Visualizing the strain evolution during the indentation of colloidal glasses

Elastic criterion for shear-banding instability in amorphous solids

In amorphous solids, plastic flow is prone to localization into shear bands via an avalanche of shear-transformation (ST) rearrangements of constituent atoms or particles. However, such banding instability still remains a lack of direct experimental evidence. Using a real 3D colloidal glass under shear as proof of principle, we study STs' avalanches into shear banding that is controlled by strain rates. We demonstrate that, accompanying the emergent shear banding, the elastic response fields of the system, typical of a quadrupole for shear and a centrosymmetry for dilatation, lose the Eshelby-type spatial symmetry; instead, a strong correlation appears preferentially along the banding direction. By quantifying the fields' spatial decay, we identify an elastic criterion for the shear-banding instability, that is, the strongly correlated length of dilatation is smaller than the full length of shear correlation. Specifically, ST-induced free volume has to be confined within the elastic shear domain of ST so that those STs can self-organize to trigger shear banding. This physical picture is directly visualized by tracing the real-space evolution of local dilatation and ST particles. The present work unites the two classical mechanisms: free volume and STs, for the fundamental understanding of shear banding in amorphous solids.

Cooling-rate induced softening in a colloidal glass

Contrary to crystalline solids, amorphous solids always become softer when vitrifying the melts under higher cooling rates. Understanding this phenomenon is of utmost importance in providing a basis for the mechanical-performance control of amorphous solids. However, the underlying mechanisms leading to this cooling-rate-induced softening of amorphous solids have remained elusive, especially the dynamic reasons are neglected. Here, we use a colloidal glass as the model system to directly study this issue. Shear modulus is used as the representative parameter to monitor the stress-bearing properties of colloidal glass. The space-spanning immobile particles, whose population is sensitive to the cooling rate, are found to make the dominant contribution to the shear modulus. The rapid solidification induced softening of colloidal glass is observed to originate from fewer immobile particles formed at higher cooling rates.

Direct Observation of Percolation in the Yielding Transition of Colloidal Glasses

When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Because of the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow us to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of nonaffine deformation percolating at yielding. In agreement with percolation theory, the spanning cluster is fractal with a fractal dimension d_{f}≃2, and the correlation length diverges upon approaching the critical yield strain. These results indicate that percolation of highly nonaffine particles is the hallmark of the yielding transition in disordered glassy systems.

Direct visualization of free-volume-triggered activation of β relaxation in colloidal glass

β relaxation, which is predicted by mode coupling theory and involves the localized motions of particles, initiates in a supercooled liquid and continues into glassy state. It correlates essentially with many fundamental properties of amorphous materials. Despite its importance, the underlying mechanisms leading to the β relaxation have remained elusive. As natural heterogeneity, the original distributed free volume has been supposed to be associated with the activation of β relaxation in amorphous solids. However, there has been no direct experimental proof for this hypothesis. Here we used a colloidal glass to directly observe the β relaxation and free-volume distribution. We found a spatial correlation between the β relaxation and free volume. The large free volume regions were observed to possess a low-energy cost of relaxation-induced strain, indicating that the large free volume region presenting a low-energy barrier for structural relaxation benefits the β relaxation.

Strain fluctuations and elastic moduli in disordered solids

Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses.

Local shear transformations in deformed and quiescent hard-sphere colloidal glasses

We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50,000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10(-5) s(-1)] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Experimental signatures of a nonequilibrium phase transition governing the yielding of a soft glass

We present direct experimental signatures of a nonequilibrium phase transition associated with the yield point of a prototypical soft solid-a binary colloidal glass. By simultaneously quantifying single-particle dynamics and bulk mechanical response, we identified the threshold for the onset of irreversibility with the yield strain. We extracted the relaxation time from the transient behavior of the loss modulus and found that it diverges in the vicinity of the yield strain. This critical slowing down is accompanied by a growing correlation length associated with the size of regions of high Debye-Waller factor, which are precursors to yield events in glasses. Our results affirm that the paradigm of nonequilibrium critical phenomena is instrumental in achieving a holistic understanding of yielding in soft solids.