Edge length-dependent interlayer friction of graphene

Edge effects have significant implications in friction at the nanoscale. Despite recent progress, a detailed understanding of the relationship between nanoscale friction and contact edges is still sorely lacking. Here, using molecular dynamics simulations, we investigate the intrinsic effect of the edge size on the nanoscale friction between graphene layers in the incommensurate case based on the model of graphene flakes on a supported graphene substrate. An original rectangular graphene sheet is cut and divided into two independent parts, namely, the inside and outside zones, according to a certain path with a hexagonal boundary. The friction of the inside and the outside flakes placed on a substrate is calculated. The results interestingly reveal that the sum of the friction forces on the inside and outside of flakes, termed the “equivalent friction force”, is substantially greater than that of the original rectangular graphene sheet because the additional edge friction of the former two systems is more than that of the latter system. More importantly, the equivalent friction force is linearly proportional to the edge size due to the larger cropped edge size having more edge friction. This work demonstrates the intrinsic dependence of friction on the contact edge size of incommensurate graphene layers.