Stiffness-dependent interlayer friction of graphene

The friction of graphene depends on thickness, but little is known how it is dependent on stiffness. Based on a graphene-spring model, using molecular dynamics simulations, we investigate the friction behavior of a graphene flake sliding on a supported graphene substrate. We show that the friction force increases exponentially with the decreasing stiffness. The stiffness is a dominant parameter for the friction of a soft substrate, e.g., where superlubricity may be completely impeded. We relate the friction to the substrate deformation and find that the indentation depth can be an indicator for the friction of soft substrates. These findings may provide a fundamental understanding for the stiffness dependent nanoscale friction.