Discrepancies between linear viscoelastic measurements and double-reptation predictions for commercial polystyrene samples

We have found discrepancies between the predictions of two double-reptation models and the corresponding linear viscoelasticity measurements for commercial, polydisperse polystyrene samples with weight-average molecular weights ranging from 140 to 300kg/mol. The accuracy of the experimental data has been confirmed by conducting viscoelasticity measurements in different laboratories using different types of rheometers and by verifying that small distortions in chromatographic measurements cannot account for the discrepancies seen in the viscoelastic response. In addition, we show that the discrepancies between predictions and measurements are systematic, suggesting that gaps in the theory are responsible for the mismatch. Is it concluded that commercial polystyrene resins may pose additional challenges for rheological modeling because of their relatively high polydispersity and low degree of entanglement. The experimental data given here can be used to validate future modeling efforts.     

Linear viscoelastic behavior of asphalt and asphalt based mastic

The rheological properties of an asphalt mastic and its matrix are investigated. For the purpose of comparison a sample of thermal aged asphalt matrix is also considered. Dynamic and creep shear measurements are reported. The reduced shear rate concept proposed by Ohl and Gleissle is used to correlate mechanical properties of the three materials at the same temperature. We found that the concept gives only qualitative trends. A similar conclusion is found concerning the applicability of the time-temperature superposition principle for each sample. Our experimental results show also that the increase in viscosity due to thermal treatment or to the inclusion of solid particles is not uniform with temperature. The differences in the increase of the Vogel temperature from the asphalt to the mastic, or to the thermally aged asphalt, relate to the different mechanisms involved. Sedimentation of steel spheres in asphalt and mastic, is studied next. The Newtonian wall correction factor for the Stokes drag law holds for the three samples. Despite the similar behavior observed in conventional shear tests, Stokes' law gives the correct trend for the two asphalts although it overestimates the experimental settling velocity by a factor of approximately two in the case of the mastic. Received: 8 June 1999/Accepted: 19 October 1999     

Linear viscoelastic behavior of perfluorooctyl sulfonate micelles: effects of counter-ions

Linear viscoelastic behavior was investigated for aqueous solutions of perfluorooctyl sulfonate (C₈F₁₇SO⁻ ₃; abbreviated as FOS) micelles having a mixture of tetraethylammonium (N⁺(C₂H₅)₄; TEA) and lithium (Li⁺) ions as the counter-ions. The solutions had the same FOS concentration (0.1 mol l⁻¹) and various Li⁺ fractions in the counter-ions, φ_Li = 0−0.6, and the FOS micelles in these solutions formed threads which further organized into dendritic networks. At T ≤ 15 °C, the terminal relaxation time τ and the viscosity η, governed by thermal scission of the networks, increased with increasing φ_Li up to 0.55. A further increase of φ_Li resulted in decreases of τ and η and in broadening of the relaxation mode distribution. These rheological changes are discussed in relation to the role of TEA ions in thermal scission: Previous NMR studies revealed that only a fraction of TEA ions were tightly bound to the FOS micellar surfaces and these bound ions stabilized the thread/network structures. The concentration of non-bound TEA ions, C_TEA ^*, decreased and finally vanished on increasing φ_Li up to φ_Li ^* ≅ 0.6, and the concentration of the bound TEA ions significantly decreased on a further increase of φ_Li. The non-bound TEA ions appeared to catalyze the thermal scission of the FOS threads, and the observed increases of τ and η for φ_Li < 0.55 were attributed to the decrease of C_TEA ^*. On the other hand, the decreases of τ and η as well as the broadening of the mode distribution, found for φ_Li > 0.55 (where C_TEA ^* ≅ 0), were related to destabilization of the FOS threads/networks due to a shortage of the bound TEA ions and to the existence of concentrated Li⁺ ions. Viscoelastic data of pure FOSTEA and FOSTEA/FOSLi/TEACl solutions lent support to these arguments for the role of TEA ions in the relaxation of FOSTEA/FOSLi solutions. Received: 12 October 1999/Accepted: 1 November 1999     

Effect of interfacial tension on linear viscoelastic behavior of immiscible polymer blends

When interfacial tension is increased from zero to infinity, the storage dynamic modulus predicted by Palierne's model varies in a nearly Gaussian fashion with almost equal asymptotic values at the limits of low and high interfacial tension. We report a simple physical discussion of such an effect. Received: 13 January 1999 Accepted: 22 March 1999     

Linear viscoelastic behavior of the Hookean dumbbell with internal viscosity

The linear viscoelastic modulus G(t) predicted by the analytical formulations of Schieber (1993), Wedgewood (1993), Dasbach et al. (1992), and Booij and van Wiechen (1970) for the free-draining Hookean dumbbell with internal viscosity (IV) are compared with exact analytical results and exact numerical results obtained from Brownian dynamics simulations. All of these analytical formulations employ the Booij and van Wiechen expression for the IV force, thereby eliminating errors associated with linearization of the deformational velocity, however the theories differ in the approximations employed to solve configuration moment equations. Comparison with the exact G(t) results provides a means of testing these approximations. The approximate theories all correctly predict the singular part of G(t) at t = 0, providing correct predictions of , however deviations from the exact G(t) are seen in all cases for t > 0.     

Comparison of the predictions of viscoelastic and plastic-viscoelastic fluid model to the rheological behaviour of polystyrene and polystyrene-carbon black compounds

The rheological properties of a polystyrene melt and its compounds with carbon black are compared with a non-linear viscoelastic fluid theory and a plastic-viscoelastic fluid model. Shear viscosities, principal normal stresses and elongational viscosities are investigated for melt and compound. The relaxation spectra for the melt was determined with an eccentric disc rheometer. The Bogue-White model gave satisfactory agreement for the melt with an a parameter of 0.5. For the plastic-viscoelastic fluid theory, a Bogue-White model was used to represent theH functional. The _i and a parameters were taken to be the same as for the pure melt while theG _i were increased by a hydrodynamic factor. A yield value was obtained from the compound data. Generally good agreement was found but some discrepancy exists for the elongational flow experiments.     

Linear viscoelastic behavior of copper phthalocyanine dispersions used in printing inks

In this paper we describe the linear viscoelastic properties of copper phthalocyanine (CuPCN) dispersions that are used in the manufacturing of offset lithographic printing inks. Transmission electron microscopy shows that the primary pigment particles are rod-like and have sizes in the range of 10 to 300 nm. Steady shear measurements show that the dispersions are Newtonian at a pigment volume fraction of 0.073 and become increasingly shear thinning as the pigment volume fraction is increased. The strong shear-thinning nature of these dispersions can be attributed to the highly flocculated nature of the dispersions, which is due to interparticle attractions. The structural complexity of the dispersions also results in an unexpected linear viscoelastic response. While at low frequencies (0.1 and 1.0 Hz) the ex tent of the linear region decreases with increasing pigment concentration, at a higher frequency (10 Hz) the extent of the linear region increases with increasing pigment concentration. This increase in the linear region with increasing pigment concentration suggests that at higher frequencies the dispersion is less brittle, and that the rheological behavior is dominated by intra-aggregate associations. In addition, frequency sweeps show that the dispersions behave like a viscoelastic liquid at low pigment concentrations. However, at higher pigment concentrations (yet significantly lower than the maximum packing fraction) the dispersions behave like a cross-linking polymer at its gel point.     

Rheology of compatibilized immiscible viscoelastic polymer blends

Rheological behavior of a PS/PE model viscoelastic immiscible blend compatibilized by two types of interfacial modifiers was investigated. Dynamic, steady shear, and transient experiments were performed to probe the effect of the interfacial modification on the rheological behavior of the blend. While the effect was relatively small in dynamic and steady shear experiments, significant signature of the presence of the copolymer was observed in transient experiments after start up of shear flow. The magnitude of the departure from Doi-Otha theory (worked out for non-compatibilized blends) was evaluated. Received: 6 March 2000 Accepted: 15 June 2000     

Rheology of polymer blends: linear model for viscoelastic emulsions

 Kerner's model for flow of composite elastic media is extended to an emulsion of viscoelastic phases with interfacial tension undergoing deformations of small amplitude. A privileged internal structure inside the suspended drops is discussed in terms of fluid circulation across the interface. It is shown that for usual drop radius and interfacial tension values of emulsions, the rheological behavior predicted by the model, with very simple expression for the complex shear modulus, is quantitatively similar to that predicted by Palierne's model. Predictions of the model are compared with experimental data obtained on a polystyrene/polyethylene blend sheared in a small-amplitude oscillatory mode. Received: 10 August 1998 Accepted: 18 December 1998     

Electrical conductivity, phase behavior, and rheology of polypropylene/polystyrene blends with multi-walled carbon nanotube

The electrical, rheological properties and phase change behavior of polypropylene (PP)/polystyrene (PS) blends filled with multi-walled carbon nanotube (MWNT) were investigated. Two kinds of masterbatch were used to prepare ternary blends of PP, PS, and MWNT, and the effects of the kinds of masterbatch were confirmed by phase morphology of ternary blends and the distribution of MWNT. From thermodynamic analysis, MWNT is expected to locate in PS phase and it shows a good agreement with the TEM observations. The ternary composites show the lowest conductive percolation threshold and fine morphologies when most MWNT particles are located at the interface. Time sweep test were carried out to monitor the phase coalescence of the ternary blends and MWNT migration and agglomeration in the PS phase during annealing. The enhancement of thermal properties of MWNT-filled blends was also investigated by DSC and TGA.     

Linear viscoelastic behavior of narrow molecular weight distribution 1,4 polybutadiene: Comparison with Doi-Edwards theory of reptation

Linear viscoelastic behavior of narrow molecular weight distribution 1,4 polybutadiene samples with molecular weights between 42500 and 779000 has been correlated with molecular structure using a simple modification of the Doi-Edwards theory of reptation. The entire GPC curve is required for the calculations of viscoelastic behavior.The plateau modulus obtained from the experimental data is comparable to literature values, while the equilibrium compliance (which is indicative of polydispersity) is greater than values reported in the literature for nearly monodisperse polybutadienes. Reasonable agreement between theory and experiment is obtained over the entire molecular weight range. The agreement between theory and experiment using the GPC curve is better than that obtained by assuming the polymer to be monodisperse or by using the Doi fluctuation model. The model appears to break down for a more polydisperse sample . This study indicates that it may be possible to use the Doi-Edwards theory to explain the viscoelastic behavior of narrow MWD polybutadienes without introducing any new concepts into the theory (fluctuations, constraints release, etc.).     

Numerical predictions of bubble growth in viscoelastic stretching filaments

In this study, we investigate the growth of bubbles within predominately extensional-deformation flows of thin film stretching form. This involves more than one free-surface to the flow (multiple surfaces), typically as inner (bubble) and outer (filament) boundaries that introduces fluid–gas interfacial treatment. Various bubble initial states and locations may be considered. The problem is discretised in space–time through a hybrid-finite element/volume pressure-correction formulation, coupled with an arbitrary Lagrangian–Eulerian (ALE) coupled with VOF scheme to track domain-mesh and free-surface movement. We contrast these results against the results from a complete ALE algorithm. Various fluid-filament materials have been considered, covering such properties as constant viscosity fluids (Newtonian), low-polymeric/high-solvent viscosity Boger-type (Oldroyd-B) fluids and high-polymeric/low-solvent viscosity elastic-type fluids (Oldroyd-B and Phan-Thien/Tanner). Numerical solutions are presented in terms of comparison between algorithms (ALE versus hybrid ALE/VOF), shapes (bubble shapes, filament shapes), contours of extra-stress (magnitude and location), mid-filament radius and extensional viscosity.     

Quantitative predictions of linear viscoelastic rheological properties of entangled polymers

The “dual constraint” model developed by Mead, Van Dyke et al. is here extended by inclusion of “early-time” contour-length fluctuations and constraint-release Rouse relaxation, and then evaluated by comparing its predictions with literature data for over 50 different linear and star polymers. By combining the reptation model of Doi and Edwards with contour-length fluctuations and constraint release, the model provides a systematic approach to prediction of the rheological properties of polymers. The parameters are taken from the literature and used consistently for linear polymers, star polymers, and their mixtures having the same chemical compositions. In most cases, the predictions of the model appears to agree well with data for monodisperse, bidisperse, and polydisperse linear and star polymers, except at low molecular weights. Received: 23 December 1999 Accepted: 28 March 2000     

Droplet relaxation in blends with one viscoelastic component: bulk and confined conditions

Using a counter rotating parallel plate shear flow cell, the shape relaxation of deformed droplets in a quiescent matrix is studied microscopically. Both the effects of geometrical confinement and component viscoelasticity are systematically explored at viscosity ratios of 0.45 and 1.5. The flow conditions are varied from a rather low to a nearly critical Ca number. Under all conditions investigated, viscoelasticity of the droplet phase has no influence on shape relaxation, whereas matrix viscoelasticity and geometrical confinement result in a slower droplet retraction. Up to high confinement ratios, the relaxation curves for ellipsoidal droplets can be superposed onto a master curve. Confined droplets with a sigmoidal shape relax in two stages: the first consists of a shape change to an ellipsoid with a limited amount of retraction, and the second is the retraction of this ellipsoid. The latter stage can be described by means of one single relaxation time that can be obtained from the relaxation of initially ellipsoidal droplets. The experimental results are compared to the predictions of a recently published phenomenological model for droplet dynamics in confined systems with viscoelastic components (Minale et al., Langmuir 26:126–132, 2010). However, whereas the model predicts additive effects of geometrical confinement and component viscoelasticity, the experimental data reveal more complex interactions.     

Bitumen/polyethylene blends: using m-LLDPEs to improve stability and viscoelastic properties

The stability and the rheological properties of blends of a 60/70 penetration-grade bitumen with conventional HDPEs and metallocene catalysed LLDPEs (m-LLDPE) are investigated. Considerably better stability results are obtained using m-LLDPEs instead of conventional polyethylenes, allowing one to avoid phase separation of the emulsion-like system during storage at high temperature. Thermodynamical interaction between bitumen and polyethylene is discarded as a cause of the observed difference, because the solubility parameter is practically the same for all the investigated polyethylenes. The result is explained on the basis of the lower melt elasticity of m-LLDPEs (attributed to their narrow molecular weight distribution), which facilitates the drop breakup during mixing process. The modification of bitumen with any of the m-LLDPEs considered in this work gives a new material with considerably improved viscoelastic properties.     

Quantitative evaluation of extrudate swell from viscoelastic properties of polystyrene

A theory of extrudate swell for short, intermediate or long dies is presented. In our experiment, we consider that the swelling phenomenon is mainly due to the recoverable elongational strain induced by the converging flow at the die entrance, as well as by recoverable shear strain originating within the die. From these concepts, an equation has been derived for the quantitative prediction of extrudate swell from the elastic material properties such as the entrance pressure drop, the relaxation modulus and the recoverable shear strain. Excellent agreement is found between predicted and measured values of extrudate swell obtained on commercial polystyrene melt, using capillaries of length-to-diameter ratios ranging from 1 to 20 and in a wide range of shear rates.     

Elongational flow behavior of viscoelastic liquids: Modelling bubble dynamics with viscoelastic constitutive relations

Summary Earlier parts of this series have described a technique based on the collapse of single bubbles in the fluids for studying the elongational rheology of viscoelastic solutions and melts of moderate viscosities ( ₀ > 10²p) at relatively high strain rates . The present paper describes the modelling of bubble collapse with both rate and integral type constitutive relations using a body coordinate system. Predictions of the stress at the bubble wall as a function of time during collapse from a BKZ model and a modified corotational Maxwell model compared favorably with experimental data for two polymer solutions, 1% polyacrylamide in water/glycerine and 2% hydroxypropyl cellulose in water.

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Zusammenfassung In vorangehenden Veröffentlichungen dieser Reihe wurde eine Methode beschrieben, mit Hilfe derer man aus dem Zerfall von einzelnen Blasen in einer Flüssigkeit auf die Dehn-Rheologie viskoelastischer Lösungen und Schmelzen mittlerer Viskosität ( ₀ > 10² P) bei relativ hohen Dehngeschwindigkeiten schließen kann. Die vorliegende Untersuchung beschreibt Modelle des Blasenzerfalls mit Hilfe von Stoffgleichungen sowohl vom rate- als auch vom Integral-Typ, wobei ein körperfestes Koordinatensystem benutzt wird. Die Voraussagen der Spannung an der Blasenwand als Funktion der Zeit während des Zerfalls bei Verwendung eines BKZ- und eines modifizierten korotatorischen Maxwell-Modells zeigen eine recht gute Übereinstimmung mit experimentellen Werten, die an zwei Polymerlösungen, nämlich einer 1%igen Polyacrylamid-Lösung in einer Wasser-Glycerin-Mischung und einer 2%igen wäßrigen Hydropropylcellulose, erhalten worden sind.

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Nomenclature a material constant - b material constant - g metric tensor, space coordinates - m material constant - n material constant - p pressure - P _G pressure within bubble - P _R pressure outside bubble at the wall - P pressure far away from the bubble - R bubble radius - dR/dt - R ₀ initial bubble radius - t time - u velocity - U potential function - Y R/R ₀ Greek symbols covariant body metric tensor - surface tension - rate of deformation matrix, II -second invariant of - strain rate - ₀ zero shear rate viscosity - _e elongational viscosity - _ef effective viscosity - ¹, ², ³ coordinates in body system - ^{1 1}/R ₀ ³ - body stress tensor - density - space stress tensor - relaxation time - _ef effective relaxation time - bubble pressure function, defined in eq. [19] - vorticity tensor With 11 figures and 1 table