Analytical Expression for the Atomic Friction of a Single Asperity Based on the Prandtl-Tomlinson Model

The Prandtl-Tomlinson(PT)model has been widely applied to interpret the atomic friction mechanism of a single asperity.In this study,we present an approximate explicit expression for the friction force in the one-dimensional PT model under quasi-static conditions.The‘stick-slip’friction curves are first approximated properly by sawtooth-like lines,where the critical points before and after the‘slip’motion are described analytically in terms of a dimensionless parameterη.Following this,the average friction force is expressed in a closed form that remains continuous and valid forη>1.Finally,an analytical expression for the load dependence of atomic friction of a single asperity is derived by connecting the parameterηwith the normal load.With the parameters reported in experiments,our prediction shows good agreement with relevant experimental results.

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.