Rheology of polymers containing carbon black

In order to elucidate the flow behavior of electrophotographic toner systems, shear stress was measured as a function of shear rate in a cone and plate rheometer for polymer melts containing carbon blacks of surface area 24 and 625 m²/g at several concentrations and temperatures. Polymers included high and low molecular weight polystyrene and poly(butyl methacrylate). The addition of carbon black to the polymers caused a large increase in viscosity, especially at low shear rates and shear stresses. As the concentration of carbon black was increased, the viscosity at low shear rates became unbounded below a value of the shear stress designated the yield stress. The absolute magnitude of the yield stress depended primarily on the concentration and surface area of the carbon black and was independent of the polymer and temperature. Apparently, carbon black forms an independent network within the polymer at low shear rates which precludes flow. In some cases, the viscosity of polymers filled with carbon black was lower than that of the pure polymer. This effect was favored for polystyrene compared to poly(butyl methacrylate) and was facilitated by increasing the molecular weight of polystyrene, reducing the surface area and concentration of carbon black, and by increasing the temperature and shear rate.     

Temperature shifting of convergent flow measured effective elongational viscosity

The effective elongational viscosity data on a series of polyolefins as a function of temperature are shifted to a reference temperature using the approach for shifting shearing viscosity data. The temperature shift factors are obtained from complex and capillary shear rheology, and these are the same factors used for shifting the shear rheology. A Carreau rheological model was used to determine the zero shear rate viscosity at different temperatures, and an Arrhenius expression was used to determine the temperature shift factors. The same shift factors are shown to produce separate master curves for shear and elongational rheology at reference temperatures. The commercial grades of polyolefins studied include an extrusion grade of polypropylene and metallocene and conventionally catalyzed low and high density polyethylene materials. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1387–1396, 2003     

魔芋溶胶对苯丙乳液流变性能的影响

研究了不同组成的魔芋溶胶(KGM sol)/苯丙复合乳液的粘度与剪切转速、剪切应力与剪切速率、剪切弹性模量、剪切粘性模量与角频率、温度之间的关系,并对复合乳液的抗电解质性能进行了测试。结果表明,KGM溶胶/苯丙复合乳液是剪切变稀流体,剪切应力随剪切速率的增大而增大,当KGM溶胶含量>4%时,复合乳液体系由牛顿型流体变为非牛顿型流体,且变化满足Herschel-Bukley方程;KGM溶胶含量增大,复合乳液的粘度、剪切弹性模量、剪切粘性模量明显增大,尤其是温度扫描曲线;复合乳液离子稳定性好。     

Flow properties of plasticized PVC: Reduction to composition and interaction variables

Existing theory of polymer flow has been applied to a definition of shift factors which reduce the widely different melt viscosity/shear rate diagrams of plasticized PVC compounds to well-defined master curves. The master curves are temperature dependent and also define the flow properties of the unplasticized polymer on which a group of plasticized compounds is based. For given plasticizers, the value of the shift factor was found to depend on melt temperature and plasticizer volume fraction. Explicit relationships have been generated for three plasticizer systems; for these, melt viscosity/shear rate data can be precalculated over several decades of shear, and in the temperature range of 150–200°C. Absolute values of the shift factors depend on the type of plasticizer, and a correlation with polymer/diluent interaction parameters has been attempted. Initial results, valid only at high plasticizer volumes and near the reduced melt temperature of a polymer/plasticizer mixture, support the existence of such a correlation.     

Rheological characterization of filled polyamide 11 and polyamide 12 solutions in polyols

A thorough understanding of the rheological properties of real-world, formulated polymer melts and solutions is important to fabricate articles via typical melt processing techniques. Polyamides have been studied extensively in the area of water purification applications. In this work, the viscosity of these homogeneous polyamide 11 and polyamide 12 solutions in specific polyols was measured in the single phase region as a function of shear rate and temperature via capillary rheometry. In addition, the viscosity of the same polyamide solutions containing various levels of dispersed, nanoscale calcium carbonate particles was characterized in order to understand the rheology of the filled systems. Viscosity-reduced shear rate master curves were constructed by applying the principle of time–temperature superposition, and the activation energies were measured for the polyamide-polyol solutions. The observed increase in viscosity caused by the addition of nanofiller could not be explained by simply applying a vertical shift to the master curve, and a density exponent was required to account for the stiffening mechanism. Also, the dependence of the relative viscosity on the filler loading was shown to be consistent with the hypothesis that the filler particles were organized in the form of small fractal aggregates. The filled polyamide 11 systems exhibited higher relative viscosities than the filled polyamide 12 systems, indicating a higher level of particle aggregation and larger mean cluster size for the filled polyamide 11 systems. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 48244.     

Effects of stearic acid coated talc,CaCO3, and mixed talc/CaCO3 particles on the rheological properties of polypropylene compounds

The effect of the stearic acid coated fillers and their geometry on the shear/dynamic viscosity and complex viscosity has been investigated using polypropylene (PP) compounds filled with stearic acid uncoated and coated talc, calcite, and mixed talc/calcite particles. The viscosity was measured over a wide range of shear rates (10^?8 to 10³) using a capillary, cone‐plate and sandwich rheometer. Overall, the rheological properties of the compounds exhibited different behavior upon different filler systems, stearic acid involvement, shear stress or strain, and frequencies due to stearic acid involvement. This implies that the stearic acid lowers the interfacial force between the filler surface and the resin matrix, followed by a favorable processing. In addition, at very low shear stresses, the viscosity of talc(un) compounds was higher than calcite(un) ones; at very high shear stresses, on the other hand, talc compounds became lower than calcite(un) compounds. This is interpreted as due to the different geometry between talc and calcite. The yield value as a function of shear stress was observed for all filler systems and exhibited lower than that obtained from the extrapolation. Furthermore, the Cox–Merz relation between the complex and shear viscosity for both the stearic acid uncoated and coated compounds is found not valid. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2105–2113, 2004     

The influence of non-Newtonian flow on effective viscosity and channel efficiency in screw pumps

A method is given for selecting the “effective viscosity” for isothermal flow of non-Newtonian liquids in screw pumps or melt extruders. Effective viscosity is the Newtonian viscosity that would give the same screw-pump performance with non-Newtonian liquids at the same flow rate and speed. When effective viscosity is known, it can be inserted in performance equations for simple Newtonian flow. The analysis is restricted to shallow screw-pump channels with large aspect ratios and to shear stress/shear rate curves with modest curvatures when shown in a double logarithmic plot. The shear stress/shear rate curve is replaced by a power-law tangent to that curve in the domain of prevailing shear rates, but the analysis could be extended to more complex behavior. Curves are also included for calculating the efficiency of the screw-pump channel, which can be used to estimate the energy dissipated in screw-pumps. It is shown that efficiency decreases with decreasing power-law exponent.     

A rheological study of the low molecular weight butyl polymer

A rheological study has been performed to characterize the low molecular weight butyl polymers using a couette coni-cylindrical viscometer. The bulk viscosity was determined as a function of temperature, weight-average molecular weight, viscosity-average molecular weight, and shear rate. The temperature dependence of the viscosity, while adequately represented by the Williams, Landel, and Ferry equation, is best described by an Arrhenius equation for the temperature range investigated. The viscosity is shown to vary with the 3.5th power of the weight-average molecular weight above a critical molecular weight and to the 1st power below this molecular weight. Although the ratio of the weight-average molecular weight to the number-average molecular weight usually affects the flow properties of polymers, this was not true for the polymers investigated. The bulk viscosity was found to be independent of the molecular weight distribution for the temperature and shear rate range studied. It has been shown that a definite relationship exists between the bulk viscosity and the viscosity-average molecular weight as determined by dilute solution viscosity. A mathematical model has been developed to relate these two parameters as a function of temperature and shear rate.     

New generalized Newtonian fluid models for quantitative description of complex viscous behavior in shear flows

Two semiempirical models of generalized Newtonian fluid are discussed. Special attention was focused on the stress dependent model based on the free volume theory. However, the strain‐rate dependent model in form of a modified viscosity function resulting from Oldroyd equation is also presented. Both models (along with specific cases) reflecting pseudoplastic or dilatant behavior of liquids in shear flows are generalized to multimode models (defined as products of two or more basic models), which are able to describe quantitatively the behavior of more complex systems, for example, systems with pseudoplastic and dilatant properties in different shear stress (shear rate) ranges. A number of practical examples for viscosity curves of non‐Newtonian fluids described by these models are given. The questions of inverse models and model efficiency are also discussed. POLYM. ENG. SCI., 58:1446–1455, 2018. © 2017 Society of Plastics Engineers     

Viscosity of concentrated clay suspensions: effect of solids volume fraction,shear stress,and deflocculant content

Abstract

Using the same clay, 28 concentrated clay suspensions were prepared with varied solids volume fractions and deflocculant contents. T he apparent viscosity of each suspension was determined at a range of shear stresses to produce flow curves. A functional relationship was derived based on the K rieger equation, describing the combined effect of solids volume fraction, deflocculant content, and shear stress on suspension viscosity when suspension behaviour is shear thinning. Intrinsic viscosity, a K rieger equation parameter, may be considered to be independent of deflocculant content. In contrast, intrinsic viscosity decreases significantly as shear stress rises, tending asymptotically to a constant value at high shear. Maximum solids volume fraction, the other K rieger equation parameter, rises as shear stress and suspension deflocculant content increase.     

Rheology of rubber-modified polymer melts

The influence of rubber particles on rheological properties of styrene-acrylonitrile, and poly(vinyl chloride) was investigated. The temperature dependence of the viscosity functions was found to be independent of the kind of rubber and its concentration. The extrudate swell becomes smaller with increasing particle concentration, the entrance pressure loss remaining nearly unaffected. The strong viscosity increase at small shear rates is more pronounced the higher the concentration and the smaller the size of the particles. It can be interpreted by the assumption of a yield stress caused by the fillers. This yield stress is independent of temperature within the accuracy of the measurements and comes out distinctly higher in elongation than in shear. An analytical expression of the dependence of the viscosity on particle concentration cannot be given. It is demonstrated how sensitively an agglomeration of particles is reflected in elongation and recoverable strain. Based on the morphology shown by electron micrographs of acrylonitrile-butadiene-styrene and acrylonitrile-styreneacrylic ester copolymers, two different models for the occurrence of a yield stress are discussed qualitatively.     

氯化聚醚/氯醇橡胶多相共混体系熔体流变行为的研究

本文研究了氯化聚醚/氯醇橡胶偶联共混物和非偶联共混物的流变性能,证实了不同配比的共混物熔体具有假塑性流体的流动行为,并在流变曲线的温度迭加和组成迭加基础上,建立了流变模型.     

Anomalous behavior of unplasticized PVC compounds in capillary flow

Capillary rheometry was performed over a temperature range of 170°–200°C and a shear-rate range of 3–3000 sec^?1 on an unplasticized poly(vinyl chloride) compound. The data were corrected for the effect of pressure on viscosity, for pressure loss in the barrel and at the capillary entrance, and for the non-Newtonian velocity profile. The pressure coefficient of viscosity was found to be in the same order of magnitude as those previously found with linear polyethylene and butadieneacrylonitrile copolymers. The pressure–shear-rate superposition of the flow curves is valid at least approximately, although the temperature–shear-rate superposition is inapplicable. The shape of flow curves at 180°, 190°, and 200°C are concave downward when they are expressed as log-shear-stress-log-shear-rate. Similar plots at 170° and 175°C, however, are very different; shear stress is independent of shear rate at low shear rates, increases somewhat and becomes independent of shear rate again at high shear rates. There is no detectable temperature dependence of flow behavior at 170° and 175°C. Irregularly shaped extrudates were obtained at higher shear rates. At constant shear rate the irregularity increased with the length of the capillary. The effect of thermal-mechanical history on the particulate and crystalline structure is discussed with possible influence on the reproducibility of the rheological data.     

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.     

Nonlinear viscoelastic behavior of butadiene–acrylonitrile copolymers filled with carbon black

Various viscoelastic measurements including dynamic mechanical measurements in tension at 110 Hz from ?60° to 160°C, tensile stress relaxation measurements with 100% elongation at 25°, 54°, and 98°C, capillary flow measurements at 70°, 100°, and 125°C, and high-speed tensile stress–strain measurements carried to break at 25°, 56°, and 98°C were performed on four samples of carbon black-filled butadiene–acrylonitrile copolymers. All the data were treated with the same equation for time–temperature conversion. The capillary viscosity–shear rate curves were significantly lower than the complex viscosity–angular frequency curves, indicating “strain softening” with extrusion. The viscosity was estimated from the stress–strain relationship at the yield point. The viscosity as a function of the strain rate is significantly higher than the complex viscosity as a function of angular frequency, indicating “strain hardening” with extension. The strain softening and strain hardening are attributable to the structural changes upon deformation of the carbon black-filled elastomers. With the unfilled elastomers, neither strain softening nor strain hardening were observed in similar measurements.     

Observation of melt fracture of polypropylene resins in capillary flow

Melt fracture, shear viscosity, extensional viscosity, and die swell of two polypropylene resins were studied using a capillary rheometer. A modified Bagley plot with consideration of pressure effects on melt viscosity and end effect was used. From the true wall shear stress the shear viscosity was calculated. Extensional viscosity was calculated from the end effect. Both shear and extensional viscosities of different molecular weights and temperatures correlated well under the time-temperature Williams-Landel-Ferry (WLF) superposition. Die swell increased when shear stress increased, and was higher for shorter dies at a given shear rate. When shear rates increased the extrudate staged from smooth to gross melt fracture with regular patterns (spurt), and then turned into irregular shapes. In the regular stage the wavelength of extrudates was measured, and corresponding frequency was calculated. The frequency increased when molecular weight decreased and when melt temperature increased. The shift factor based on shear viscosity also brought frequency data of different molecular weights and temperatures into master curves. The frequency decreased slightly when die lengths increased from L/R=10 to 60. A small maximum was observed when shear rates increased.     

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     

EFFECT OF TEMPERATURE ON THE RHEOLOGY OF POLYMERIC LIQUID CRYSTALS

As part of a more general effort to elucidate the flow of polymeric liquid crystals, the effect of temperature on the rheological properties has been investigated. A lyotropic sample of poly(γ-benzyl-L-glutamate) in m-cresol has been used throughout the measurements. Under steady state shear flow the viscosity and the first normal stress difference have been measured. Oscillatory flow after cessation of steady shear flow reveals a time effect which led to the determination of initial and final moduli; both have been measured as a function of temperature. Finally some transients have been considered as well.

The limiting zero frequency value of the dynamic viscosity and the zero shear value of the steady state viscosity have different activation energies. The dynamic moduli can be scaled for temperature effects by means of the zero frequency viscosity. Because of the difference in activation energies this scaling does not hold for the steady state properties. An alternative scaling procedure is suggested. The time scale of the transients is nearly independent of temperature. None of the available theoretical models describes the measured phenomena.     

Time-dependent properties of versamid cured epoxies

Versamid cured-epoxy specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine the yield stress and strain, and tangent, secant, and relaxation moduli. A torsion pendulum was used to measure the dynamic properties as a function of temperature and frequency. The time-temperature superposition principle was used to reduce this data to master curves. It was concluded that the time-temperature shift factors for secant moduli up to the yield point, for stress relaxation and for dynamic moduli were identical and were independent of the mode of loading. It was also shown that the presence of fillers or reinforcing agents likewise had no effect on the shift factors.     

The Influence of a Titanate Coupling Agent on the Rheological Properties of PP/CaCO3

The present work deals with the study of the rheological properties of polypropylene/calcium carbonate composites treated with a titanate coupling agent. The study focused on the examination of the flow behavior of the material under different conditions of shear rate and temperature. A more pronounced pseudoplastic behavior was observed for the filled material than for neat polypropylene. It was also found that the power law index increases slightly with increasing temperature and increased concentration of the coupling agent; but decreases with the amount of filler and shear rate. On the other hand, the viscosity increased with increased amount of the filler, especially at low shear rates, but showed a substantial reduction with increased temperature and concentration of the coupling agent. The activation energy, too, was found to decrease with shear rate and concentration of the titanate agent, confirming, hence, the lubricating action of this coupling agent. Finally, through the shift factor that was calculated for both the viscosity and the shear stress functions, the flow master curves superposed for all the materials that were studied.