Elongational viscosity of polymer melts: A lubricated skin-core flow approach

Previous work by this research group has shown that the use of a lubricated skin/core flow of polymer melts and a hyperbolic converging die results in an essentially pure elongational flow at a constant elongational strain rate in the core. The previous work was carried out on a laboratory-scale coextrusion system in a planar slit die; tracer particles and an image analysis system were used to confirm the predicted behavior. In this work, the technique was implemented first on the coextruder assembly, as a planar elongational rheometer, and then on a commercial capillary rheometer, as a uniaxial elongational rheometer for polymer melts. The later is achieved by replacing the standard capillary die with a hyperbolic axisymmetric die. A two-laycred billet is prepared for placement in the rheometer barrel by completely encapsulating the core polymer (the polymer to be analyzed) with a low-viscosity polyethylene skin. Commercial grades of polypropylenes, syndiotactic polystyrene, and nylon-66 were analyzed using this technique. Elongational viscosity at high extensional rates can be determined with this method; values in excess of 500 s⁻¹ have already been achieved. © 1996 John Wiley & Sons, Inc.     

Measurement of the equibiaxial elongational viscosity of polystyrene using lubricated squeezing

The equibiaxial elongational viscosity of polystyrene was determined using a lubricated squeezing technique. Constant strain rates up to Hencky strains of 4.5 could be maintained by a newly constructed instrument. Test results from controlled stress and controlled strain rate measurement were consistent and yielded well-defined steady-state viscosities. Measurements appeared to be unaffected by sample geometry, although proper lubrication is important in achieving steady state. The measured biaxial viscosity appeared to be strain rate thinning above a biaxial strain rate of ≈ 0.01 s⁻¹ at 160°C. As anticipated in the Newtonian region, biaxial elongational viscosity was approximately six times the shear viscosity. Thinning indices of both shear and biaxial elongational viscosities were 0.75. Data obtained at various temperatures were shifted following the timetemperature superposition principle. The resulting master curve could be fitted by a Carreau model with n ≈ 0.3 and a time constant of 110 s.     

Shear and elongational rheology of polyethylenes with different molecular characteristics. II. Elongational rheology

The elongational viscosities of polyethylenes with different molecular characteristics were measured at different Hencky strains and temperatures with a capillary rheometer by the replacement of the capillary cylindrical die with a hyperbolic converging die. The hyperbolic shape of the die established a purely elongational flow field at a constant elongational strain rate throughout the die. The effects of molecular characteristics such as the molecular weight, molecular weight distribution, and long‐chain branching and processing conditions such as the temperature and Hencky strain on the elongational rheology of the polyethylene samples were studied. Good master curves were generated for temperature and Hencky strain shifting and simultaneous shifting with respect to both the temperature and Hencky strain. Both the molecular weight distribution and long‐chain branching seemed to promote strain rate thinning and reduce the elongational viscosity. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 1184–1194, 2007     

Effect of chain structure on the melt rheology of modified polypropylene

The effect of molecular structure of polypropylene (PP) on the melt rheological properties were investigated for electron irradiated polymer and di-2-ethylhexyl peroxy dicarbonate (EHPC)-treated polymer. The modifications were examined in terms of the rheological behaviors, molecular weight distribution, and the degree of branching. The high melt strength PP was obtained by irradiating with 50 and 80 kGy and adding EHPC. The modified PPs showed the strain hardening in the uniaxial elongational viscosity, though the linear elongational viscosity was lower than that of the unmodified PP. Low angle laser light-scattering measurements of the modified PPs showed the interesting results; high irradiation doses such as 50 and 80 kGy caused higher molecular weight chains branching. Nevertheless, the long branching chains were not detected for the EHPC modified PP, which also showed the strain hardening in uniaxial elongational flow. In this article, the relation between chain structure and rheological properties is discussed. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 1493–1500, 1999     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. III. Elongational rheology

The elongational rheology of solutions of cellulose in the ionic liquid solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was measured at 80, 90, and 100°C; 8, 10, and 12 wt% cellulose; Hencky strains 5, 6, 7; and strain rates from 1 to 100 s^?1. Master curves were generated by shifting the elongational viscosity curves with respect to temperature and Hencky strain. Also, general master curves were generated by simultaneously shifting with respect to both temperatures and Hencky strain. From the Arrhenius plots of the temperature shift factors, the activation energy for elongational flow was determined. The elongational rheology of these solutions was elongational strain rate thinning similar to that of their shear behavior and polymer melts and they were also strain hardening. Both effects and the viscosity increased with cellulose concentration. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Correlation between entry pressure losses and elongation viscosity of polyethylene melts

The correlation between the entry pressure drop and elongation viscosity during entry converging flow of polymer melts was discussed in this article. The entry pressure drop during extrusion of a low density polyethylene (LDPE) melt and a linear low density polyethylene (LLDPE) melt was measured by means of a capillary rheometer under test conditions with temperature of 170 °C and shear rate varying from 10 to 300 s⁻¹. The results showed that the entry pressure drop increased nonlinearly with an increase of the shear stain rate, and the variation of entry pressure drop of the two melts was close to each other. The melt elongation viscosity of the two resins was estimated using Cogswell equation from the measured entry pressure drop data, and the predictions were compared with the melt extension viscosity measured by using a melt spinning technique published in literature. It was found that the melt extension viscosity from entry converging flow was slightly lower than that from melt spinning technique under the same temperature and extension strain rate.     

Rheological Properties of Different Film Blowing Polyethylene Samples Under Shear and Elongational Flow

Summary: The rheological behavior of polyethylenes is mainly dominated by the molecular weight, the molecular weight distribution and by the type, the amount and the distribution of the chain branches. In this work a linear metallocene catalyzed polyethylene (m‐PE), a branched metallocene catalyzed polyethylene (m‐bPE), a conventional linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE) have been investigated in order to compare their rheological behavior in shear and in elongational flow. The four samples have similar melt flow index and in particular a value typical of film blowing grade. The melt viscosity has been studied both in shear and in isothermal and non‐isothermal elongational flow. The most important features of the results are that in shear flow the m‐PE sample shows less pronounced non Newtonian behavior while in the elongational flow the behavior of m‐PE is very similar to that of the linear low density polyethylene: the narrower molecular weight distribution and the better homogeneity of the branching distribution are reasonably responsible for this behavior. Of course the most pronounced non‐linear behavior is shown, as expected, by the LDPE sample and by the branched metallocene sample. This similar behavior has to be attributed to the presence of branching. Similar comments hold in non‐isothermal elongational flow; the LDPE sample shows the highest values of the melt strength and the other two samples show very similar values. As for the breaking stretching ratio the opposite is true for LDPE while m‐PE and LLDPE show higher values. The transient isothermal elongational viscosity curves show that the branched samples show a strain hardening effect, while LLDPE and m‐PE samples present a linear behavior.

Dimensionless flow curves of different polyethylene samples.     

Studies on blown film extrusion. I. Experimental determination of elongational viscosity

Blown-film extrusion experiments were carried out to investigate the elongational flow behavior of viscoelastic polymer melts at different melt temperatures. Materials chosen for study were high-density polyethylene, lowdensity polyethylene, and polypropylene. In the study, isothermal blown-film extrusion experiments were carried out in which the molten blown film traveled upward through a heated chamber of about 13 in. in length maintained at the same temperature as the melt. Axial tension was measured at the take-up roller, the axial profiles of bubble diameter were determined by a photographic technique, and, from the samples collected, the variation in the film thickness along the axial direction was found. These measurements were used later to determine the elongational viscosity, using the force balance equations. It was found, in the experiment, that a careful control of the pressure difference across the thin film permitted one to maintain the bubble diameter constant, and, therefore, depending on the choice of the extrusion conditions, either a uniaxial or biaxial elongational flow was made possible. The experimental results show that, depending on the materials, elongation rate, and melt temperature tested, the elongational viscosity may decrease or increase with elongation rate, and may also stay constant independent of elongation rate. It was observed that the data of elongational viscosity obtained under uniaxial stretching in blown film extrusion is consistent with the data of elongational viscosity obtained earlier by use of the melt-spinning operation.     

New extensional rheometer for elongational viscosity and flow birefringence measurements: some results on polystyrene melts

A new extensional rheometer allowing the simultaneous measurement of elongational viscosity and flow birefringence is described. Polystyrene melts have been tested at different temperatures and strain rates. It appears that the time-temperature superposition principle holds for elongational tests in the temperature range investigated, with the same shift factors as for linear shear experiments. It has been verified that the stress optical behaviour of the melts is linear for small values of the stress whereas significant deviations appear at higher stresses.     

Study of kinematics and dynamics of film blowing of different polyethylenes

An extensive experimental study of the effects of material characteristics and processing parameters on the kinematics and dynamics of film blowing is presented. Three polyethylene resins, a high-density polyethylene (HDPE), a low-density polyethylene (LDPE), and a linear low-density polyethylene (LLDPE) were investigated. The convergent flow analysis of Cogswell was used to characterize the elongational flow behavior of the polymers. Strain rates and pressure inside the bubble (P_i) have been determined over a wide range of film blowing conditions. Moreover, on-line bubble temperature and birefringence measurements have been carried out along the length of the bubble. The experimental results reveal that the three polymers display different behaviors. The LLDPE requires the highest P_i value and the LDPE, the lowest. Consistent with this, the LLDPE shows the lowest in-plane birefringence and the LDPE, the highest. Interactions between various process parameters affecting the P_i value are characterized. Bubble instability is correlated to the apparent uniaxial elongational viscosity and P_i. The most stable polymer (LDPE) has the highest elongational viscosity and requires the lowest P_i. Stresses have been calculated with the help of the birefringence and P_i data. The stress and strain rate data were used to calculate an apparent nonuniform biaxial elongational viscosity of the melts, but could not be correlated through any simple constitutive equation.     

Rheological effects of polyethylenes in film blowing

The aim of this work is to correlate the rheological properties and processability of various polyethylenes during the film‐blowing process. The effect of rheology on the kinematics and dynamics of film blowing for five different polyethylene resins has been extensively studied using a fully instrumented laboratory unit. The complex viscosity, shear viscosity, uniaxial elongational viscosity, and non‐uniform biaxial elongational viscosity, as well as the strain rates and stresses during film blowing, have been determined and correlated to the bubble stability. G′ versus G″ plots were found to be virtually independent of temperature for all polymers investigated. The more elastic polymers (larger G′ values) were found to be more stable in film blowing. Also, the more stable polymer melts were found to be those possessing larger elongational properties.     

Elongational behavior of polyethylene melts—effect of deformation

Transient elongational viscosity of linear low density polyethylene (LLDPE) and two low density polyethylenes (LDPE1 and LDPE2) was measured at one temperature and different deformation rates in constant strain rate elongational rheometer. The elongational viscosity measurements revealed stronger strain hardening characteristics for LDPEs than that observed for LLDPE. The different response to stretching of these polymers is thought to relate to the presence of long chain branches in LDPEs, which affect the elongation viscosity profoundly. The onset of strain hardening for all long chain branched LDPEs as well as for linear LLDPE occurs at the same value of the critical strain, which is independent of temperature or deformation rate. An attempt has been made to explain this phenomenon in terms of the changes that occur in the macromolecular network upon stretching.     

Elongational rheology of polyethylene melts

Effective elongational viscosities were measured for high‐ and low‐density polyethylene samples using a capillary rheometer fitted with semihyperbolic dies. These dies establish a purely elongational flow field at constant elongational strain rate. The effective elongational viscosities were evaluated under the influence of the process strain rate, Hencky strain, and temperature. Enthalpy and entropy changes associated with the orientation development of semihyperbolic‐processed melts were also estimated. The results showed that elongational viscosities were primarily affected by differences in the weight‐average molecular weight rather than in the degree of branching. This effect was process‐strain‐rate‐ as well as temperature‐dependent. An investigation of the melt‐pressure relaxation and the associated first decay time constants revealed that with increasing strain rate the molecular field of the melt asymptotically gained orientation in approaching a limit. As a result of this behavior, molecular uniqueness became much less distinct at high process strain rates, apparently yielding to orientation development and the associated restructuring of the melt's molecular morphology. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2170–2184, 2001     

Modeling of nonlinear extensional and shear rheology of low-viscosity polymer melts

The hierarchical multi-mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low-density polyethylenes (1840H and 2426 k), and a linear poly-(ethylene-co-α-butene), PEB A-780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear-viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus G_D for extensional flows, and in addition a constraint release parameter for shear flow.     

Supercritical carbon dioxide-assisted reactive extrusion for preparation long-chain branching polypropylene and its rheology

An environmental benign process, which uses supercritical carbon dioxide (ScCO₂) as a processing aid, is developed in this work to prepare long chain branching polypropylene (LCB-PP). Results from the oscillatory shear rheology, melt elongational behavior and Fourier transformed infrared spectroscopy (FTIR) show that long chains have been linked as branches to the original linear PP chains using scCO₂-assisted reactive extrusion in the presence of cumene hydroperoxide and 1,6-hexanediol diacrylate. Compared to the initial linear PP, the branched samples show higher storage modulus (G′) at low frequency, distinct strain hardening of elongational viscosity, lower melt flow rate, increased crystallization temperature and improvement of the melt strength. ScCO₂ can improve the branching efficiency of modified PPs. The elastic response, melt strength and strain hardening parameter of the modified PPs increase with increasing scCO₂ concentration, which is ascribed to scCO₂ acting as a plasticizer for reducing PP viscosity and a carrier for active chemical species.     

An experimental study of the influence of carbon black on the rheological properties of a polystyrene melt

A broad range of experiments on carbon black filled polystyrene melts shows the reinforcing effect of the filler. This study represents one of the most extensive investigations of a series of highly filled polymer melts. Stress relaxation and dynamic experiments characterize the small strain behavior while the steady state shear viscosity, normal stresses, and elongational flow experiments describe the large strain deformation rate response. Extrudate swell and unconstrained shrinkage of extrudates are also measured. Highly filled systems exhibit yield values. This is seen in the dynamic experiments and in the shear and elongational viscosities. Viscosity does not level off at finite values with decreasing deformation rate but continues to increase in an approximately inverse manner. This corresponds to yield values of order 5 × 10⁵ dynes/cm². The storage modulus also does not tend to zero at low frequencies. The small strain dynamic properties and stress relaxation results suggest high memories for small strain experiments. Txtrudate swell values are however small and the systems exhibit minimal delayed recovery. The implications of this are considered. Generally it is argued that at volume loadings between 10 and 20 percent, the system takes on the characteristics of a gel and the response is similar to that of a Schwedoff body.     

Relationships between processing conditions and rheological behavior of polyethylenes

The rheological properties of high‐density polyethylene melts were found to change drastically after treatment with oxygen or peroxide. Unusual features of the treated melts in shear flow (190°C) included (a) increase in length of time to reach steady state values of shear stress in start‐up experiments; (b) a non‐reproducibility of the low‐shear rate sections of the flow curves measured at increasing and decreasing shear rate; (c) an increase of viscosity at low shear rates compared to the neat sample. Under non‐stationary extensional flow (a regime of constant force) the treatment leads to a change in shape of the strain development with time, an increase of the apparent elongational viscosity, and an increase in time to break. At 150–170°C, the rheological behavior of the treated polyethylenes is completely identical to the corresponding behavior of the untreated. These results, together with data from IR‐spectroscopy and GPC suggest the following mechanism: The oxidation or peroxidation leads to reactive sites in the polymer chain that incorporate a few long branches during the initial contact with oxygen or peroxide. These reactive sites remain in the polymer after cooling/solidification and can become activated again upon heating to 190°C causing additional changes in molecular structure. Formation of the long‐chain branches results in an increased resistance of the melt to extensional deformation, and an improvement in processing behavior, as well as the quality of bottles produced by the blow‐molding process. Polym. Eng. Sci. 44:615–624, 2004. © 2004 Society of Plastics Engineers.     

Shear and elongational flow properties of peroxide‐modified wood/low‐density polyethylene composite melts

Adding fillers to a polymer melt may result in a strain softening behavior in elongational flow in long‐chain branched materials, showing strain‐hardening behavior when compared with unfilled one. To improve the strain‐hardening properties in wood/LDPE composites, the effect of peroxide concentration on both the molecular architecture and molar mass distribution, and the rheological quantities in shear and elongation is studied. Addition of wood flour increases the viscosity according to a logarithmic mixing rule, as expected from the large particle size and the filler fractions used. The peroxide has multiple effects on the molar architecture of the polymer. First, a gel fraction of cross‐linked material is formed, the concentration of gel being dependent of the amount of peroxide used. Second, a higher molar mass component is detected, leading to higher value of M_w and to a broader molar mass distribution. Finally, the degree of long‐chain branching unexpectedly decreases with increasing peroxide content. The changes in molecular architecture are hardly influenced by addition of the wood flour. The peroxide treatment leads to an improved strain‐hardening behavior, detected by elongational viscosity and melt strength measurements. However, the addition of wood flour decreases the amount of strain hardening.POLYM. COMPOS., 33:2084–2094, 2012. © 2012 Society of Plastics Engineers     

The effect of long chain branching on the processability of polypropylene in thermoforming

Linear polypropylene was modified by reaction with peroxydicarbonates in a twin screw extruder to obtain varied degrees of long chain branching. The melt strength and the elasticity of the modified polymers were found to increase with the modification. The processability in foaming and thermoforming processes improved with branching and showed an optimum, beyond which higher degrees of long chain branching appeared not to help any further. The branched PP samples showed distinct strain hardening in the elongational viscosity, which was absent from the original linear melts. Melt strength, elasticity and strain hardening increased with the increase of the number of long chain branches on the main chain. The effect of molecular weight and molecular weight distribution of the precursor on the improvement of the processability of the polymer was examined. Polym. Eng. Sci. 44:973–982, 2004. © 2004 Society of Plastics Engineers.     

Experimental study of elongational flow and failure of polymer melts

A new and simple instrument for measurement of elongational flow response of polymer melts in constant uniaxial extension rate experiments is described. Quantitative stress development data are presented for a series of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polystyrene (PS), polypropylene (PP), and poly(methyl methacrylate) (PMMA) melts. For small elongation rate E, linear viscoelastic behavior was observed; while for large E, LDPE and PS showed exponential stress growth, while HDPE and PP showed only linear stress growth. Stress relaxation experiments were carried out for several of the same melts in the instrument. Elongation to break and mechanisms of filament failure were studied. HDPE and PP have a tendency to neck and exhibit ductile failure, while at high E, LDPE and PS seem to show cohesive fracture. The elongational flow stress response data were compared to predictions of nonlinear viscoelastic fluid theory, specifically the Bogue-White formulation. The qualitative differences in responses of the melts studied were explained in terms of different dependences of the effective relaxation times on deformation rate and, more specifically, on values of the a parameter in the theory.