Volume 48, Issue 1, January 2004
Index of content:
48(2004); http://dx.doi.org/10.1122/1.1634988View Description Hide Description
The viscoelasticproperties of a 4-branched poly(ethylene oxide)-poly(propylene oxide)- poly(ethylene oxide) copolymer in aqueous solutions have been studied in all parts of its phase diagram. In the unimer zone, the solution behaves like a Maxwellian fluid. The formation of micelles induces the presence of a secondary relaxation process on the dynamic mechanical response of the system. When the micelles condense into a crystalline body centered structure, the solution exhibits rheological properties similar to the behavior of an entangled polymer. The crystal’s terminal relaxation time τ is strongly dependent on the value of the stress used in the dynamic mechanical test. Stress-time relationships can also be observed with yield stress measurements. First of all, the structural origin of these phenomena has been explored. The relevance of several already proposed mechanisms has been analyzed and discrepancies between rheological results and SANS experiments discussed. We have been able to demonstrate that the evolution of the crystalline phase’s terminal relaxation time with stress can be described with an approach derived from Eyring’s theory. Moreover, this rheological relaxation time has been interpreted as being characteristic of a micelle’s diffusion in a crystalline structure. Finally, the values of the diffusion length and the intermicellar energy have been calculated and compared to already existing theories.
The effect of (2-hydroxypropyl)-β-cyclodextrin on rheology of hydrophobically end-capped poly(ethylene glycol) aqueous solutions48(2004); http://dx.doi.org/10.1122/1.1631422View Description Hide Description
(2-Hydroxypropyl)-β-cyclodextrin (HPBCD), a modified cyclic oligosaccharide, changes the flow behavior of aqueous solutions of a model telechelic associative polymer,hydrophobically end-capped poly(ethylene glycol) (ODU-12), because the inclusion complexation of HPBCD and octadecyl end-capping groups interferes with aggregation of the polymer end groups. The HPBCD-induced decrease in the high-frequency modulus can be well described assuming a 1:1 binding isotherm, but cannot fully explain the decrease in the low shear rate Newtonian viscosity, because HPBCD also strongly decreases the relaxation time. Consequently, besides decreasing low shear rate Newtonian viscosity, HPBCD also extends the Newtonian behavior to higher shear rates as predicted by the free-path version of the transient network theory [Marrucci et al., Macromolecules26, 6483–6488 (1993)].
Structural effects on the viscoelasticity of polydimethylsiloxane networks close to the sol-gel threshold48(2004); http://dx.doi.org/10.1122/1.1631421View Description Hide Description
Polydimethylsiloxane(PDMS) networks were obtained by hydrosilation of a difunctional vinyl-terminated PDMS prepolymer with three crosslinkers of different functionality and molecular weight. These samples were studied using dynamic viscoelastic experiments as a function of time and frequency. Critical parameters were determined close to and above the sol-gel threshold. Rheological master curves could be built for the three PDMS networks above the gel point. The results obtained suggest that the critical exponents are not universal and depend on the chemical structure of the incipient networks.
48(2004); http://dx.doi.org/10.1122/1.1631424View Description Hide Description
In a recent paper, Ottinger and Beris assert that the celebrated Doi–Edwards (DE) model for entangled polymer dynamics is incompatible with the so-called “GENERIC” form of nonequilibrium thermodynamics. Simply put, they claim that the DE model for tube dynamics is inconsistent with the principle of virtual work. I show that with the correct choice of effective Hamiltonian, namely the full tube configurational entropy, the DE stress tensor does in fact result from a virtual work argument.
New technique for reconstructing instantaneous velocity profiles from viscometric tests: Application to pasty materials48(2004); http://dx.doi.org/10.1122/1.1626677View Description Hide Description
We present a new technique for reconstructing the instantaneous velocity profiles during creep, dynamic, or ramp tests under controlled stress in wide-gap Couette flows, from a series of similar tests under smaller stress amplitudes. This approach is based on a rigourous theory, and since it requires that the fluid does not flow close to the outer cylinder, it is particularly suitable for yield stress fluids. The interest of this reconstruction technique is that it is simpler than direct techniques (nuclear magnetic resonance,light scattering, particle imagingvelocimetry, etc.) and has almost no limitations in time and space resolution. Thus, one can obtain the velocity profiles under steady-state and transient flows. We show that for a commercial hair gel the velocity profile obtained with this technique is in excellent agreement with that found from magnetic resonance imaging rheometry within the range of measurement (four decades of velocity). From other tests with a mustard and a kaolin–water suspension we demonstrate that the “viscosity bifurcation” effect observed with various pasty materials [Coussot et al., Phys. Rev. Lett. (2002a)] is directly associated with an abrupt change in the slope of the velocity profiles at the interface between the sheared and unsheared regions. We also show that the effect of wall slip on the reconstructed velocity profile is to shift the level of the unsheared region to a virtual, constant, finite, velocity level.
48(2004); http://dx.doi.org/10.1122/1.1626675View Description Hide Description
A phenomenological model for the dynamics of a single drop immersed in an immiscible matrix is proposed with the two incompressible component liquids being in general viscoelastic. The model is formulated by assuming that the drop is always ellipsoidal, and the model parameters are determined once and for all in the small deformation limit. The model is thereafter applicable to whatever flow condition is imposed at infinity, and for whatever intensity of flow field. Predictions of steady state deformation,drop breakup, and drop relaxation display the effects of constitutive elasticity on the dropdynamics.
48(2004); http://dx.doi.org/10.1122/1.1631423View Description Hide Description
An elongational rheometer is used to study the rheological behavior of gelled propellant simulants in uniaxial elongational flow. In simple shear such fluids typically exhibit a shear thinning behavior which could be described by a power-law constitutive equation. Knowledge of the elongational behavior of these fluids is important for understanding the processes of their atomization and spray formation. The results of the present work demonstrated that the three-dimensional power-law model permits description of uniaxial elongation of these fluids as well. Moreover, the values of the rheological parameters of the tested fluids measured in simple shear and in uniaxial elongation agree fairly closely. Therefore the elongational behavior of gelled propellant simulants can be inferred from their shear behavior.
48(2004); http://dx.doi.org/10.1122/1.1626678View Description Hide Description
We examine if a microrheological interpretation of probe diffusion in modeldispersions dominated by excluded-volume interactions and hydrodynamics captures the underlying viscoelastic relaxation mechanisms reasonably accurately. Standard dynamic light scattering is used to measure mean-squared displacements (MSDs) of visible probe particles in a refractive-index-matched model hard-sphere dispersion [poly(methyl methacrylate) particles in cycloheptyl alcohol]. The loss and storage moduli of the dispersion are extracted as functions of frequency ω from the measured MSDs. We suggest a semiempirical modification of the generalized Stokes–Einstein relation to convert the MSD to the viscoelasticmodulus The results show a volume-fraction-dependent plateau at high frequencies in the storage modulus consistent with the domination of lubrication stresses. Viscoelasticity sets in at volume fractions φ above 0.2, and for the ratio of the mean viscoelasticrelaxation time 〈τ〉 to the Péclet time remains constant as had been observed previously for index-matched silica dispersions, but the microrheological measurements show a narrower spectrum of relaxation times. Master curves could be constructed for as sole functions of frequencies scaled with in the above volume-fraction range. The microrheological method used provides moduli over a large range of frequencies from single measurements and avoids the need for time–temperature superposition to reach high frequencies. The effects of fast relaxation phenomena caused by soft surface layers and the deviations from hydrodynamic interactions expected for ideal hard-sphere systems can also be examined.
48(2004); http://dx.doi.org/10.1122/1.1634987View Description Hide Description
Shear-induced coalescence was studied in immiscible blends of polydimethylsiloxane(PDMS) and polyisoprene (PI) with a droplet-matrix morphology, using both rheology and scanning electron microscopy. Dynamic moduli of the blends compatibilized with different amounts of a PDMS–PI diblock were measured. The experimental results indicate that the blend response is characterized by two relaxation mechanisms. The general Palierne model with an interfacial shear modulus was used to analyze the data, since this model can describe the dynamic response of polymer blends in which interfacial tension gradients induce an extra relaxation mechanism besides droplet relaxation. Scanning electron microscopy was used to investigate the droplet size evolution in the blends during coalescence. For systems with a high amount of compatibilizer, it is shown that coalescence is completely suppressed under the conditions studied here.
48(2004); http://dx.doi.org/10.1122/1.1631425View Description Hide Description
The effect of a delicate balance of forces on the interparticle dynamics and structure of monodisperse spherical polystyrene particles suspended at the interface between decane and water was observed as shear flow was applied to the system. A strong dipole–dipole repulsion, due to ionizable surface sulfate groups, induces the particles to arrange themselves on a hexagonal lattice under quiescent conditions. The application of a shear flow to the interface, however, forces the lattice into a new semiordered, anisotropic state over which great control is exerted by particle concentration and applied shear rate. At low particle concentrations or high shear rates, the forces applied by the flow dominate the system and cause strings of particles to align in the flow direction to facilitate their movement past each other. A remarkable contrast to this behavior is seen at high concentrations or low shear rates, where the interparticle forces gain importance and tend to more strongly keep the particles in their lattice positions. Consequently, domains of particles are forced to rotate in the flow. The transition between these two regimes and the nature of this rotation, including an associated cyclic melting and crystallization of the lattice, is discussed.
Structure scaling properties of confined nematic polymers in plane Couette cells: The weak flow limit48(2004); http://dx.doi.org/10.1122/1.1626676View Description Hide Description
One of the confounding issues in laminar flow processing of nematic polymers is the generation of molecular orientational structures on length scales that remain poorly characterized with respect to molecular and processing control parameters. For plane Couette flow within the Leslie–Ericksen continuum model, theoretical results since the 1970s yield two fundamental predictions about the length scales of nematic distortion: a power law scaling behavior, where Er is the Ericksen number (ratio of viscous to elastic stresses); the exponent varies according to whether the structure is a localized boundary layer or an extended structure. Until now, comparable results which incorporate molecular elasticity (i.e., distortions in the shape of the orientational distribution) have not been derived from mesoscopic Doi–Marrucci–Greco (DMG) tensor models. In this paper, we derive asymptotic, one-dimensional gap structures, along the flow-gradient direction, in “slow” Couette cells, which reflect self-consistent coupling between the primary flow, in-plane director (nematic) and order parameter (molecular) elasticity, and confinement conditions (plate speeds, gap height, and director anchoring angle). We then read off the small Deborah number, viscoelastic structure predictions: The flow is simple shear. The orientation structures consist of: two molecular-elasticity boundary layers with the Marrucci scaling which are amplified by tilted plate anchoring; and a nonuniform, director-dominated structure that spans the entire gap, with average length scale, present for any anchoring angle. We close with direct numerical simulations of the DMG steady, flow-nematic boundary-value problem, first to benchmark the small Deborah number structure formulas, and then to document onset of new flow-orientation structures as the asymptotic expansions become disordered.
Tensorial constitutive models for disordered foams, dense emulsions, and other soft nonergodic materials48(2004); http://dx.doi.org/10.1122/1.1634985View Description Hide Description
In recent years, the paradigm of soft glassy matter has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting soft glassy rheology (SGR) model treats the shear stress in isolation, effectively scalarizing the stress and strain rate tensors. Here we offer generalizations of the SGR model that combine its nontrivial aging and yield properties with a tensorial structure that can be specifically adapted, for example, to the description of fluid film assemblies or disordered foams.
On the polymer entropic force singularity and its relation to extensional stress relaxation and filament recoil48(2004); http://dx.doi.org/10.1122/1.1626679View Description Hide Description
We examine the use of transient extensional rheology as a means of examining worm-like and freely jointed chain behavior of polymers in dilute solution at high extension. We demonstrate theoretically that both chain types follow different power-law stress decay functions for short times after cessation of strong extensional flow. The different power laws are universal for different strain and strain-rate histories and, moreover, are signatures of the singularities in the entropic-spring force laws that develop close to full extension. We also demonstrate that these power-law exponents are directly related to the inertialess elastic recoil of an extensionally stretched filament of polymer solution. Finally, these theoretical predictions are compared to experimental results for the relaxation of stress following extension for monodisperse polystyrene solutions. When modeled as freely jointed chains, we find excellent agreement with the theoretical predictions.
The Newtonian viscosity of concentrated stabilized dispersions: Comparisons with the hard sphere fluid48(2004); http://dx.doi.org/10.1122/1.1634986View Description Hide Description
The Newtonian shear viscosity, of near-hard-sphere colloidal particle liquids from many sources at various packing fractions is compared with that of the pure hard sphere fluid which can be calculated essentially exactly by molecular dynamics, MD, computer simulations. The experimental relative viscosities for the colloidal systems, where is the viscosity of the solvent, generally lie in between two curves formed from the hard-sphere data, namely, as an upper bound and the inverse self-diffusion coefficient, as the lower bound, where and are the Boltzmanntransport coefficients accurate at low densities. Brownian dynamics simulation values of and where is the long-time self-diffusion coefficient are close to this lower bound which indicates that Brownian motion alone without hydrodynamic interactions underestimates the viscosity of the system. Hydrodynamic effects increase the viscosity closer to the pure hard-sphere curve obtained by MD. The ratio, obtained from the experimental data increases slightly more rapidly than at high packing fractions. There is a near-linear relationship between the inverse viscosity (fluidity) and self-diffusion coefficient with inverse packing fraction for the hard-sphere fluid, the former proposed by Dymond (1974). This analytic form accounts reasonably well for the corresponding quantities of the colloidal systems as well. We analyzed the values of the relative viscosities at 50% packing fraction. We conclude that the value is ∼40 for the pure hard sphere fluid itself from recent molecular dynamics simulations by of Sigurgeirsson and Heyes (2003), and probably ∼25±5 from experiments on real near-hard sphere colloids (although the experimental scatter is quite large), and ∼10 by Brownian dynamicscomputer simulations. For the long time self-diffusion coefficient the ratio is ∼40±10 for experimental colloidal systems, and ∼10 from simulation by molecular dynamics and Brownian dynamics. The infinite frequency shear viscosity has a ratio ∼10 and the short-time self-diffusion coefficient ratio is ∼4, both of which are somewhat lower than their long-time counterparts. The shear viscosity at finite shear rates in the second Newtonian plateau typically lies in between the values of the Newtonian viscosity and the infinite frequency viscosity (i.e., ∼15±5).