Steady-state Elongational Viscosity Research Articles

Rheological properties of grafted maleic anhydride based polypropylene composites filled with organoclay and glass fibers

AbstractExfoliated polypropylene/layered silicate nanocomposites and chopped glass fiber reinforced composites were prepared by a melt compounding process using maleic anhydride modified polypropylene (PP-g-MAH). The effect of fillers on morphological and rheological properties in melt mixing of polypropylene matrix with compatibilizer was investigated and compared with various measurements. It was observed that polypropylene/layered silicate nanocomposites exhibited remarkable reinforcement compared with the conventional composites filled with glass fibers which were dispersed at micrometer scale. The nanocomposites had larger storage modulus at low frequency region and outstanding strain hardening behavior than those of pure polypropylene or glass fiber reinforced composites. It was shown that glass fiber reinforced composites had lower elastic properties and steady state elongational viscosities than pure polypropylene melt. Contrary to glass fiber reinforced composites, it was confirmed that 3-dimensional network structure due to strong intermolecular bonding between polypropylene matrix and layered silicates affected particular rheological properties of nanocomposites.

Modeling non-Gaussian extensibility effects in elongation of nearly monodisperse polystyrene melts

Elongational viscosity and birefringence of two nearly monodisperse polystyrene melts with molar mass MW of 206000gmol−1 (PS206k) and 465000gmol−1 (PS465k), respectively, were measured simultaneously by Luap et al. [Rheol. Acta. 45, 83–91 (2005)]. The samples did not follow the stress optical rule (SOR). Elongational viscosity data can be modeled quantitatively by the molecular stress function (MSF) model of Wagner et al. [J. Rheol. 49, 1317–1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934–3942 (2004)], and which is modified here to account for non-Gaussian chain extension using the Padé approximation of the inverse Langevin function. The tube diameter relaxation time scales with MW2. While the transient elongational viscosity shows a small dependence on finite extensibility, the predicted steady-state elongational viscosity is not affected by non-Gaussian effects. The power-law exponent of the relation between steady-state elongational stress and Deborah number predicted is found to be 0.59 for PS465k, confirming a previous result of 0.6 for a similar molecular mass sample [Wagner et al. (2005)]. The power-law exponent is invariant with respect to temperature but slightly dependent on molar mass, thereby increasing with decreasing molar mass. Deviations from the SOR are described quantitatively by the MSF model by taking into account finite chain extensibility, and within the experimental window investigated, deviations from the SOR are predicted to be strain rate-, temperature-, and molar mass independent, in good agreement with experimental data.

Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts

Elongational behavior of four narrow molar mass distribution polystyrene melts of masses 50 000, 100 000, 200 000, and 390 000, g∕mol, respectively was investigated up to Hencky strains of 5. All melts show strain hardening behavior. For the two highest molar mass polystyrenes, strain hardening starts at elongation rates larger than the inverse reptation time, and the steady-state elongational viscosities decrease with increasing elongation rate according to a power law with a power-law index of approximately −1∕2 instead of −1 as predicted by the original Doi–Edwards tube model. Marrucci and Ianniruberto [Macromolecules 37, 3934 (2004)] have introduced an interchain pressure term arising from lateral forces between the chain and the tube wall into the Doi–Edwards model to account for the latter effect. Based on the molecular stress function theory allowing for a strain-dependent tube diameter, we show that the transient and steady-state elongational viscosities of the nearly monodisperse polystyrene melts can be modeled quantitatively by assuming affine chain deformation balanced by the interchain pressure term of Marrucci and Ianniruberto. The interchain pressure is governed by a tube diameter relaxation time τa, which is found to be larger than the Rouse time τR of the chain, and which is the only parameter of the model. For monodisperse polystyrene melts of sufficient low molar mass, τa is larger than the reptation time, and a maximum in the steady-state elongational viscosity is predicted.

Rheological measuring techniques and their relevance for the molecular characterization of polymers

The zero shear viscosity η 0, the linear steady-state compliance and the elongational viscosity are rheological quantities, which can preferably be used for a molecular characterization of polymers. The techniques applied to obtain reliable results are described. It is demonstrated that linear polyethylenes of high-density fulfill the relationship η 0 ∼ M w 3.6 independently of the polydispersity. M w is the absolute mass-average molar mass. Long-chain branched polyethylenes significantly deviate from this relation. The results from polyethylenes are used to characterize electron beam irradiated polypropylenes. It is clearly shown that long-chain branches are introduced by irradiation the topography of which changes with the dose. Measurements of the elongational viscosities support the conclusions from shear experiments. Creep tests in extension show the existence of steady-state elongational viscosities for the irradiated polypropylenes. The viscosities run through a maximum as a function of the elongational rates reached at steady state. The shape of the curves depends on the dose indicating once more a change in molecular structure by irradiation.

Determination of elongational viscosity of polymer melts by RME and Rheotens experiments

Several linear (LLDPE, HDPE, PS) and long-chain-branched (LDPE, PP) polymer melts were investigated by an elongational rheometer (RME Rheometrics) and by Rheotens (Gottfert). The Molecular Stress Function (MSF) theory is briefly reviewed and used to extrapolate the steady-state elongational viscosity. To evaluate Rheotens experiments, a new process model is introduced which assumes that the elongational viscosity in the Rheotens test is a function of the draw ratio only. The apparent elongational viscosities extracted from Rheotens curves are found to lie in between the steady-state elongational viscosity and three times the shear viscosity.

Frequency-Dependent Elongational Viscosity by Nonequilibrium Molecular Dynamics

The elongational viscosity of a liquid describes the response of the liquid to simultaneous stretching and compression in various directions, subject to the restriction that the trace of the rate of the strain tensor is zero (or the density is constant). Despite the growing popularity and usefulness of nonequilibrium molecular dynamics methods in studies of the shear viscosity of simple and complex fluids, the elongational viscosity remains a relatively neglected property in computer simulation studies. This stems from some significant technical difficulties that arise when standard methods such as the constant strain rate SLLOD algorithm are applied to elongational flow. For example, if planar elongational flow with a constant elongation rate is applied in a computer simulation with periodic boundary conditions, the box size in the contracting direction quickly becomes smaller than twice the range of the potential, violating the minimum image convention. The time at which this occurs may be less than the time required for the system to reach a steady state, making it impossible to compute the steady-state elongational viscosity. This difficulty can be avoided by applying an oscillating elongational strain rate to the liquid, and computing frequency dependent elements of the stress tensor, which can then be extrapolated to zero frequency to evaluate the steady-state elongational viscosity. We have used this method to compute the elongational viscosity of a simple atomic liquid and discuss its possible application to a model polymeric liquid.

Determination of steady-state elongational viscosity for rubber compounds using bell-mouthed dies

A bell-mouthed die geometry was designed to cause convergent flow at a constant, uniform, elongational strain rate. An equation was derived, which showed that steady-state elongational viscosity could be calculated from a plot of pressure drop due to elongation against a simple function of die length. To obtain values of pressure drop due to elongation, it was necessary to correct the total pressure drop measured across the bell-mouthed dies for the contribution from shear occurring near the die wall. For this purpose, a simplified shape for the bell-mouthed dies was assumed, comprising several parallel sided segments. Applying a formula to pressure drop data measured across straight dies corresponding to these segments gave an estimate of the pressure drop due to shear across the bell-mouthed dies. Pressure drops due to elongation were determined by subtracting the pressure drop due to shear from the total pressure drop measured across the bell-mouthed dies. Measurements were also carried out with lubrication to validate the shear correction method. The results indicate that for the compound used in this study, a combination of bell-mouthed and straightsided dies can be used in a conventional capillary rheometer to determine steady-state elongational viscosity. An elongational viscosity of 190 kPa s at 90°C and at a strain rate of 10 s−1 was determined for a simple styrene-butadiene rubber compound. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1139–1150, 1997

Comparison between uniaxial and biaxial elongational flow behavior of viscoelastic fluids as predicted by differential constitutive equations

Behavior of polymer melts in biaxial as well as uniaxial elongational flow is studied based on the predictions of three constitutive models (Leonov, Giesekus, and Larson) with single relaxation mode. Transient elongational viscosities in both flows are calculated for three constitutive models, and steady-state elongational viscosities are obtained as functions of strain rates for the Giesekus and the Larson models.

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.

Extensional flow of mica‐filled polyethylene

AbstractExtensional flow of mica‐filled high density polyethylene was studied at 150°C in a Rheometrics elongational rheometer. The constant strain‐rate mode at a rate of 10−3 to 1.0 s−1, and the constant stress mode were used. The mica content was 0, 25, 40, and 60 weight percent. In both testing modes, the steady state elongational viscosities were obtained; those for the filled samples were about ten to twenty times larger than the shear viscosity at corresponding (low) rates of deformation.

INVITED REVIEW Polymer Kinetic Theories and Elongational Flowsdagger;

Abstract Steady-state elongational viscosity and various time-dependent elongational properties are generally much more difficult to measure than their shear flow counterparts. In kinetic theory, on the other hand, elongational phenomena are easier to describe than shear phenomena. A summary is presented of the available theoretical results for dilute polymer solutions, in which the macromolecules are modeled as various kinds of bead-rod-spring models, designed to simulate the orientability, distortion, and stretchability of the molecules. Then a summary of theoretical results for undiluted polymers (“polymer melts”) is given. For melts one has available two classes of theories: (i) those in which the melt is envisaged as a temporary network formed by physical junctions with various lifetimes, and (ii) those in which the melt is pictured as a collection of interacting and reptating chains. Future data comparisons will be very important in assessing the merits of the various molecular theories that have been proposed.

Elongational properties and molecular structure of polyethylene melts

The viscosity and the recoverable strain in the steady state of elongation have been measured on several polyethylenes of different molecular structures. The elongational viscosity as a function of tensile stress runs through a more or less pronounced maximum in the nonlinear range whereas in the linear range the Trouton viscosity is reached. For low density polyethylenes it could be demonstrated that the maximum of the steady-state elongational viscosity and the elasticity expressed by the steady-state compliances in shear and tension sensitively increase if the molecular weight distribution is broadened by the addition of high molecular weight components. A variation of the weight average molecular weight does only shift the elongational viscosity curve but leaves its shape unchanged. Two of the four high density polyethylenes investigated do not show a maximum of the steady-state elongational viscosity, for the others it is less pronounced than in the case of low density polyethylenes. The influence of branching on the elongational behaviour of polyethylene melts in the steady-state and the transient region is qualitatively discussed.

Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt

A single integral constitutive equation is presented, which gives a reasonable description of the non-linear shear and elongational behavior of a low-density branched polyethylene melt at constant strain rate observed byMeissner. The memory function of this integral equation is a product of the memory function of Lodge's rubber like-liquid theory and a damping functionh = exp [ —n\(h = \exp [ - n\sqrt {I_2 - 3} ]\)], whereI2 is the second invariant of the Finger tensor. Stress- and normal stress overshoot are described as well as shear rate dependence of the transient shear viscosity and the first normal stress coefficient. Tensil stress overshoot and a finite, rate-dependent steady-state elongational viscosity is predicted in simple elongational flow.