Active microrheology in a colloidal glass

Abstract

We study the dynamics of a probe particle driven by a constant force through a colloidal glass of hard spheres. This nonequilibrium and anisotropic problem is investigated using a new implementation of the mode-coupling approximation with multiple relaxation channels and Langevin dynamics simulations. A force threshold is found, below which the probe remains localized, while above it the probe acquires a finite velocity. We focus on the localized regime, comparing theory and simulations concerning the dynamics in the length scale of the cage and the properties of the transition to the delocalized regime, such as the critical power-law decay of the probe correlation function. Probe van Hove functions predicted by the theory show exponential tails reminiscent of an intermittent dynamics of the probe. This scenario is microscopically supported by simulations.

Critical force in active microrheology

“…The dynamics of this probe correlation function is derived from a microscopic overdamped Smoluchowski equation within the framework of mode-coupling theory (MCT) [20]. It is given by a integrodifferential equation (2) with initial condition Φ s q (0) = 1.…”

“…The numerical solution algorithm is described in Appendix C of [20] and in more detail in Chapter 3 of [21]. We choose a cutoff of q max d = 14 for q r and q z on a uniform grid from 0 to q max d with step size ∆qd = 0.5 with N = 29 points, which is refined towards 0 by adding N log = 10 nonuniformly spaced grid points given by 2 −i ∆qd (i = 1, .…”

“…for ϕ > ϕ g , we find f s q = 0 for small external forces, while f s q = 0 if the force is large enough. The smallest force for which f s q = 0 is the critical force and determines the delocalization transition [20]. The predictions for the behavior of the correlation function close to this critical point will provide us with several means to characterize the critical force in simulations and experiments.…”

“…Hence, this system is as far from the glass transition as the system used for the theoretical calculations. The preparation and properties of this glass have been discussed previously [20,30]. In essence, the system is equilibrated in a fluid state with the same density and moderate attractions; the attractions are then suddenly removed, leaving only the repulsive interactions.…”

“…In a previous study, active microrheology in a colloidal glass was analyzed with a model based on the modecoupling approximation, and tested against simulations [20]. It was found in that work that there are two regimes for the dynamics of the tracer: a localized regime, found when the external force is small, and where the tracer is trapped in the cage formed by its own neighbours, and a delocalized regime, when the force is large enough to break the cage, and the tracer exhibits motion over long distances.…”