Separating anisotropic and isotropic friction between atomic force microscope tips and atomically flat surfaces

Mengzhou Liao, Paolo Nicolini, and Tomas Polcar

Phys. Rev. B 107, 195442 – Published 31 May 2023

Abstract

Layered materials are the most important class of solid lubricants. Friction on their surfaces has complex origins. Most experimental methods so far only give total friction force and cannot separate contributions from different origins. Here, we report a method to separate anisotropic and isotropic friction forces on atomically flat surfaces such as ${MoS}_{2}$ , graphite, h-BN, and mica by combining a two-dimensional friction force microscope technology and a two-dimensional friction model. We found that the friction force of most atomically flat surfaces is anisotropic, the total force on the tip misaligns with the scan direction, and the friction anisotropy vanishes under low sliding velocity. Our two-dimensional friction model explains experimental observations. It reveals the existence of elemental hopping combinations and the isotropic component in total friction. The misalignment angle can be used to calculate the ratio of anisotropic and isotropic friction components and the ratio of resistance forces from different lattice directions. The separation of anisotropic and isotropic friction forces will offer an avenue for studying the properties of individual friction components, which can boost the study of friction mechanisms in the future and benefit the application of solid lubricants.

Received 3 January 2023
Revised 15 April 2023
Accepted 15 May 2023

DOI:https://doi.org/10.1103/PhysRevB.107.195442

Physics Subject Headings (PhySH)

Friction

Layered crystals Surfaces

Ab initio molecular dynamics Atomic force microscopy Materials modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mengzhou Liao ^1,*, Paolo Nicolini ^1,2,†, and Tomas Polcar^1,3

¹Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, 16627 Prague 6, Czech Republic
²Institute of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Prague 8, Czech Republic
³National Centre for Advanced Tribology (nCATS), Department of Mechanical Engineering, University of Southampton, Highfield, SO17 1BJ Southampton, United Kingdom

^*Corresponding author: mengzlia@fel.cvut.cz
^†Corresponding author: nicolini@fzu.cz

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Issue

Vol. 107, Iss. 19 — 15 May 2023

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Images

Figure 1
Friction anisotropy of the ${MoS}_{2}$ surface. (a) Diagram of the 2DFF-AFM friction measurement. (b),(c) Diagrams depicting the measurement of the signals in the $Y$ and $X$ directions. (d) Image of an exfoliated ${MoS}_{2}$ flake on a Si substrate with 300-nm ${SiO}_{2}$ . (e)–(i) $Y$ -direction force (e), $X$ -direction force (f), total force (g), misalignment angle (h), and friction force (i) as a function of the scan and sample angles.
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Figure 2
Friction anisotropy of other 2D surfaces: graphite, h-BN and mica. (a) Top and side view of the graphite structure. (b)–(d) Friction anisotropy results between the silicon tip and the graphite surface: $x, y$ directions and total force (b), misalignment angle (c), and friction force (d) as a function of the scan angle. (e) Top and side views of the h-BN structure. (f)–(h) Friction anisotropy results between the silicon tip and the h-BN surface: $x, y$ directions and total force (f), misalignment angle (g), and friction force (h) as a function of the scan angle. (i) Top and side views of the mica structure. (j)–(l) Friction anisotropy results between the silicon tip and the mica surface: $x, y$ directions and total force ( $j$ ), misalignment angle ( $k$ ), and friction force ( $l$ ) as a function of the scan angle.
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Figure 3
The evolution of the friction anisotropy on the bulk ${MoS}_{2}$ surface with different sliding velocities. (a)–(e) $Y$ -direction force (a), $X$ -direction force (b), total force (c), misalignment angle (d), and friction force (e) as a function of the scan and sample angles with different sliding velocities. The normal load is set to 216.83 nN.
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Figure 4
Diagrams of EHCs. (a) Potential energy surface of an amorphous ${SiO}_{2}$ slab interacting with a ${MoS}_{2}$ layer. (b) Diagram illustrating the 2D sliding model with two EHCs. (c)–(e) The trajectory of the PT particle with $T = 0$ K, $k = 1 N / m, v = 2000 nm / s$ , and in the critical damping regime. Trajectories followed by the PT particle when sliding along (c) $0^{\circ}$ (zigzag direction), (d) $15^{\circ}$ , and (e) $30^{\circ}$ (armchair direction). (f)–(h) The trajectory of the PT particle with $T = 300$ K, $k = 1 N / m, v = 2000 nm / s$ , and in the critical damping regime. Trajectories followed by the PT particle when sliding along (f) $0^{\circ}$ (zigzag direction), (g) $15^{\circ}$ , and (h) $30^{\circ}$ (armchair direction).
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Figure 5
Theoretical calculations of friction on an atomically flat surface with two EHCs. ( $a_{1}$ ),( $a_{2}$ ) Misalignment angle ( $a_{1}$ ) and normalized friction force ( $a_{2}$ ) as a function of the sliding angle at $T = 0$ K with $F_{v} = 0$ and different $F_{2}^{*} / F_{1}^{*}$ ratios, $F_{c}^{*} = F_{2}^{*} \frac{sin α}{sin θ_{c}}$ ( $θ_{v} \neq n α$ ). ( $b_{1}$ )–( $b_{3}$ ) Normalized total force ( $b_{1}$ ), misalignment angle ( $b_{2}$ ), and normalized friction force ( $b_{3}$ ) as a function of the sliding angle at $T = 0$ K with $F_{2}^{*} / F_{1}^{*} = 10$ and different $F_{v}, F_{c \max} = F_{2}^{*} \frac{sin α}{sin θ_{c}}$ . (c) An example of $F_{c 1}$ and $F_{c 2}$ as functions of $ln (v_{i})$ for $T > 0$ K; parameters come from Ref. [4]. ( $d_{1}$ )–( $d_{3}$ ) Normalized total force ( $d_{1}$ ), misalignment angle ( $d_{2}$ ), and normalized friction force ( $d_{3}$ ) as functions of sliding angles at different sliding velocities with $F_{v} = 0$ ; $F_{c 1}$ and $F_{c 2}$ are from (c). ( $e_{1}$ )–( $e_{3}$ ) Normalized total force ( $e_{1}$ ), misalignment angle ( $e_{2}$ ), and normalized friction force ( $e_{3}$ ) as functions of sliding angles at different sliding velocities, with $F_{v} = F_{c}^{*}$ ; $F_{c 1}$ and $F_{c 2}$ are from (c).
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