Steady Elongational Viscosity Research Articles

Rheology and Entanglement Structure of Well-Entangled Polymer Melts: A Slip-Link Simulation Study

We have extended the slip-link model originally developed by Doi and Takimoto [Philos. Trans. R. Soc. London, A 2003, 361, 641] to calculate fast shear and uniaxial elongational flows. The original Doi–Takimoto (DT) model shows that steady elongational viscosity increases when the elongational strain rate is larger than WiR(e) > 1, which is not observed in experiments for entangled polymer melts. To improve the predictions of the DT model, we have extended the DT model by incorporating the stretch/orientation-induced reduction of friction (SORF) developed by Yaoita et al. [Macromolecules 2012, 45, 2773]. Consequently, we can successfully reproduce thinning behavior in steady uniaxial elongational viscosities for fast flows WiR(e)>1. Through use of a decoupling approximation, we have found that the reduction of chain stretch has a major effect on the thinning behavior in the strain rate region WiR(e)>1 when employing SORF. Meanwhile, under shear flows, the effect of SORF can be observed in a relatively hig...

Diluting Entangled Polymers Affects Transient Hardening but Not Their Steady Elongational Viscosity

It is now established that the huge qualitative difference in flow behavior between entangled polymer melts and solutions in nonlinear elongational flows cannot be explained in the framework of the...

Test of Orientation/Stretch-Induced Reduction of Friction via Primitive Chain Network Simulations for Polystyrene, Polyisoprene, and Poly(n-butyl acrylate)

Entanglement dynamics of polymers under fast elongation has not been fully understood. Namely, the steady-state uniaxial elongational viscosity of entangled polystyrene (PS) solutions increases with an increase of strain rate above the reciprocal Rouse time, whereas the viscosity of PS melts monotonically decreases even at such high rates. This qualitative difference between solution and melt has been hypothesized to result from the orientation/stretch-induced reduction of friction (SORF). This study examines universality of the mechanism of SORF for narrowly distributed PS, polyisoprene (PI), and poly(n-butyl acrylate) (PnBA). For this purpose, SORF was incorporated in the multichain slip-link simulation through an empirical relationship between the magnitude of friction reduction and the stretch/orientation order parameter for PS [reported in Macromolecules 2012, 45, 2773–2782]. This empirical SORF relationship adopted a mean-field view for contacts between polymer backbone and solvent, and the simulation having this mean-field feature was confirmed to reproduce satisfactorily the transient and steady elongational viscosity data for PS melts and solutions. Assuming that the magnitude of SORF is insensitive to the chemical structure of polymers, we further made the simulation with the same SORF relationship for PI and PnBA. For PI, the simulation reasonably described the viscosity data of a melt and solutions. However, for PnBA melt, the data were well described by the simulation but without SORF. This result suggests that the magnitude of SORF is not universal but changes with the chemical structure of polymers. Specifically, for PnBA, the flexible side chains always surround the PnBA backbone and may behave as a solvent to screen the direct interaction between the backbone segments even in melt. For this case, the mean-field type SORF relationship obviously fails. Nevertheless, a non-mean-field type SORF could result in negligible friction reduction even under fast elongation, thereby allowing the simulation without SORF to describe thet data for PnBA.

Primitive Chain Network Simulation of Elongational Flows of Entangled Linear Chains: Stretch/Orientation-induced Reduction of Monomeric Friction

Well-entangled monodisperse linear polystyrene melts exhibit monotonic thinning of the steady state elongational viscosity with increasing the strain rate ε̇ even beyond the Rouse relaxation frequency, τR-1. This behavior is quite different from the thinning followed by hardening at ε̇ > τR-1 observed for entangled semidilute solutions. We attempt to elucidate the molecular origin of this difference by focusing on the concept of stretch/orientation-dependent monomeric friction ζ recently proposed by Ianniruberto and co-workers. Specifically, literature data of the stress relaxation after cessation of transient elongational flow, reported for both PS melts and solutions, are analyzed to evaluate the stretch/orientation-dependent decrease of ζ. In our working hypothesis, ζ is expressed as a function of the factor Fso = λ̃2S̅, where λ̃ is the normalized stretch ratio of entangled subchains defined with respect to the fully stretched state, and S̅ is an average orientational anisotropy of the components (polymer plus solvent if any) in the system. The factor Fso was estimated from the stress decay data after flow cessation. The resulting functional form of ζ(Fso) was then used in the primitive chain network (PCN) simulation including finite extensible nonlinear elasticity (FENE) to examine the elongational behavior of melts and solutions. For melts the simulation indicates that ζ decreases significantly under fast elongation because the entangled subchains are short and approach the fully stretched (and fully oriented) limit rather easily. Hence, the steady elongational viscosity ηE follows this decrease of ζ to exhibit the monotonic thinning even at ε̇ > τR-1. In contrast, for solutions, the simulated ηE exhibits thickening at ε̇ > τR-1 because the average anisotropy S̅ is governed by the solvent and remains small, thus overwhelming the increase of the subchain stretch λ̃. The simulated results proved to be in satisfactory agreement with the experiments.

Selective withdrawal of polymer solutions: Computations

This paper reports numerical simulations of selective withdrawal of Newtonian and polymeric liquids, and complements the experimental study reported in the accompanying paper (Zhou and Feng [2]). We use finite elements to solve the Navier–Stokes and constitutive equations in the liquid on an adaptively refined unstructured grid, with an arbitrary Lagrangian–Eulerian scheme to track its free surface. The rheology of the viscoelastic liquids are modeled by the Oldroyd-B and Giesekus equations, and the physical and geometric parameters are matched with those in the experiments. The computed interfacial deformation is in general agreement with the experimental observations. In particular, the critical condition for interfacial rupture is predicted to quantitative accuracy. Furthermore, we combine the numerical and experimental data to explore the potential of selective withdrawal as an extensional rheometer. For Newtonian fluids, the measured steady elongational viscosity is within 47% of the actual value, apparently with better accuracy than other methods applicable to low-viscosity liquids. For polymer solutions, an estimated maximum error of 300% compares favorably with prior measurements.

Rheological properties of blends of linear and long‐chain branched polypropylenes

AbstractBlends of a long‐chain branched polypropylene (LCB‐PP) and a linear polypropylene (L‐PP) were prepared using a twin‐screw extruder. Linear viscoelastic properties such as complex viscosity, storage modulus, and weighted relaxation spectrum were determined as functions of LCB‐PP content. Shear data obtained from commercial rheometers as well as from a slit‐die rheometer were used to verify the Cox‐Merz relation for the neat components as well as for a blend. Elongational properties were obtained using a Sentmanat Extensional Rheometer (SER) unit mounted on an Advanced Rheometric Expansion System (ARES) rheometer and the converging die. A significant strain hardening was observed for the neat LCB‐PP as well as for all the blends, but the strain hardening decreased with increasing strain rate. The apparent steady elongational viscosity values evaluated using the converging die were observed to be comparable at high deformation rates to those obtained from the SER unit, but the differences increased as the strain rate decreased. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers

Rheological behavior and theoretical modeling of uniaxial elongational flow properties of polypropylene/layered silicate nanocomposites

AbstractRheological behaviors of polypropylene/layered silicate nanocomposites were investigated in both shear and uniaxial elongational flows. They were analyzed by using the K‐BKZ constitutive equation with two damping functions, for example, the WD‐FÖ and PSM‐LT models in transient and steady elongational viscosities. Although pure PP matrix and uncompatibilized nanocomposite did not show the strain hardening, compatibilized nanocomposite showed outstanding strain‐hardening behavior due to three‐dimensional network structure. Predictions of WD‐FÖ and PSM‐LT models gave good agreement with the experimental results at low elongational rate region. However, the elongational viscosity calculated with the WD‐FÖ model did not predict the steady‐state value and diverged to infinity when $\dot{\varepsilon} {\lambda}_{\bf max}\ {\geq}\ {\bf 1}$. The PSM‐LT model offered good description on transient and steady elongational viscosities even at higher elongational rates as well as on strong strain‐hardening behavior of compatibilized nanocomposites. Through the numerical analysis, using the K‐BKZ model with two types of damping functions, it was found that the PSM‐LT model was superior to that of the WD‐FÖ model in rheological modeling of PP/layered silicate nanocomposites. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers

Large amplitude oscillatory elongation flow

A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as $\epsilon(t) = \dot{\epsilon}_0 t + \Lambda [1 - \cos( 2 \pi \Omega \dot{\epsilon}_0 t )]$ where e is the Hencky strain, $\dot{\epsilon}_0$ is a constant elongational rate for the base elongational flow, Λ the strain amplitude (Λ ≥ 0), and Ω the strain frequency. A narrow molecular mass distribution linear polystyrene with a molecular weight of 145 kg/mol was subjected to the oscillative flow. The onset of the steady periodic regime is reached at the same Hencky strain as the onset of the steady elongational viscosity ( Λ = 0). The integral molecular stress function formulation within the ‘interchain pressure’ concept agrees qualitatively with the experiments.

Elongational viscosity of monodisperse and bidisperse polystyrene melts

The start-up and steady uniaxial elongational viscosity have been measured for two monodisperse polystyrene melts with molecular weights of 52 and 103kg∕mole, and for three bidisperse polystyrene melts. The monodisperse melts show a maximum in the steady elongational viscosity vs. the elongational rate, ϵ̇, of about two times the limiting value of 3η0 expected for a Newtonian fluid, whereas the bidisperse melts have a maximum of up to a factor of seven times the Trouton limit of 3η0. The Wiest model which incorporates anisotropic drag and finite extensibility may be used to interpret the results in molecular terms.

Viscosity overshoot in the start-up of uniaxial elongation of low density polyethylene melts

The transient uniaxial elongational viscosity of BASF Lupolen 1840D and 3020D melts has been measured on a filament stretch rheometer up to Hencky strains of 6–7. The elongational viscosity of both melts was measured at 130°C within a broad range of elongational rates. At high elongation rates, an overshoot or maximum in the transient elongational viscosity followed by a steady viscosity was observed. The steady elongation viscosity was about 40%–50% less than the maximum at high strain rates. The steady elongational viscosity as a function of the elongation rate, ϵ̇, decreases approximately as ϵ̇−0.6 in both melts at high strain rates. The transient elongational viscosity, measured at a specific elongation rate at 170°C on the BASF Lupolen 3020D melt, did not follow the time temperature superposition principle based on linear viscoelasticity during the decrease in the transient elongational viscosity towards the steady state.

125 二次元対向流れにおける流動複屈折測定を用いた定常平面伸張粘度測定(S34-1 複雑流体の流れとその応用(1),S34 複雑流体の流れとその応用)

125 二次元対向流れにおける流動複屈折測定を用いた定常平面伸張粘度測定(S34-1 複雑流体の流れとその応用(1),S34 複雑流体の流れとその応用)

Elongational Viscosity of Narrow Molar Mass Distribution Polystyrene

Transient and steady elongational viscosity has been measured for two narrow molar mass distribution polystyrene melts of molar masses 200 000 and 390 000 by means of a filament stretching rheometer. Total Hencky strains of about five have been obtained. The transient elongational viscosity rises above the linear viscoelastic prediction at intermediate strains, indicating strain hardening. The steady elongational viscosities are monotone decreasing functions of elongation rate. At elongation rates larger than the inverse reptation time, the steady elongational viscosity scales linearly with molar mass at fixed elongation rate.

Introduction

You have accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article McLeish Tom C. B., Cates Mike E., Higgins Julia S. and Olmsted Peter D. 2003IntroductionPhil. Trans. R. Soc. A.361637–639http://doi.org/10.1098/rsta.2002.1169SectionYou have accessIntroduction Tom C. B. McLeish Tom C. B. McLeish Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK Google Scholar Find this author on PubMed Search for more papers by this author , Mike E. Cates Mike E. Cates School of Physics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK Google Scholar Find this author on PubMed Search for more papers by this author , Julia S. Higgins Julia S. Higgins Department of Chemical Engineering, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2AZ, UK Google Scholar Find this author on PubMed Search for more papers by this author and Peter D. Olmsted Peter D. Olmsted Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK Google Scholar Find this author on PubMed Search for more papers by this author Tom C. B. McLeish Tom C. B. McLeish Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK Google Scholar Find this author on PubMed Search for more papers by this author , Mike E. Cates Mike E. Cates School of Physics, The University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK Google Scholar Find this author on PubMed Search for more papers by this author , Julia S. Higgins Julia S. Higgins Department of Chemical Engineering, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2AZ, UK Google Scholar Find this author on PubMed Search for more papers by this author and Peter D. Olmsted Peter D. Olmsted Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:28 February 2003https://doi.org/10.1098/rsta.2002.1169AbstractIt is an exciting thing to be involved in a young science. Though tracing a lineage from the polymer and colloid sciences of the last century, and the foundations of statistical mechanics of the century before, the newly self-aware – eld of ‘soft matter physics’ is clearly coming of age. Increasing interaction between research communities focused once exclusively on surfactants, liquid crystals, colloids or polymers has produced more than a comparison of notes and the sharing of techniques, important though such activity is. The signs of real new growth are everywhere: – rst-order questions abound, directed both at equilibrium (‘what is the phase diagram for polymer–colloid mixtures?’) and kinetics (‘how do polymer chains' mutual entanglements affect collective dynamics?’). Quite new phases of matter are coming to light, such as the counter–intuitive soft elasticity of nematic networks. Deceptively familiar materials, such as granular media, are revealing deep new puzzles. Furthermore, all this new science is much more than the application of old tools and methods to new applications. The new questions have rebounded on fundamental concepts of physics as familiar as electrostatics, and reshaped them. They have motivated the rapid development of less familiar, but no less basic, frameworks such as non–equilibrium statistical mechanics. Tentatively, progress in synthetic soft–matter systems might have something to say about the delicate complexity of biological matter. Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Chakraborty S and Das S (2020) Relaxation in a phase-separating two-dimensional active matter system with alignment interaction, The Journal of Chemical Physics, 10.1063/5.0010043, 153:4, (044905), Online publication date: 28-Jul-2020. de Castro P and Sollich P (2019) Phase separation of mixtures after a second quench: composition heterogeneities, Soft Matter, 10.1039/C9SM01706B, 15:45, (9287-9299) Shahid T, Clasen C, Oosterlinck F and van Ruymbeke E (2019) Diluting Entangled Polymers Affects Transient Hardening but Not Their Steady Elongational Viscosity, Macromolecules, 10.1021/acs.macromol.8b02701, 52:6, (2521-2530), Online publication date: 26-Mar-2019. This Issue15 April 2003Volume 361Issue 1805Discussion Meeting Issue ‘Slow dynamics in soft matter’ organized by T. C. B. McLeish, M. E. Cates, J. S. Higgins and P. D. Olmsted Article InformationDOI:https://doi.org/10.1098/rsta.2002.1169Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online28/02/2003Published in print15/04/2003 License: Citations and impact PDF Download

スピンラインレオメータにより測定される希薄高分子溶液の見かけの伸長粘度の評価

The relationship between apparent elongational viscosity obtained by using a spinline rheometer and a variety of flow conditions in its measurement is investigated for a dilute polymer solution. The numerical calculations are carried out for a FENE-P dumbbell model and the experiments are performed for a 100 ppm aqueous solution of polyacrylamide.Elongational rates and elongational stress are significantly changed along the spinline. The apparent elongational viscosity depends on the flow rate and the spinline length. It is found that this dependence of the apparent elongational viscosity is due to the effect of inertia. Finally, a comparison is made between the apparent elongational viscosity and the steady elongational viscosity.

Hydrodynamic interactions of dilute polymer solutions in elongational flow

Dumbbell models are only crude representations of actual polymer molecules, but their simplicity allows for explicit calculations which in many instances have shed light on the connection between molecular properties and rheological behavior. On the other hand, hydrodynamic interactions are known to strongly influence the dynamic response of polymer solutions and this makes the representation of the hydrodynamic drag an important aspect in the calculations. In the present work, the effects of the state of flow are incorporated explicitly in the frictional properties of the FENE model of a dilute polymer solution. Results for the steady elongational viscosity and the mean square end-to-end distance arc presented.

A differential constitutive equation for polymer melts

A modification of the Giesekus constitutive equation is derived by incorporating (approximately, via the Peterlin approximation) the finite extensibility of polymer molecules into dumbbell kinetic theory along with the anisotropic hydrodynamic drag suggested by Giesekus. The constitutive equation that is obtained retains much of the simplicity of Giesekus' constitutive equation, but it involves terms that are cubic in the stress as well as those that are quadratic. It is shown that the constitutive equation quantitatively describes the steady elongational viscosity of the IUPAC polymer melt A (including the strain softening of the melt), but it cannot describe the elongational and shear viscosities simultaneously. It is also shown that the constitutive equation satisfies the Lodge-Meissner relation for shear strains less than unity.

Elongational Viscosity Measurements on Polymer Melts by a Meissner-type Rheometer

The elongational flow behavior of various polymer melts has been measured using a new Meissner-type uniaxial extensional rheometer. The following results are obtained for polystyrene melts :(1) When the strain rate ε is sufficiently low, transient elongational viscosity function ηE+(t) agress with 3η+(t), where η+(t) is the corresponding function in shear. ηE+(t, ε) at high ε still agrees with 3η+(t) when the strain is smaller than a critical value. At large strains, ηE+(t, ε) becomes larger than 3η+(t) and approaches asymptotically to a steady value.(2) The steady value of ηE+ for a broad-distribution polystyrene is somewhat larger than 3η0, where η0, is the zero-shear viscosity. The steady elongational viscosity ηE(ε) of a narrow-distribution polystyrene is equal to 3η0, in the strain-rate region where the shear viscosity ε(γ) decreases with γ, while it begins to decrease with ε at high ε.(3) The nonlinear function ΛηNL(=ηE+(t, ε)/ηE+(t)) becomes more strongly dependent on strain ε(=εt) with increasing strain rate. For a low-density polyethylene melt, ηE+(t, ε)(or elongational stress σ) at low ε increases smoothly with time t (or ε), approaching asymptotically to a steady value. ηE+ (or σ) at high ε increases in two stages with t (or ε). Finally, it has been emphasized that the measurement of ε through observation of the sample diameter is very important, especially for polyolefin samples.

Kinetic theory of polymer melts. IX. Comparisons with experimental data

The modification to the Curtiss–Bird model to account for polydispersity is used to compare predictions of several material functions to experimental data. The data were taken from samples of polymer melts and concentrated solutions with two types of molecular weight distributions, log-normal and Flory–Schulz. The Curtiss–Bird model is also compared to predictions of the Doi–Edwards model for viscosity of polydisperse samples. Experimental data for first normal stress coefficient, elongational stress growth viscosity, and steady elongational viscosity were also compared to the predictions of the Curtiss–Bird model. In all cases, the best fit to the experimental data were found for nonzero values of the link tension coefficient ε. It is found that HDPE η̄ data (and η̄+ data) can be fit by ε≂0.05, a value of ε that is low enough to predict rod dipping for this material.

Kinetic theory of polymer melts. VIII. Rheological properties of polydisperse mixtures

The Curtiss–Bird model of polymer melts has been extended to include polydisperse mixtures. The formula for the stress tensor derived in the last paper is used here to give explicit expressions for material functions in shear and elongational flow. Predictions are shown for viscosity, first normal stress coefficient, elongational stress growth viscosity, and steady elongational viscosity for Flory–Schulz and log–normal molecular weight distributions. It is also shown how generalizations that are observed experimentally for viscosity are predicted by the Curtiss–Bird model. In the next paper, these calculations are compared with experimental data.

Elongational behavior of short glass fiber reinforced polypropylene melts

AbstractThe Rheometrics Elongational Rheometer was employed to study the uniaxial extensional flow of glass fiber filled polypropylene melts, in which the fiber concentration, c, varied between zero and 40 weight percent. The constant strain rate mode was used for strain rates, \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document}, between 0.003 and 0.6 s−1. Steady state elongational viscosities were observed in most cases for fiber filled polypropylene melts, even at rates at which the stress continued to increase for unfilled polypropylene. The rate of relative stress growth increased with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and was affected by the addition of fibers. The steady elongational viscosity of the fiber reinforced melts was found to decrease with increasing \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^. $\end{document} and to increase with increasing c. Yield stresses were observed in elongational flow at high concentrations, although there was no clear evidence of yield in steady shear.