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.