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1.
The time—temperature superposition principle is well-established for linear viscoelastic properties of polymer systems. It is generally supposed that the same principle carries over into nonlinear phenomena, such as the relationship between viscosity η and shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}. Guided by this principle and the forms of various molecular theories, one would expect that η—\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} data on the same polymer at different temperatures would superimpose when plotted as η/η0 versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}η0/ρT, η0 being the limiting viscosity at low shear rates, ρ the polymer density, and T the absolute temperature. Data on polystyrene melts, obtained in a plate-cone viscometer, appear systematically to violate this principle in the range 140–190°. Such anomalies are absent in concentrated solutions of polystyrene. The trends are similar to those reported by Plazek in the steady-state compliance of polystyrene melts near Tg, but they appear to persist to higher temperatures than the compliance anomaly.  相似文献   

2.
Poly(acrylonitrile‐co‐itaconic acid) (poly(AN‐co‐IA)) precursor required for carbon fiber production is made into a dope and spun into fibers using a suitable spinning technique. The viscosity of the resin dope is decided by the polymer concentration, polymer molecular weight, temperature, and shear force. The shear rheology of concentrated poly(AN‐co‐IA) polymer solutions in N,N‐dimethylformamide (DMF), in the range of 1 × 105–1 × 106 g mol?1, has been investigated in the shear rate (γ′) range of 1 × 101–5 × 104 min?1. The zero shear viscosity (η0) has been evaluated at different temperatures. The temperature dependence of zero shear viscosity conformed to the Arrhenius–Frenkel–Eyring model. The free energy of activation of viscous flow (ΔGV) values were in the range 5–32 kJ mol?1 and this value increased with increase in polymer concentration and molecular weight. A master equation for the ΔGV value of the polymer solution of any and concentration (c) is suggested. The power law fitted well for the shear dependency of viscosity of these polymer solutions. The pseudoplasticity index (n) diminished with increase in polymer concentration and molecular weight. An empirical relation between viscosity (η) and was found to exist at constant shear rate, concentration and temperature. For each , the equation relating n, c, and T was established. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

3.
Summary: The miscibility behavior and intermolecular interactions among Dextran (Dx) with different molecular weight and Polyvinylpyrrolidone (PVP) blends were studied as dilute aqueous solutions at 25 °C by viscosity method. The intrinsic viscosity and the interaction coefficient were experimentally measured for each polymer-water as well as for Dx-PVP-water systems. These results served for the prediction of miscibility of the Dx/PVP blends with various blend compositions by using , , , , and parameters. Except Dx4/PVP with its all compositions (Dx4 with nominal molecular weight of 110 000), other blend systems are found to be almost miscible. The density measurements of these polymer solutions and their blends were conducted in order to compare with the viscosity findings. Lastly, all Dx with different molecular weight, PVP and their blends were characterized by infrared spectroscopy (FT-IR), and differential scanning calorimetry (DSC).  相似文献   

4.
Four samples containing 40, 60, 80, and 97 wt-% of poly(vinyl chloride), the rest being plasticizer and stabilizer, were tested by using the Weissenberg Rheogoniometer in the steady-shearing mode at temperatures between 155 and 235°C and rates of shear \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma = 0.01 - 400 $\end{document} sec?1. The viscosity η versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} follows Graessley's theoretical dependence for infinitely entangled system. The primary normal-stress difference coefficient ψ versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is well described by the same theoretical function, used with the square of its argument. The temperature dependence of η0 and ψ0 shows discontinuities at T = Tb. The numerical values of Tb can be calculated from the theory of the melting point depression due to diluent. The activation energy of viscous flow Eη below Tb is 5–9 times as large as above this temperature. The activation energy of normal stress is found to be Eψ ≈ 5Eη. The characteristic relaxation times τo, ψp, calculated from superposition of η versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} and ψ versus \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} data, respectively, onto Graessley's master curves, and τN, computed from zero shear parameters η0 and ψ0, differ in their sensitivity to the melting of microcrystalline regions. It is postulated that in the systems investigated, aggregates with long lifetimes are being formed, increasing the effective molecular weight and introducing changes in the effective polydispersity.  相似文献   

5.
We theoretically investigate polymer deformation and shear thinning, i.e., a decrease of intrinsic viscosity, in a dilute polymer solution as a function of the applied shear rate $ \dot \gamma $. We use a bead-and-spring model with hydrodynamic interaction in the Rouse-Zimm framework, approximately accounting also for excluded-volume effects, and impose a constraint on the average mean-square spring length to prevent its stretching at large $ \dot \gamma $. When suitably normalized, both the intrinsic viscosity [η] and the components of the mean gyration tensor 〈SS〉 depend on the single variable $ \xi = {{\dot \gamma \tau _1^{\left( 0 \right)} } \mathord{\left/ {\vphantom {{\dot \gamma \tau _1^{\left( 0 \right)} } {N^{1 - v} }}} \right. \kern-\nulldelimiterspace} {N^{1 - v} }} $ where τ is the longest relaxation time for $ \dot \gamma = 0 $, N is the number of chain springs and v is the Flory exponent. The full shear-rate dependence is obtained numerically, and compared with analytical results obtained under free-draining conditions both for low and for very large shear rates. The shortcomings of the theory are also discussed, in particular a substantial stretching under shear of the central springs, where the intramolecular tension is largest, with a corresponding strong contraction of the end springs due to the average character of the constraint.  相似文献   

6.
7.
The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 105 to 7.62 × 106 and 0.112–0.329 g/cm3, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10?4 < k < 1 sec?1. The Cox–Merz relation η(k) = |η*(ω)|ω=k was tested with the experimental result (|*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η*(ω)|ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ1 > τ2 > …, and the values of τ1, τ2 η1 and η2 were determined for some solutions. The relaxation times τ1 and τ2 were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η1 and η2 were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η1 and η2 with increasing k. It was shown that η1(k) may be evaluated from the relaxation strength G1(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high cM systems as well as for low cM systems.  相似文献   

8.
Extensional tests at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document} have been carried out on polystyrene melts with different molecular weight distributions at various temperatures and strain rates. The true tensile stress is found to be well approximated by the sum of two contributions: (1) a neo-Hookean expression involving the recoverable strain and (2) a contribution rapidly reaching a steady-state value. Two experimental parameters can be defined: an elasticity modulus \documentclass{article}\pagestyle{empty}\begin{document}$ G(\dot \varepsilon ) $\end{document} from (1) and a viscosity \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{\rm v} (\dot \varepsilon ) $\end{document} from (2). It is further shown that time-temperature equivalence applies not only to the stress but also to the recoverable strain and to G and ηv. The dependence of G and ηv on strain rate is then discussed. For high strain rates, G is close to the linear viscoelastic plateau modulus of PS melts and decreases with decreasing strain rate. The value of ηv is found to a good approximation to be equal to three times the shear viscosity taken at a shear rate equivalent to the elongational strain rate.  相似文献   

9.
Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τRZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τL > τRZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ1) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ2)?1/2, where γ is the magnitude of shear. Contributions to η and Ψ1 from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τst = τ + (τRZ ? τ)/(1 + 0.35τRZ γ˙) instead of τRZ. Here, γ˙ is the rate of shear, and τ is the τRZ value at the infinite dilution limit. η and Ψ1 at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002  相似文献   

10.
We investigate relaxation dynamics in a series of six‐arm star/linear 1,4‐polybutadiene blends with mechanical rheometry measurements. Blend systems are formulated to systematically probe constraint release and arm relaxation dynamics. Zero shear viscosity and terminal relaxation times of star/linear polymer blends with fixed star arm molecular weights (Ma) and compositions (?S) are found to follow nonmonotonic dependencies on the linear polymer molecular weight (ML). At low values of ?S, at least two scaling regimes are apparent from the data (ξ0M and ξ0M), where ξ0 refers to the zero shear viscosity or terminal relaxation time of the blend. The two regimes are separated by a critical linear polymer molecular weight M* that is more than 20 times larger than the critical molecular weight for entanglements. When the linear polymer contribution to blend properties is removed, a clear transition from dilution dynamics, ξ0M, to Rouse‐like constraint‐release dynamics, ξ0M, is apparent at low values of ?S. At higher ?S values, a new activated constraint‐release dynamic regime is evident in which ξ0M and ξ0 ~ ?, where α changes continuously from approximately 2 to 0.5 as ?S increases and β varies from 2.0 to 1.0 as ML increases. The experimental results are compared with theoretical predictions based on a drag coupling model for entangled polymer liquids. All features observed experimentally are captured by this model, including the value of M* for the transition from dilution to Rouse constraint‐release dynamics. Predictions of the drag coupling model are also compared with published data for the zero shear viscosity and terminal relaxation time in bidisperse linear polymer blends and pure entangled starlike molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2501–2518, 2001  相似文献   

11.
Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n12 ≈ Cσ) and first normal stress differences (n1 = n11 ? n22 ≈ CN1) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 106 MW PS), steady‐state n12 and n1 results manifest unusual power‐law dependencies on shear rate [n12,ss 0.4 and n1,ss 0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χSS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χp in the range 20–24° is observed; χp values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001  相似文献   

12.
It is shown that the energy of a hydrogen‐like atom confined inside a spherical cavity of radius, R, and potential barrier, V0, is quantitatively defined by the ratio . Here, the conventional spherical density (r) is scaled as ηl(r) = and the ratio of the second derivative η(r) to ηl(r) is evaluated at the nucleus. Numerical results of the ratios are presented for 1s, 2s, 2p, and 3d states at several values of V0. For such states, the characteristic radii of confinement leading to the well‐defined values of energy are identified. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009  相似文献   

13.
Shear stress P21 and normal stress P11P22 functions of moderately concentrated aqueous solutions of sodium poly (acrylate) were measured under steady shear flow at various shear rates \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma$\end{document} with a Weissenberg rheogoniometer. The compliance function Js = (P11P22)/2P212 is found to vary with shear rate. The double logarithmic plot of Js versus \documentclass{article}\pagestyle{empty}\begin{document}$\dot \gamma$\end{document} can be superposed with respect to molecular weight at constant concentrations of added neutral salt and polymer. These reduced plots differ markedly as the concentration of added salt is varied but converge to a single line at high shear rates.  相似文献   

14.
The surface stresses in Ag stepped surfaces (910), (710), (510), (410), (310), (210), (320), (430) and (540) have been calculated by using the modified embedded atom method (MEAM). The surface stresses in the surface plane τxx (along the step edge) and τyy (normal to the step edge) have similar orders of magnitude as the surface energy. For surfaces having the (100) and (110) terraces, the change of τxx and τyy is very small and the variation of the surface energy is smooth. The stress τzz (normal to the surface plane) is always tensile in the unrelaxed state. The linear variation of the change in surface energy per unit change in elastic strain , and (i.e. τxx ? γ, τyy ? γ and τzz) with the angle α between the (hk0) and (100) planes has a turning point corresponding to the (210) surface. The anisotropic ratio in the stepped surface having the (110) terrace is larger than that having the (100) terrace, and the wider the (110) terrace or the narrower the (100) terrace, the larger the ratio τyyxx. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

15.
The effect of a layer of electrochemically grafted 4‐diazo‐N,N‐diethylaniline (DEA) groups on the electron transfer kinetics of redox systems, displaying fast and slow heterogeneous electron transfer rate constants at edge and basal planes of carbon, was investigated. The properties of the modified electrode were characterized by cyclic voltammetry using four different inorganic redox systems (Fe(CN) , Co(phen) , Ru(NH3) , and IrCl in acidic, neutral, and basic media. Two distinct blocking behaviors and electrostatic effects were observed. More precisely, a strong blocking effect of the grafted layer on Fe(CN) and Co(phen) was found, whereas Ru(NH3) and IrCl showed to be rather unaffected by the presence of the DEA grafted layer.  相似文献   

16.
The imidazolium salt 3‐methyl‐1‐(naphthalen‐2‐yl)‐1H‐imidazolium iodide ( 2 ) has been treated with silver(I) oxide and [{Pt(μ‐Cl)(η3‐2‐Me‐C3H4)}2] (η3‐2‐Me‐C3H43‐2‐methylallyl) to give the intermediate N‐heterocyclic carbene complex [PtCl(η3‐2‐Me‐C3H4)(H$\widehat{CC}$ *‐κC*)] ( 3 ) (H$\widehat{CC}$ *‐κC*=3‐methyl‐1‐(naphthalen‐2‐yl)‐1H‐imidazol‐2‐ylidene). Compound 3 undergoes regiospecific cyclometallation at the naphthyl ring of the NHC ligand to give the five‐membered platinacycle compound [{Pt(μ‐Cl)($\widehat{CC}$ *)}2] ( 4 ). Chlorine abstraction from 4 with β‐diketonate Tl derivatives rendered the corresponding neutral compounds [Pt($\widehat{CC}$ *)(L‐O,O′)] {L=acac (HL=acetylacetone) 5 , phacac (HL=1,3‐diphenyl‐1,3‐propanedione) 6 , hfacac (HL=hexafluoroacetylacetone) 7 }. All of the compounds ( 3 – 7 ) were fully characterized by standard spectroscopic and analytical methods. X‐ray diffraction studies were performed on 5 – 7 , revealing short Pt?Pt and π–π interactions in the solid‐state structure. The influence of the R‐substituents of the β‐diketonate ligand on the photophysical properties and the use of the most efficient emitter, 5 , as phosphor converter has also been studied.  相似文献   

17.
We review recent hole growth measurements performed at elevated temperatures in freely-standing polystyrene (PS) films, using optical microscopy and a differential pressure experiment (DPE). In the hole growth experiments, which were performed at temperatures close to the bulk glass-transition temperature of PS, T = 97 °C, we find evidence for nonlinear viscoelastic effects, which markedly affect the growth of holes in freely-standing PS films. The hole radius R initially grew linearly with time t before undergoing a transition to exponential growth characterized by a growth time τ. The time scale τ1 for the decay of the initial transient behavior prior to reaching steady state was consistent with the convective constraint release mechanism of the tube theory of entangled polymer dynamics, while the characteristic hole growth times τ of the holes were consistent with significant reductions in viscosity of over eight orders of magnitude with increasing shear strain rate due to shear thinning. DPE measurements of hole growth on very thin freely-standing films revealed that hole formation and growth occurs only at temperatures that are comparable to or greater than T, even for films for which the Tg value was reduced by many tens of degrees Celsius below the bulk value. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B:Polym Phys 44: 3011–3021, 2006  相似文献   

18.
An electron spin resonance (ESR) spin probe study was performed on 1 : 1 by weight poly(acrylic acid) (PAA)/poly(ethylene oxide) (PEO) complex over the 100–450 K temperature range with a series of tetramethylpiperidyloxy‐based spin probes. Measurements of the parameters T5mT, Ta and Td demonstrated the effects of probe size and the strength of hydrogen bonding. The probes in the series Tempone, Tempo, Tempol and Tamine (respectively 4‐oxo‐, unsubstituted, 4‐hydroxy‐ and 4‐amino‐2,2,6,6,‐tetramethylpiperidine ‐1‐oxyl) displayed noticeable increases in the hydrogen‐bonding effect, as indicated by Ta and Td. These increases correlated with increasing hydrogen bond acceptor strength. On the other hand, as the probe size became larger, T5mT gradually increased due to the free volume decrease. These effects were analyzed using the established theoretical relationship of T5mT to probe volume expressed by f. Meanwhile, in order to investigate the effect of polymer matrix rigidity, a similar study was performed with a nitroxide spin probe, 2,2,6,6‐tetramethyl‐1‐piperidine‐1‐oxyl (Tempo), on PAA/PEO complexes of different weight compositions. The quantitative fast motion fraction in the composite ESR spectrum was calculated. The influence of changes in the composition of PAA on the molecular mobility was characterized by changes of the spectral parameters and τc. The molecular mobility was shown to diminish with increasing content of PAA in PAA/PEO blends duo to the restriction of the polymer matrix rigidity increase. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

19.
The γ-distonic radical ions R$ \mathop {\rm O}\limits^ + $CHR′CH2?HR″ and their molecular ion counterparts R$ \mathop {\rm O}\limits^{{\rm + } \cdot } $CHR′CH2CH2R″ have been studied by isotopic labelling and collision-induced dissociation, applying a potential to the collision cell in order to separate activated from spontaneous decompositions. The stability of CH3$ \mathop {\rm O}\limits^ + $HCH(CH3)CH2?HCH3, C2H5$ \mathop {\rm O}\limits^ + $HCH(CH3)CH2?HCH3, CH3$ \mathop {\rm O}\limits^ + $HCH(CH3)CH2?H2, CH3$ \mathop {\rm O}\limits^ + $HCH2CH2?HCH3 and C2H5$ \mathop {\rm O}\limits^ + $HCH2CH2?HCH3, has been demonstrated and their characteristic decomposition, alcohol loss, identified. For all these γ-distonic ions, the 1,4-H abstraction leading to their molecular ion counterpart exhibits a primary isotope effect.  相似文献   

20.
Methyl methacrylate/styrene (MMA/S), ethyl methacrylate/styrene (EMA/S) and butyl methacrylate/styrene (BMA/S) feeds (>90 mol % methacrylate) were copolymerized in 50 wt % p‐xylene at 90 °C with 10 mol % of additional SG1‐free nitroxide mediator relative to unimolecular initiator (BlocBuilder®) to yield methacrylate rich copolymers with polydispersities w/ n = 1.23–1.46. kpK values (kp = propagation rate constant, K = equilibrium constant) for MMA/S copolymerizations were comparable with previous literature, whereas EMA/S and BMA/S copolymerizations were characterized by slightly higher kpK's. Chain extensions with styrene at 110 °C initiated by the methacrylate‐rich macroinitiators (number average molecular weight n = 12.9–33.5 kg mol?1) resulted in slightly broader molecular weight distributions with w/ n = 1.24–1.86 and were often bimodal. Chain extensions with glycidyl methacrylate/styrene/methacrylate (GMA/S/XMA where XMA = MMA, EMA or BMA) mixtures at 90 °C using the same macroinitiators resulted frequently in bimodal molecular weight distributions with many inactive macroinitiators and higher w/ n = 2.01–2.48. P(XMA/S) macroinitiators ( n = 4.9–8.9 kg mol?1), polymerized to low conversion and purified to remove “dead” chains, initiated chain extensions with GMA/MMA/S and GMA/EMA/S giving products with w/ n ~ 1.5 and much fewer unreacted macroinitiators (<5%), whereas the GMA/BMA/S chain extension was characterized by slightly more unreacted macroinitiators (~20%). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2574–2588, 2009  相似文献   

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