Rheotens-mastercurves and elongational viscosity of polymer melts

In a Rheotens experiment, the tensile force needed for elongation of an extruded filament is measured as a function of the draw ratio. For thermo-rheologically simple polymer melts, the existence of Rheotens-mastercurves was proved by Wagner, Schulze, and Göttfert (1995). Rheotens-mastercurves are invariant with respect to changes in melt temperature and changes in the average molar mass. By use of purely viscous models, we convert Rheotens-mastercurves of a branched and a linear polyethylene melt to elongational viscosity as a function of strain rate. The resulting elongational viscosity from constant force extension experiments is found to be in general agreement with what is expected as steady-state viscosity of polyethylene melts measured in either constant strain-rate or constant stress mode.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Determination of the elongational viscosity of polymer melts by melt spinning experiments. A comparison with different experimental techniques

In this work, melt spinning experiments were tentatively used for the determination of the elongational viscosity of polymer melts at different levels of tensile strain and strain rate. The materials examined were two high-density polyethylene grades for blow moulding with similar number-average molecular mass but different polydispersity index. The data from melt spinning tests were compared with transient extensional viscosity data obtained by uniform isothermal tensile tests, performed by means of an extensional rheometer, as well as with those produced by converging flow tests (Cogswell model). The results showed that for high strain and strain rate levels, the melt spinning experiments provide elongational viscosity data quite close to the transient extensional viscosity values obtained from the tensile tests.     

Miniature universal testing platform: from extensional melt rheology to solid-state deformation behavior

Described is a detachable fixture for a rotational rheometer, the Sentmanat Extensional Rheometer Universal Testing Platform, which incorporates dual wind-up drums to ensure a truly uniform extensional deformation during uniaxial extension experiments on polymers melts and elastomers. Although originally developed as an extensional rheometer, this highly versatile miniature test platform is capable of converting a conventional rotational rheometer host system into a single universal testing station able to characterize a host of physical properties on a variety of polymer melts and solid-state materials over a very wide range of temperatures and kinematic deformations and rates. Experimental results demonstrating these various testing capabilities are presented for a series of polymers of varying macrostructure and physical states.     

Sources of error and other difficulties in extensional rheometry revisited: commenting and complementing a recent paper by T. Schweizer

In a recent paper by T. Schweizer (Schweizer 2000) a large collection of experimental difficulties associated with the measurement of uniaxial extensional properties of polymer melts in the Rheometrics RME extensional rheometer is described. The work covers topics such as sample preparation for different types of polymers (sensitive or not to moisture) supplied in different shapes (pellets or powder), the necessary corrections to the tensile force, and the ever-present problem of determining the true strain rates of the experiments. The aim of the present paper is to complement and expand the work of Schweizer by pointing out other experimental problems that are the cause of errors in extensional rheometry of polymer melts. The present analysis, however, is not exclusively dedicated to the RME, unlike that of Schweizer, being directed instead to a general class of apparatus that work according to the principle of stretching a constant length sample between pairs of counter-rotating rollers; for example, all the data shown was obtained with our own extensional rheometer (Maia et al. 1999). This work will focus on the importance of the correct choice of the supporting media used for sample heating and support, the importance of end-effects, and the influence that the griping surfaces can have in such measurements. Received: 23 February 2001 Accepted: 15 May 2001     

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 (Göttfert). 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.     

A novel technique for conducting creep experiments in equibiaxial elongation

A recently developed rheological technique known as continuous lubricated squeezing flow (CLSF) is adapted to perform constant stress, or creep, experiments in equibiaxial elongation flows of polymer melts. By modifying the CLSF technique, which was developed for constant strain rate deformations, we demonstrate that the technique can also be used to generate constant stress flows. Measured steady state viscosities are compared to constant rate elongation results for polymer melts having different molecular characteristics. Linear polymers show strain softening and compare well in constant stress and constant strain rate deformations. The branched polymer shows strain hardening and a viscosity that is slightly higher in constant stress for low rates. Limitations of the current version of the CLSF technique for creep flows are also briefly discussed.     

The strain-hardening behaviour of linear and long-chain-branched polyolefin melts in extensional flows

By generalizing the Doi-Edwards model to the Molecular Stress Function theory of Wagner and Schaeffer, the extensional viscosities of polyolefin melts in uniaxial, equibiaxial and planar constant strain-rate experiments starting from the isotropic state can be described quantitatively. While the strain hardening of four linear polymer melts (two high-density polyethylenes, a polystyrene and a polypropylene) can be accounted for by a tube diameter that decreases affinely with the average stretch, the two long-chain-branched polymer melts considered (a low-density polyethylene and a long-chain branched polypropylene) show enhanced strain hardening in extensional flows due to the presence of long-chain branches. This can be quantified by a molecular stress function, the square of which is quadratic in the average stretch and which follows from the junction fluctuation theory of Flory. The ultimate magnitude of the strain-hardening effect is governed by a maximum value of the molecular stress, which is specific to the polymer melt considered and which is the only free non-linear parameter of the theory. Received: 1 June 1999/Accepted: 24 November 1999     

Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts

From stress-strain experiments in extensional and shearing flows, nonlinear strain measures and effective damping functions are derived for a polyisobutylene melt. The strain measures determined in planar extensional flow and in simple shear flow coincide. Experimental results are compared with predictions of two molecular theories, the Doi-Edwards model and the molecular stress function approach of Wagner and Schaeffer. Discrepancies between theories and experiment lead to a reconsideration of the classification of extensional flows. The symmetry of the flow field is identified and quantified as an important parameter influencing the strain measure, and a unifying strain measure for general extensional and shearing flows of polymer melts is presented.     

Extensional rheology of a shear-thickening cornstarch and water suspension

A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.     

Equibiaxial extensional flow of polymer melts via lubricated squeezing flow. II. Flow modeling

A model for lubricated squeezing flow of a viscoelastic fluid is developed in order to study the viability of this flow as a rheological technique for generating equibiaxial extensional deformations in polymer melts. In this simple flow model, the melt, described by an upper-convected Maxwell fluid, is squeezed between thin films of a Newtonian fluid. Comparisons of the model predictions for constant strain rate and constant stress flows are made with experimental results presented in the first paper. Predictions from the model are able to describe the effects of lubricant viscosity and experimental configuration and indicate the technique fails for these flows at Hencky strains of approximately one. The cause for this failure is lubricant thinning, which leads to significant errors in both the measured stress difference and the strain. Received: 31 January 2000 Accepted: 31 May 2000     

Elongational flow behavior of polymeric fluids according to the Leonov model

The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) the stress growth at constant speed and (iii) the elastic recovery in elongational flow. The model parameters have been determined from the available rheological data obtained either in steady shear flow (shear viscosity and first normal-stress difference as a function of shear rate) or oscillatory flow (storage and loss moduli as a function of frequency in the linear region) or from extensional flow at very small strain rates (time-dependent elongation viscosity in the linear viscoelastic limit). In addition, the effect of the parameter characterizing the strain-hardening of the material during elongation has also been studied. The estimation of this parameter has been based upon the structural characteristics of the polymer chain which include the critical molecular weight and molecular weight of an independent segment. Five different polymer melts have been considered with varying number of modes (maximum four modes). Resulting predictions are in fair agreement with corresponding experimental data in the literature.     

The relevance of entry flow measurements for the estimation of extensional viscosity of polymer melts

The extensional viscosity of some flexible chain polymers and a thermotropic liquid crystalline polymer was measured in uniaxial extensional flow at constant extension rate. Power law functions were found for the dependence of the extensional viscosity at constant accumulated strain on strain rate. The stress growth curves were compared with measurements in axisymmetric entry flow, where both elongation and shear occur. The comparison showed that the values of the extensional viscosity calculated from the measurements in the entry flow correspond to the ones calculated from the viscosity growth measured in uniaxial elongation and averaged over extensional strain equal to what is accumulated on the fluid as it flows from the barrel into the capillary.     

Effect of a controlled pre-deformation history on extensional viscosity of dilute polymer solutions

We use a modified filament stretching rheometer to quantify the influence of a known controlled pre-shear history on the transient extensional viscosity of a dilute polymer solution. Two different types of pre-deformation are explored; both influence the subsequent stretching significantly, albeit in opposite ways. Small-amplitude oscillatory straining parallel to the direction of stretching enhances strain hardening and accelerates the tensile stress growth toward the steady-state value. Conversely, steady torsional shearing orthogonal to the direction of stretching retards strain hardening and results in a delayed approach to steady-state elongational flow. In both cases, the final steady-state extensional viscosity is the same as that observed with no pre-shearing. Calculations using a finitely extensible nonlinear elastic Peterlin dumbbell model qualitatively capture the trends observed in experiments, enabling interpretation of these observations in terms of the degree of polymer chain stretching imposed by the flow before extensional stretching.     

Tensile properties of an extruded polyethylene-melt

Summary Isothermal continuous stretching experiments with a Rheotens apparatus were carried out on an extruded polyethylene melt. Measurements of the tensile force, the thread velocity and the thread profiles for various mass flow rates resulted in the determination of the elongational viscosity as a function of the strain rate and the deformation time. It was found that the deformation time is a more suitable general parameter than the strain rate for the characterization of the elongational viscosity of extruded polymer melts.

---

Zusammenfassung Experimente zum isothermen Schmelzspinnen wurden mit dem Rheotens an einer extrudierten Polyäthylenschmelze durchgeführt.Messungen von Abzugskraft, Abzugsgeschwindigkeit und Querschnittsprofil des extrudierten Stranges bei variierenden Ausstößen führten zur Bestimmung der Dehnviskosität als Funktion von Dehngeschwindigkeit und Deformationszeit. Es konnte nachgewiesen werden, daß die Deformationszeit besser als die Dehngeschwindigkeit zur Charakterisierung der Dehnviskosität von extrudierten Schmelzen geeignet ist.

---

---

Vortrag, gehalten auf der Jahrestagung der Deutschen Rheologischen Gesellschaft e.V., Universität Dortmund, 9. bis 11. März 1977.

---

With 8 figures     

Design of new HDPE/silica nanocomposite and its enhanced melt strength

Linear polymers are restricted to use in processes that involve severe extensional deformation, such as fiber spinning, film blowing, and thermoforming. To extend their applicability, the extensional properties of polymer melts should be enhanced such that strain hardening, which is defined as an increase in extensional viscosity under a large strain that deviates from the linear viscoelastic curve, is pronounced. In this study, a novel preparation method of linear polymer/inorganic nanocomposites was proposed with a main focus on enhanced melt strength. The design of molecular structure consists of three components—linear polymer, compatibilizer, and surface-modified particles. High-density polyethylene was used as a linear polymer while polyethylene grafted with maleic anhydride was used as a compatibilizer. Silica particles were synthesized and modified on their surfaces by 3-aminopropyltriethoxysilane. The strain hardening behavior of the surface-modified silica composites was pronounced. However, such a result was not observed for the composites of the same composition with pure-silica. In addition, the dispersion of the modified silica was much better than that of pure-silica.     

Rheometer zur Untersuchung der deformationsmechanischen Eigenschaften von Kunststoff-Schmelzen unter definierter Zugbeanspruchung

Zusammenfassung Es wird ein neues Rheometer beschrieben, mit dem Zugversuche mit konstanter Dehnungsgeschwindigkeit an einer Poly?thylen-Schmelze ausgeführt werden. Als Klemmen finden in dem Ger?t Zahnradpaare Verwendung, die mit konstanter Drehzahl laufen, w?hrend ihr Abstand fixiert ist. Die horizontale Me?anordnung taucht in Silikon?l, auf dem bei Me?temperatur (in den Me?beispielen 150 °C) die strangf?rmige Probe schwimmt. Mit dieser Anordnung ist es m?glich, das Spannungs-Dehnungs-Diagramm über gro?e Gesamtdeformationen zu messen und au?erdem die Gesamtdehnung in einen irreversiblen, viskosen und einen reversiblen, elastischen Anteil aufzuteilen. Mit weiteren Zusatzeinrichtungen k?nnen die Relaxation der Spannung und die Retardation der Dehnung an jeder Stelle des Spannungs-Dehnungs-Diagramms gemessen werden. Die Ergebnisse zeigen, da? bei niedrigen Dehnungsgeschwindigkeiten die Zugspannung im Laufe der Verformung in einen Endwert einmündet, dem eine Zugviskosit?t entspricht. Bei h?heren Dehnungsgeschwindigkeiten bildet sich dieser Endwert nicht aus, vielmehr nimmt das Spannungs-Dehnungs-Diagramm einen Sf?rmigen Verlauf, wie das von Gummi bekannt ist. Der elastische Dehnungsanteil steigt mit zunehmender Dehnungsgeschwindigkeit und mit zunehmender Gesamtdehnung an. Tr?gt man die auf die Dehnungsgeschwindigkeit bezogenen Zugspannungen über die Deformationszeit auf, so erh?lt man „Anlaufkurven“, die bei niedrigen -Werten dem Dreifachen der Anlaufkurven für die Scherstr?mung im linearen Beanspruchungsbereich entsprechen.

---

Summary In order to investigate the rheological behaviour of polymer melts subjected to an extensional deformation a new rheometer was developed which is described in detail. The test specimen consists of an extruded polymer rod of about 5,4 mm diameter which is molten and brought to test temperature in a bath of silicone oil. Swimming on this bath the molten rod is clamped in two pairs of gears which have a constant distance and which operate at constant rate of rotation thus deforming the specimen at constant extensional strain rate. Large extensional strains can be obtained easily and the separation of the total strain in an irrecoverable, viscous and in a recoverable, elastic portion is possible. Additional equipment allows the determination of the stress relaxation and the retardation of the deformation at each point of the stressstrain-curve. Stress-strain-curves of a low density polyethylene melt at 150 °C show at low strain rates an increase of the stress up to a limiting value which corresponds to an extensional viscosity. At higher strain rates no limiting value of the stress is obtained but the stress-strain-relation has aS-shape curve similar to the tensile behaviour of a rubberlike material. The recoverable portion of the total strain increases with increasing strain rate and increasing total strain. If the tensile stresses are reduced to strain rate their time dependence corresponds at low -values to the threefold of the time dependence of the reduced shear stress measured in a shear experiment in the linear viscoelastic (Newtonian) range.

---

---

HerrnF. Landmesser danke ich für die Hilfe bei der Entwicklung der Me?methode und für die Ausführung der Messungen.     

Measurement of extensional viscosity of polymer solutions

A filament stretching technique for measuring the extensional viscosity of polymer solutions at constant stretch rate is presented. The liquid sample is held between two coaxial discs and stretched by moving the bottom disc downwards with a speed that increases exponentially with time. This is illustrated using a constant viscosity, elastic fluid consisting of 0.185% polyisobutylene in a solvent of kerosene and polybutene. For the case of this particular fluid, two distinct stretch rate regions are found to arise. The stretch rate in the first region is much higher than in the second, which is, in most cases, close to the overall stretch rate imposed on the sample. Nonetheless, all the results of any given run can be represented using an average extensional rate. The extensional stress growth data, plotted as the Trouton ratio against time, show an initial linear viscoelastic region where T_R rises to a value of 3, independent of extensional rate. Beyond this region, T_R depends on the stretch rate and rises dramatically to values in excess of 10³; the higher the extensional rate, the faster is the increase in T_R. These data do not seem to reach a steady state and appear to be similar to polymer melt data obtained by others in the past. The reproducibility of the results is very good and all this suggests that it is now possible to obtain unambiguous constant-stretch-rate stress-growth data for polymer solutions stretched from a state of rest.     

Step planar extension of polymer melts using a lubricated channel

A technique to do step planar extension on polymer melts has been developed using a rectangular channel with lubricated walls and the linear motor of the Rheometrics System Four rheometer. Using this method we probe the stress relaxation of two polymer melts, a linear low density polyethylene (LLDPE) and a highly branched low density polyethylene (IUPAC X), and compare the step planar extensional data to step shear data. Since a step planar deformation is theoretically equivalent to a step shear in a rotating frame of reference, we expect that the nonlinear modulus for step planar extension should be equivalent to that for step shear. Although we find the time dependence of the stress relaxation modulus to be the same in both shear and planar extension, the strain dependence is surprisingly different for the two experiments.     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

Interchain tube pressure effect in extensional flows of oligomer diluted nearly monodisperse polystyrene melts

We have derived a constitutive equation to explain the extensional dynamics of oligomer-diluted monodisperse polymers, if the length of the diluent has at least two Kuhn steps. These polymer systems have a flow dynamics which distinguish from pure monodisperse melts and solutions thereof, if the solvent has less than two Kuhn steps, e.g. is not a chain. The constitutive equation is based on a phenomenological tube-based model within the methodology of the molecular stress function approach. The nonlinear dynamics have been explained as a consequence of a constant thermal interchain pressure originating from the short polymer chains (e.g. the oligomers) on the wall of the tube containing the long chains. The nonlinear dynamics are uniquely defined by the Rouse time and the maximal extensibility of the long polymer chains. Both are linked to the entanglement length. The relation between the Rouse times and entanglements have been established based on published extensional experiments on nearly monodisperse polystyrene melts. The constitutive equation has shown agreement with the experimental startup of and steady extension data from Huang et al. (Macromolecules 46:5026–5035, 2013a) based on 285 and 545 kg/mol polystyrenes diluted in styrene oligomers containing 3.3 (1.92 kg/mol) and 7.3 (4.29 kg/mol) Kuhn steps.