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.

基于滑动势能面的二维材料原子尺度摩擦行为的量化计算

近年来,二维材料优异的摩擦特性成为人们关注的焦点,然而目前缺乏理论上对其摩擦力进行快速、有效、精确的计算预测方法.本文提出采用密度泛函理论计算真实体系的滑动势能面,利用得到的"数值型势能面"替代传统的解析势函数,并结合Prandtl-Tomlinson模型,量化求解具有复杂形状势能面的真实二维材料体系的摩擦行为.基于该方法,揭示了原子力显微镜实验中观察到的石墨烯Moire纹超晶格结构的双周期"黏-滑"摩擦现象;理论预测了二维材料异质结构的层间超低摩擦现象,相对于同质材料,其静摩擦力和滑动摩擦力均成数量级降低,发现势能面起伏和驱动弹簧刚度均会影响层间相对滑动路径,进而对层间的摩擦行为产生影响.该方法同样可拓展到其他van der Waals作用主导的界面摩擦体系.

Vibration-induced nanoscale friction modulation on piezoelectric materials

Mechanical vibration,as an alternative of application of solid/liquid lubricants,has been an effective means to modulate friction at the macroscale.Recently,atomic force microscopy(AFM)experiments and model simulations also suggest a similar vibration-induced friction reduction effect for nanoscale contact interfaces,although an additional external vibration source is typically needed to excite the system.Here,by introducing a piezoelectric thin film along the contact interface,we demonstrate that friction measured by a conductive AFM probe can be significantly reduced(more than 70%)when an alternating current(AC)voltage is applied.Such real-time friction modulation is achieved owing to the localized nanoscale vibration originating from the intrinsic inverse piezoelectric effect,and is applicable for various material combinations.Assisted by analysis with the Prandtl–Tomlinson(P–T)friction model,our experimental results suggest that there exists an approximately linear correlation between the vibrational amplitude and the relative factor for perturbation of sliding energy corrugation.This work offers a viable strategy for realizing active friction modulation for small-scale interfaces without the need of additional vibration source or global excitation that may adversely impact device functionalities.