Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Results are reported for the dynamic moduli,G andG, measured mechanically, and the dynamic third normal stress difference, measured optically, of a series bidisperse linear polymer melts under oscillatory shear. Nearly monodisperse hydrogenated polyisoprenes of molecular weights 53000 and 370000 were used to prepare blends with a volume fraction of long polymer, _L, of 0.10, 0.20, 0.30, 0.50, and 0.75. The results demonstrate the applicability of birefringence measurements to solve the longstanding problem of measuring the third normal stress difference in oscillatory flow. The relationship between the third normal stress difference and the shear stress observed for these entangled polymer melts is in agreement with a widely predicted constitutive relationship: the relationship between the first normal stress difference and the shear stress is that of a simple fluid, and the second normal stress difference is proportional to the first. These results demonstrate the potential use of 1,3-birefringence to measure the third normal stress difference in oscillatory flow. Further, the general constitutive equation supported by the present results may be used to determine the dynamic moduli from the measured third normal stress difference in small amplitude oscillatory shear. Directions for future research, including the use of birefringence measurements to determineN ₂/N ₁ in oscillatory shear, are described.     

On the role of stress-induced migration on time-dependent terminal velocities of falling spheres

There is experimental evidence to suggest that even under steady-state conditions the velocity of solid spheres or bubbles moving through viscoelastic fluids can become time dependent. One of the possible explanations offered for interpreting this phenomenon has been the generation of a polymer depleted layer in the line of passage of the particles, which disappears due to the counterbalancing effect of molecular diffusion in the long range. We have done some careful experiments and measured these concentrations to show that no such depletion layers are formed. Alternative explanations of the phenomenon have been examined and the importance of the possible effects of microstructures generated through temporary associations has been emphasised.     

Measurement of the shear viscosity using a newly developed GRLDA-viscometer

A two-point laser-Doppler anemometer is used to determine velocity gradients. Measuring additionally the pressure drop in channel flow allows one to use this instrument as a viscometer. This is demonstrated by measuring two polymer solutions as well as water. Besides the velocity gradient, the system also furnishes the velocity as well as velocity fluctuations. For surfactant solutions the sudden increase in these fluctuations go hand-in-hand with the sudden shear thickening reported. This behavior thus seems to be caused by a change in type of flow field (structural turbulence) rather than a change in the rheology of the surfactant solutions.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Elastic recovery and polymer-polymer interactions

i) Elastic recovery in polymeric liquids is a cooperative phenomenon in the sense that individual polymer molecules undergoing retraction must interact with one another in order to generate recovery. Stress generated by polymer molecules under an externally imposed flow field may or may not be a cooperative phenomenon. We suggest that the ability to describe the large elastic recovery exhibited by many polymeric liquids furnishes a crucial test of the validity of methods used to model the interaction of a given polymer molecule with its neighbors. Temporary-junction network models appear to be capable of explaining observed recoveries. Elastic recovery cannot be explained by single-molecule-in-a-mean-field theories which involve no calculation of the effect of the single molecule on the mean field. ii) A Gaussian network theory equation for the change of volume with elongation for a cross-linked elastomer is generalized in order to allow the bulk compliance to depend on elongation. iii) It is proved that two classes of flow history, namely shear-free and shear, are constitutively independent in the sense that, for a given viscoelastic liquid of unknown constitutive equation, the behavior in one class cannot be predicted from rheological measurements (however extensive) made solely in the other class.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

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.     

Nonlinear viscoelasticity of polymer melts in different types of flow

The nonlinear viscoelastic properties of a fairly large class of polymeric fluids can be described with the factorable single integral constitutive equation. For this class of fluids, a connection between the rheological behaviour in different flow geometries can be defined if the strain tensor (or the damping function) is expressed as a function of the invariants of a tensor which describes the macroscopic strain, such as the Finger tensor. A number of these expressions, proposed in the literature, are tested on the basis of the measuring data for a low-density polyethylene melt. In the factorable BKZ constitutive equation the strain-energy function must be expressed as a function of the invariants of the Finger tensor. The paper demonstrates that the strain-energy function can be calculated from the simple shear and simple elongation strain measures, if it is assumed to be of the shape proposed by Valanis and Landel. The measuring data for the LDPE melt indicate that the Valanis-Landel hypothesis concerning the shape of the strainenergy function is probably not valid for polymer melts.     

Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Attempts to find a molecular theory for which the high-frequency dynamic viscosity is less than the solvent viscosity

It has been found that for some dilute polymer solutions the dynamic viscosity at very high frequencies is less than the zero-shear-rate solvent viscosity. Such an effect cannot be explained by the usual kinetic theories using bead-spring-rod models. Here we examine several modifications of the kinetic theories that might be expected to explain the experimental facts.This paper is dedicated to Prof. Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (M _w 1.8 10⁶). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Matheson's theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.     

A study of swelling and collapse in polyelectrolyte gels

Swelling and collapse of a polyelectrolyte are shown to be the result of a delicate balance of three thermodynamic forces, viz. osmotic pressure, polymer elasticity, and van der Waals attraction. The behaviour of the polyelectrolyte gel is studied under isotropic pressure and under uniaxial and biaxial loading.     

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.     

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.     

Statistical mechanics of temporary polymer networks

The statistical theory of temporary polymer networks developed in parts I and II of this work is closed by a discussion on dynamical effects, including comparison with experiments. After a short review of the theory developed in parts I and II we discuss the situation in which a prescribed velocity gradient is imposed on the physical system formed by the temporary network and the solvent. The dynamical equation for the 2nd moments (derived from a generalized bead-spring model) contains the configuration-dependent transition probability, which depends on the second moments in a complex way. An approximate solution of these equations is obtained from a computer program. It shows the experimentally observed behavior, in particular the stress overshoot maximum after a sudden start of the flow.The derivation of the above equations contains simplifying assumptions which, however, leave the essential physics intact. The most important assumptions concern the relaxation time approach and the decay and formation processes. These were supposed to be dilute enough to break up the many-junction processes into one-junction processes. Both assumptions are analogous to frequently used assumptions in Boltzmann's kinetic theory.     

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.     

Prediction of stress in a linear viscoelastic solid strained while cooling

A simplethermoelastic method is proposed, and justified, for predicting stresses arising during cooling of a linearviscoelastic solid. It is equivalent to representing the material by an array of spring-switch thermoelastic elements. The final stress resulting from an increment of strain is calculated using isochronal modulus data applying to the temperature at which the strain was applied, modified to accommodate temperature dependence of the limiting moduli. The method is exact for a material whose relaxation times and limiting moduli scale uniformly with change in temperature, with time-temperature shift factora _T obeying the Arrhenius equation, cooled such that reciprocal absolute temperature is linear in time. For other cooling sequences it is useful as an approximation. In particular, it assists the computational prediction of stresses arising during cooling in polymer processes.     

Wall effects in the flow of flexible polymer solutions through small pores

Effective viscosities of dilute and semidilute flexible solutions flowing through small cylindrical pores were determined in the Newtonian regime for various pore diameters. The low viscosities relative to the bulk were associated with a depletion phenomenon due to a steric exclusion of macromolecules from the pore wall. Using a two-fluid flow model, the depletion layer thickness was determined and discussed as a function of polymer concentration, ionic strength, and molecular weight. This thickness, which was constant and close to the macromolecule gyration radius in dilute regime, was found to decrease rapidly with polymer concentration in the semidilute regime.     

Formation des gels d'agar et seuil d'écoulement

Résumé Les seuils de plasticité de gels d'agar a différentes concentrations ont été déterminés par différentes méthodes et comparé entre eux. Le seuil de contrainte qui apparaît au cours du refroidissement de la solution indique le début de la formation du réseau gélifié. II définit une température d'apparition du seuil de plasticite. La determination de cette temp6rature critique montre que la formation du gel est soumis aux conditions de refroidissement de la solution: le processus de gelification est accéléré par un refroidissement rapide des solutions et débute à une température plus basse. La formation du gel peut être suivie dans des conditions plus proches des réalités industrielles de fabrication de ces milieux.

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The yield stress of agar gels has been measured by different methods and the results compared. The yield stress which occurs during cooling of polymer solutions indicates the beginning of crystalline network formation. This point defines the temperature of plastic flow; its determination shows that the gel formation is subordinated to cooling conditions of the solution: the process of gelification is retarded by very fast cooling, and is induced at a lower temperature than occurs with slow cooling. We follow the formation of gels in conditions similar to those used in manufacturing processes.

     

Does N 1 or N 2 control the onset of edge fracture?

The edge fracture instability which occurs at the air/liquid interface in a cone-and-plate rheometer is studied for six elastic polymer solutions. Theoretical models for the onset of edge fracture are evaluated in light of the experimental data. The data are well-described by the Tanner-Keentok model, which predicts that fracture will occur whenever a critical value of the second normal stress difference is exceeded in magnitude.