Energy dissipation of atomic-scale friction based on one-dimensional Prandtl-Tomlinson model

Zi-Jian Wang,Liang Xu,Tian-Bao Ma,Hui Wang,Yuan-Zhong Hu

doi:10.1007/s40544-015-0086-2

Abstract

Abstract The energy transition and dissipation of atomic-scale friction are investigated using the one-dimensional Prandtl-Tomlinson model. A systematic study of the factors influencing the energy dissipation is conducted, indicating that the energy that accumulated during the stick stage does not always dissipate completely during stick-slip motion. We adopt the energy-dissipation ratio (EDR) to describe the relationship between the energy dissipated permanently in the system and the conservative reversible energy that can be reintroduced to the driving system after the slip process. The EDR can change continuously from 100% to 0, covering the stick-slip, intermediate, and smooth-sliding regimes, depending on various factors such as the stiffness, potential-energy corrugation, damping coefficient, sliding velocity, and the temperature of the system. Among these, the parameter η, which depends on both the surface potential and the lateral stiffness, is proven in this paper to have the most significant impact on the EDR. According to η-T phase diagrams of the EDR, the smooth-sliding superlubricity and thermolubricity are found to be unified with regard to the energy dissipation and transition. An analytical formulation for the EDR that can be used to quantitatively predict the amount of energy dissipation is derived from a lateral-force curve.

Highlights

Friction is mechanical kinetic-energy loss or the transformation of sliding motion into heat and other excitations [1,2,3]
To clearly illustrate the energy transitions, a complete stick-slip period can be divided into four stages, the first of which is the accumulation of potential energy
To measure the degree of energy dissipation or energy reversibility, we present two definitions for the energy-dissipation ratio (EDR): EDRW and EDRP, which are described in Eqs. (12) and (13), respectively

Summary

Introduction

Friction is mechanical kinetic-energy loss or the transformation of sliding motion into heat and other excitations [1,2,3]. Atomic-scale frictional behavior and its influencing factors have been studied extensively, the process and amount of energy transfer and dissipation during stick-slip friction—which are essential for an in-depth understanding of atomic-scale friction—are rarely quantified. The elastic energy that accumulates during the stick stage can be dissipated irreversibly by heat generation during the slip stage [4,5,6]. Berman and Israelachvili postulated that in the cobblestone model, upon each molecular collision during sliding, only part of the kinetic energy is Friction 3(2): 170–182 (2015). The energy transition and dissipation under stick-slip friction are quantitatively examined using the Prandtl–Tomlinson (PT) model [10,11,12]. The formulation of the energy-dissipation ratio (EDR) is derived analytically to characterize the ratio between the dissipative energy and the total energy that accumulates during sticking

Methods

Results

Conclusion