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.

Statistical Characterization of the Yield Stress of Nanoparticles

Atomistic simulations are performed to study the statistical mechanical properties of gold nanoparticles.It is demonstrated that the yielding behavior of gold nanoparticles is governed by the dislocation nucleation around surface steps.Since the nucleation of dislocation is an activated process with the aid of thermal fluctuation,the yield stress at a specific temperature should vary statistically rather than being a definite constant value.Molecular dynamics simulations reveal that the yield stress follows a Gaussian distribution at a specific temperature.As the temperature increases,the mean value of yield stress decreases while the width of distribution becomes larger.Based on the numerical analysis,the dependence of mean yield stress on temperature can be well described by a parabolic function.This study illuminates the statistical features of the yielding behavior of nanostructured elements.