Dynamics of the contacts reveals Widom lines for jamming

We experimentally study the vicinity of the jamming transition by investigating the statics and the dynamics of the contact network of a horizontally shaken bi-disperse packing of photo-elastic discs. Compressing the packing very slowly, while maintaining a mechanical excitation, yields a granular glass, namely a frozen structure of vibrating grains. In this glass phase, we observe a remarkable dynamics of the contact network, which exhibits strong dynamical heterogeneities. Such heterogeneities are maximum at a packing fraction φ, distinct and smaller than the structural packing fraction φ, which is indicated by an abrupt variation of the average number of contacts per particle. We demonstrate that the two crossovers, one for the maximum dynamical heterogeneity, and the other for static jamming, converge at point J in the zero mechanical-excitation limit, a behavior reminiscent of the Widom lines in the supercritical phase of a second-order critical point. Our findings are discussed in the light of recent numerical and theoretical studies of thermal soft spheres. Copyright c © EPLA, 2012 At large packing fraction, disordered packings of particles with repulsive contact interactions jam into a rigid state. For frictionless and athermal particles, the jamming transition coincides with the onset of isostaticity and a number of geometrical and mechanical quantities exhibit clear scaling laws with the distance to jamming [1]. One prominent signature of jamming is the singular behavior of the average number of contacts per particle z− zJ ∝ (φ− φJ), where zJ = 2d, d being the space dimension [2,3]. The distribution of the gaps between particles displays a delta function at zero and a square-root decay for increasing gaps, which is key to the singular behavior of the average contact number [4–7]. Although the average coordination number singularity is the hallmark of jamming at zero temperature, its behavior is less clear at finite temperature. Both experimentally [8] and numerically [6,8–11], it has been observed that the first peak of the partial pair correlation function has a finite maximum at a packing fraction φj(T )> φj(0) = φJ . This maximum has been interpreted as a vestige of the divergence of the pair correlation function at point J , the T = 0 jamming transition (fig. 1). However, it was later argued [12] that this structural anomaly can be accounted for using equilibrium liquid-state theory, and is therefore not specific to jamming. The vicinity of point J has also been explored in a mean-field–like replica description of thermal soft and hard spheres [13]. This description recovers all the observed scalings in temperature and packing fraction but the square-root singularity of the pair correlation function when T = 0 and φ= φ+J . This discrepancy, together with the onset of a diverging length in the vibrational properties of the jammed state [14], suggests that largerscale correlations must be taken into account, and calls for a better characterization of the vicinity of point J. In the present letter, we focus on the dynamics of the contact network, a natural quantity of interest as soon as dynamics is present, which, to our knowledge, has never been explored so far. To this end, we experimentally investigate a vibrated two-dimensional bi-disperse packing of photo-elastic grains, close to its jamming transition. We control both the packing fraction, φ, and the mechanical excitation, γ, to be defined precisely below. This mechanically driven and dissipative system is far from equilibrium and the mechanical excitation is different from a temperature in