Low friction and rotational dynamics of crystalline flakes in solid lubrication

Solids at incommensurate contact display low-friction, ’superlubric’, sliding. For graphene flakes on a graphite surface, superlubric sliding is only temporary due to rotation of the flakes from incommensurate to commensurate contact with the substrate. We examine this rotational channel of friction in a prototype geometry of mesoand macroscopic solid lubrication. By molecular dynamics simulations and theoretical arguments we find that two surfaces lubricated by mobile, rotating graphene flakes exhibit stable superlubric sliding as for ideally incommensurate contacts also when they are covered by randomly oriented pinned graphene patches. For commensurate surfaces, we find a low friction state at low temperature where incommensurate states are not destroyed by thermal fluctuations. Superlubricity between incommensurate surfaces provides a desired low-friction state essential for the function of small-scale machines and function of solid lubricants. Vanishing static friction has been first predicted by Aubry and Peyrard [1, 2] for infinite lattices on an incommensurate periodic potential. Later, Shinjo and Hirano [3] predicted that for infinite incommensurate contacts also the kinetic friction would vanish and called this effect superlubricity. Extremely low friction has been observed for small contacts in AFM experiments by Dienwiebel et al. [4] for the sliding of small graphite flakes on a single surface of graphite. However, the superlubric sliding is experimentally found to be only temporary, going over to stick-slip behavior after several scans along the surface [5]. Direct molecular dynamics simulations [5] as well as a theoretical analysis of the nonlinear dynamics [6] demonstrated that this increase of friction is due to the rotation of the flakes to a commensurate contact with the single surface. The incommensurate orientations of the flakes are stable but not robust against thermal fluctuations particularly if the center of mass of a flake travels on top of the substrate atoms [6]. The rotation of nano-scale crystals such as graphene flakes is the simplest nontrivial issue in lubrication with lamellar solids such as graphite and MoS2. Fig. 1: (Color online) The system describes two infinite plates with graphene flakes embedded in between. The plate surfaces are covered by single-domain or randomly oriented multi-domain graphite layers, as shown for the bottom substrate. The top plate is pulled by a spring, the tension in which gives a measure of friction. The pulling angle θ, relative orientation of lattices on the two plates β, and flake orientation φ are indicated. In this Letter, we propose a model system that can be used to investigate solid lubrication at both nano and macro scales, and which exhibits stable super-low friction. The system, shown in Fig. 1, consists of two infinite plates covered either by single-domain or randomly oriented multi-domain (graphite) layers with (graphene) flakes embedded between them that act as a solid lubricant. As such, the model contains all key elements of