Intermediate range structure in packing of frictional particles

Including friction between particles can have profound effects on particle packing compared to frictionless packings. Friction leads to looser granular sphere packings than frictionless packings: the more friction present the lower the packing fraction attainable. Using discrete element simulations, we show that the inclusion of various modes of friction – which is concomitant with decreasing packing fraction – is characterized by the development of intermediate range order as identified by the emergence of a pre-peak at lower values of the wavenumber q than that of the nearest-neighbor primary peak as seen in the static structure factor S(q). For mono and weakly dispersed particle packings with sliding friction, the position of the pre-peak increases with the coefficient of friction and occurs at a distance scale d ~ 30 particle diameters. Including rolling and twisting friction, to account for dissipation on these degrees of freedom, leads to lower density packings with fewer contacts, with a stronger pre-peak, which shifts to lower q. The length scale of this intermediate range structure is correlated with spatial fluctuations in the excess number of neighbors a particle has within a distance d compared to the global average.