On the asymptotic expressions of critical energy barrier in Prandtl-Tomlinson model

The Prandtl-Tomlinson (PT) model is the most widely used and successful minimalistic model to describe atomistic scale friction. It can describe the thermally activated, stress assistant process which shows stick-slip frictional behavior. The relationship between the energy barrier and lateral force is critical to determine how the frictional force depends on velocity and temperature. There is some confusion in the literature to derive such relationship. The underlying assumption and approximations are not stated in a clear way and the rigorous derivations are missing. This study discusses the asymptotic behavior of the energy barrier as the support-spring coupling lowers it to zero and gives a detailed derivation of the asymptotic expression of the energy barrier within the framework of PT model.