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

Abstract

The majority of atomic-scale friction models inwhich sliding is proposed to occur over the atomic-scaleenergy corrugation at the sliding interface assume a simplesinusoidal potential. An analysis of these models showsthat the energy barrier is reduced by the imposition of anexternal force F, becoming zero at a critical force definedas F*. It was first suggested by Prandtl that the energybarrier approaches a limiting value with a force dependencethat is proportional to (F*-F)^3/2. In order toexplore the effects of the shape of the energy potential onthe sliding behavior, this model is analyzed for constantforcesliding with a non-sinusoidal potential of the form(sin(pi*x/a))^n, where n is an even integer >=2. The sameasymptotic dependence is found as suggested by Prandtl,where the proportionality constant depends on the shape ofthe potential. These results are used to calculate thevelocity and temperature dependences of sliding frictionfor constant-force sliding over non-sinusoidal surfacepotentials.Ke