Influence of Potential Shape on Constant-Force Atomic-Scale Sliding Friction Models

The majority of atomic-scale friction models in which sliding is proposed to occur over the atomic-scale energy corrugation at the sliding interface assume a simple sinusoidal potential. An analysis of these models shows that the energy barrier is reduced by the imposition of an external force F , becoming zero at a critical force defined as F *. It was first suggested by Prandtl that the energy barrier approaches a limiting value with a force dependence that is proportional to F ∗ - F 3 2 . In order to explore the effects of the shape of the energy potential on the sliding behavior, this model is analyzed for constant-force sliding with a non-sinusoidal potential of the form sin n π x a , where n is an even integer ≥2. The same asymptotic dependence is found as suggested by Prandtl, where the proportionality constant depends on the shape of the potential. These results are used to calculate the velocity and temperature dependences of sliding friction for constant-force sliding over non-sinusoidal surface potentials.