Nonlinear Area Dependence of Graphene Friction at the Nanoscale

How friction changes with contact area remains a fundamental
topic
of friction. Classical laws suggested that for macroscopic friction
the friction force between two solids is independent of the nominal
contact area, and then the linear relation between friction force
and the real contact area is established. In this work, we show with
molecular dynamics that at the nanoscale, however, there exists a
more complicated relation between friction and contact area. We systematically
simulated how the friction between a graphene substrate and a sliding
monolayer square graphene tip varies with the contact area (from a
single atom to 1000 nm2). The results show that in commensurate
contact mode the friction stress oscillates violently with the tip
area and the oscillatory behavior gradually disappears until the area
is larger than 100 nm2. Detailed analysis indicates that
the friction stress is sensitive to the edge structure of tips: the
ultralow friction occurs for the tips in bearded edge configuration,
and friction increases abruptly when all the edge configurations are
either zigzag or armchair. Characterization of the potential energy
surface and the tip motion pathway demonstrate that the presence of
the bearded edge configuration distorts the potential energy surface
sensed by the tip, which modifies the tip motion paths and causes
a dramatic drop in friction.