Hencky strain shifting of convergent flow measured effective elongational viscosity

The effective elongational viscosity data on a series of polyolefins as a function of the Hencky strain are shifted to a reference Hencky strain using an approach similar to that used for temperature shifting, shearing viscosity data. The basis of this shifting is the order that develops (i.e., the decrease in entropy that occurs) during forced flow through semihyperbolically convergent dies. The entropy decrease is proportional to the orientational contribution to the effective elongational viscosity. The Hencky strain shift factors are obtained from the convergent flow effective elongational rheology and the complex and capillary shear rheology. The commercial grades of polyolefins studied include polypropylene, high density polyethylene, and metallocene and conventionally catalyzed low density polyethylene. The combination of the temperature shift factors given in our companion article and the Hencky strain shift factors in this article enable the creation of master curves for the effective elongational rheology. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1397–1404, 2003     

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     

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     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. I. Shear rheology

In this article, shear rheology of solutions of different concentrations obtained by dissolution of cellulose in the ionic liquid (IL) solvent 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl) was studied by measuring the complex viscosity and dynamic moduli at different temperatures. The obtained viscosity curves were compared with those of lyocell solutions and melt blowing grade polypropylene melts of different melt flow rates (MFR). Master curves were generated for complex viscosity and dynamic moduli by using Carreau and Cross viscosity models to fit experimental data. From the Arrhenius plots of the shift factors with respect to temperature, the activation energies for shear flow were determined. These varied between 18.99 and 24.09 kCal/mol, and were compared with values for lyocell solutions and different polymeric melts, such as polyolefins, polystyrene, and polycarbonate. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

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.     

Rheology of LLDPE,LDPE and LLDPE/LDPE blends and its relevance to the film blowing process

The relevance of polymer melt rheology in film blowing process for linear low‐density polyethylene (LLDPE) and its blends with three different low‐density polyethylenes (LDPEs) has been discussed. The effect of different LDPE components as well as their concentration on shear and elongational viscosity has been investigated. A good correlation has been observed between the extensional rheological parameters of LDPEs measured by different experimental techniques. The molecular structure of parent polymers as well as blend composition play an important role in the rheology of these blends and consequently their performance in the film blowing process. © 2000 Society of Chemical Industry     

Well-mixed blends of HDPE and ultrahigh molecular weight polyethylene with major improvements in impact strength achieved via solid-state shear pulverization

Compared with conventional polyolefins, ultrahigh molecular weight polyethylene (UHMWPE) possesses outstanding impact strength and crack resistance that make it desirable for a wide variety of applications. Unfortunately, UHMWPE has an ultrahigh viscosity that renders common, continuous melt-state processes ineffective for making UHMWPE products. Attempts to overcome this problem by blending UHMWPE with lower molecular weight high-density polyethylene (HDPE) by melt processing have typically led to poorly dispersed blends due to the vast viscosity mismatch between blend components. Here, we present solid-state shear pulverization (SSSP) as a mild, continuous, and simple approach for achieving effective and intimate mixing in UHMWPE/HDPE blends. These SSSP blends are easily processed by post-SSSP melt extrusion; for an SSSP blend with 50 wt% UHMWPE, we observe more than a factor of 1000 increase in viscosity at a shear rate of 0.01 s⁻¹ but less than a factor of 5 increase at 100 s⁻¹, the latter being more typical of melt-processing operations. Using extensional rheology, we confirm the strain hardening behavior of SSSP blends. Shear rheology and crystallization data show that the mixing between UHMWPE and HDPE can be improved with subsequent passes of SSSP and single-screw extrusion. Finally, we show that blending via SSSP leads to dramatic improvements in impact strength: as compared to literature results, injection-molded sample bars made from SSSP blends with 30–50 wt% UHMWPE exhibit very high values of notched Izod impact strength, 660–770 J/m (the impact strength of neat HDPE was 170 J/m).     

The influence of molecular weight on the melt rheology of polypropylene

Melt viscosity and melt elasticity data were obtained over a broad range of temperatures and shear rates on a series of four polypropylenes of different molecular weight but approximately the same molecular weight distribution. The superposition technique was used with both temperature and molecular weight to shift flow curves for all four materials at three temperatures each along the shear rate axis to generate a master flow curve at a given temperature and molecular weight. For polypropylenes of this type, and molecular weight distribution shift, factors which can be used to extend the useful range of experimentally obtained flow data were determined. The dependency of apparent viscosity on weight average molecular weight at shear stresses as high as 10⁶ dynes/cm² is shown. The dependency of melt elasticity on molecular weight and temperature is discussed.     

Rheological properties of polypropylene/hemp fiber composites

This study investigates the effect of hemp fibres on the shear and elongational rheology of polypropylene (PP). The parameters studied were hemp content (0‐30%) and maleic anhydride polypropylene (MAPP) addition (0‐0.6%). Shear rheology revealed that fibre content mainly influences low shear rate properties like yield stress and zero‐shear‐viscosity while coupling agent addition mainly influences intermediate to high shear rate parameters like relaxation time, power‐law index and Yasuda parameter. On the other hand, elongational rheology results showed a strain softening behaviour of the composites with increasing consistency and decreasing strain at break as fibre concentration increases. MAPP addition is also shown to improve the fibre‐polymer compatibility, but at the same time produces a plasticizing effect having a significant effect on rheological properties. POLYM. COMPOS., 2009. © 2009 Society of Plastics Engineers     

Rheology of cellulosic N‐methylmorpholine oxide monohydrate solutions

Shear dynamic and elongational rheology of concentrated solutions of cellulose in N‐methylmorpholine oxide monohydrate (lyocell) were investigated at different temperatures and for two Hencky strains. Shear thinning and strain thinning behavior is characteristic for dynamic viscosity and effective elongational viscosity of lyocell solutions. Body forces, enthalpy, and entropy of orientation are high at low temperature and high deformation rates, showing a strong orientation effect. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1369–1377, 2000     

Structure and dynamics of polyethylene/clay films

The relationships between structure and rheology of polyethylene/clay hybrid composite blown films were investigated through rheological tests both in shear and elongational flow. Two polymer matrices (low density polyethylene, LDPE and linear low density polyethylene, LLDPE) with different relaxation kinetics were used. Independently from the matrix, morphological analyses (TEM, XRD, and SEM) indicate that the hybrid structures are similarly constituted of delaminated platelets or tactoids having a relevant degree of orientation along the draw direction. This strongly affects the rheological behavior of materials. However, despite the similarities emerged from morphological analyses, both shear (steady shear and oscillatory) and elongation measurements show a negligible effect upon the rheology of LDPE‐based nanohybrids. Conversely, relevant increases of shear viscosity, dynamic moduli and melt strength of LLDPE‐based nanohybrids have been detected. The effects of homopolymer relaxation kinetics have been investigated by means of stress relaxation tests. The results obtained seem to be consistent with the existence of a roughly bimodal population of dynamical species: a matrix component behaving like the homopolymer, and a fraction interacting with the filler, whose rheological behavior is controlled by the particles and their interactions with the polymer. Mechanical properties of hybrid films were also investigated. Differently from what happens in the melt state, the solid‐state properties mainly depend on the filler amount. The relative increases of tensile modulus and melt strength are of the same order of magnitude for both the matrices used, indirectly confirming the similarities in hybrids structures. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 4749–4758, 2006     

An experimental study of threadline dynamics with emphasis on the effect of molecular weight on the elongational viscosity of melt-spun poly(ethylene terephthalate)

A study of a melt-spun threadline has been carried out to determine the effect of molecular weight on the elongational viscosity of the polymer being spun. Polymer chosen for this study was poly(ethylene terephthalate) having different molecular weights. Conventional nonisothermal spinning of the polymers was carried out with cooling by free convection. Threadline surface temperatures were measured by a null-balance technique. Threadline tension at the take-up device was measured, and samples of the threadline were taken to obtain linear density profiles. Nonlinear least-squares fits were applied to the linear density data to obtain equations for velocity and elongation rate. These measurements were then used to determine the threadline elongational viscosity. Least-squares fits were made to a polynomial relating absolute temperature and elongation rate to the elengational viscosity. These results were then used to determine an activation energy of elongational flow which was found to decrease with elongation rate. Elongational viscosity was found to increase with molecular weight.     

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.     

Entry pressure and elastic behavior of a branched polyethylene

Die entry pressures and elastic parameters derived from these have been determined for one low-density polyethylene (LDPE) at four temperatures using three dies having different entry angles. The elongational viscosity shows a somewhat different behavior with respect to temperature than the shear viscosity. Mostly the elastic parameters show a temperature-independent relation to the shear stress but only if the data at the lowest temperature used (130°C) are ignored. The latter data show that the material is much more elastic at this temperature than at higher ones; this is so even when the temperature is increased by only 20°C, after which any further increase gives negligible difference in elasticity. This behavior is probably due to a structural difference which may be a result of increased crosslink sites created by flow-induced crystallization. © 1995 John Wiley & Sons, Inc.     

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.     

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.     

Structure and melt rheology of long‐chain branching polypropylene/clay nanocomposites

Long‐chain branching polypropylene (LCB‐PP)/clay nanocomposites were prepared by melt blending in a twin‐screw extruder. The microstructure and melt rheology of these nanocomposites were investigated using x‐ray diffraction, transmission electron microscopy, oscillatory shear rheology, and melt elongation testing. The results show that, the clay layers are intercalated by polymer molecular chains and exfoliate well in LCB‐PP matrix in the presence of maleic anhydride grafted PP. Rheological characteristics, such as higher storage modulus at low‐frequency and solid‐like plateau in tan‐ω curve, indicate that a compact and stable filler network structure is formed when clay is loaded at 4 phr (parts per hundred parts of) or higher. The response of the nanocomposite under melt extension reveals an initial decrease in the melt strength and elongational viscosity with increasing clay concentration up to 6 phr. Later, the melt strength and elongational viscosity show slight increases with further increasing clay concentration. These results might be caused by a reduction in the molecular weight of the LCB‐PP matrix and by the intercalation of LCB‐PP molecular chains into the clay layers. Increases in the melt strength and elongational viscosity for the nanocomposites with decreasing extrusion temperature are also observed, which is due to flow‐induced crystallization under lower extrusion temperature. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Characterization of electron beam irradiated polypropylene: Influence of irradiation temperature on molecular and rheological properties

The aim of the investigations was to analyze the influence of the temperature during the irradiation process of polypropylene on the molar mass, the formation of long chain branching and the final branching topology. A linear isotactic polypropylene homopolymer was modified by electron beam irradiation at different temperatures, with two irradiation doses to insert long chain branching. The samples were analyzed by size exclusion chromatography coupled with a multiangle laser light scattering detector, by differential scanning calorimetry, and by shear and elongational rheology. The shear and elongational flow behavior is discussed in terms of the influence of molecular parameters and used to analyze the topology of the irradiated samples. With increasing temperature, a slight reduction of the molar mass, an increase of long chain branching and an increase of crystallization temperature were found. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2770–2780, 2006     

Rheology of 1‐butyl‐3‐methylimidazolium chloride cellulose solutions. II. Solution character and preparation

The focus of this article of a three part series is the effects of preparation and composition on the shear rheology of cellulose in the ionic liquid 1‐butyl‐3‐methylimidazolium chloride ([Bmim]Cl). Included are the effects of three different degrees of polymerization, (i.e., average molecular weight), manual versus high shear mixing, a range of cellulose concentrations, and the effects of controlled amounts of lignin and a hemicellulose. The rheology implies that a gel phase develops at higher degrees of polymerization, higher concentration, and at lower temperatures. The first article focused primarily on shear rheology of cellulose in [Bmim]Cl with a high shear preparation technique, one degree of polymerization, a narrow range of cellulose concentrations, and temperature. The third article focuses on elongational rheology of cellulose in [Bmim]Cl. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Prediction of melt viscosity flow curves at various temperatures for some olefin polymers and copolymers

A knowledge of the variation of melt viscosity of thermoplastic polymers with both shear rate and temperature is of considerable importance to plastics engineers as well as to polymer rheologists. The actual measurement of melt viscosity at a large number of temperatures and shear rates is frequently a tedious and time-consuming task. A technique has been developed, based upon the applicability of shear rate-temperature superposition, for predicting the flow curves of a number of olefin polymers and copolymers at various temperatures from experimental data obtained at one temperature for the material in question. The experimental validity for superimposing log shear stress—log shear rate curves at different temperatures along the log shear rate axis has been established for both high and low density polyethylenes, polypropylene, polybutene-1, and poly (ethylene vinyl acetate) copolymers. The temperature dependence of the resultant shift factors has been determined for each system, and the method of utilizing this information to predict viscosities as a function of temperature and shear rate is discussed.