Theoretical description of nanomechanics of the contact state of twisted graphene interface

抄録

Superlubricity due to the incommensurate contact between twisted crystal lattices of layered material reduces friction to the order of magnitude of less than several hundreds of pN [1, 2]. Twisted graphene is one of such typical superlubric interfaces, and can be formed by rotating a graphene sheet stacked on a graphite substrate as shown in Fig. 1(a). While the sheet is slid on the substrate, the nanoscale real contact region between the sheet and the substrate plays an important role in superlubricity, but its microscopic mechanism has yet to be discussed. Because of the microscopic roughness, the real contact area is smaller than the apparent contact area. Since the frictional force is represented by the sum of the force to shear the real contact region, in order to control the nanoscale friction, it is important to clarify the behavior of the real contact region during the sliding process of the sheet. Therefore, in this work, the mechanical behavior of the contact state of a twisted graphene interface is studied by a molecular simulation of the sliding process of the sheet. Furthermore, the mechanics of the contact state in a general twisted crystal lattices of layered material is mathematically discussed. By applying this discussion to the twisted graphene, the contact state behavior observed in the simulation is theoretically explained.

First, the molecular simulation of the sliding process of the sheet of the twisted graphene interface was performed. Fig. 1(b) shows the model of the twisted graphene. Twisted graphene interface is comprised of the pseudo AA and AB stacking regions which can be locally approximated as AA and AB stacking regions, respectively. The pseudo AA stacking regions are arranged on the lattice points of a triangular lattice as shown as red circles in Fig. 1(b). Similarly, the pseudo AB stacking regions are arranged on the lattice points of a hexagonal lattice as shown as blue circles in Fig. 1(b). Here, in AA stacking, every carbon atom in the sheet locates on the substrate carbon atom and the contact state is energetically unstable. By contrast, in AB stacking, every other carbon atom in the sheet locates on the substrate carbon atom and the contact state is stable. Thus, the contact state of the twisted graphene interface is not energetically flat although graphene is geometrically flat in nanoscale. In addition, from the results of the simulation, it was found that the stacking pattern moves while the sheet is slid. It indicates that the contact state of the twisted graphene interface varies during the sliding process of the sheet.

Next, for a general twisted crystal lattices of layered material, we consider a case when the sheet is rotated by the misfit angle θ and is translated by the sliding vector Δτ. When the deviation between the crystal lattices of the sheet and the substrate is expressed by σ₁ and σ₂, any lateral position τ can be written by the formula as a function of the rotation angle θ, the translational movement vector Δτ, and the crystal lattice deviations σ₁ and σ₂. According to the formula obtained above, when the sheet is slid, the stacking pattern also slides in the direction rotated by π/2 - θ/2 from the sliding direction of the sheet. This transelational movement of the stacking pattern can explain the smulated results. Thus the formula obtained above in this work can give a clear explanation to the contact mechanics of the twisted graphene interfaces.

[1] M. Hirano and K. Shinjo, Phys. Rev. B41, 11837 (1990).

[2] M. Dienwiebel et al., Phys. Rev. Lett. 92, 126101 (2004).