Dynamics of the contacts reveals Widom lines for jamming

Abstract

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.