A new statistical mechanics for out-of-equilibrium soft materials
Whereas one can think of liquids or suspensions consisting of particles which move very slowly compared to gases, there comes a point where all particles are in close contact with one another and therefore experience structural arrest or “jamming” In granular systems and compressed emulsions there is no kinetic energy of consequence; the typical energy required to change the positions of the jammed particles is very large compared to the thermal energy at room temperature. As a result, the material remains arrested in a metastable state and is able to withstand an applied stress. The focus of this project is the study of a thermodynamic formulation for systems undergoing structural arrest or approaching the jammed state. In particular we will study: densely packed granular materials and compressed emulsion systems, colloidal glasses and supercooled fluids. These seemingly distinct disordered systems are examples of out-of-equilibrium systems belonging to a new class of ‘jammed materials’, characterized by slow relaxation dynamics. These systems involve many-body interactions leading to a collective structural evolution, much slower than the microscopic motion of the constitutive particles. Jammed matter is very often out of equilibrium, since a laboratory experiment generally takes place on time scales shorter than their characteristic relaxation time. Consequently, the behavior of these systems is very difficult to understand as the general tools of statistical mechanics are insufficient. The thermodynamic picture which we are aiming to explore is the application of the powerful tools of equilibrium statistical mechanics to help explain a different set of natural phenomena – the physics of static and weakly driven jammed matter.
A densely packed granular system, in which all the grains are in contact with their neighbors, is an example of jammed matter. Since there is no thermal energy of consequence within the system, the exploration of the available jammed configurations of the constituent particles must be facilitated by an external energy input, such as tapping or slow shear. Provided that all the jammed configurations are equally probable and bear no memory of their creation, we arrive at the ergodic hypothesis, implying that a statistical mechanics approach is justified. This forms the basic tenet of the thermodynamic formulation for jammed matter, which characterizes the packing state by the `compactivity’ or ‘effective temperature’ and the entropy. The existence of jammed reversible states has been suggested by compaction experiments employing tapping, oscillatory compression or sound propagation as the external perturbation. On the other hand, macroscopic variables, such as effective temperatures, have not been previously measured in the laboratory. Until present, the only evidence of their significance in describing the system has emerged from theoretical mean-field models of glasses and computer simulations of glassy systems and granular matter. This line of research has led to the design of a decisive experiment which we recently published in PNAS. The measurement of the effective temperature is realized in the laboratory by slowly shearing a jammed ensemble of spherical beads confined by an external pressure in a Couette geometry. The particle trajectories yield the diffusivity and the mobility from which the temperature is deduced. All the particles, independent of their properties, equilibrate at the same temperature, which is in turn independent on the slow shear rate, thus satisfying the condition of a true thermodynamic variable for the jammed system. This result suggests that the problem of jammed matter could be a generalization of the statistical mechanics introduced by Boltzmann. This work is supported by the Department of Energy.
Graduate students: Ping Wang and Chaoming Song, CCNY, Jorge Kurchan, ESPCI, Paris, J. Brujic and S. Edwards, Cambridge University.