The effect of molecular weight distribution on the elongational properties of linear polymers

The elongational properties of a series of six polypropylene and two polystyrene samples have been studied at constant rate of strain. A Wagner-type constitutive equation has been used to fit the experimental data, and the shape of the damping function has been correlated with the polydispersity index of the samples. As the memory function or relaxation function of linear viscoelasticity may be derived from the molecular-weight distribution using either molecular or phenomenological models, it is therefore possible to calculate the stress growth function of a linear polymer in elongation from its molecular-weight distribution.     

The peculiar rheo-optical behavior of bisphenol A-polycarbonate and polymethylmethacrylate

The rheological and stress-optical behavior of the melts of several grades ob bisphenol-A-polycarbonate (PC) and polymethylmethacrylate (PMMA) is investigated. Pertinent flow birefringence measurements are carried out in a remodelled cone-plate apparatus [1]. The shear stress in the polymer melt is calculated from the dynamic moduli, which are determined separately. It is shown that the linear stress optical rule is obeyed. In this way, the stress-optical coefficient C of the melt can be determined. The low-Mw polycarbonates all behave as Maxwellian fluids. The main stress direction does not deviate significantly from 45°. In the temperature range from 160° to 260°C the stress-optical coefficients of the different grades lie between 3 and 4×10^–9 Pa^–1 and show a weak temperature dependence. The stress-optical coefficient of PMMA is about a factor of 100 lower and shows a peculiar temperature-dependence, changing its sign at 144°C. The results are discussed in terms of the anisotropy of the polarizability of the polymer chain.     

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.     

Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

Rheological determination of peptizing agents in bentonite clays

This paper presents the results of an evaluation of the rheological properties of commercial bentonite suspensions made from peptized and unpeptized clay samples collected over a six year time span. The rheological properties of these suspensions were measured between shear rates of 5.11 to 1022 s^–1 at concentrations of 15, 30, 45, 64.2 and 70 kg/m³. Bingham, power-law and Casson models were then fitted to the shear stress and shear rate values. Parameters derived from these models were then subjected to further analyses. Four rheological methods (termed peptization index tests) were developed to differentiate between peptized and unpeptized bentonite samples.     

Comportement rheologique de sols d'acide polysilicique. II. Etude de la gélification

Résumé L'analyse du comportement rhéologique de sols d'acide polysilicique en solution aqueuse de concentration supérieure à 7 g 1^–1 de silice en fonction du pH entre 6 et 11 et de la température entre 25 et 45 °C a permis de situer la gélification dans un domaine de pH compris entre 8 et 10. Ce processus prend une intensité maximale à 30°C. Le comportement rhéofluidifiant à bas gradients de cisaillement et antithixotrope donne naissance sur les rhéogrammes à un point d'inversion à pH = 9. L'ionisation des groupes silanols à la surface des particules colloïdales permet la réorganisation du milieu après cisaillement. Un état d'ionisation trop élevé est responsable d'un effet electro-répulsif à pH = 10. L'influence de la concentration et de la température sur ces processus est discutée.

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The rheological behavior of polysilicic acid in aqueous solutions at higher concentrations than 7 g 1^–1 of silice is studied for pH between 6 and 11 with temperature varying from 25° to 45°C. This study indicates that gelification takes place between pH 8 and 10. The process of gel formation attains the highest intensity at 30°C. The shear-thinning behavior at low shear rate gives rise to an inversion point at pH = 9 in shear stress—shear rate curves. The state of ionization at the surface of colloïdal silice particles after shear involve shear thickening observed at pH = 9. A high ionization degree causes an electrostatic repulsion at pH = 10. The concentration and temperature effects upon the organization of network are discussed.

     

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.     

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.

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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.

     

Representation of the rheological properties of polymer melts in terms of complex fluidity

In dynamic rheological experiments melt behavior is usually expressed in terms of complex viscosity ^* () or complex modulusG ^* (). In contrast, we attempted to use the complex fluidity ^* () = 1/µ ^* () to represent this behavior. The main interest is to simplify the complex-plane diagram and to simplify the determination of fundamental parameters such as the Newtonian viscosity or the parameter of relaxation-time distribution when a Cole-Cole type distribution can be applied. ^* () complex shear viscosity - () real part of the complex viscosity - () imaginary part of the complex viscosity - G ^* () complex shear modulus - G() storage modulus in shear - G() loss modulus in shear - J ^* () complex shear compliance - J() storage compliance in shear - J() loss compliance in shear - shear strain - rate of strain - angular frequency (rad/s) - shear stress - loss angle - ^* () complex shear fluidity - () real part of the complex fluidity - () imaginary part of the complex fluidity - ₀ zero-viscosity - ₀ average relaxation time - h parameter of relaxation-time distribution     

Effect of secondary zone dimensions on melt fracture manifestations of high density polyethylene

An experimental study was performed on melt fracture phenomena in extrusion of high density polyethylene. The purpose of the work was to study the sensitivity of melt fracture driven roughness to the size of recirculation zones, viz. secondary zones. The experimental apparatus consists of a right angle die and a hypodermic needle used as a capillary. The position of the needle relative to the die was adjusted using a special fixture. The roughness of the extrudate was studied as a function of penetration depth. A developed procedure provides a comparison between profile lengths of extruded strands. The computed mean, median, and mode values for roughness were presented as a function of capillary position. A qualitative analysis was conducted for the force oscillations during extrusion with a separate set of dies, equipped with the fixed capillaries of identical lengths and different depths of penetration. It was observed that the oscillatory pattern is sensitive to the sizes of the secondary zones. This qualitative observation supports the conclusions from the quantitative analysis that the roughness of the extrudate can be controlled through an adjustment of the secondary zone sizes.Partly presented at the 58th Annual Meeting of the Society of Rheology, Tulsa, Oklahoma, October 20–23, 1986     

Evaluating Herschel-Bulkley fluids with the back extrusion (annular pumping) technique

A mathematical model was developed to describe the behavior of Herschel-Bulkley fluids in a back extrusion (annular pumping) device. A technique was also developed to determine the rheological properties (yield stress, flow behavior index, and consistency coefficient) of these fluids. Mathematical terms were expressed in four dimensionless terms, and graphical aids and tables were prepared to facilitate the handling of the expressions.Nomenclature a radius of the plunger, m - dv/dr shear rate, s^–1 - F force applied to the plunger, N - F _b buoyancy force, N - F _cb force corrected for buoyancy, N - F _T recorded force just before the plunger is stopped, N - F _Te recorded force after the plunger is stopped, N - g acceleration due to gravity, m/s² - H(t) momentary height between plunger and container bottom, m - K a/R, dimensionless - L length of annular region, m - L(t) depth of plunger penetration, m - n flow behavior index, dimensionless - p static pressure, Pa - P _L pressure in excess of hydrostatic pressure at the plunger base, Pa - p ₀ pressure at entrance to annulus, Pa - P pressure drop per unit of length, Pa/m - Q total volumetric flow rate through the annulus, m³/s - r radial coordinate, measured from common axis of cylinder forming annulus, m - R radius of outer cylinder of annulus, m - s reciprocal of n, dimensionless - t time, s - T dimensionless shear stress, defined in Eq. (3) - T ₀ dimensionless yield stress, defined in Eq. (4) - T _w dimensionless shear stress at the plunger wall - _p velocity of plunger, m/s - velocity, m/s - mass density of fluid, kg/m³ - Newtonian viscosity, Pa s - P p ₀ –p _L , Pa - consistency coefficient, Pa sⁿ - value of where shear stress is zero - _–, ₊ limits of the plug flow region (Fig. 1) - r/R - shear stress, Pa - _y yield stress, Pa - _w shear stress at the plunger wall, Pa - dimensionless flow rate defined in Eq. (24) - dimensionless velocity defined by Eq. (5) - _–, ₊ dimensionless velocity outside the plug flow region - _max dimensionless maximum velocity in the plug flow region - _p dimensionless velocity at the plunger wall     

The effect of dissolved polymers on the rheological properties of coating colours

Coating colours used for the coating of paper and board consist mainly of a mineral pigment, which is very often clay, a synthetic binder such as a styrenebutadiene latex, dispersion agents and water retention aids. The latter are often water soluble polymers. These polymers have a very strong influence on the rheological properties of the coating colours, both on the strain rate dependence of the apparent viscosity and on the viscoelasticity. The effects of two different grades of carboxymethylcellulose (CMC) and one grade of hydroxyethylcellulose (HEC), on the rheological properties at room temperature of a clay-based coating colour at pH 8, have been investigated. It is concluded that the high values of the dynamic modulus of the colours are due to interactions between the cellulose derivatives and the solid particles, i.e. mainly the clay particles. For HEC this interaction is associated with adsorption of the polymeric molecules on the clay particles. In the case of CMC, the adsorption is strongly retarded by the presence of the dispersant (a polyacrylate salt). It is suggested that the marked elasticity of the CMC-containing colour in addition to a possible polymer adsorption may be due to charge interactions and/or depletion flocculation. The effect of CMC and HEC on the water-retention properties of the colour is also discussed.     

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.

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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.     

Zum Einfluß von Füllstoffen auf das rheologische Verhalten von hochmolekularen Polyethylenschmelzen

Zusammenfassung Zur Sichtbarmachung der Strömungsvorgänge im Bereich der konvergenten Strömung vor einer Kapillaren wurde ein Verfahren entwickelt, das die Eigenschaften bestimmter teilkristalliner Polymere bei der Kristallisation unter Scherung bzw. aus einer vorgescherten Schmelze nutzt. Diese zeigen im erstarrten Zustand sogenannte Fließlinien, die aus in bestimmter Weise auf reihenförmig angeordnete Keime aufgewachsenen Kristallitstrukturen bestehen. Solche linienförmigen Aggregate sind in der Lage, ein Stromlinienbild der Strömung in der Schmelze im erstarrten Polymer wiederzugeben. Für ein LDPE vom Spritzgußtyp konnte die Entwicklung der Einlaufwirbel mit wachsender Schergeschwindigkeit dargestellt werden. Die hochmolekularen Polymertypen erwiesen sich schon bei geringsten Durchsätzen als instabil, die Einlaufwirbel verschwanden dabei vollständig, und die Bilder des erstarrten Polymers legen einen Mechanismus der Instabilitäten nahe, bei dem jeweils unterschiedliche Teilvolumina zeitweise in die Kapillare einströmen, bei Überschreiten einer kritischen Deformation jedoch abreißen und zurückschnellen, während andere Volumenelemente ihren Platz einnehmen. Das Verhalten der Suspensionen unterscheidet sich diesbezüglich nicht von dem der ungefüllten Schmelzen.Ein signifikanter Einfluß der Füllstoffe zeigt sich jedoch beim Einströmen in Kapillaren. Während die ungefüllten Schmelzen nach sehr kurzer Zeit ein laminares Strömungsprofil ausbilden, findet man mit zunehmender Füllung im Bereich stabiler Einströmbedingungen einen sehr hohen Einlaufdruckverlust bei kurzen Kapillaren, nicht jedoch bei Lochdüsen. Dies deutet auf einen Verfestigungsmechanismus bei der Ausbildung des laminaren Strömungsprofils hin, der durch Aggregierungsvorgänge im Bereich der hohen Dehnbeanspruchung in der konvergenten Einlaufströmung bewirkt wird.

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For the visualization of polymer flow in the entry region of a capillary, a method has been developed that uses distinct crystallization phenomena of the partially crystalline polymer itself solidifying from a presheared melt. The solid polymer shows so-called flow lines made up of transcrystalline overgrowth on rows of nuclei capable of showing a picture of the past melt-flow streamlines. The development of circulating flow in the entry region of capillaries could be shown with an injection-molding type LDPE. The higher molecular-weight types appeared to show unstable flow with disappearing circulating flow in the corners even at very low flow rates. The bulk polymer seems to flow into the capillary from certain parts of the reservoir until a critical strain is reached, then snaps back, giving way for the same flow type from another part of the reservoir. The behaviour of the suspensions does not differ in this respect from that of the pure melts.A significant filler influence is, however, shown within the capillary. While unfilled polymer melts reach steady flow conditions only one or two diameters downstream of the capillary entrance, an entry pressure loss increasing with increasing filler content is found in short capillaries (l/d = 5 – 15), but not in no-land dies (l/d 1). This seems to indicate a flow hardening mechanism in the region where the steady laminar flow profile develops and which might result from the very high extensional strain (next to instability) in the converging flow of the capillary entrance.

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

The rheology of a smectic main-chain polymer

The rheology of a smectic main-chain polymer shows that the activation energy is high (275 kJ mol^–1) and that the viscosity is more than two orders of magnitude higher than in the isotropic phase. The recoverable strain in the smectic phase is largely due to the reformation of the smectic layers after cessation of shear.     

Some extended Giesekus-type theorems for non-Newtonian flows

Giesekus discovered in 1963 that the creeping second-order velocity field in the three-dimensional case is sometimes the same as the Newtonian velocity field. The paper reviews some extensions of this idea especially for plane and parallel flows. Some consideration is given to the case where the viscosity and normal stress coefficients vary with shear rate. An application of the results is made to the pressure-hole problem and it is shown that the well-known Higashitani-Pritchard formula can be derived.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Stabilität der ebenen Couette-Strömung bezüglich Störungen in der viskosimetrischen Ebene

Zusammenfassung Die Stabilität der ebenen Scherströmung eines einfachen Fluids wird im Rahmen der Kurzwellenapproximation für Störungen in der viskosimetrischen Ebene untersucht. Für kurze Wellen ist eine Stabilitätsanalyse unabhängig von der speziellen Form der Stoffgleichung möglich. Die vorliegende Analyse stellt einen ersten Schritt in diese Richtung dar und führt zu einem hinreichenden Stabilitätskriterium. Für kurze Wellen sind die Maxwell-FlüssigkeitenA undB bezüglich ebener Störungen stabil.

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The stability of a plane shear flow of simple fluids is investigated for perturbations in the viscometric plane within the framework of the short wave approximation. For short waves it is possible to carry out a stability analysis, which is independent of the type of constitutive equation. The analysis presented is the first step in this direction and leads to a sufficient stability criterion. For short waves Maxwell fluidsA andB are stable for perturbations in the viscometric plane.

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Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p _c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.