Jamming of frictional spheres and random loose packing

The role of friction coefficient, $\mu$, on the jamming properties of disordered, particle packings is studied using computer simulations. Compressed, soft-sphere packings are brought towards the jamming transition - the point where a packing loses mechanical stability - by decreasing the packing fraction. The values of the packing fraction at the jamming transition, $\phi^{\mu}_{c}$, gradually decrease from the random close packing point for zero friction, to a value coincident with random loose packing as the friction coefficient is increased over several orders of magnitude. This is accompanied by a decrease in the coordination number at the jamming transition, $z^{\mu}_{c}$, which varies from approximately six to four with increasing friction. Universal power law scaling is observed in the pressure and coordination number as a function of distance from the generalised, friction-dependent jamming point. Various power laws are also reported between the $\phi^{\mu}_{\rm c}$, $z^{\mu}_{\rm c}$, and $\mu$. Dependence on preparation history of the packings is also investigated.