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Register a new userMedium Amplitude Parallel Superposition (MAPS) Rheology of a Wormlike Micellar Solution
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The weakly nonlinear rheology of a surfactant solution of wormlike micelles is investigated from both a modeling and experimental perspective using the framework of medium amplitude parallel superposition (MAPS) rheology. MAPS rheology defines material functions, such as the third order complex compliance, which span the entire weakly nonlinear response space of viscoelastic materials to simple shear deformations. Three-tone oscillatory shear deformations are applied to obtain feature-rich data characterizing the third order complex compliance with high data throughput. Here, data for a CPyCl solution are compared to the analytical solution for the MAPS response of a reptation-reaction constitutive model, which treats micelles as linear polymers that can break apart and recombine in solution. Regression of the data to the model predictions provides new insight into how these breakage and recombination processes are affected by shear, and demonstrates the importance of using information-rich data to infer precise estimates of model parameters.
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A new mathematical representation for nonlinear viscoelasticity is presented based on application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and experimental framework, which we call Medium Amplitude Parallel Superposition (MAPS) Rheology, reveals a new material property, the third order complex modulus, which describes completely the weakly nonlinear response of a viscoelastic material in an arbitrary simple shear flow. In this first part, we discuss several theoretical aspects of this mathematical formulation and new material property. For example, we show how MAPS measurements can be performed in strain- or stress-controlled contexts and provide relationships between the weakly nonlinear response functions measured in each case. We show that the MAPS response function is a super-set of the response functions that have been previously reported in medium amplitude oscillatory shear and parallel superposition rheology experiments. We also show how to exploit inherent symmetries of the MAPS response function to reduce it to a minimal domain for straightforward measurement and visualization. We compute this material property for a few constitutive models to illustrate the potential richness of the data sets generated by MAPS experiments. Finally, we discuss the MAPS framework in the context of some other nonlinear, time-dependent rheological probes and explain how the MAPS methodology has a distinct advantage over these others because it generates data embedded in a very high dimensional space without driving fluid mechanical instabilities, and is agnostic to the flow protocol.
An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This experimental protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies. Imposing this deformation and measuring the mechanical response reveals a rich data set consisting of up to 19 measurements of the third order complex modulus at distinct three-frequency coordinates. We discuss how the choice of the input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting data set is indeed large and feature-rich, while still being acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represents measurements of an intrinsic material function by studying its internal consistency, its compatibility with low-frequency predictions for Coleman-Noll simple fluids, and its agreement with data obtained via MAOS amplitude sweeps. Finally, the data is compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a materials time-dependent response.
We present results of temperature dependent measurements of dynamics of micellar nanoparticle - polymer composites of fixed volume fraction and variable polymer chain grafting density. For nanoparticles with lower grafting density we observe dynamically arrested state at low temperatures corresponding to an attractive glass while at high temperature the same system shows relaxation typical of a repulsive glass. For higher grafting density, the low temperature dynamics resembles more of a gel which crosses over to a repulsive glass at high temperature. Possible reasons for such fascinating dynamical transitions is delineated.
The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted by the oppositely charged confinement on the polyelectrolyte chains. Furthermore, by altering the placement of the charged confinement counterions, enhanced polyelectrolyte separation can be achieved by utilizing surface polarization effect due to dielectric mismatch between the media inside and outside the confinement.
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $phi_R$. Chains with degree of entanglement $Zapprox14$ mixed to produce 10 well-entangled systems with $phi_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a function of $phi_R$, and identify with simple arguments a ring fraction $phi_Rapprox0.4$ where the topological constraints of the entanglement network are maximized. These topological analyses are used to rationalize the $phi_R$-dependence of ring and linear chain dynamics, conformations, and blend viscosity. Complimentary simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments, and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymer conformations that is caused by the convective unthreading of rings from linear chains. This produces significant changes in the entanglement structure of blends that we directly visualize and quantify with primitive path analyses during flow.
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