Study of Nanoscale Friction Behaviors of Graphene on Gold Substrates Using Molecular Dynamics

Abstract

In this paper, we investigate the friction behaviors of graphene flakes sliding on a gold substrate using molecular dynamics simulations. The effects of flake size, flake shape, relative rotation angle between flake and substrate, and crystal orientation of substrate on the friction process are thoroughly studied. It is found that under the same load, the average friction forces per atom are smaller for a bigger graphene flake, which exhibits an obvious size effect. It is also shown that flake shape is critical in determining the friction in the sliding process. The average friction forces per atom for the square flake are much bigger than those for the triangular and round flakes. Moreover, the average friction forces per atom for the triangular flake are the smallest. We also find that the orientation of graphene flake relative to gold substrate plays a vital role in the friction process. The friction forces for the graphene flake sliding along the armchair direction are much bigger than those for the flakes with rotation. In addition, it is also found that single crystalline gold substrate exhibits a significant anisotropic effect of friction, which is attributed to the anisotropic effect of potential energy corrugation. These understandings not only shed light on the underlying mechanisms of graphene flake sliding on the gold substrates but also may guide the design and fabrication of nanoscale graphene-based devices.

Keywords: Friction; Graphene; Molecular dynamics; Single crystalline gold.

Fig. 1

Simulation model of friction process

Fig. 2

Friction force as a function of sliding distance at various normal loads (L). The flake has a square shape with a size of 5.8 nm. Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction

Fig. 3

The variation of friction force and average friction force for different flake sizes. The typical friction force as a function of sliding distance for the 2.0 nm (N = 160 atoms) flake (a) and 10 nm (N = 3936 atoms) flake (b). c The average friction force per atom (F_fric/N) as a function of load per atom (L/N). Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction

Fig. 4

The variation of friction force and average friction force for different flake shapes. The typical friction force as a function of sliding distance for the round (N = 1080 atoms) flake (a) and triangular (N = 654 atoms) flake (b). c The average friction force per atom (F_fric/N) as a function of load per atom (L/N). Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction

Fig. 5

The friction force vs sliding distance of the 5.8 nm square flake at L = 240 nN for different rotation angles (θ = 0°, 15°, 30°, 45°, 60°, 90°). a–f correspond to the rotation angle 0°~90°, respectively. Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction

Fig. 6

The average friction force Ffric of the 5.8-nm square flake for different rotation angles at different normal loads

Fig. 7

The friction force of the 5.8-nm square flake sliding on the (a) Au(001) and (b) Au(110) surfaces as a function of sliding distance at different normal loads. Here, a1 (= 4.08 Å) is the lattice spacing of Au(001) along the sliding direction and a2 (= 4.08 Å) is lattice spacing of Au(110) along the sliding direction

Fig. 8

The average friction force F_fric of the 5.8-nm square flake sliding on the Au substrates with different crystal orientation at different normal loads

Fig. 9

Contour maps of the potential energy for the Au(111), Au(110), and Au(001) surface at L = 120 nN are shown in a–c, respectively. The 5.8-nm square graphene flake is adopted. In a–c, a black solid line (y = 0) on the maps is used to show the sliding path of the flake. The graphene-gold interaction potential energy along the sliding path for the Au(111), Au(110), and Au(001) surface is also plotted in d–f, respectively. The unit of the potential energy is eV. The average height of the flake at L = 120 nN for the Au(111), Au(110), and Au(001) surface is 2.36 Å, 2.1 Å, and 2.17 Å, respectively

Fig. 10

Friction force as a function of sliding distance at various normal loads (L) for the friction process without the movement constraint of graphene in the y direction. The flake has a square shape with a size of 5.8 nm. Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction

Fig. 11

The variation of friction force and average friction force for different flake sizes for the friction process without the movement constraint of graphene in the y direction. The typical friction force as a function of sliding distance for the 2.0 nm (N = 160 atoms) flake (a) and 10 nm (N = 3936 atoms) flake (b). c The average friction force per atom (F_fric/N) as a function of load per atom (L/N). Here, a0 (= 9.99 Å) is the lattice spacing of Au(111) along the sliding direction