Nonlinear elasticity and yielding of depletion gels

Abstract

A microscopic activated barrier hopping theory of the viscoelasticity of colloidal glasses and gels has been generalized to treat the nonlinear rheological behavior of particle-polymer suspensions. The quiescent cage constraints and depletion bond strength are quantified using the polymer reference interaction site model theory of structure. External deformation (strain or stress) distorts the confining nonequilibrium free energy and reduces the barrier. The theory is specialized to study a limiting mechanical description of yielding and modulus softening in the absence of thermally induced barrier hopping. The yield stress and strain show a rich functional dependence on colloid volume fraction, polymer concentration, and polymer-colloid size asymmetry ratio. The yield stress collapses onto a master curve as a function of the polymer concentration scaled by its ideal mode-coupling gel boundary value, and sufficiently deep in the gel is of an effective power-law form with a universal exponent. A similar functional and scaling dependence of the yield stress on the volume fraction is found, but the apparent power-law exponent is nonuniversal and linearly correlated with the critical gel volume fraction. Stronger gels are generally, but not always, predicted to be more brittle in the strain mode of deformation. The theoretical calculations appear to be in accord with a broad range of observations.

Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear

“…As Masschaele et al have shown in a study on yielding in two-dimensional gels [42], the characteristic scale of structural deformations becomes increasingly localized as gel concentration increases and the typical spatial scale is only a few particle diameters in the concentrated regime. Further, effective theories based on mode-coupling ideas have successfully predicted many features of yielding in concentrated colloidal gels [43,44]. These theories consider only local structural properties, specifically those contained in the static structure factor S(q), and issues such as large-scale heterogeneity, the connectivity of the gel structure, and bond percolation are not taken into account.…”

The influence of shape on the glassy dynamics of hard nonspherical particle fluids. II. Barriers, relaxation, fragility, kinetic vitrification, and universality

“…34 This is in contrast to our results for hard nonspherical objects where the smooth hard sphere is characterized by an intermediate level of dynamic fragility, larger than the fragility of rods and disklike particles but smaller than the compact Conway and non-Conway cluster particles. Our theory as it stands can be applied to study nonlinear viscoelasticity 36 and the linear and nonlinear dynamics of fluids of attractive nonspherical particles that form gels or attractive glasses. 36,37 The theory employed in this work is oversimplified in the sense that it does not describe rotational dynamics.…”

“…Our theory as it stands can be applied to study nonlinear viscoelasticity 36 and the linear and nonlinear dynamics of fluids of attractive nonspherical particles that form gels or attractive glasses. 36,37 The theory employed in this work is oversimplified in the sense that it does not describe rotational dynamics. This limitation has recently been overcome at the NMCT and NLE levels for uniaxial rigid objects where both CM forces and torques are present.…”

Derivation of a microscopic theory of barriers and activated hopping transport in glassy liquids and suspensions

“…23 Kawasaki 24 proposed a dynamic density-functional theory ͑DDFT͒ for the collective density field which employs the equilibrium densityfunctional theory 25 as input. The theory is sufficiently general and simple that it has been extended and quantitatively applied to treat slow activated dynamics in hard-sphere colloidal and nanoparticle glasses, 34,38,39 polymer-particle depletion gels, 40,41 nonlinear rheological phenomena in particle gels 42 and glasses, 43 isotropic polymer melts, 44,45 and anisotropic polymer systems including oriented liquid crystals, strained cross-linked networks, and thin films. 26 Conceptually different thermodynamic-based approaches that focus on an "entropy catastrophe" have also been pursued.…”