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.     

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.     

Effect of vinyl acetate content and silicate loading on EVA nanocomposites under shear and extensional flow

In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems.     

Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state

The flow curves of linear (linear-low and high density) and branched polyethylenes are known to differ significantly. At increasing shear rates, the linear polymers exhibit a surface melt fracture or sharkskin region that is followed by an unstable oscillating or stick-slip flow regime when a constant piston speed capillary rheometer is used. At even higher shear rates, gross melt fracture appears. Unlike their linear counterparts, branched polyethylenes rarely exhibit sharkskin melt fracture and although gross melt fracture appears at high shear rates there is no discontinuity in their flow curve. The various flow regimes of these two types of polyethylenes are examined by performing experiments in the melt state using a unique extensional rheometer (the SER by Xpansion Instruments) that is capable of performing accurate extensional flow and peel experiments at very high rates not previously realized. The peel strength curves of these linear and branched polyethylenes exhibit all of the distinct flow regimes exhibited in their respective flow curves, thereby providing a fingerprint of their melt flow behavior. Moreover, these extensional flow and peel results in the melt state provide insight into the origins and mechanisms by which these melt flow phenomena may occur with regard to rapid tensile stress growth, melt rupture, and adhesive failure at the polymer wall interface.     

Measurements and model predictions of transient elongational rheology of polymeric nanocomposites

Transient elongational rheology of two commercial-grade polypropylene (PP) and the organoclay thermoplastic nanocomposites is investigated. A specifically designed fixture consisting of two drums (SER Universal Testing Platform) mounted on a TA Instruments ARES rotational rheometer was used to measure the transient uniaxial extensional viscosity of both polypropylene and nanoclay/PP melts. The Hencky strain rate was varied from 0.001 to 2 s^− 1, and the temperature was fixed at 180°C. The measurements show that the steady-state elongational viscosity was reached at the measured Hencky strains for the polymer and for the nanocomposites. The addition of nanoclay particles to the polymer melt was found to increase the elongation viscosity principally at low strain rates. For example, at a deformation rate of 0.3 s^− 1, the steady-state elongation viscosity for polypropylene was 1.4 × 10⁴ Pa s which was raised to 2.8 × 10⁴ and 4.5 × 10⁴ Pa s after addition of 0.5 and 1.5 vol.% nanoclay, respectively. A mesoscopic rheological model originally developed to predict the motion of ellipsoid particles in viscoelastic media was modified based on the recent developments by Eslami and Grmela (Rheol Acta 47:399–415, 2008) to take into account the polymer chain reptation. We show that the orientation states of the particles and the rheological behavior of the layered particles/thermoplastic hybrids can be quantitatively explained by the proposed model.     

The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements

Extensional rheometry has only recently been developed into a commercially available tool with the introduction of the capillary breakup extensional rheometer (CaBER). CaBER is currently being used to measure the transient extensional viscosity evolution of mid to low-viscosity viscoelastic fluids. The elegance of capillary breakup extensional experiments lies in the simplicity of the procedure. An initial step-stretch is applied to generate a fluid filament. What follows is a self-driven uniaxial extensional flow in which surface tension is balanced by the extensional stresses resulting from the capillary thinning of the liquid bridge. In this paper, we describe the results from a series of experiments in which the step-stretch parameters of final length, and the extension rate of the stretch were varied and their effects on the measured extensional viscosity and extensional relaxation time were recorded. To focus on the parameter effects, well-characterized surfactant wormlike micelle solutions, polymer solutions, and immiscible polymer blends were used to include a range of characteristic relaxation times and morphologies. Our experimental results demonstrate a strong dependence of extensional rheology on step-stretch conditions for both wormlike micelle solutions and immiscible polymer blends. Both the extensional viscosity and extensional relaxation time of the wormlike micelle solutions were found to decrease with increasing extension rate and strain of the step-stretch. For the case of the immiscible polymer blends, fast step-stretches were found to result in droplet deformation and an overshoot in the extensional viscosity which increased with increasing strain rates. Conversely, the polymer solutions tested were found to be insensitive to step-stretch parameters. In addition, numerical simulations were performed using the appropriate constitutive models to assist in both the interpretation of the CaBER results and the optimization of the experimental protocol. From our results, it is clear that any rheological results obtained using the CaBER technique must be properly considered in the context of the stretch parameters and the effects that preconditioning has on viscoelastic fluids.     

The effect of pre-shear on the extensional rheology of wormlike micelle solutions

The effect of initial microstructural deformation, alignment, and morphology on the response of wormlike micelle solutions in transient uniaxial extensional flows is investigated using a pre-shear device attached to a filament stretching rheometer. In filament stretching experiments, increasing the strength and the duration of the pre-shear just before stretch is found to delay the onset of strain hardening. In these experiments, the wormlike micelle solution filaments fail through a rupture near the axial midplane. The value of the elastic tensile stress at rupture is found to decrease with increasing pre-shear rate and duration. The most dramatic effects are observed at shear rates for which shear banding has been independently observed. The reduction in the strain hardening suggests that pre-shear before filament stretching might break down the wormlike micelles reducing their size before stretch. Strain hardening is also observed in capillary breakup rheometry experiments; however, the pre-sheared wormlike micelle solutions strain harden faster, achieve larger steady-state extensional viscosities and an increase in the extensional relaxation time with increasing shear rate and duration. The difference between the response of the wormlike micelles in filament stretching and capillary breakup experiments demonstrates the sensitivity of these self-assembling micelle networks to pre-conditioning.     

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.     

Transient shear and elongational behavior of blends of PET with a LCP

Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer. The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function was measured in a cone and plate rheometer. The elongational growth function was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend. The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET. The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend had an intermediate behavior between both blends.     

On the pressure correction of capillary melt rheology data

In this paper, the importance of a pressure correction of viscosity data obtained in capillary melt rheology is demonstrated. A linear polycarbonate has been chosen as a highly pressure-sensitive material for which data obtained by rotational rheometry does not overlap with capillary data. This apparent problem with the Cox–Merz relation is attributed to the existence of a mean pressure inside the capillary which is significantly different from atmospheric conditions. Different methods to determine the pressure coefficient of polycarbonate have been evaluated based on experiments performed with a capillary rheometer equipped with a pressure chamber. It is demonstrated that the pressure coefficient obtained at constant shear stress and the pressure coefficient obtained by the superposition method represent accurate pressure coefficient values. Two approaches are proposed to correct the original capillary data. In the direct methodology, the pressure coefficient is used to rescale the mean pressure inside the capillary to atmospheric conditions. The indirect approach consists of first constructing a mastercurve at a certain reference pressure using capillary data obtained with a pressure chamber. The resulting mastercurve can then be rescaled to atmospheric conditions. It is shown that both methods lead to viscosity curves on which both rotational and capillary data overlap, hence confirming the Cox–Merz relationship for polycarbonate. The indirect method is proven to be advantageous since it opens the possibility to significantly extend the shear rate window in which viscosities can be measured.     

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.     

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].     

Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient?

We investigate a variety of different semidilute polymer solutions in shear and elongational flow. The shear flow is created in the cone-plate-geometry of a commercial rheometer. We use capillary thinning of a filament that is formed by a polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) as an elongational flow. We compare the relaxation time measured in the CaBER with relaxation times based on the first normal stress difference and the zero shear polymer viscosity that we measure in our rheometer. All of these three measurable quantities depend on different fluid parameters—the viscosity of the solvent, the polymer concentration within the solution, and the molecular weight of the polymers—and on the shear rate (in the shear flow measurements). Nevertheless, we find that the first normal stress coefficient depends quadratically on the CaBER relaxation time. Several scaling laws are presented that could help to explain this empirical relation.     

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     

Measuring uniaxial extensional viscosity using a modified rotational rheometer

Knowledge of the extensional behaviour of polymer melts is extremely important due to the industrial relevance of extensional flows in common processing techniques and sequences such as blow moulding, film blowing, fibre spinning, melt flow through extrusion dies and injection mould filling. One of the main problems both researchers and industrialists come across is the fact that, unlike shear flows, steady-state extensional flows are not easy to generate and maintain experimentally. This fact limits the extent to which one can characterise the materials and, therefore, the degree of optimisation of the productive process. In this paper, a modification to a commercially available controlled rate rotational rheometer is proposed in order to produce a cheap, easy to set-up, flexible extensional rheometer. This is based on the well-known Meissner-type extensional rheometer and makes use of the accurate velocity control and torque measurement possibilities of the rotational apparatus. In this case, the adaptation was performed on a TA Instruments Weissenberg Rheogoniometer, but the idea is applicable to most other similar devices. The feasibility of the modification will be discussed and confirmed, results being presented for two materials at different temperatures. These include the calculation of transient uniaxial extensional viscosity and a study of rupture conditions.     

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.     

Exponential shear flow of branched polyethylenes in rotational parallel-plate geometry

Exponential shear flow, as a strong flow with the potential to generate a high degree of molecular stretching, has attracted considerable interest in recent years. So far, exponential shear flow has been realized by either sliding-plate or cone-and-plate (CP) geometry. Both geometries guarantee homogeneous shear flow. Here, we present experimental data on exponential shear flow of several long-chain branched polyethylene melts with different degrees of strain hardening obtained by using parallel-plate (PP) geometry in a rotational rheometer. This type of geometry, which is standard in linear-viscoelastic characterization of polymer materials, produces inhomogeneous shear flow. A comparison of exponential shear flow data obtained by PP and CP geometry is made. Additionally, the experimental data are compared to predictions of the rubber-like liquid (RLL) and the molecular stress function (MSF) theories. For this purpose, the relaxation spectra of the polymer melts considered were obtained by standard linear-viscoelastic characterization. In addition, two irrotational parameters and one rotational parameter are required by the MSF theory. While the irrotational parameters were obtained from fitting to elongational viscosity data, the value of the rotational parameter was used as given in the literature. It can be concluded that viable experimental data in exponential shear flow can be obtained by PP geometry. For finite linear-viscoelasticity (RLL theory), predictions of reduced shear stress for CP and PP geometry coincide, but nonlinear material behavior (as modeled by the MSF theory) leads to small differences between both geometries. Furthermore, it is shown that the MSF predictions are in excellent agreement with the experimental data in exponential shear flow and that this type of flow leads to much less chain stretching than elongational flow.Dedicated to the memory of Prof. Arthur S. Lodge (1922–2005).     

Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Viscoelastic behaviour and flow instabilities of biodegradable poly (ε-caprolactone) polyesters

The viscoelastic behaviour of a number of commercial and newly synthesized linear biodegradable polyesters—poly (ε-caprolactone) (PCLs) with different molecular characteristics was investigated using both rotational and extensional rheometry. The variation of the zero-shear viscosity and relaxation spectrum with molecular weight was studied in detail. The damping function of these PCLs was also determined in order to model their viscoelastic behaviour. The classic Wagner constitutive equation was found to represent the rheology of all PCL polymers quite well. Finally, the PCL processing instabilities were studied by capillary extrusion using a number of capillary dies having various diameter and length-to-diameter ratios. Sharkskin and gross melt fracture was observed at different shear rates depending on the molecular characteristics of the resins and the geometrical details of the capillary dies.