Effects of Anisotropy and Substrate Shape on Atomic Friction Force in Two-Dimensional Model

Understanding the effects of anisotropy and substrate shape on atomic friction force is critically needed for the designed development of nanoscale friction devices. The simulation of atomic force microscope on various substrate shapes using the 2D Prandtl–Tomlinson model is investigated in the framework of three representative surface lattices: MoS2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {MoS}}_2$$\end{document}, NaCl and highly oriented pyrolytic graphite surfaces. The results show that the lateral force map reveals a significant contrast between different surface lattice shapes yielding lattice rows which differ from their neighboring ones. Careful analysis of the friction force during the individual friction scanning revealed that the friction forces over the narrow maxima domains were lower than those over the narrow wells domains. Depending on crystal orientation and the potential shape, variations in the frictional force can also be seen in the simulations. It has been numerically observed that frictional force depends on the crystal orientation as well as on the shape of the substrate potential. Velocity dependence of the kinetic friction force has the form of a power law Fk-Fk0=cstvs2/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{k}-F_{k0}={\hbox {cst}} \, v_{\mathrm{s}}^{2/3}$$\end{document}, for small scanning velocities. The effects of the shape parameter r on this law have been shown.