Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.     

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.     

Material functions for constant-strain-rate elongational flows

The problem of determination of invariant material functions for elongational flows in which two components of the constant strain-rate tensor are equal is briefly discussed, and a method of its solution described. The method is based on simultaneous modeling of the elongational viscosity as measured in uniform uniaxial elongational flow, and the shear viscosity as measured in steady viscometric flow. A single integral model with a strain-rate dependent memory is used to correlate both viscosities over a given experimental range of strain rates. The procedure has been applied to a set of experimental data obtained for a low-density polyethylene melt by Laun and Münstedt.     

Influence of molecular structure on the extensional behaviour of polyethylene melts

The elongational behaviour of polyethylene samples having different molecular structure has been tested. Elongational viscosity measurements have been carried out using the isothermal melt spinning technique. The extensional behaviour of the different samples is analysed as a function of total strain. The effect of long-chain branching on elongational viscosities is described. A comparison is presented between elongational viscosity and melt strength data.Some of the results reported here were presented at the VIIIth International Congress on Rheology, Naples, September 1–5, 1980, cf. [16].     

Modelling elongational and shear rheology of two LDPE melts

Experimental data of two low-density polyethylene (LDPE) melts at 200°C for both shear flow (transient and steady shear viscosity as well as transient and steady first normal stress coefficient) and elongational flow (transient and steady-state elongational viscosity) as published by Pivokonsky et al. (J Non-Newtonian Fluid Mech 135:58–67, 2006) were analysed using the molecular stress function model for broadly distributed, randomly branched molecular structures. For quantitative modelling of melt rheology in both types of flow and in a very wide range of deformation rates, only three nonlinear viscoelastic material parameters are needed: Whilst the rotational parameter, a ₂, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter describing maximum stretch of the polymer chains.     

Elongational properties and molecular structure of polyethylene melts

Summary 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.With 11 figures and 4 tables     

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.

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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.

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

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With 8 figures     

Flow instability for binary blends of linear polyethylene and long-chain branched polyethylene

The rheological properties and flow instability are studied for binary blends composed of a long-chain branched polyethylene and a linear polyethylene. It is found that the blends containing a linear-polyethylene with high shear viscosity exhibit higher oscillatory moduli, drawdown force, and strain-hardening behavior. The blends showing the anomalous rheological phenomena show sharkskin failure in low shear rate region as compared with a pure linear polyethylene. Moreover, the blends exhibit severe gross melt fracture at low output rate. Enhanced strain-hardening in elongational viscosity and large entrance angle at a die entry will be responsible for the severe gross melt fracture for the blends.     

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.     

Comparison of the elongational behaviour of a polyethylene melt at constant stress and constant strain rate

Summary Two different apparatuses for measuring the elongational behaviour of polymer melts at constant tensile stress and constant elongational strain rate are described. Measurements on a low density polyethylene were carried out up to stretching ratios of 400. The homogeneity of sample deformation in both test methods was sufficient to reach a steady-state of elongational flow where the tensile stress and the strain rate as functions of time are constant. By unloading the molten rod the recoverable strain can be determined at any state of deformation. The recoverable strain increases with growing deformation and reaches a constant value in the steady-state. The elongational viscosity calculated from the rate of viscous flow agrees with the Trouton viscosity in the case of very small deformations only. With growing deformation the elongational viscosity increases up to a constant value in the steady-state which is greater than the Trouton viscosity by about a factor of six at measured strain rates of 0.03 s^–1 and 0.1 s^–1, respectively. The elongational viscosity and the recoverable strain in the steady-state measured with the two different test methods under the same experimental conditions are in good agreement.

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Zusammenfassung Zwei verschiedene Apparaturen zur Untersuchung des Dehnverhaltens von Polymerschmelzen unter konstanter Zugspannung und konstanter Dehngeschwindigkeit werden beschrieben. An einem Polyäthylen niedriger Dichte wurden Messungen bis zu Verstreckgraden von 400 durchgeführt. Die ausreichend homogene Probenverformung erlaubt in beiden Versuchsführungen das Erreichen eines stationären Dehnfließens mit zeitlich konstanter Zugspannung und Dehngeschwindigkeit. Durch Entlasten des Schmelzestranges ist der reversible Dehnungsanteil für jeden Verformungszustand direkt zu messen. Die reversible Dehnung steigt mit wachsender Dehnverformung an, bis sich im stationären Bereich ein konstanter Wert einstellt. Die aus der Geschwindigkeit des viskosen Dehnfließens berechnete Dehnviskosität stimmt nur für den Grenzfall kleiner Deformationen mit der Trouton-Viskosität überein. Mit wachsender Dehndeformation steigt die Dehnviskosität bis zu einem Gleichgewichtswert an, der bei den gemessenen Dehngeschwindigkeiten von 0,03 s^–1 und 0,1 s^–1 um etwa einen Faktor 6 über dem Wert der Trouton-Viskosität liegt. Die unter gleichen Versuchsbedingungen mit beiden Apparaturen bestimmten Dehnviskositäten und reversiblen Dehnungen im stationären Bereich stimmen überein.

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Parts of this paper were presented at the VII^th Internat. Congress on Rheology, Gothenburg, Sweden.

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With 10 figures and 2 tables     

Rheological behaviour of nano-composites based on polyamide 6 under shear and elongational flow at high strain rates

In this work, the rheological behaviour of high molecular mass polyamide 6 (PA6)/organo-montmorillonite nano-composites, obtained via melt blending, was investigated under shear and extensional flow. Capillary rheometry was used for the measurement of high shear rate steady state shear viscosity and die entrance pressure losses; further, by the application of a converging flow method (Cogswell model) to these experimental results, elongational viscosity data were indirectly calculated. The extensional behaviour was directly investigated by means of melt spinning experiments, and data of apparent elongational viscosity were determined. The results evidenced that the presence of the organo-clay in filled PA6 melts modifies the rheological behaviour of the material, with respect to the unfilled polymer, in dependence on the type of flow experienced by the fluid. In shear flow, the nano-composites showed a slightly lower viscosity than neat PA6, whereas in elongation, they appeared much more viscous, in dependence on the organo-clay content.     

Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes

To enhance the melt strength of a conventional linear polypropylene (L-PP), blends with a long-chain branched polypropylene (LCB-PP) were produced by adding 2, 5, 10, 25, 50, and 75 wt% of LCB-PP to L-PP and mixing in a twin screw extruder. It was found that, already, an addition of 10% or less of LCB-PP to L-PP leads to significant strain hardening. Elongational viscosity data of L-PP and LCB-PP and those of their blends were analyzed by the use of the molecular stress function (MSF) theory. While L-PP is characterized by the MSF parameter, β=1 (typical for linear melts), and shows very little chain stretch (), melt elongational behavior of LCB-PP is characterized by the MSF parameters, β=2 (typical of LCB melts), and (which corresponds to a maximum stretch of molecular chains by a factor of 15). By extruding LCB-PP, a refining effect is observed similar to the refining effects seen in low density polyethylene (LDPE), which reduces the steady-state elongational viscosity and reduces to 121. A second-order mixing rule for the fractional relaxation moduli, g _i , was found to show good agreement with the linear-viscoelastic data of the blends. To simulate the elongational viscosities of the L-PP/LCB-PP blends, a similar second-order mixing rule was used for the MSF parameter, β, while a first-order mixing rule was found to be appropriate for . This allows for a quantitative prediction of the time-dependent elongational viscosities of all L-PP/LCB-PP blends on the basis of the linear and nonlinear parameters of the mixing components L-PP and LCB-PP only. Comparison between the steady-state elongational viscosities as obtained from creep experiments shows good agreement with predictions.     

An experimental and theoretical study of the effect of the elongational history on the dynamics of isothermal melt spinning

Isothermal spinning of a low-density polyethylene (LDPE) melt has been compared with isothermal creep under a constant force. Although the same initial stress was applied in both measurements, there was a tremendous difference in the stretch ratio vs. time curves, which demonstrates the enormous effect the flow before and in the capillary has on the rheological behaviour of a polymer melt.The modelling of the upstream flow as a plug flow with velocity inversely proportional to the square of the channel radius has been the basis of the development of a computer program incorporating the effect of the prehistory on the velocity profile during spinning. The constitutive equation used was a well tested, single integral constitutive equation containing a memory function and a nonlinearity function. The calculated results have been compared with isothermal spinning data for various boundary conditions. The agreement between calculation and experiment is encouraging and indicates the importance of the elongational component in the upstream flow.     

Mechanism of gross melt fracture elimination in the extrusion of polyethylenes in the presence of boron nitride

The mechanism by which the addition of a small amount of boron nitride into a polyethylene eliminates gross melt fracture is elucidated. Simple elongational viscosity measurements at high rates revealed that the presence of boron nitride decreases the extensional viscosity of polyethylenes. The extensional rates at which these effects are present were found to be about the same with those at which gross melt fracture is obtained (calculated from Cogswells analysis). Thus, it can be argued that the well dispersed boron nitride particles decrease extensional stresses that are responsible for gross melt fracture and/or their presence dissipate the release of energy resulting from isolated rupture or slip planes within the melt originating at the entrance to the capillary.     

Correlation between rheological behaviour in uniaxial elongation and film blowing properties of various polyethylenes

Six various low density polyethylenes and one blend were rheologically characterized in elongation. Their different strain-hardening behaviour could qualitatively be related to their molecular structure. All the materials were blown to films on laboratory equipment under various conditions. The take-up force and the film homogeneity were determined quantitatively, the bubble stability was visually assessed. The bubble stability increased with growing take-up force. The take-up force was found to be the stronger the higher the elongational viscosity was. The homogeneity of film thickness is not related to the bubble stability but to the occurrence of strain hardening in the uniaxial elongational experiment at high Hencky strains. Measurements of the uniaxial elongational behaviour of polyethylene melts are a valuable and promising way to assist the development and optimisation of film blowing materials.

Linear viscoelastic model for elongational viscosity by control theory

Flows involving different types of chain branches have been modelled as functions of the uniaxial elongation using the recently generated constitutive model and molecular dynamics for linear viscoelasticity of polymers. Previously control theory was applied to model the relationship between the relaxation modulus, dynamic and shear viscosity, transient flow effects, power law and Cox–Merz rule related to the molecular weight distribution (MWD) by melt calibration. Temperature dependences and dimensions of statistical chain tubes were also modelled. The present study investigated the elongational viscosity. We introduced earlier the rheologically effective distribution (RED), which relates very accurately and linearly to the viscoelastic properties. The newly introduced effective strain-hardening distribution (RED_H) is related to long-chain branching. This RED_H is converted to real long-chain branching distribution by melt calibration and a simple relation formula. The presented procedure is very effective at characterizing long-chain branches, and also provides information on their structure and distribution. Accurate simulations of the elongational viscosities of low-density polyethylene, linear low-density polyethylene and polypropylene, and new types of MWDs are presented. Models are presented for strain-hardening that includes the monotonic increase and overshoot effects. Since the correct behaviour at large Hencky strains is still unclear, these theoretical models may aid further research and measurements.     

Branched viscoelastic surfactant solutions and their response to elongational flow

Several years ago, Münstedt and Laun reported on the influence of branching on the elongational flow properties of polymer chains (Münstedt and Laun, 1981). They concluded that, in addition to the molecular weight distribution, the degree of branching strongly affects the degree of strain thickening of the elongational viscosity in such a way that the maximum in this material function increases with branching. In a recent paper by Lin, a ternary system of dodecyldimethylamine oxide-sodium laureth sulphate-sodium chloride surfactant solutions was investigated by CryoTEM and rheology (Lin, 1996). He reported a linear relation between the added sodium chloride and the branching of the wormlike micelles. In this paper we present an investigation of these surfactant solutions in elongational flow. Our results indicate that for branched micellar systems the presence of branching enhances the maximum of the elongational viscosity in the same manner as in the case of polymer melts.     

液晶高分子-各向异性流体挤出拉伸分岔研究

应用共转导数型本构方程研究了液晶高分子纺丝挤出过程的拉伸黏度,应用计算机符号运算软件 Maple得出解析表达式,拉伸黏度与拉伸率之间关系(随剪切速率变化)表明存在分岔现象,得出拉伸黏度显著高于相应的剪切黏度,解释了液晶高分子熔体挤出时不发生挤出胀大的物理机制．     

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.