCP concentration.     

Elastic modulus of the crystalline phase of poly(cis 1,4-isoprene)

The crystalline elastic modulus of poly(cis 1,4-isoprene) has been measured by x rays and calculated by molecular mechanics. The experimental modulus is E = (2.3 ± 0.3) × 10⁹N m^?2. The calculated modulus is E = (8.8 ± 0.1) × 10⁹N m^?2 for chains in S⁺ cis S^?T conformation and E = (6.1 ± 0.1) × 10⁹N m^?2 for chains in S⁺ cis S+T conformation. The modulus calculated for a statistical structure including both conformation is E = (6.7 ± 0.1) × 10⁹N m^?2. The experimental modulus is thought to be a lower limit because of partial crystallinity of the sample. The chief mechanism of deformation is rotation around single bonds adjacent to the double bond.     

Low-temperature processing of sol-gel derived Pb(Zr,Ti)O<Subscript>3</Subscript> thick films using CO<Subscript>2</Subscript> laser annealing

Fabrication of ferroelectric Pb(Zr_0.52Ti_0.48)O₃ (PZT) thick films on a Pt/Ti/SiO₂/Si substrate using powder-mixing sol-gel spin coating and continuous wave CO₂ laser annealing technique to treat the specimens with at a relatively low temperature was investigated in the present work. PZT fine powders were prepared by drying and pyrolysis of sol-gel solutions and calcined at temperatures from 400 to 750°C. After fine powder-containing sol-gel solutions were spin-coated on a substrate and pyrolyzed, CO₂ laser annealing was carried out to heat treat the specimens. The results show that laser annealing provides an extremely efficient way to crystallize the materials, but an amorphous phase may also form in the case of overheating. Thicker films absorb laser energy more effectively and therefore melt at shorter periods, implying a significant volume effect. A film with thickness of 1 μm shows cracks and rough surface morphology and it was difficult to obtain acceptable electrical properties, indicating importance of controlling interfacial stress and choosing appropriate size of the mixing powders. On the other hand, a thick film of 5 μm annealed at 100 W/cm² for 15 s exhibits excellent properties (P _r = 36.1 μC/cm², E _c = 19.66 kV/cm). Films of 10 μm form a melting zone at the surface and a non-crystallized bottom layer easily at an energy density of 100 W/cm², showing poor electrical properties. Besides, porosity and electrical properties of thick films can be controlled using appropriate processing parameters, suggesting that CO₂ laser annealing of modified sol-gel films is suitable for fabricating films of low dielectric constants and high crystallinity.     

Physicochemical Properties and Surface Tension Prediction of Mixed Surfactant Systems: Triton X‐100 with Dodecylpyridinium Bromide and Triton X‐100 with Sodium Dodecylsulfonate

Dependences of the surface tension of aqueous solutions of ionic (dodecylpyridinium bromide, sodium dodecylsulfonate) and nonionic (Triton X‐100) surfactants and their mixtures on total surfactant concentration and solution composition were studied, and the surface tension of the mixed systems were predicted using different Miller's model. It was found that how to select the model for calculation of ω is corresponding to the degree of the deviation from the ideality during the adsorption of mixed surfactants. The compositions of micelles and adsorption layers at air‐solution interface as well as parameters (β^m, β^ads) of headgroup‐headgroup interaction between the molecules of ionic and nonionic surfactants were calculated based on Rubingh model. The parameters (B₁) of chain‐chain interaction between the molecules of ionic and nonionic surfactants were calculated based on Maeda model. The free energy of micellization calculated from the phase separation model (ΔG ₂ ^m ), and by Maeda's method (ΔG ₁ ^m ) agree reasonably well at high content of nonionic surfactant. The excess free energy ΔG _ads ^E and ΔG _m ^E (except α=0.4) for TX‐100/SDSn system are more negative than that TX‐100/DDPB system. These can be probably explained with the EO groups of TX‐100 surfactant carrying partial positive charge.     

Low temperature preparation and electric properties of highly (100)-oriented Pb<Subscript>0.8</Subscript> La<Subscript>0.1</Subscript>Ca<Subscript>0.1</Subscript>Ti<Subscript>0.975</Subscript>O<Subscript>3</Subscript> thin films prepared by a sol–gel route

Highly (100)-oriented Pb_0.8La_0.1Ca_0.1Ti_0.975O₃ (PLCT) thin films deposited on Pt/Ti/SiO₂/Si substrate were successfully achieved by a sol–gel route. The influence of annealing temperature on microstructures and electric properties was investigated; it was found that the PLCT film could be crystallized only at 450 °C. When the annealing temperature increased to 500 °C, the PLCT film exhibited highly (100)-oriented, which also possessed higher remnant polarization Pr (27 μC/cm²) and better pyroelectric figure of merit (F _d = 205 μC/m²k) at room temperature. It was also found too high annealing temperature (625 °C) could lead to recrystallization of film, and the small grains caused by recrystallization could make polarization reversal difficult and disturbed the preferred crystal growth in film, which was not benefit to obtain enhanced electric properties.     

Expansion and Shrinkage of Fibers: Load- and temperature modulated TMA measurements temperature calibration of fiber attachments

The thermal behavior of a drawn PET fiber has been investigated by thermomechanical analysis, TMA, and by differential scanning calorimetry, DSC. Above the glass transition temperature of 79°C, the fiber shrinks to a maximum of 8% of the initial length. Temperature modulated TMA enabled the separation of the thermal expansion from the overlapping shrinkage during the first heating and to calculate the expansivity, _e and the shrinkage coefficient, _s, independent of each other. Young's modulus, E, was measured by TMA with modulation of the tensile stress. Hence, it was possible to record the behavior of _e, _s and E during the structural changes by combining both modulations in a single measurement.A new technique was developed to calibrate the sample temperature. With this, accurate control of the modulated temperature of the specimen was achieved, independent of the changing heating rate.This revised version was published online in November 2005 with corrections to the Cover Date.     

The flexibility of rodlike micelles in aqueous solutions and the crossover concentrations among dilute,semidilute, and concentrated regimes

A flexibility parameter, the persistence length, has been evaluated from the radii of gyration and the contour lengths for rodlike micelles of heptaoxyethylene alkyl ethers (C _n E₇,n=12, 14, 16) and tetradecyldimethylammonium chloride (C₁₄DAC) and bromide (C₁₄DAB) at the observed crossover concentrations between dilute and semidilute regimes. The persistence length range is 43–73 nm, except for C₁₂E₇, for which it is 32 nm. The crossover concentrations between dilute and semidilute regimes for the semiflexible rodlike micelles calculated according to Ying and Chu as a function of the molecular weight, the contour length, and the persistence length are consistent with the observed values. The crossover concentration between semidilute and concentrated regimes was, on the other hand, calculated by using the same micelle parameters, including the value of thickness of cross-section of the rodlike micelles. The obtained values are at variance with the observed values. This means that rodlike micelles in semidilute and concentrated solutions might differ in size and/or flexibility from those in dilute solution.     

Quantitative evaluation of stress distribution in bulk polymer samples through the comparison of mechanical behaviors between giant single‐crystal and semicrystalline samples of poly(trans‐1,4‐diethyl muconate)

The Raman shift and crystallite modulus were measured under the application of tensile force for a giant single crystal and a series of uniaxially oriented semicrystalline samples of poly(trans‐1,4‐diethyl muconate) (polyEMU). The apparent Raman shift factor α^app or a vibrational frequency shift per 1 GPa tensile stress was higher for the semicrystalline samples with lower crystallinity or lower bulk modulus. The apparent crystallite modulus E or Young's modulus along the chain axis in the crystalline region was not constant but varied remarkably between the giant single crystal and semicrystalline samples. A systematic change in α^app and E among the polyEMU samples with different preparation history could be interpreted quantitatively on the basis of a mechanical series parallel model consisting of crystalline and amorphous phases. The origin of different E and α^app was speculated to be a stress concentration on the taut‐tie chain contained as a parallel crystalline component in the mechanical model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 444–453, 2003