The oscillation of a graphene flake on a substrate with undulated surface is investigated by classical molecular dynamics simulation. The gradient in amplitude of the undulation is found to provide the driving force for the motion of the graphene flake, which slides on top of a graphene layer that well conforms to the substrate. The oscillatory motion of the flake can be well described by the equation of motion of a damped oscillator, with damping factor corresponding to the friction coefficient between the flake and the graphene layer on which it glides. When the amplitude gradient increases, the oscillation frequency increases as well. The shape of the graphene flake is found to have a strong influence on friction, as some geometries promote in-plane rotation. The results in the present study point to an alternative approach to transport or manipulation of nanosized objects.

It has been demonstrated through experiments and simulations that friction decreases significantly when graphene is used as a solid lubricant on various materials. However, the effect of increasing the number of graphene layers on lubrication is controversial. Some studies predict an increase of friction with the number of layers that can be imputed to increased contact area, others a decrease in friction attributed to increased flexural rigidity of the layers. Herein, atomistic simulations are performed to investigate the atomic mechanisms by which few-layers graphene lubricate rough copper surfaces when probed by a smooth tip. The results of the simulations show that increasing the number of graphene layers drastically reduces friction, while the deformation mechanism is found to change from atomic wear to recoverable flattening of surface steps, as the amount of interlocking between the surfaces is reduced.

Graphene is well known as a solid lubricant for nanoscale devices and is generally used to decrease friction between flat surfaces. In this work, we investigate its performance as a lubricant for rough surfaces. To this end, the problem of a silicon tip sliding on a rough copper single crystal, bare or covered by a graphene layer, is addressed through molecular dynamics simulations. To simplify the analysis, the copper crystal is taken to be quasi-three dimensional, so that the roughness profile is constant along the short periodic dimension. Results show markedly different deformation mechanisms in copper, depending on whether the rough surface is bare, covered with a stretched graphene layer, or with a wrinkled graphene layer. The wrinkled layer appears to be the best solution to reduce friction.