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Register a new userAnalyzing Onset of Nonlinearity of a Colloidal Gel at the Critical Point
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In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.
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We introduce a model gel system in which colloidal forces, structure, and rheology are measured by balancing the requirements of rheological and microscopy techniques with those of optical tweezers. Sterically stabilized poly(methyl methacrylate) (PMMA) colloids are suspended in cyclohexane (CH) and cyclohexyl bromide (CHB) with dilute polystyrene serving as a depletion agent. A solvent comprising of 37% weight fraction CH provides sufficient refractive index contrast to enable optical trapping, while maintaining good confocal imaging quality and minimal sedimentation effects on the bulk rheology. At this condition, and at a depletant concentration c = 8.64 mg/mL (c/c* = 0.81), results from optical trapping show that 50% of bonds rupture at 3.3 pN. The linear strain-dependent elastic modulus of the corresponding gel (volume fraction = 0.20) is G = 1.8 Pa, and the mean contact number of the particles in the gel structure is 5.4. These structural and rheological parameters are similar to colloidal gels that are weakly aggregating and cluster-like. Thus, the model gel yields a concomitant characterization of the interparticle forces, microstructure, and bulk rheology in a single experimental system, thereby introducing the simultaneous comparison of these experimental measures to models and simulations.
We use numerical simulations and an athermal quasi-static shear protocol to investigate the yielding of a model colloidal gel. Under increasing deformation, the elastic regime is followed by a significant stiffening before yielding takes place. A space-resolved analysis of deformations and stresses unravel how the complex load curve observed is the result of stress localization and that the yielding can take place by breaking a very small fraction of the network connections. The stiffening corresponds to the stretching of the network chains, unbent and aligned along the direction of maximum extension. It is characterized by a strong localization of tensile stresses, that triggers the breaking of a few network nodes at around 30% of strain. Increasing deformation favors further breaking but also shear-induced bonding, eventually leading to a large-scale reorganization of the gel structure at the yielding. At low enough shear rates, density and velocity profiles display significant spatial inhomogeneity during yielding in agreement with experimental observations.
We report a molecular dynamics simulation study of a model gel whose interaction potential is obtained by modifying the three body Stillinger-Weber model potential for silicon. The modification reduces the average coordination number, and suppresses the liquid-gas phase coexistence curve. The low density, low temperature equilibrium gel that can thus form exhibits interesting dynamical behavior, including compressed exponential relaxation of density correlations. We show that motion responsible for such relaxation has ballistic character, and arises from the motion of chain segments in the gel without the restructuring of the gel network.
The thermal conductivity $kappa$ of underdoped Y was measured in the $T to 0$ limit as a function of hole concentration $p$ across the superconducting critical point at $p_{SC}$ = 5.0%. ``Time doping was used to resolve the evolution of bosonic and fermionic contributions with high accuracy. For $p leqslant p_{SC}$, we observe an additional $T^3$ contribution to $kappa$ which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, manifest as a linear term in $kappa$, is seen to persist unaltered through $p_{SC}$, showing that the state just below $p_{SC}$ is a thermal metal. In this state, the electrical resistivity varies as log$(1/T)$ and the Wiedemann-Franz law is violated.
Dynamic Light Scattering (DLS) measurements were performed on colloidal suspensions of Laponitetextsuperscript{textregistered} at different concentrations in the range $C_text{w}= (1.5{div}3.0)$%. The slowing down of the dynamics induced by aging was monitored by following the temporal evolution of autocorrelation functions at different concentrations towards the gel and glass transition. Exploiting analogies with supercooled liquids approaching their glass transitions, an Angell plot for the structural relaxation times was drawn. Finally, the fragility of Laponitetextsuperscript{textregistered} suspensions at different concentrations, in different solvents, at two salt concentrations and with the addition of a polymer was reported and discussed.
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