Index of content:
Volume 47, Issue 4, July 2003
Linear viscoelastic behavior of densely grafted poly(chloroethyl vinyl ether)-g-polystyrene combs in the melt47(2003); http://dx.doi.org/10.1122/1.1579688View Description Hide Description
We have measured the linear viscoelastic behavior in the melt of two densely grafted poly(chloroethyl vinyl ether)-g-polystyrene comb polymers. Both samples have a backbone of approximately 800 ethyl vinyl ether monomers and the fractions of grafted backbone monomers are 98% and 10%, respectively. The viscoelastic behavior shows remarkable features. The comb polymer with the highest grafting density shows a power law behavior over five orders of magnitude in frequency. The power law can be understood through a “Rouse-like” motion of the entire chains with an apparent friction coefficient coming from the fast Rouse dynamics of the short grafts. Alternatively, the same behavior can be described as the signature of a “fluctuating” physical gel. The less densely grafted comb polymer has a more complex behavior.
47(2003); http://dx.doi.org/10.1122/1.1579687View Description Hide Description
The relation between morphology and the steady state rheological behavior has been investigated for blends of immiscible polymers, i.e., polydimethylsiloxane and polyisobutylene, and this over the full composition range. Cryogenicscanning electron microscopy has been used to obtain information about the morphology during shearing. By means of relaxation experiments the stresses have been decomposed in interfacial and component contributions. From the interfacial stress components the orientation of the inclusions could be estimated. These stresses do not provide a clear indication of the location of the phase inversion as they hardly change with concentration in the midconcentration range, they even seem to develop a local minimum around the 50/50 concentration. In this region fibrils can be observed that are nearly oriented in the flow direction. The values of the interfacial stress components are consistent with such a structure. The component contributions to the viscosity can also be explained on the same basis although the normal stresses are underestimated.
47(2003); http://dx.doi.org/10.1122/1.1574023View Description Hide Description
Evidence of wall slip and magnitude of yield stress are examined for colloidalgels consisting of hydrophobicsilica, polyether, and lithium salts using geometries with serrated, smooth, hydrophilic and hydrophobicsurfaces. Serrated plates, which provide minimal wall slip, are used to compare different methods of measuringyield stress: conventional extrapolation of shear stress in steady shear experiments and dynamic experiments at large strain amplitudes. In the latter, the yield stress is denoted by the maximum in the elastic stress, the product of the elastic modulus and strain when plotted as a function of strain amplitude. Although excellent agreement is observed in the yield stress values using both these techniques, the dynamic method seems preferable considering its experimental ease, accuracy, and lack of extrapolation. In the presence of smooth geometries, the silicagels show evidence of wall slip with a concomitant decrease in yield stress. Using underestimation of yield stress as a measure of wall slip, we find slip to be unaffected by changes in the gel modulus obtained through incorporation of additional silica or salts. The use of smooth surfaces compared to serrated surfaces leads to approximately a 60% reduction in yield stress for all such samples. Finally, control of wall slip is attempted using plates modified to have different surface energies. Hydrophobic plates reduce slip significantly and produce data comparable to those with the serrated plates. In contrast, hydrophilic plates have minimal effect on slip and produce data analogous to those obtained using smooth plates. These results can be explained based on the fact that the particle-lean layer, responsible for slip, remains so with hydrophilic plates as it repels the hydrophobicsilica particles in favor of the polar solvent. In contrast, the hydrophobicsilicainteracts with the hydrophobic plates, thus reducing slip.
Viscosity of solutions of low-density polyethylene in ethylene as a function of temperature and pressure47(2003); http://dx.doi.org/10.1122/1.1566036View Description Hide Description
The viscosity, η, of solutions of low-density polyethylene kg/mol) in ethylene containing 18.4, 22.5, 27.4, and 35.0 wt % polymer, respectively, was measured over a wide range of temperatures, pressures, and shear rates. The equipment used consisted of a high-pressure autoclave in which the solutions were prepared and a rotational viscometer which was operated by a computer. The solution with a polymer concentration of 35 wt % was found to be shear thinning. Due to experimental inaccuracy the shear influence on the viscosity of the mixtures with lower polymer content could not be identified clearly. The zero-shear viscosities show the expected increase of η according to the pressure or polymer concentration and a corresponding reduction of η as the temperature is increased. The results are consistent with current theories and can be described well by a mathematical expression based on activation energies, and activation volumes, and on exponential growth of η with a rise in polymer concentration.
Three-dimensional dynamics simulation of electrorheological fluids under large amplitude oscillatory shear flow47(2003); http://dx.doi.org/10.1122/1.1582854View Description Hide Description
Large amplitude oscillatory shear (LAOS) behavior of electrorheological (ER) fluids has been investigated using three-dimensional particle-level dynamics simulation. As an ER device usually operates in a dynamic mode with large deformation, it is important to understand the LAOS behavior as well as its underlying mechanism for the development of an effective ER fluid. Simulation predicted most of the experimental observations including strain overshoot, distorted stress signal, dogbone-type Lissajous curve, and stripe pattern formation, to list a few. By careful investigation of cluster statistics as well as microstructures, we found that the strain overshoot phenomenon, which is often observed in complex fluid systems with little explanation, arises from the cluster reformation process in addition to a slight rearrangement within a cluster. Fourier transformationanalysis was also performed, and the scaling behavior of the intensities of higher harmonics was investigated. The intensities of higher harmonics were found to increase according to the power of harmonic order. As it becomes more important to understand the nonlinear behavior of complex fluids, it is expected that our results increase our understanding on the complex nonlinear behavior as well as Fourier transformation rheology of ER fluids in relation with the microstructural changes.
47(2003); http://dx.doi.org/10.1122/1.1574020View Description Hide Description
The flow behavior of glass bead, limestone, and powdered quartzsuspensions was examined in steady and oscillatory shear tests. The solids content was varied up to a maximum of 25 vol % and the mean particle diameter ranged from 3 to 31 μm. The suspending liquid consisted of one of two silicone oils, which had limiting viscosities at zero shear rate slightly greater than and respectively. The concept of shear stress equivalent inner shear rate, which describes the response of suspensions in steady shear experiments, was applied here to dynamic tests. Application of this concept yielded uniform descriptions of the flow curves that result from oscillatory deformations. In the region dominated by hydrodynamic forces, a modified Cox–Merz rule was derived. The shear stress function and complex modulus can be expressed as a function of the solid concentration using the parameters in this modified Cox–Merz relation.
47(2003); http://dx.doi.org/10.1122/1.1579686View Description Hide Description
We show that flow-induced coalescence is facilitated when the molecular weight of the matrix fluid becomes large enough. For a system that consists of polybutadiene drops in a suspending fluid of polydimethylsiloxane, and a viscosity ratio of the drop to the suspending fluid of 0.5, the critical molecular weight is found to be approximately For the range of molecular weights and drop sizes studied here, the shear rates remain low enough that bulk viscoelastic effects are negligible. Instead, we hypothesize that coalescence is facilitated because there is slip at the boundaries of the thin film between the drops, and this facilitates its drainage to a point where the film ruptures. This suggestion is tested in two indirect ways. First, we extend the film drainage analysis to include slip and show that the analysis seems to be qualitatively consistent with the data. Second, we carry out additional experiments in which the interface of the drops is covered with a “compatibilizer.” These experiments show that the molecular weight effect is largely suppressed, due apparently to the fact that the copolymers span the interfacial zone and are entangled with the bulk polymers on the two sides of the interface, thus largely eliminating the possibility for slip.
Direct visualization of flow-induced microstructure in dense colloidal gels by confocal laser scanning microscopy47(2003); http://dx.doi.org/10.1122/1.1579689View Description Hide Description
Unconstrained uniaxial compression (or squeeze flow) of high volume fraction gels of fluorescent silica particles of diameter 832 nm results in the formation of voids (at and cracks (at that are of scale 10–100 μm. This evidence of inhomogeneous material deformation was obtained by direction visualization of three-dimensional structure by confocal laser scanning microscopy. Flow-induced void and crack microstructures are quantified by locating all particle centroids with quantitative image processing, by performing Voronoi volume tessellation with computational geometry and by analyzing the particle number densityfluctuations as a function of averaging volume. Average short-range real space structural measures, such as the pair correlation function, are little changed by the flow. However, the probability distribution of excess normalized Voronoi polyhedra volume is profoundly extended by squeeze flow, particularly at large polyhedra volumes. Comparison of the Voronoi polyhedra volume distributions and particle bond distributions indicates that: (1) in the low φ gel, large flow-induced voids are formed by the reorganization of the existing quiescent voids without significant effect on the local structure; and (2) in the high φ gel,cracks are formed by reorganization of the local structure itself. Analysis of the number densityfluctuations shows that the gels respond to applied squeeze flow deformation with structural distortion on the length scale of 5–10 particle diameters.
47(2003); http://dx.doi.org/10.1122/1.1579691View Description Hide Description
In recovery experiments after melt elongation, binary blends of immiscible polymers display large values of the recovered stretch that strongly exceed the recovery of the pure components. This unusual behavior is caused by the interfacial tension: It attempts to minimize the interfacial area between the two phases and thus predominantly promotes the macroscopic retraction of the sample. In this article, the transient recovery of binary blends of immiscible polymers is studied theoretically by applying an effective medium approximation. Numerical solutions of the time evolution equations for the stretch ratio of the sample and of the disperse phase allow quantitative prediction of the recovery of the sample. Our analysis shows that matrix and disperse phase deform with different Hencky strain rates during recovery. The equilibrium value of the recovered stretch and the characteristic time scale of the recovery are functions of the volume concentration Φ of the disperse phase. The equilibrium value of the recovered stretch increases with Φ and with the maximum elongational strain of the sample. Finally, we consider the breakup of single droplets and show that Rayleigh instabilities can frequently occur during recovery if the volume concentration Φ remains below an upper limit.
47(2003); http://dx.doi.org/10.1122/1.1574022View Description Hide Description
We investigate the nonlinear rheological behavior of colloidalsuspensions of Laponite, a synthetic clay, driven by steady homogeneous shear strain. We show that the external drive leads to drastic slowing down of the aging dynamics or even, in some cases, in rejuvenation of the system. Under shear, after a surprisingly long time, the spontaneous aging process observed at rest is suppressed. The system then reaches a nonequilibrium stationary state that is characterized by complex viscosity depending on the shear rate applied. In addition, the glass exhibits non-Newtonian shear-thinning behavior. This rheological behavior confirms recent numerical and theoretical predictions.
47(2003); http://dx.doi.org/10.1122/1.1574021View Description Hide Description
In a new rheometer for polymer melts equibiaxial and planar elongations were performed at 150 °C with a low and a high density polyethylene (LDPE and HDPE, respectively), and equibiaxial elongations at 170 °C with a commercial polystsyrene (PS); for simple elongations a previously described rheometer was used. Each sample is clamped by metal belts that introduce the elongation and measure the forces that act upon each clamp. The samples are small and are supported by inert gas. By particle tracking and video recording the deformation history and the test performance are determined. The resulting elongational viscosities e, p for the different elongational modes) are newly defined such that at small strain rates they are equal to the linear viscoelastic shear viscosity, The ratio represents the nonlinear behavior: means strain hardening and strain softening. Hardening occurs in simple and in planar elongation in the flow direction, more for LDPE than for HDPE and is smallest for PS (simple elongation only). In equibiaxial elongation, there is softening followed by much (LDPE), little (HDPE), and no (PS) hardening. Planar elongation causes softening in the cross direction (more for HDPE than for LDPE). At the end of planar elongation, the samples become hazy and form holes.
47(2003); http://dx.doi.org/10.1122/1.1582853View Description Hide Description
An ellipsoidal model for droplet deformation in mixtures of Newtonian fluids is proposed. The model makes a bridge between the phenomenological description of the ellipsoidal deformation of the droplet [Eshelby (1957); Maffetonne and Minale (1998); Jackson and Tucker (JT model) (2003); Wetzel and Tucker (WT model) (2001)] and the interfacial velocity calculation between two Newtonian liquids. The bridging was obtained by the use of the general boundary integral formalism. The velocity at the interface was decomposed into a flow dominated term and an interfacial term. The flow term is the same as in JT and WT models and arises from Eshelby’s theory, while the interfacial term was calculated by assuming a linear, uniform velocity gradient tensor over the entire surface of the droplet. The model for droplet deformation is applicable to mixtures of two Newtonian liquids with arbitrary viscosity ratio and nonzero interfacial tension. The predictions of the present model in terms of shape evolution of the droplet agree well with many experiments and numerical simulations including transient deformation for small and large capillary numbers, transient shear widening for small viscosity ratio and large capillary numbers, and steady shear deformation. The rheology of dilute emulsions based on the morphological predictions by the present model was calculated according to Batchelor’s formalism (1970). The predicted rheological material functions agree reasonably well with the experimental data. The limitations of the present model are also discussed.
Enhancement of the first normal stress coefficient and dynamic moduli during shear thickening of a polymer solution47(2003); http://dx.doi.org/10.1122/1.1579690View Description Hide Description
Viscosity results of a solution of poly(2-hydroxyethyl methacrylamide) in glycerine, obtained from a continuous increase of shear rate and under steady state (constant shear rate) conditions, reveal the existence of a shear thickening region. The analysis of normal stresses shows that the first normal stress coefficient exhibits the same shear-thickeningeffect as the viscosity. The increase of the solutionelasticity during shear thickening is also noticed by an enhancement of the storage modulus,measured in experiments using parallel superposition of oscillations on steady flows, as the shear stress is increased. Thermorheological simplicity, observed in dynamic measurements in absence of steady flow, is broken when shear stresses corresponding to the shear thickening region are applied. The results are explained by the presence of shear-induced hydrogen bonds, which provoke a reinforcement of the plateau modulus and an enlargement of the relaxation time spectrum.
47(2003); http://dx.doi.org/10.1122/1.1584429View Description Hide Description
We use a finite-difference algorithm to simulate the shear flow of nematic liquid crystals based on the Leslie–Ericksen theory, and investigate how unequal elastic constants affect the formation, oscillation, and breakup of roll cells, the nucleation of defects, and the coarsening of texture upon cessation of flow. With elasticanisotropy, the so-called Ericksen number (Er) cascade comprises the same regimes previously documented for isotropic elasticity: stable simple shear, steady roll cells, oscillatory roll cells, and an irregular pattern with thick disclinations. The onset of roll cells is most sensitive to the elastic constant for bend. Increasing stabilizes the shear flow against the formation of rolls. For reduced a second Er cascade may appear for higher Er, with regularization and eventual reappearance of the defect-laden irregular pattern. The twist constant is the most important for defectformation; a weaker causes roll cells to breakup and pairs of ±1 defects to nucleate at lower Er. The defects show distinctive structures depending on the elasticanisotropy; typically a weaker elastic constant gives rise to patterns that incur greater distortion in the corresponding mode. After cessation of shear, all textures relax completely to a monodomain. The longest-lasting orientational pattern is again attributable to the weakest of the elastic constants. By analyzing the amount of distortion in each mode and the associated free energy, we are able to elucidate the role of elasticanisotropy in defining the orientational patterns in sheared nematics.
47(2003); http://dx.doi.org/10.1122/1.1584428View Description Hide Description
For a polystyrene melt with a zero shear rate viscosity of 44.5 kPa s at shear stress and first normal stress difference in step shear rate experiments with cone-standard plate and cone-partitioned plate tools are compared. The cone angle α is throughout. With the partitioned plate and a central stem of radius 4 mm, steady state viscosities can be obtained up to shear rates of about a factor of 3 higher than for the standard plate tool. The strain at the maximum viscosity grows from 2.3 below to 6.5 at This increase can hardly be seen with the standard plate tool. The ratio of the maximum to the steady state viscosity shows a tendency to saturate beyond and reaches 1.75 at This finding is again beyond the scope of the standard plate tool. The ratio of the maximum to the steady state first normal stress difference only shows a minor increase to 1.03 at beyond this strain rate cannot be determined because the maximum thrust of 20 N narrows the range of sample radii too much. It is found that experiments at high shear rates are not limited by edge fracture but by insufficient normal force transducer capacities and by viscous dissipation heating. Calculations show that small cone angles (below should be used beyond to deal with this. Small cone angles necessarily require very stiff rheometers for a good short time resolution.