Contents

Transient and Steady State Rheological Behaviour of the Thermotropic Liquid Crystalline Polymer Vectra B950

F. Beekmans, A.D. Gotsis, and B. Norder

A Model with Two Coupled Maxwell Modes

B.J. Edwards, A.N. Beris, and V.G. Mavrantzas

Use of Rheological Measurements to Estimate the Molecular Weight Distribution of Linear Polyethylene

Paula M. Wood-Adams and John M. Dealy

A Model of Adaptive Links for Aging Viscoelastic Media

Aleksey D. Drozdov

On Capillary Instability of Jets of Magneto-Rheological Fluids

V.M. Entov, M. Barsoum, and L.E. Shmaryan

A Structure-Related Model to Describe Asphalt Linear Viscoelasticity

Didier Lesueur, Jean-François Gerard, Pierre Claudy, Jean-Marie Letoffe, Jean-Pascal Planche, and Didier Martin

The Transient Extensional Behavior of Polystyrene-Based Boger Fluids of Varying Solvent Quality and Molecular Weight

M.J. Solomon and S.J. Muller

Kinetic Theory and Transport Phenomena for a Dumbbell Model under Nonisothermal Conditions

Hans Christian Öttinger and Fabrizio Petrillo

An Anomalous Electrorheological Behaviour of Magnesium Hydroxide Suspensions in Silicone Oil

J. Trlica, O. Quadrat, P. Bradna, V. Pavlínek and P. Sáha

A Multi-Mode Approach to Finite, Three-Dimensional, Nonlinear Viscoelastic Behaviour of Polymer Glasses

T.A. Tervoort, E.T.J. Klompen, and L.E. Govaert

Reversible Shear Thickening in Monodisperse and Bidisperse Colloidal Dispersions

Jonathan Bender and Norman J. Wagner

Concentration Effects on the Rheology and Texture of PBG/m-cresol Solutions

Lynn M. Walker, Martine Mortier, and Paula Moldenaers

Exploring Molecular Origins of Sharkskin, Partial Slip and Slope Change in Flow Curves of Linear Low Density Polyethylene

Shi-Qing Wang, Patrick A. Drda, and Yong-Woo Inn

Shear History Dependence of the Viscosity of Aggregated Colloidal Dispersions

W. Wolthers, M.H.G. Duits, D. van den Ende, and J. Mellema

Transient and Steady State Rheological Behaviour
of the Thermotropic Liquid Crystalline Polymer Vectra B950

F. Beekmans, A.D. Gotsis, and B. Norder
Delft University of Technology
Fac. Chemical Technology and Materials Science
Dept. Polymer Technology
Julianalaan 136, 2628 BL Delft, The Netherlands

Synopsis

The shear stress and the first normal stress difference in steady and transient shear flows of the commercial thermotropic liquid crystalline polymer Vectra B950 are measured at 300°C. The viscosity curve shows the typical three region flow curve of LCPs. The first normal stress difference is everywhere positive and its steady state value increases linearly with the shear rate throughout Regions I and II. The growth curves of the shear and the normal stresses for shear rates in Region II show slow oscillations that scale with strain. The stress transients during flow reversal and stepwise increase or decrease of the shear rate also scale with strain. The damping of the transients is slower than what is found in other thermotropic LCPs. The oscillations of N_l after reversal and after stepwise increase of the shear rate do not have a clear phase difference. The relaxation of the stresses after cessation of flow shows a fast initial part and a long strain scaling tail. The elastic texture contribution to the total stress is lower than in other semi-flexible systems. Either the viscous/elastic molecular contribution or an additional viscous contribution of the defects seems to be responsible for this low value.

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A Model with Two Coupled Maxwell Modes

B.J. Edwards¹, A.N. Beris, and V.G. Mavrantzas²
Department of Chemical Engineering
University of Delaware
Newark, DE 19716

Synopsis

In an effort to quantitatively examine the effect of coupling between multiple relaxation modes, a new model involving two coupled Maxwell modes is developed as a generalization of the upper-convected Maxwell and the Giesekus models. The model contains, in addition to the parameters inherent to a Maxwell model with two uncoupled modes (i.e., lambda₁, lambda₂ and eta₁ = G₁ lambda₁, eta₂ = G₂ lambda₂), a dimensionless coupling coefficient theta which multiplies a quadratic coupling term. In the two characteristic limits theta = 0 or (eta₁ lambda₁ = eta₂ lambda₂), the Maxwell model with two uncoupled relaxation modes or the Giesekus constitutive model is obtained, respectively.

The rheological behavior of the model is investigated in the linear and nonlinear deformation-rate regimes. Calculation of the linear viscoelastic behavior shows that the linear stress relaxation modulus is the sum of two decaying exponentials with characteristic times and pre-exponential factors which are quite different from lambda₁, lambda₂ and G₁, G₂, respectively. In slow, slowly-varying flows, the zero shear-rate ratio PSI⁰₂/PSI⁰₁ assumes small negative values when theta takes on small positive values. The nonlinear rheological behavior of the model is examined under the imposition of shear and extensional flow fields, from both a steady-state and transient perspective. The qualitative behavior observed is remarkably rich in describing the experimental trends seen in polymer melts and Boger fluids for a constant value of theta = 0.1.

¹Permanent address: 7305 S. Colony Ct., Nashville, TN 37221
²Permanent address: Department of Chemical Engineering, University of Patras, Patras, Greece

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Use of Rheological Measurements to Estimate
the Molecular Weight Distribution of Linear Polyethylene

Paula M. Wood-Adams and John M. Dealy
Department of Chemical Engineering
McGill University
3480 University Street
Montreal, Canada

Synopsis

An important characteristic of a polymer is its molecular weight distribution (MWD). The MWD affects its processing characteristics and its solid state performance The traditional analytical method for determining MWD is gel permeation chromatography (GPC). However, GPC results depend strongly on the skill and experience of the operator and are not sensitive to small amounts of high molecular weight material that can have an important effect on processing and product properties. It is known that rheological properties depend on MWD, and it has been proposed that viscosity or complex viscosity data can be used to infer the MWD for commercial polymers. Although there has been some controversy as to whether this is feasible, recent results of Shaw, Tuminello and others indicate that for linear polymers this is, in theory, possible. However, limitations in the accessible frequency range, as well as inevitable experimental errors, pose serious barriers to the use of such a procedure. We have investigated the severity of these barriers and have shown that within certain limits, complex viscosity data can be used to infer a realistic MWD for linear polyethylenes.

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A Model of Adaptive Links for Aging Viscoelastic Media

Aleksey D. Drozdov
Institute for Industrial Mathematics
Ben-Gurion University of the Negev
22 Ha Histadrut Street, Be'ersheba, 84213 Israel

Abstract

A new model is derived for the mechanical behavior of linear viscoelastic materials subjected to physical aging. According to the model, a viscoelastic medium is treated as a system of elastic springs (links between polymeric molecules) which replace each other. Two types of links are distinguished: links arisen at the instant of quenching (type-I), and links emerging in the quenched material at a constant temperature (type-II).

The mechanical behavior of an aging medium is determined by three material functions which characterize (i) the collapse of links of type-I, (ii) the breakage of links of type-II, and (iii) the rate of emergence of new links of type-II. We derive integral equations for these functions and find their solutions using data of the standard relaxation tests.

To verify the model, we calculate the material response in the creep tests and compare results of numerical simulation with experimental data for an epoxy adhesive. The results obtained demonstrate fair agreement between experimental observations and their prediction.

By using the model developed, we analyze numerically the behavior of a viscoelastic medium under time-varying loads. We study elongation of a specimen with a constant rate of strain, its recovery after creep tests, and steady shear oscillations of a layer. In the latter case, numerical results are compared with experimental data for polypropylene samples.

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On Capillary Instability of Jets of Magneto-Rheological Fluids

V.M. Entov^l, M. Barsoum² and L.E. Shmaryan³

^lInstitute for Problems in Mechanics of Russian Academy of Sciences
pt.Vernadskogo, 101, 117526, Moscow, RUSSIA

²Mechanical Engineering Department, Worcester Polytechnic Institute
100 Institute Road, Worcester, MA 01609, USA

³Moscow Gubkin Oil and Gas Academy, Moscow, RUSSIA

Abstract

Capillary instability and breakup of jets of magneto-rheological fluids is studied theoretically in the framework of one-dimensional theory. Linear instability is considered and the nonlinear jet profile evolution is followed using numerical modelling. The magnetic field is assumed to be trapped within the liquid and both produces magnetic pressure and causes an increase in viscosity due to the magneto-rheological effect. Both effects of the magnetic field result in slowing down the necking and lead to development of a beads-on-string structure at the late stage of jet evolution. It is shown, that the magneto-rheological effect by itself may prevent early breakup even in suspensions with strongly shear-thinning rheological behavior.

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A Structure-Related Model to Describe Asphalt Linear Viscoelasticity

Didier Lesueur, Jean-François Gerard,
Laboratoire des Matériaux Macromoléculaires
UMR CNRS 5627 - INSA Lyon Bat. 403 - 69621 Villeurbanne Cedex - FRANCE

Pierre Claudy, Jean-Marie Letoffe,
Laboratoire de Thermochimie Minérale
URA CNRS 116 - INSA Lyon Bat. 401 - 69621 Villeurbanne Cedex - FRANCE

Jean-Pascal Planche and Didier Martin
Centre de Recherche ELF Solaize
BP22 - 69360 St- Symphorien d'Ozon - FRANCE

Synopsis

Viscoelastic properties of paving grade asphalt cements (AC) were measured on a Rheometrics RDA II. Thermal properties were studied with a Mettler TA 2000 B Differential Scanning Calorimeter. A review of the literature showed that most authors proposed that the Time-Temperature Superposition Principle (TTSP) applies to asphalt over the whole temperature range. However, the results presented herein demonstrate that it indeed fails at high temperatures, especially for high asphaltene content and high crystalline content materials. This paper focuses on the role of asphaltenes, which are, by definition, insoluble in n-heptane. Asphaltenes are suspended in a colloidal manner within the AC matrix and are peptizided by the species called resins. Thus, a temperature dependent solid fraction exists within a liquid (or glassy) matrix. This paper shows that the viscoelastic properties of asphalt are bimodal: they are governed by both solid and continuous phases.

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The Transient Extensional Behavior of Polystyrene-Based Boger Fluids
of Varying Solvent Quality and Molecular Weight

M.J. Solomon and S.J. Muller
Department of Chemical Engineering, University of California at Berkeley
and Center for Advanced Materials, Lawrence Berkeley Laboratories
Berkeley CA 94720

Synopsis

The behavior under transient uniaxial elongation of a homologous series of variable extensibility polystyrene-based Boger fluids has been investigated in an apparatus similar to that developed by Sridhar and co-workers. The test fluids are dilute solutions of either 2.0 × 10⁷ or 2.0 × 10⁶ g/mole monodisperse polystyrene dissolved in poor, dioctyl phthalate-based or good, tricresyl phosphate-based solvents. This rational manipulation of Boger fluid solvent quality (assessed based on previously reported light scattering and intrinsic viscometry measurements) and chain length yields a unique opportunity to correlate viscoelastic extensional response to finite extensibility and molecular interactions: here we search for such effects in transient filament extension between parallel plates, an approximation of purely extensional flow. The test device, which can impart a maximum Hencky strain, epsilon, of 4.5 at rates, epsilon-dot, between 0.3 s^-l and 3.0s^-1, is similar to that reported by Sridhar et al. (1991). In agreement with results communicated there and in Tirtaatmadja and Sridhar (1993), large strain hardening is observed for these polymer solutions, as well as certain deviations of the experimental flow from ideal uniaxial extension. As opposed to Tirtaatmadja and Sridhar (1993), no steady state extensional viscosities are obtained for the comparatively small strains of our experiment. The transient experimental results are roughly consistent with simple one dimensional FENE-P calculations. However, uncertainties due to the non-ideal nature of the flow at short times and the sensitivity of the measured extensional stress growth coefficient to the details of the imposed elongation make it difficult to unambiguously assign L based solely on short time filament stretching results. These results are considered in light of the substantial effects solvent quality and molecular weight have on the measured drag in flow past a sphere (Chmielewski et al., 1990; Solomon and Muller, 1996b).

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Kinetic Theory and Transport Phenomena for a Dumbbell Model
under Nonisothermal Conditions

Hans Christian Öttinger and Fabrizio Petrillo
ETH Zürich, Department of Materials, Institute of Polymers
CH-8092 Zürich, Switzerland

Abstract

A Hookean dumbbell model for polymers in dilute solutions undergoing homogeneous flow is generalized to include arbitrary imposed temperature profiles. In order to obtain the "nonisothermal diffusion equation" for the probability density in polymer configuration space we generalize the approach of Schieber and Öttinger [J. Chem. Phys. 89, 6972-6981 (1988)] to Brownian motion out of equilibrium. In addition, we derive the polymer contributions to the mass flux vector, stress tensor and heat-flux vector by means of the kinetic theory approach of Curtiss and Bird [Adv. Polym. Sci. 125, 1-101 (1996)] for the case of a slowly varying temperature gradient, and we find coupled constitutive equations for the mass, momentum and energy fluxes. For a simple steady shear flow it is then possible to calculate the heat-flux vector explicitly, at least for small temperature gradients and shear rates. We compare our approach and results with previous works on this subject, and we finally discuss some extensions.

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An Anomalous Electrorheological Behaviour
of Magnesium Hydroxide Suspensions in Silicone Oil

J. Trlica¹, O. Quadrat², P. Bradna², V. Pavlínek¹ and P. Sáha¹

¹Technical University, Faculty of Technology
762 72 Zlín, Czech Republic

²Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic
162 08 Prague 6, Czech Republic

Summary

In contrast to the usual electrorheological behaviour manifesting in an increase in viscosity of suspensions of various materials in electrical field, a negative electrorheological effect, i.e., a decrease in viscosity of suspensions of magnesium hydroxide particles in silicone oil was observed.

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A Multi-Mode Approach to Finite, Three-Dimensional,
Nonlinear Viscoelastic Behaviour of Polymer Glasses

T.A. Tervoort^1†, E.T.J. Klompen², and L.E. Govaert²

Centre for Polymers and Composites
¹Faculty of Chemical Engineering and Chemistry
²Faculty of Mechanical Engineering
Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

In this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behaviour of glassy polymers up to the yield point. It is assumed that the deformation behaviour of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three-dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the (elastic) hydrostatic and (viscoelastic) deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of parameters, the multi-mode Leonov model is capable of describing realistic constant strain rate experiments, including the strain rate dependent yield behaviour. It is also capable of giving a quantitative description of nonlinear stress-relaxation experiments.

^† Current address: ETH Zürich, Institut für Polymere, ETH Zentrum, UNO C 15, Universitatstrasse 41, CH-8092 Zürich

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Reversible Shear Thickening in Monodisperse and Bidisperse Colloidal Dispersions

Jonathan Bender^† and Norman J. Wagner
Center for Molecular and Engineering Thermodynamics
Department of Chemical Engineering
University of Delaware
Newark, DE 19716

Abstract

Reversible shear thickening is measured in model colloidal suspensions of silica that exhibit near hard-sphere behavior. Flow dichroism measurements and the colloidal stress-optical relationship prove that hydrodynamic interactions drive the shear thickening transition. Turbidity and flow small angle neutron scattering (flow-SANS) demonstrate that particles cluster reversibly in the shear thickened state. Further, SANS measurements show that shear thickening occurs without any shear induced order-disorder transition, in contrast to observations for dispersions of charged colloids. A simple force balance predicts the scaling of the critical stress for the onset of shear thickening with particle size and volume fraction. Measurements on bimodal mixtures verify the scaling laws derived from the force balance and provide a strategy for controlling the shear thickening transition.

^† Current address: Lord Corporation, 405 Gregson Drive, Cary NC 27511-7900

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Concentration Effects on the Rheology and Texture of PBG/m-cresol Solutions

Lynn M. Walker, Martine Mortier, and Paula Moldenaers
Department of Chemical Engineering
Katholieke Universiteit Leuven, de Croylaan 46
B-3001 Leuven, Belgium

Abstract

In this work, the rheology of PBG/m-cresol systems is re-evaluated with the specific goal of understanding the influence of concentration on low shear rate rheology. Comparisons of steady-state and transient rheology and the behavior after cessation of shear allow for the separation of the contributions to the stress from the nematic fluid and defect texture. Stress relaxations demonstrate that the textural contribution to the stress increases nonlinearly from 30% to 55% as the concentration increases from 12 to 37 wt%. Recoil shows a similar nonlinear trend in the magnitude of the ultimate recovered strain gamma_infinity. Stress relaxations and recoil, once normalized, have universal dynamics dependent only on gamma-dot₀ t and independent of concentration. Two different regions of concentration are identified and correlated to a distinct change in the nature and behavior of the textural contribution to the stress.

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Exploring Molecular Origins of Sharkskin, Partial Slip and Slope Change
in Flow Curves of Linear Low Density Polyethylene

Shi-Qing Wang, Patrick A. Drda, and Yong-Woo Inn^†
Department of Macromolecular Science
Case Western Reserve University
Cleveland, OH 44106-7202

Synopsis

This paper explores the molecular mechanism for sharkskin formation on extrudate of linear low density polyethylenes (LLDPE) and investigates the rheological origin of a characteristic curvature (i.e., a slope change) in the flow curve of LLDPE. Rheological measurements, performed at various temperatures from 160 to 240°C with a controlled-pressure capillary rheometer and a variety of dies, suggest that the slope change in the flow curve, interpreted by many as demonstrating wall slip in the die land, arises from a combination of interfacial slip and cohesive failure due to chain disentanglement, first initiated on the die wall in the exit region. Since the disentanglement state is unstable for the adsorbed chains within a certain stress range below the critical stress for the global stick-slip transition, a partial slip flow cannot sustain itself and occurs only periodically. This time-dependent molecular entanglement-disentanglement fluctuation produces the sharkskin like extrudate in the regime where the slope change takes place. Sharkskin dynamics are found to precisely correlate with chain relaxation processes. Specifically, the characteristic time scale tau (i.e., the sharkskin periodicity) is found to be of the same magnitude and have the same WLF temperature dependence as that of the characteristic molecular relaxation time tau* as determined by oscillatory shear measurements in a parallel-plate flow cell. The LLDPE resins are also observed to undergo interfacial stick-slip transitions as well as a rarely seen cohesive slip-slip transitions at various temperatures.

^† Current address: Institute of Materials Science U136, University of Connecticut, Storrs, CT 06269-3136

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Shear History Dependence of the Viscosity of Aggregated Colloidal Dispersions

W. Wolthers, M.H.G. Duits, D. van den Ende, and J. Mellema
Rheology Group, Faculty of Applied Physics
University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands

Abstract

The shear history dependence of the viscosity of a depletion flocculated dispersion of colloidal spheres has been studied with two different rheometrical geometries. The observed rheological behavior is found to depend on the geometry, due to effects of thixotropy and sedimentation. By comparing the results of a cone-plate and a Couette geometry, we were able to obtain reliable data. The shear history dependence is explored by measuring a flow curve before and after subjecting the aggregated dispersion to a constant shear rate during one hour. The viscosity values of the flow curve after this hour turned out to be considerably lower than the initial flow curve. The results have been interpreted with a micro rheological model for fractal aggregation in shear flow. The drop in viscosity is attributed to a shear induced compaction of the aggregates. Combination of this model and the concept of compaction results in a satisfactory description of the experimental results.

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