Velocity dependence of atomic-scale friction: a comparative study of the one- and two-dimensional Tomlinson model

TL;DR

This study analyzes how atomic-scale friction depends on velocity using the Tomlinson model in 1D and 2D, revealing a universal power-law behavior at low velocities and discussing thermal effects and surface corrugation influences.

Contribution

It provides a comprehensive comparison of velocity-dependent friction in 1D and 2D Tomlinson models, including analytical and numerical insights into thermal effects and damping.

Findings

Friction exhibits a power-law velocity dependence with an exponent of 2/3 at low velocities.

Thermal fluctuations increase the velocity dependence of friction.

The velocity dependence is universal across dimensions and damping values in the absence of thermal noise.

Abstract

We present a comparative analysis of the velocity dependence of atomic-scale friction for the Tomlinson model, at zero and finite temperatures, in 1D and 2D, and for different values of the damping. Combining analytical arguments with numerical simulations, we show that an appreciable velocity dependence of the kinetic friction force $F_{fric}$, for small scanning velocities $v_s$ (from 1 nm/s to 2 $\mu$m/s), is inherent in the Tomlinson model. In the absence of thermal fluctuations in the stick-slip regime, it has the form of a power-law, $F_{fric}-F_0\propto v_s^{\beta}$ with $\beta=2/3$, irrespective of dimensionality and value of the damping. Since thermal fluctuations enhance the velocity dependence of friction, we provide guidelines to establish when thermal effects are important and to which extent the surface corrugation affects the velocity dependence.