Slow Relaxations in Complex Fluids: Origin and Nature of Dynamical HeterogeneitiesB. Chakraborty, Brandeis University, DMR 0549762

Materials as diverse as molecular liquids, foams and granular matter experience a transition from a fluid-like to a solid-like state characterized only by the arrest of their dynamics. It has been proposed that the phenomena associated this dynamical arrest can explained within the unified framework of a jamming phase diagram[Liu+Nagel, 1997]. This phase diagram exists in the space of Temperature, Density, and Shear Stress and there are indications from simulations and experiments that a zero temperature critical point separates a jammed from an unjammed phase.

We have investigated granular systems in mechanical equilibrium, extending the framework of statistical mechanicsThe constraint of force balance can be used to construct a height vector field for any grain packin.

Using this field, we can construct a “canonical” ensemble for soft granular matter, where the trace, , and determinant, , of the stress tensor play roles analogous to the energy in a thermal system:

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Experimental data from Behringer group, Duke University

Leading to a natural phase-space of grain packings

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Scaling verification of ensemble in shear-free packings (Simulations of Corey O’Hern)

A field theory (S. Henkes + B. C., Phys. Rev. Lett. 95, 198002 (2005)) predicts a critical point on the 1/ axis, in qualitative agreement with experiments and simulations

ORIGIN: CRITICAL POINT?

Transition rates between metabasins

The origin of the anomalously slow dynamics of supercooled liquids approaching the glass transition is not yet fully understudied. With a Lennard-Jones binary mixture as a mode system, we have studied the dynamics projected on to the space of metabasins involving set of mechanically stable states which are connected by low barriers.

Slow Relaxations in Complex Fluids: Origin and Nature of Dynamical HeterogeneitiesB. Chakraborty, Brandeis University, DMR 0549762

ORIGIN: A phase transition in inherent-structure space?

To construct metabasins, we constructed clusters of inherent structures (local enengy minima) by throwing ``bond’’ between two structures if they had the highest transition rate from one to the other.

We found that the transition rates from each metabasin can be characterized with a activation energy and a factor .

doesn’t have a linear dependency on the metabasin energy.

varies strongly among metabasins, thus it is of importance as E* for understanding the glass transition.

Slow Relaxations in Complex Fluids: Origin and Nature of Dynamical HeterogeneitiesB. Chakraborty, Brandeis University, DMR 0549762

Nature of dynamical Heterogeneities in a dense, driven, 2D granular flow

Spatial map of the time taken by a particle to travel a distance r, showing that the dynamics is most heterogeneous at a lengthscale ~ 0.4 (grain diameter)

Size of heterogeneity () and the cage size (rpeak) for decreasing flow velocities approaching jamming.

The motion of “fast” and “slow” particles become increasingly separates as the system approaches jamming.

Allison Ferguson, B.C.To be submitted to Nature Physics