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.