(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

Abstract

The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size ($A^0$) and two commensurate ones which scale differently (with $A^{1/2}$ and $A$) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found ($A^{1/4},A^{3/4},A$). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed.

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• Atomic-scale defects restricting structural superlubricity: Ab initio study study on the example of the twisted graphene bilayer
• Slider Thickness Promotes Lubricity: from 2D Islands to 3D Clusters
• The twisting dynamics of large lattice mismatch van der Waals heterostructures
• Friction and Nonlinear Dynamics
• Kinetic Friction of Structurally Superlubric 2D Material Interfaces
• Current trends in the physics of nanoscale friction
• How square ice helps lubrication
• Emergent friction in two-dimensional Frenkel-Kontorova models
• Static friction boost in edge-driven incommensurate contacts
• Molecules on rails: friction anisotropy and preferential sliding directions of organic nanocrystallites on two-dimensional materials
• Frictionless nanohighways on crystalline surfaces
• Size-dependent commensurability and its possible role in determining the frictional behavior of adsorbed systems
• Pervasive orientational and directional locking at geometrically heterogeneous sliding interfaces
• Effective stick-slip parameter for structurally lubric 2D interface friction
• Friction of Physisorbed Nanotubes: Rolling or Sliding?
• Restriction of macroscopic structural superlubricity due to structure relaxation by the example of twisted graphene bilayer