Volume 53, Issue 2, March 2009
Index of content:
53(2009); http://dx.doi.org/10.1122/1.3045803View Description Hide Description
The way a colloidal glass flows under the influence of external shear is still not fully understood. Here, we study the rheology of glasses of soft thermosensitive core-shell particles with particular emphasis on nonlinear oscillatory and steady measurements and present a comprehensive set of data which display strong nonlinear effects. Step rate experiments exhibit stress overshoots which increase with shear rate, while dynamic strain sweeps reveal a peak in the loss modulus and a yield strain that increases with volume fraction and frequency. Moreover, a Fourier transform analysis of oscillatory measurements yields a significant contribution of high harmonics in the stress which peaks in the shear thinning regime acquiring values up to 25%. A key question is whether shear induced melting is caused by a simple advection process where the shear induced relaxation time,, scales inversely proportional with the shear rate,, or is governed by the energy flow in the system, thus depending on both stress, , and shear rate as . Using a simple phenomenological model based on that of Derec et al. [Phys. Rev. E67, 061403 (2003)] we managed to reproduce the main features of our rheological data, the shape of the stress oscillations in the dynamic measurements, as well as the strain dependence of the higher harmonic contribution. This analysis suggests that nonlinearities are important during the yielding process, and the shear induced relaxation time follows a nontrivial dependence on both the stress and strain rate.
53(2009); http://dx.doi.org/10.1122/1.3072013View Description Hide Description
The conformational properties of a model macromolecule, namely DNA, in an oscillatory shear flow have been investigated using Brownian dynamics (BD) simulations. To elucidate the influence of time periodic motion on the chain dynamics, the simulation results have been compared to previous experimental and BD simulation studies in steady simple shear flow. Based on these comparisons, we have determined that when the Deborah number (De), defined as the product of polymerrelaxation time and the angular forcing frequency, is less than a critical , which corresponds to , where is the tumbling frequency of the chain in a corresponding simple steady shear flow,macromolecules exhibit similar dynamics as their steady shear flow counterpart in each half-cycle. Specifically, at the polymer chain experiences end-over-end tumbling events in each half-cycle, which give rise to odd harmonics in the power spectral density (PSD) of the orientation angle, where the fundamental mode of frequency corresponds to the forcing frequency . At , chain flipping is the predominant event observed. Thus there are two distinct regions in the parameter space: (1) a plateau regime at , where the chain dynamics and average conformational properties of the macromolecules are essentially the same as the corresponding steady shear flow, and (2) a power-law regime at , where the chain dimension approaches its equilibrium value as is significantly enhanced.
Influence of anionic surfactant on the rheological properties of hydrophobically modified polyethylene-oxide/cyclodextrin inclusion complexes53(2009); http://dx.doi.org/10.1122/1.3059563View Description Hide Description
Associative polymers, such as hydrophobic ethoxylated urethane (HEUR), interact with various cyclodextrins (CDs) to form inclusion complexes in aqueous solution. The rheological behavior of HEUR/CD inclusion complex solutions can be manipulated by the introduction of an anionic surfactant, such as sodium dodecyl sulfate (SDS), and such behavior is dependent on the characteristics and types of CD. The introduction of SDS partially restores the viscoelastic behavior of the HEUR/methylated system, but it completely recovers the viscoelastic behavior of the system. Such difference is attributed to the different binding affinity of SDS and CDs. Temperature dependence of the viscoelastic behavior revealed that the activation energy and plateau modulus for system were higher than those of the system. In excess amounts of SDS, the interaction between SDS and HEUR/CD inclusion complexes was similar to that of SDS and HEUR. Isothermal titration calorimetric study provided physical insights on the binding mechanism responsible for the recovery of the viscoelastic properties of HEUR/CD/SDS ternary systems.
A generalized differential constitutive equation for polymer melts based on principles of nonequilibrium thermodynamics53(2009); http://dx.doi.org/10.1122/1.3059429View Description Hide Description
Based on principles of nonequilibrium thermodynamics, we derive a generalized differential constitutive equation for polymer melts which incorporates terms that account for anisotropic hydrodynamic drag in the form suggested by Giesekus, finite chain extensibility with nonlinear molecular stretching, nonaffine deformation, and variation of the longest chain relaxation time with chain conformation. In the new equation, the expression for the Helmholtz free energy of deformation is defined such that the entropy remains bounded even at high deformation rates, as it should from a physical point of view. Key elements in the new constitutive model are the functions describing the dependence of the nonequilibrum free energy and the relaxation matrix on the conformation tensor. With suitable choices of these two functions, the new equation reduces to a number of well-known viscoelastic models. However, it is more general in the sense that it permits incorporating into a single constitutive differential equation more accurate expressions for the description of chain elasticity and relaxation. Restrictions on the parameters entering these two functions are obtained by analyzing the thermodynamic admissibility of the model. By analyzing the asymptotic behavior of the new constitutive equation at low and high shear rates in steady shear, one can fix all of its parameters from available rheological data for the conformation tensor except for one which should be fitted. We illustrate the procedure here where the new model is used to fit available rheological data for short polyethylene melts obtained through direct nonequilibrium molecular dynamics simulations in shear and planar elongation, with remarkable success.
53(2009); http://dx.doi.org/10.1122/1.3056631View Description Hide Description
A procedure is described and analyzed for the determination of the relative placement of linear viscoelastic functions and their relative relaxation∕retardation spectra for a commercial polycarbonate (LEXAN GE). The complete set of viscoelastic functions in creep and relaxation was obtained from two simple experimental data, namely the linear viscoelastic response in shear and the pressure volume temperature (PVT) behavior. The dimensionless bulk compliance was extracted from PVT data showing that it coincides with the memory function appearing in the Kovacs, Aklonis, Hutchinson, Ramos phenomenological theory [Kovacs, A. J., J. J. Aklonis, J. M. Hutchinson, and A. R. Ramos, J. Polym. Sci., Polym. Phys. Ed.17, 1097 (1979)]. Our results are compared with the relevant literature data obtained on different polymers and show that polycarbonate fulfills simultaneously the responses features concerning the relative placement of the bulk and shear moduli [Kono, R. J., Phys. Soc. Jpn.15, 4 (1960)], the shapes of the bulk and the shear retardation spectra [Bero, C. A., and D. J. Plazek, J. Polym. Sci., Part B: Polym. Phys.29, 39–47 (1991)], the relative placement of the bulk and shear compliance [Deng, T. H., and W. G. Knauss, Mech. Time-Depend. Mater.1, 33–49 (1997); Sane, S. B., and W. G. Knauss, Mech. Time-Depend. Mater.5, 293–324 (2001)], the relative placement of bulk modulus and shear compliance [Meng, Y., and S. L. Simon, J. Polym. Sci., Part B: Polym. Phys.45, 3375–3385 (2007)], the relative placement of the bulk compliance and the axial relaxationmodulus [Knauss, W. G., and I. Emri, Polym. Eng. Sci.27, 86–100 (1987)], and the shape of the Poisson’s ratio [Lakes, R. S., Cell. Polym.11, 466–469 (1992); Von Koppelmann, J., Rheol. Acta1, 20–28 (1958); Ferry, J. D., Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1980)], and its scaling with the shear modulus [O’Brien, D. J., N. R. Sottos, and S. R. White, Exp. Mech.47, 237 (2007)].
53(2009); http://dx.doi.org/10.1122/1.3058438View Description Hide Description
We measure the microviscosity of a colloidalsuspension using active, oscillatory laser tweezer microrheology. Our results are compared to a new theoreticalmodel that explicitly accounts for different bath and probe particle sizes and the three independent contributions to the stress: direct interactions (collisions) between the probe and suspension particles; indirect interactions between suspension particles; and the Einstein contribution of the suspension particles. Notably, direct and indirect interactions give rise to two characteristic and highly separated dimensionless frequencies or Peclet numbers as the probe diameter becomes large relative to the average suspension particle diameter, but are identical in the limit that the diameters are equal. The experimental microviscosities are consistent with indirect interactions dominating the direct bath-probe collisions in the large probe limit. This enables a reinterpretation of previous drag microrheology experiments in the large probe limit, further confirming the promise that microrheology can, by actively driving the probe particle, be adapted to measure the nonlinear rheology of complex fluids.
53(2009); http://dx.doi.org/10.1122/1.3073753View Description Hide Description
We present measurements of the rheology of suspensions of rigid spheres in a semi-dilute polymer solution from experiments of steady and oscillatory shear. For a given value of the shear rate, addition of particles enhances the viscosity and the first normal stress difference but decreases the magnitude of the second normal stress difference. The viscosity exhibits a power law variation in for a range of that grows with . The first normal stress is positive and its value grows with ; it exhibits a clear power law variation for the entire range of that was studied. The second normal stress difference is negative for the pure polymer solution and much smaller in magnitude than ; on addition of particles, its magnitude further decreases, and it appears to change sign at large . The behavior of and is at odds with the findings of recent studies on particle-loaded dilute polymer solutions and polymer melts. The small-amplitude oscillatory shear experiments show the linear viscoelasticproperties, and , increasing with at a given value of the angular frequency . The dynamic viscosity of the suspension differs substantially from its steady shear viscosity, and the difference increases as , .
53(2009); http://dx.doi.org/10.1122/1.3059575View Description Hide Description
The startup of uni-axial elongational flow followed by stress relaxation and reversed bi-axial flow has been measured for a branched polystyrene melt with narrow molar mass distribution using the filament stretching rheometer. The branched polystyrene melt was a multiarm pom-pom polystyrene with an estimated average number of arms of . The molar mass of each arm is about with an overall molar mass of . An integral molecular stress function constitutive formulation within the “interchain pressure” concept agrees reasonably well with the experiments.
53(2009); http://dx.doi.org/10.1122/1.3073754View Description Hide Description
Shear-induced ordering is known to occur in sheared suspensions. The range of parameters for which this order occurs is probed here by simulation of monodisperse Brownian hard-sphere suspensions using accelerated Stokesian Dynamics. The simulations are performed for particle volume fractions of at Péclet numbers of , where is the suspending fluid viscosity, is the imposed shear rate, is the sphere radius, and is the thermal energy. At , when particle volume fraction is above , the suspensions undergo ordering over extended periods at the onset of flow, with remarkable reduction in the shear viscosity and self-diffusivity. The thixotropic response is a result of microstructural ordering, which is characterized both by the real space pair distribution function and its Fourier transform, the static structure factor. Both show that the particles tend to flow in chains with hexagonal packing in the plane normal to the flow. An order parameter is formulated to quantitatively describe the strength of this hexagonal packing. This ordering is not observed at . Step changes in Pe are found to result in transitions of the structure and rheology. Hence the steady state rheology determined is uniquely associated with the flow conditions and particle fraction for most of the parameter space studied. However, near the boundary with respect to Pe between flow-induced order and disordered states of suspension at , the ultimate structure is history dependent within the typical simulation duration of material strain of .
53(2009); http://dx.doi.org/10.1122/1.3072077View Description Hide Description
The shear rheology of a model wormlike micellar solution exhibits moderate shear thinning and curved flow velocity profiles without discontinuity (nonbanding case). The shear rheology and the flowkinematics are analyzed within the framework of the Giesekus constitutive equation. Macroscopically, the steady state flow curve of the solution exhibits shear thinning with a shear exponent without hysteresis, indicative of a sample that does not shear band. The microstructure of the micellar network is probed by the combination of dynamic rheology, rheo-optics, and SANS. Flowkinematics in a Couette geometry are measured by particle tracking velocimetry and found to be consistent with predictions of the Giesekus constitutive equation fit to the bulk shear rheology. 1-2 plane SANS measurements of the segmental alignment under shear are also found to be in agreement with predictions of the constitutive equation, providing a coherent picture of the mechanisms by which wormlike micellesflow and shear thin. The degree of segmental alignment is found to lag behind predictions of the model, which is postulated to be a consequence of the long, branched topology of the wormlike micelles.
Rotation of a sphere in a viscoelastic liquid subjected to shear flow. Part II. Experimental results53(2009); http://dx.doi.org/10.1122/1.3073052View Description Hide Description
The effect of the viscoelastic nature of the suspending medium on the rotation of spherical particles in a simple shear flow is studied experimentally using a counter-rotating device. To evaluate the effect of variations in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features. These include a reference Newtonian fluid, a constant viscosity, high elasticity Boger fluid, a single relaxation time wormlike micellar surfactant solution, and a broad spectrum shear-thinningelasticpolymer solution. It is shown that particle rotation slows down, when compared to the Newtonian case, as elasticity increases, in qualitative agreement with computer simulation studies. Despite the variation in constitutive properties and the wide range of time scales of the fluids, it is found that the Weissenberg number suffices to scale the data: the dimensionless rotation speed of the spheres in the different fluids scales onto a single master curve as a function of the Weissenberg number. This indicates that the slowing down in rotation finds its main origin in (indirect) normal stress effects.