The Jamming Transition

Abstract

In Chap. 2 we presented a rather broad overview of renowned theories about the glass transition. In the last decades, the study of glasses at low temperature has also attracted significant interest, both from a theoretical and an experimental point of view [29, 39, 40, 42]. This is motivated by the fact that a different solidity transition, the jamming transition, can be observed in hard spheres and in many other out-of-equilibrium systems, such as foams, emulsions, granular matter. The jamming phenomenon defines a purely geometrical problem where the thermal energy does not play any role in determining or facilitating the transition. It has been studied for years but only recently new advancements have been achieved by analyzing systems of granular media. Liu and Nagel first proposed a compelling unifying phase diagram [40] in an attempt to group molecular glasses, colloids, foams, emulsions, hard spheres-in one word glassy systems together with granular ones-and connecting various rigidity transitions. For instance, granular media flow when they are shaken or poured, but jam below a certain shaking intensity. Analogously, foams and emulsions have a liquid-like behavior for a large shear stress, but jam when the shear stress is lowered below the yield stress [20]. However, while colloids and molecular liquids are both thermal systems, granular media, dense emulsions, foams and hard spheres, are athermal. For the last category the interaction energies are orders of magnitude larger than the thermal scale k B T. Of course, the determination of a unique phase diagram might be helpful to investigate different classes of materials and the different role played by thermal fluctuations. However, one of the main difficulties in studying jammed systems is that, while thermodynamics usually provides a unique phase (or a finite number of phases) at equilibrium, defining a single phase in out-of-equilibrium systems looks unfeasible.