Contact percolation signals jamming

Using extensive computer simulations, we thermally quench spherical grains that interact via purely repulsive contact forces to zero temperature using the steepest descent algorithm as a function of packing fraction φ . We find that these systems display a percolation transition at φ _P < φ _J, where φ _J is the jamming onset at which the system is mechanically stable. Above φ _P, a connected cluster of geometric (non-force bearing) contacts spans the system, and the number of floppy modes from the dynamical matrix begins to decrease strongly. The correlation length critical exponent (but not the other exponents) that characterize the transition, differs strongly from that for the continuum percolation and jamming transitions. We argue that the percolation of geometric contacts represents a novel transition that is important for determining the structural, mechanical, and dynamical properties of jammed and nearly jammed materials.