Comparison of the rheology of polymer melts in shear,and biaxial and uniaxial extensions

The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.     

A note on the coefficient of viscosity of pure molten 2,4,6-trinitrotoluene (TNT)

The viscosity of pure molten TNT has been investigated over the temperature range 82.0°–95.4°C. The temperature dependence of viscosity was found to be best represented by a relation of the type = A e ^B/T whereA = 0.000541,B = 3570, is the viscosity in mPa s andT is the temperature in Kelvin. Earlier work, which suggests an inverse temperature dependence of the flow activation energy, is shown to include an error in the published equation for the temperature dependence of the viscosity of molten TNT.     

Anisotropic conduction of heat caused by molecular orientation in a flowing polymeric liquid

To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.     

The non-isothermal elastic dumbbell: A model for the thermal conductivity of a polymer solution

In a flowing polymeric liquid, molecular orientation will give rise to anisotropic conduction of heat. In this paper, a theory is presented relating the thermal conductivity tensor to the deformation history of the fluid. The basis of this theory is formed by the Hookean dumbbell. It is shown that the anisotropy of the thermal conductivity is proportional to the polymer contribution to the extra-stress tensor. This stress-thermal law makes it relatively simple to incorporate anisotropic heat conduction into the numerical simulation of a flowing polymeric liquid.     

The steady shear viscosity of filled polymeric liquids described by a linear superposition of two relaxation mechanisms

Filled polymeric liquids often exhibit apparent yielding and shear thinning in steady shear flow. Yielding results from non-hydrodynamic particle—particle interactions, while shear thinning results from the non-Newtonian behavior of the polymer melt. A simple equation, based on the linear superposition of two relaxation mechanisms, is proposed to describe the viscosity of filled polymer melts over a wide range of shear rates and filler volume fraction.The viscosity is written as the sum of two generalized Newtonian liquid models. The resulting equation can describe a wide range of shear-thinning viscosity curves, and a hierarchy of equations is obtained by simplifying the general case. Some of the parameters in the equation can be related to the properties of the unfilled liquid and the solid volume fraction. One adjustable parameter, a yield stress, is necessary to describe the viscosity at low rates where non-hydrodynamic particle—particle interaction dominate. At high shear rates, where particle—particle interactions are dominated by interparticle hydrodynamics, no adjustable parameters are necessary. A single equation describes both the high and low shear rate regimes. Predictions of the equation closely fit published viscosity data of filled polymer melts. n power-law index - n ₁,n ₂ power-law index of first (second) term - shear rate - steady shear viscosity - ₀ zero-shear rate viscosity - _{0, 1}, _{0, 2} zero-shear rate viscosity of first (second) term - time constant - ₁, ₂ time constant of first (second) term - µ _r relative viscosity of filled Newtonian liquid - ₀ yield stress - ø solid volume fraction - ø _m maximum solid volume fraction     

A differential constitutive equation for polymer melts

A modification of the Giesekus constitutive equation is derived by incorporating (approximately, via the Peterlin approximation) the finite extensibility of polymer molecules into dumbbell kinetic theory along with the anisotropic hydrodynamic drag suggested by Giesekus. The constitutive equation that is obtained retains much of the simplicity of Giesekus' constitutive equation, but it involves terms that are cubic in the stress as well as those that are quadratic. It is shown that the constitutive equation quantitatively describes the steady elongational viscosity of the IUPAC polymer melt A (including the strain softening of the melt), but it cannot describe the elongational and shear viscosities simultaneously. It is also shown that the constitutive equation satisfies the Lodge-Meissner relation for shear strains less than unity.     

Comparison of linear viscoelastic constitutive equations for non-uniform polymer melts

Linear-viscoelastic properties of polydisperse and randomly-branched polymer melts were fit with several proposed relaxation functions by non-linear regression. Three polymer systems were investigated, including 1) crosslinked polyethylenes, 2) polydisperse linear poly(dimethylsiloxane)s, and 3) Marlex polyethylenes, which are polydisperse and probably contain long-chain branching. Four relaxation functions were evaluated, including the Rouse, reptation, stretched-exponential, and stretched-exponential-power-law (SEPL) relaxation functions. The SEPL best described each series of polymers, and therefore may be a general relaxation function for non-uniform polymer melts. The flow activation energy for crosslinked polyethylene may be coupled to a breadth-of-relaxation index, indicating that a coupling between a characteristic short relaxation time and longest relaxation time, as suggested by Ngai and Plazek (J. Polym. Sci. Polym. Phys. Ed. 1985, 23:2159–2180), may hold for some non-uniform polymers.     

Effect of processing and particulate fillers on the rheology of a nematic polymer melt

Processing of a nematic HBA/HNA polymer melt increases the capillary diameter dependence of the viscosity and induces structural changes which are evident in oscillatory shear, but cannot be characterized by DSC. The effect of 6-m calcium carbonate particulate fillers is to increase the viscosity uniformly. Low concentrations of sub-micron carbon black particles cause an unexplained viscosity minimum in a large (30-mil) capillary.     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. II. Comparison with experimental results

The results of the theory presented in part I are compared to already published flow birefringence data obtained with dilute up to semi-dilute solutions of polyethylene oxide which have also shown shear thickening effects. The agreement with the theory is quite good so that the reversible formation of associations in flow seems to be a process which has to be taken in account for high molecular weight flexible macromolecules solutions in relatively poor solvents.     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. I. Theory

Assuming the formation of doublets in the flow according to a mass action law, the shear rate and the concentration dependence of the extinction angle, of the birefringence, and of the average coil expansion are calculated for dilute solutions of flexible macromolecules. It is shown that this reversible association process has a strong influence on the measurable parameters in a flow birefringence experiment. c concentration (g/cm³) - h ² mean square end-to-end distance at shear rate - h ₀ ² mean-square end-to-end distance at zero-shear rate - n refractive index of the solution (not very different from the solvent for a very dilute solution) - E mean coil expansion - K ₀,K constant of the mass action law - M molecular weight - R _G gas constant - T absolute temperature - ₁ – ₂ optical anisotropy of the segment - ₀ Deborah number: - Deborah number: - shear rate - ₀, reduced concentration - _s viscosity of the solvent - [] ₀ intrinsic viscosity at zero-shear rate - [] intrinsic viscosity at shear rate - extinction angle - N _a Avodagro's number - _n magnitude of the birefringence     

An automated dynamic viscometer with air bearing and inductive transducers for angular displacement detection

A dynamic viscometer is described, with which the dynamic moduli in the frequency range from 2 × 10^–3 to 10 Hz can be determined for liquids with 10^–3 Pa< |G ^* | <10² Pa. Due to the application of an air bearing and inductive transducers for the detection of the angular displacement of both the drive and the measuring cylinder a sensitive apparatus has been made. Very small strains (₀ 10^–3) can be applied and only a small amount of sample (4 ml) is needed. The operation of the apparatus is fully computer-controlled, thus, long runs at various frequencies and temperatures are possible without operator intervention. The theoretical background, calibration procedure, and operation window are described. A presentation of some measurements on two polyisoprene/polystyrene triblock copolymer solutions concludes the work.     

A network theory for the thermal conductivity of an amorphous polymeric material

A model to relate the thermal conductivity tensor to the deformation of an amorphous polymeric material above the glass transition temperature is presented. The basis of the model is formed by the transient network theory for polymer melts. With this theory it is possible to calculate the average orientation of the macromolecular segments as a function of the history of the deformation. Combined with an expression which relates the thermal conductivity to the orientation of the molecules, this provides us with the information needed to calculate the heat conduction tensor. Despite the fact that the simplest possible network model is chosen, there is good agreement with the sparse, experimental results.     

An experimental study of exit pressures for polymer melts

A slit die apparatus is used to measure exit pressures for five different polymer melts. Viscosity data obtained from the same apparatus agree well with values obtained from a cone-and-plate rheometer or a capillary rheometer. Except for a PVC sample where thermal degradation was found to occur, the exit pressures obtained by linear extrapolation of the measured pressure profiles are all positive, and increase with increasing shear stress. The values of the first normal stress difference calculated according to the exit pressure theory are of the right order of magnitude and in some cases correlate satisfactorily with values measured in a cone-and-plate rheometer. However, the high sensitivity of the exit pressure values to the method of extrapolation and the wild scatter of exit pressure data for some materials make it difficult to use the exit pressure method as a routine procedure for accurate determination of the first normal stress difference.     

Rheological behavior of water-creosote and creosote-water emulsions

The effect of temperature on the steady-shear viscosity of two base emulsions (water-in-creosote (w/o) and creosote-in-water (o/w)) and a pigment emulsified creosote (PEC) was investigated. The PEC is a water-in-creosote emulsion which contains also a solid, micronised pigment, and is used industrially as a wood preservative. All three emulsions exhibited shear thinning characteristics at different temperatures. The viscosity-shear rate relationships follow a modified Quemada model. A temperature-superposition method using the reduced variables / and t _c was applied to yield a master plot for each of these emulsions at different temperatures. The effect of creosote concentration on the viscosity of four other o/w emulsions at different temperatures was also studied. The same reduced variables were able to produce a temperature-concentration superposition plot for all of the o/w emulsion results.The effective (average) radius of the globules (dispersed phase) was found to increase with increasing temperature for the base w/o and the PEC emulsion. The collision theory could be used to explain the increase in the droplet size. However, while little overall variation in globule size was observed for the o/w emulsions, microscopic observation indicated an increase in the proportion of large diameter droplets with temperature at the highest creosote concentration (60%). A creaming effect (phase concentration) was observed with these emulsions at higher temperatures, precluding an accurate estimate of droplet size based on collision theory.Seconded from Koppers Coal Tar Products, Newcastle, N.S.W., Australia.     

Flow behaviour of molten 2,4,6-trinitrotoluene (TNT) between concentric cylinders

The flow behaviour of pure and commercial molten TNT when subjected to very high rates of shear in a rotational viscometer over the temperature range 82.0 to 95.4°C is presented. All data obtained suggest that the behaviour of molten TNT is Newtonian, contrary to the conclusions of some published work, and the temperature dependence of the viscosity of pure TNT is adequately described by an Arrhenius-type relationship of the form = A e ^B/T whereA = 0.000 541,B = 3 570 andT is the Kelvin temperature. A similar relationship is obtained for commercial TNT. Under some instrumental conditions discontinuities are seen in the shear stress—shear rate flow curves. An analysis of these discontinuities shows them to be caused by the transition from laminar to turbulent flow. Possible implications for processibility and initiation of explosives are discussed.     

Comportement rhéologique de sols d'acide polysilicique.

Résumé Le comportement rhéologique de sols d'acide silicique a été examiné au cours du temps à des pH compris entre 6 et 8 à la concentration de 10 g 1^–1 de silice, et à pH = 8 à des concentrations variant entre 0,5 et 10 g 1^–1. Les courbes d'écoulement révélent un comportement rhéologique complexe. L'analyse des rhéogrammes en fonction du temps, du pH et de la concentration contribue à la connaissance de l'état structural du polymère au cours de la formation du gel. Il ressort que le comportement initialement rhéoépaississant aux faibles concentrations correspondant à l'état d'une solution colloïdale, laisse place à un écoulement rhéofluidifiant dans les conditions favorables á la polymérisation de l'acide silicique. La transition sol-gel est marquée par un breakpoint; en prolongeant les mesures on observe un comportement plastique dû à l'apparition d'agrégats sous l'effet du cisaillement. Tous les processus rhéologiques se trouvent exacerbées à pH = 8.

---

The rheological behaviour of silicic acid in aqueous solutions was studied over a period of time for pH values between 6 and 8 at the concentration 10 g 1^–1, and at pH = 8 for different concentrations varying from 0.5 to 10 g 1^–1. The shear stress-shear rate curves indicate a very complex character of rheological behaviour. Its analysis with respect to the influence of time, pH and concentration contributes to the knowledge of the structure of the polymer during the process of gel formation. It is shown that the inital shear-thickening behaviour of the colloïdal sol at low concentrations is followed by a shear-thinning behaviour under conditions of polymerization of the silicic acid. The sol-gel transition is marked by a breakpoint. When measurements pass beyond this point, plastic flow behaviour is observed because of the shear induced formation of amorphous silicic aggregates. All rheological processes of silicic acid sols are intensified at pH = 8.

     

Apparent thickening behavior of dilute polystyrene solutions in extensional flows

An experimental investigation was undertaken to study the apparent thickening behavior of dilute polystyrene solutions in extensional flow. Among the parameters investigated were molecular weight, molecular weight distribution, concentration, thermodynamic solvent quality, and solvent viscosity. Apparent relative viscosity was measured as a function of wall shear rate for solutions flowing from a reservoir through a 0.1 mm I.D. tube. As increased, slight shear thinning behavior was observed up until a critical wall shear rate was exceeded, whereupon either a large increase in or small-scale thickening was observed depending on the particular solution under study. As molecular weight or concentration increased, decreased and, the jump in above , increased. increased as thermodynamic solvent quality improved. These results have been interpreted in terms of the polymer chains undergoing a coil-stretch transition at . The observation of a drop-off in at high (above ) was shown to be associated with inertial effects and not with chain fracture due to high extensional rates.     

Untersuchungen zum Fließverhalten verschieden konzentrierter Polyisobutenlösungen unter hoher Scherbeanspruchung.

Zusammenfassung Das Schubspannungs- und Verfestigungsverhalten verschieden konzentrierter hochmolekularer Polyisobutenlösungen wird mit Hilfe eines neu konstruierten Hochdruckkapillarviskosimeters bis zu sehr hohen Schergeschwindigkeiten untersucht. Hierbei wird gleichzeitig der Einlaufdruckverlust nach Bagley durch Messungen an Kapillaren mit unterschiedlichenL/R-Verhältnissen ermittelt und, um Informationen über das Einströmverhalten der Lösungen zu erhalten, die Einlaufströmung in die Kapillare sichtbar gemacht. Im Bereich niedriger Schergeschwindigkeiten werden die Lösungen zusätzlich mit verschiedenen Rotationsviskosimetern charakterisiert.Die anhand der durchgeführten Untersuchungen erhaltenen Fließkurven lassen sich für Lösungen mit einem Polymergehalt ab 0,5% PIB-B200 in drei Bereiche einteilen, die mit Hilfe von Strömungssichtbarmachungsuntersuchungen verschiedenen Strömungsphänomenen zugeordnet werden können. Dabei kommt es u. a. zu Verfestigungserscheinungen, die sich in einem sprunghaften Ansteigen des Druckverlustes bemerkbar machen. Durch Messungen an Kapillaren mit einem kegelförmigen Einlauf kann gezeigt werden, daß diese Verfestigungserscheinungen und der damit verbundene Druckanstieg nicht nur auf das Auftreten von Sekundärströmungen im Einlaufbereich der Kapillaren zurückgeführt werden kann, sondern daß hierfür andere Effekte wie etwa die Bildung von Assoziaten aus Makromolekülen verantwortlich gemacht werden können. Auch die starke Viskositätszunahme der Lösungen im Verfestigungsbereich und die Beobachtung der Ausbildung heller Streulichtfelder sprechen für eine Bildung von Polymerassoziaten vor der Kapillare.Des weiteren wird bei den Untersuchungen zur Bagley-Korrektur festgestellt, daß zur korrekten Ermittlung des Einlaufdruckverlustes bei höher konzentrierten Polyisobutenlösungen Kapillaren mit einemL/R-Verhältnis von mindestens 1000 verwendet werden müssen. Es zeigt sich nämlich im Bagley-plot dieser Lösungen, daß die Linien konstanter Schergeschwindigkeit bei kleinerenL/R-Verhältnissen eine auffallende Krümmung im Sinne eines mit zunehmendemL/R-Verhältnis abnehmenden Druckgradienten besitzen, der erst oberhalb eines bestimmtenL/R-Verhältnisses konstant wird.

---

A new design high-pressure capillary-viscometer is used to study the shear behavior of high-molecular polyisobutene solutions up to very high shear rates. The entry pressure loss from the Bagley-plot is estimated by the measurement in capillaries of different length-to-radius (L/R) ratios. Simultaneously, flow visualization of the entry flow is carried out. At low shear rates the flow behavior of the solutions is characterized by different rotational viscometers.The obtained flow curves for the solutions with polymer concentrations being above 0.5% PIB-B200 can be divided into three regions which can be related to different flow phenomena by means of flow visualization. A sudden increase in pressure loss can be related to a shear thickening behavior. Measurements in capillaries with a conical entry show that this thickening behavior is not only due to secondary flows in the entry region of the capillary, but also due to other effects like the association of macromolecules. The assumption of the formation of molecular associates is also supported by the large increase in the viscosity of the solutions in the thickening region and the observed formation of luminous scattered light areas.Furthermore, the investigations on the Bagley-correction show that for higher concentrated polyisobutene solutions capillaries withL/R ratios of at least 1 000 have to be used for a correct determination of the entry pressure loss. The Bagley-plots of these solutions show that lines of constant shear rate are remarkably curved at lowerL/R ratios. The gradient of the pressure loss decreases with increasingL/R ratio and approaches a constant value at a certainL/R ratio.

Erster Teil einer vom Fachbereich Chemietechnik der Universität Dortmund genehmigten Dissertation.     

Analysis of Taylor vortex flow by means of laser light scattering

Rheological measurements and light-scattering experiments were performed on dilute solutions of high molecular polystyrene. We are able to describe the orientation behavior of chain molecules under shear flow by means of light-scattering. Beyond that these investigations of light-scattering of flowing polymer solutions are an useful and suitable tool for detection and characterization of Taylor vortex formation. We can estimate the appearance of these hydrodynamic instabilities, which overlay the laminar main flow and we can observe a typical influence of the solvent power on it.Presented in part at the meeting of the Deutsche Rheologische Gesellschaft, Berlin, 13–15 May, 1991.