Thermal activation in atomic friction: revisiting the theoretical analysis

The effect of thermal activation on atomic-scale friction is often described in the framework of the Prandtl–Tomlinson model. Accurate use of this model relies on parameters that describe the shape of the corrugation potential β and the transition attempt frequency f0. We show that the commonly used form of β for a sinusoidal corrugation potential can lead to underestimation of friction, and that the attempt frequency is not, as is usually assumed, a constant value, but rather varies as the energy landscape evolves. We partially resolve these issues by demonstrating that numerical results can be captured by a model with a fitted β and using harmonic transition state theory to develop a variable form of the attempt frequency. We incorporate these developments into a more accurate and generally applicable expression relating friction to temperature and velocity. Finally, by using a master equation approach, we verify the improved analytical model is accurate in its expected regime of validity. (Some figures may appear in colour only in the online journal) 1