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Journal of RheologyVolume 42, Issue 3 (May-June 1998) |
Contents
The Effect of Temperature on the Viscoelastic Properties of Model and Industrial DispersionsNhol Kao 1, Sati N. Bhattacharya1, Robert Shanks 2, Ian H. Coopes31 Rheology and Materials Processing Centre 2 Department of Applied Chemistry, Royal Melbourne Institute of Technology, Melbourne, Australia, 3 Kodak (Australasia) Pty. Ltd. AbstractThis paper discusses the effect of temperature on the dynamic rheological properties of both the model polystyrene-gelatin and the industrial photographic coupler dispersions. The time temperature-superposition (TTS) was used to bring experimental data at various temperatures together into single master curves. An Arrhenius-type TTS principle, rather than the Williams-Landel-Ferry (WLF) equation, was used in this work to bring all dynamic moduli and dynamic viscosity curves at different temperatures into single master curves. The present investigation verified that the TTS principle which was developed for polymeric materials could also be used for model and industrial photographic coupler dispersions as well. Furthermore, not only was the TTS principle suitable for the dispersions in the sol state, but it could also be used for the data in the gel-like state as well. The TTS allowed the estimation of the rheological properties of the dispersions over the frequency range which is otherwise inaccessible to the range of experimental measurement. Therefore, the linear viscoelastic properties of these model and photographic coupler dispersions at very low frequency (which is useful in predicting the stability of the product) as well as properties at very high frequency (or large deformation e.g. during coating or pumping processes) could be estimated. Sliding Plate Rheometer Studies of Concentrated Polystyrene Solutions: Nonlinear Viscoelasticity and Wall Slip of Two High Molecular Weight Polymers in Tricresyl PhosphateMichael J. Reimers* and John M. Dealy** *Present address: CEBE Reinigungschemie GmbH Ruhrstrasse 47, 22761 Hamburg, Germany **Corresponding author AbstractTwo high molecular weight, narrow distribution polystyrenes dissolved in tricresyl phosphate were studied using a sliding plate rheometer. Shear stress and birefringence measurements in step strain allowed the determination of N3 for both solutions. Start-up of steady simple shear and large amplitude oscillatory shear measurements revealed that the critical shear stress for slip for both solutions is around 2500 Pa and that slip is dynamic in nature, allowing rheological measurements above the critical stress to be made at sufficiently high frequencies. The critical stress value was used in conjunction with data from the literature to develop a relationship between critical stress and concentration. Large amplitude oscillatory shear stress measurements revealed that the solutions exhibit a limiting behavior at high strain rate amplitudes in the intermediate frequency range when the dependence on strain rate amplitude becomes small. Birefringence measurements showed that at high frequencies, where the time scale of the deformation is short, the oscillatory component of N3 vanished. This was found to occur at lower frequencies for the lower molecular weight solution. In contrast, the average value of the third normal stress difference, reflected in the zeroth harmonic, was found to vary little between the two solutions. Relationship Between Structure and Viscoelastic Behavior of Plasticized StarchG. Della Valle1*, A. Buleon1,
P. J. Carreau2, P-A. Lavoie2, B. Vergnes3 1 INRA, Centre de Recherches Agro-alimentaires, BP 71627 44316 Nantes Cedex 3, France 2 CRASP, Ecole Polytechnique, CP 6079, Succ. Centre Ville Montreal, QC, H3C 3A7, Canada 3 CEMEF, Ecole des Mines de Paris, BP 207 06904 Sophia-Antipolis Cedex, France * Corresponding author AbstractThe linear viscoelastic behavior of starches from various origins, blended with different amounts of a plasticizer using a twin screw extruder, has been investigated. Conditions of stability for reliable measurements and linearity domain have been determined At low strain, the plasticized starch is found to behave as a viscoelastic gel-like material. This behavior is partially explained by its semi-crystalline structure, as evidenced by X-ray diffraction patterns. Crystallites are assumed to participate in the formation of an elastic network, embedded in a viscoelastic amorphous phase. Additional thermomechanical treatment reduces crystallinity and leads to a decrease of the storage and loss moduli. The plasticizing role of water is found to be important. The higher molecular weight of the potato starch is responsible for its larger moduli. In the case of maize starch, the highly branched amorphous amylopectin softens the structured behavior, resulting in lower moduli compared to those of rich-content amylose. Chemorheology of Polyurethane Systems as Predicted from Monte-Carlo Simulations of Their Evolutive Molecular Weight DistributionC. Dubois1, A. Ait-Kadi2,
and P. A. Tanguy3 AbstractThe chemorheological models used for the description of thermoset polyurethanes are too often specific to a given formulation. This paper discusses the application of a more generic modeling approach which describes the evolutive rheological behavior of a polyurethane reactive mixture from a set of fitted monomer characteristic parameters and its calculated molecular weight distribution (MWD) at a given conversion level. The MWD is evaluated numerically from stochastic simulations. Once the adjusted parameters are obtained, the model becomes applicable at any starting formulation using a liquid prepolymer built from the same monomer. The linear viscoelastic properties were obtained from MWDs using the double reptation mixing rule. The mixing rule was adapted to include a contribution of Rouse' s relaxation times to account for short chains species, as those encountered in the beginning of the polymerization reaction. This procedure was successfully applied to two different difunctional thermoset polymeric systems that included either hydroxy-terminated polybutadiene (HTPB) or polypropylene glycol (PPG). Uniaxial Elongational Flow of Particle-Filled Polymer MeltsJ. Greener* and J.R.G. Evans AbstractPolymer processes which employ elongational flows have been successfully used for shaping ceramics by using crowded (50-60vol%) suspensions of ceramic particles, but the full realization of their potential rests on an understanding of the extensional flow behaviour of filled polymer systems. A uniaxial rheometer was constructed to evaluate the extensional flow properties of crowded suspensions based on polyisobutylene. The shear viscosity was evaluated for comparison using a Weissenberg rheometer and correlated with published literature values for a similar molecular weight polyisobutylene. Trouton's Law was verified for the unfilled polymer. The shear and elongational viscosities of filled polyisobutylene, containing up to 42vol% and 45vol% ceramic respectively, were measured. The dependence of shear and elongational relative viscosities on powder volume fraction were compared. In uniaxial flow, Trouton's Law was obeyed for crowded suspensions containing up to 42vol% ceramic powder. The Time-Dependent Extrudate-Swell Problem of an Oldroyd-B Fluid With Slip Along the WallEric Brasseur, Marios M. Fyrillas1,
Georgios Georgiou1,2, and Marcel J. Crochet AbstractWe demonstrate that viscoelasticity combined with nonlinear slip acts as a storage of elastic energy generating oscillations of the pressure drop similar to those observed experimentally in extrusion instabilities. We consider the time-dependent axisymmetric incompressible Poiseuille and extrudate-swell flows of an Oldroyd-B fluid. We assume that slip occurs along the wall of the die following a slip equation, which relates the shear stress to the velocity at the wall and exhibits a maximum and a minimum. We first study the stability of the one-dimensional axisymmetric Poiseuille flow by means of a one-dimensional linear stability analysis and time-dependent calculations. Linearly unstable solutions are shown to exist in the negative slope regime of the flow curve. The numerically predicted instability regimes agree well with the linear stability ones. The Newtonian solutions are found to be stable everywhere in case the volumetric flow rate is kept fixed. Indeed, the interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model or as the Weissenberg number increases. The numerical calculations reveal that periodic solutions are obtained when an unstable steady-state is perturbed and that the amplitude and the period of the oscillations are increasing functions of the Weissenberg number. We then continue to numerically solve the time-dependent two-dimensional axisymmetric Poiseuille and extrudate-swell flows using the EVSS method for the integration of the constitutive equation. Again, oscillations are observed in the unstable regime; consequently, the surface of the extrudate is wavy. However, the amplitude and the period of the pressure drop oscillations are considerably smaller than in the one-dimensional flow. The most important phenomenon revealed by our two-dimensional calculations is that the flow in the die is periodic in the axial direction. Wall Slip in Polymer Melts: A Pseudo Chemical ModelDavide A. Hill AbstractA chemical-type theory for wall slip in polymer melts is developed by modeling the exchange of bridging sites between two, opposing, polymeric and solid surfaces. Kinetic equations, describing surface coverage by bridging monomers, are formulated and analyzed to evaluate the stability of adhesive contact and slip characteristics of the viscoelastic melt. Order of magnitude estimates of the kinetic coefficients suggest that the polymer-solid interface is always at equilibrium, even under slip. The model displays the following features. The polymer slips at all stresses; the slip velocity, vs, obeys time-free volume superposition and depends on both shear and normal stresses. At small stresses, vs is linear in shear stress and proportional to a function of the work of adhesion: the slip parameter b (the slip extrapolation length scale) takes on the same form as that proposed by de Gennes, but displays an additional dependence on adhesive energy. At constant vs the shear stress is proportional to the adhesive free energy. A catastrophic loss of adhesion occurs at a critical stress that depends on the difference between the work of adhesion (polymer-solid) and the work of cohesion (polymer-polymer). Predictions compare favorably with literature data for slip of linear low-density polyethylene on metal. Electrorheological Creep Response of Tumbling NematicsNing Yao and Alex M. Jamieson* AbstractThe shear creep response of homeotropic monodomains of 4,4'-n-octylcyanobiphenyl (8CB) and dilute solutions of a side-chain liquid-crystalline polysiloxane in N-(4-methoxybenzylidene)-4-butylaniline (MBBA) is studied in the absence and presence of electric fields applied along the director. In the absence of the field, oscillations in strain rate are observed for 8CB and the LCP/MBBA solutions, indicative of director-tumbling flow. In the presence of electric fields, the tumbling flow is suppressed and, with increasing field strength, a systematic evolution is observed toward flow-aligning, the apparent viscosity being determined by the balance in hydrodynamic and electric torques. Due to a larger dielectric anisotropy, the tumbling flow of 8CB is suppressed at a critical field strength much lower than that of the LCP/MBBA solution. Moreover, a field-induced asymmetry of the doublet peaks is observed in the creep deformation for 8CB at 34 °C. Based on Erickson's transversely isotropic fluid (TIF) theory, simulation of the influence of electric fields on the flow-tumbling behavior is performed and qualitative agreement with the experimental results is obtained.Enhanced Electrorheological Fluids Using Anisotropic ParticlesRex C. Kanu1,2 and Montgomery T.
Shaw2,3 AbstractThe electrorheological phenomenon is widely attributed to the chaining of micron-sized polarizable particles when subjected to an external electric field. It has been hypothesized that the strength of the particle-particle interactions determines the rheological properties of ER fluids. On the basis of an electrostatic polarization model, we proposed that by controlling the geometry of the particles, the dielectric properties of ER fluid can be enhanced resulting in increased strength of the particle-particle interactions. In this work, we have developed systems featuring anisotropic particles and conducted a systematic study of the role of particle geometry in the response of ER fluids. Our findings appear to be in agreement with the electrostatic polarization model. The Electrorheology of Barium Titanate SuspensionsPeter J. Rankin and Daniel J. Klingenberg AbstractBarium titanate/insulating oil suspensions were investigated to determine the dielectric polarization mechanisms that govern their electrorheological (ER) behavior. The dynamic yield stress of 19.3 volume% suspensions exhibited Maxwell-Wagner-like frequency dependence, with the dynamic yield stress increasing significantly with a.c. electric field frequency, as expected for suspensions composed of particles with large dielectric constants. The dynamic yield stress at a given frequency was proportional to Em, where E is the applied electric field strength and the exponent m increased with frequency. For electric field strengths of 2 kV/mm at 1 kHz, dynamic yield stresses were approximately 500 Pa. Rheological experiments in which particle surface and oil conductivities were varied suggest that the dielectric relaxation of these suspensions is controlled by the particles' bulk conductivity. The dielectric relaxation depended strongly on field strength, becoming broader with increasing field strength. Harmonic analysis of the current passing through the suspensions verified that the nonlinear contribution to the apparent suspension conductivity increased with E and decreased with frequency. The current harmonics for barium titanate/dry air suspensions were similar to those of the oil based suspensions, suggesting that nonlinear conduction may arise from field-enhanced dissociation of surface groups, as opposed to field-enhanced dissociation of ion pairs within the continuous phase. Experimental Studies of an Entangled Polystyrene Solution in Steady State Mixed Type FlowsDmitry Yavich,* David W. Mead,†
James P. Oberhauser, and L. Gary Leal AbstractExperimental measurements of birefringence and velocity gradient components are reported for steady mixed type flows of a 0.076 g/cm3 solution of 2.89 × 106 MW polystyrene in a mixed toluene/oligomer solvent. The flow field is produced in a co-rotating two-roll mill with a series of different ratios of the gap width to roller radius chosen so that the flow type at the stagnation point for a Newtonian fluid would range from 0.0196 £ l £ 0.20, where || E || / || W || = (1 + l)/(1 - l). Additional data are also reported, for comparison purposes, for a similar polystyrene solution in a simple Couette flow. Finally, the stress-optical relationship is used to obtain a generalized extensional viscosity as a function of strain rate. This viscosity shows a range of strain rate thinning as predicted by reptation theory, followed at a critical Weissenberg number of O(1) based on the Rouse relaxation time by the initial stages of a region of strain rate thickening, as predicted by the Marrucci-Grizzuti extension of reptation theory that allows for stretching of the primitive chain. Detailed comparisons with birefringence predictions from this model, using measured flow data as inputs, shows good qualitative agreement but a number of quantitative differences. Most notable are: the fact that the model predicts an orientation angle that is rotated further from the principal strain rate direction than what is observed experimentally, especially for the smallest l values; the lack of a distinct plateau region prior to the onset of chain stretch; and a rate of increase of steady state chain stretching with Weissenberg number that is significantly weaker in the experiments than what is predicted via the model.Viscoelastic Flow Through Fibrous Media Using the CONNFFESSIT ApproachC. C. Hua* AbstractA combined finite element and Brownian dynamics technique (CONNFFESSIT) is used to predict the steady-state flow field around an infinite array of square-arranged cylinders using kinetic theory models. A finitely extensible elastic dumbbell model (FENE) and a modified reptation model are considered. Since Brownian dynamics simulations are used to predict the stresses in the flow field, no closure approximations are necessary in the models, such as the Peterlin approximation, or independent alignment. Comparisons are made with analogous models that have closed-form constitutive equations, namely the FENE-P dumbbell, and Doi and Edwards reptation model with independent alignment using the same numerical technique. The modified reptation model contains information about the entire chain configuration instead of just single segment orientations. In this way, the problems involved with reversing flows for reptation with independent alignment can be avoided. Since the flow field presents alternately converging and diverging flows for fluid particles, it offers an important test for reptation models in reversing flows. We find significant quantitative difference between the predictions of the approximate and the more-realistic models. For example, the FENE-P dumbbell underpredicts the magnitude of the normal stresses by as much as 25%, reptation with independent alignment underpredicts the magnitude of the normal stresses by as much as 22%. The calculations presented here are a starting point towards the realistic prediction of the onset of instability seen experimentally in these flows. Obtaining MWD Information from the Viscosity Data of Linear Polymer MeltsYongming Liu1, Montgomery T.
Shaw1 and William H. Tuminello2 AbstractBased on the model of Bersted and Slee, and later Malkin and Teishev, both differential and integral methods were developed to determine the MWD from viscosity data. The more sensitive differential method can detect small inflections in the viscosity data and convert these into MWD information. The integral method is, however, capable of handling moderately incomplete viscosity data. Combining self-consistent differential and integral approaches, we are able to resolve details of a MWD and quantify reasonably broad MWDs from many sets of limited viscosity data. These methods both have very short computation times. A reported overemphasis of the high-molecular-weight end of distribution is due to the excitation of Rouse modes during the rheological measurements at high frequencies, which masks the diffusive contributions of the low-molecular-weight components to the relaxation process. A Constitutive Analysis of Uniaxial, Equibiaxial and Planar Extension of a Linear Polyethylene (HDPE) MeltM.H. Wagner, P. Ehrecke, P. Hachmann*, and
J. Meissner** AbstractFrom constant strain-rate experiments in extensional flows, nonlinear strain measures and effective damping functions are derived for a linear polyethylene (HDPE) melt. Experimental results are compared with predictions of two molecular theories, the Doi-Edwards model and the molecular stress function approach of Wagner and Schaeffer. Orientation (but not stretch) of macromolecules at small and large strains is well represented by the Doi-Edwards orientation tensor. Stretch of macromolecules is found to be isotropic as predicted by the molecular stress function model, which is in excellent agreement with the data. For the latter model, a novel strain energy function is presented. Observation of Deformation and Recovery of PIB Droplet in a PIB/PDMS Blend After Application of Step Shear StrainHideki Yamane, Masaoki Takahashi*, Rika
Hayashi, Kenzo Okamoto AbstractThe deformation and recovery of a poly(isobutylene) droplet with a lower viscosity embedded in a poly(dimethyl siloxane) matrix are directly observed from two directions after application of a large step shear strain. The droplet shape and recovery time strongly depended on the magnitude of the applied strain. Just after application of a large strain, a droplet deforms almost affinely to a flat ellipsoid. It then changes into a rod-like shape, a dumbbell and to an ellipsoid of revolution, and finally to a sphere. Model calculations show that the primary driving force for the shape recovery is the interfacial energy in order to reduce the surface area of the deformed droplet. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |