Kinetic friction of structurally superlubric 2D material interfaces

Abstract

The ultra-low kinetic friction Fk of 2D structurally superlubric interfaces, connected with the fast motion of the incommensurate moiré pattern, is often invoked for its linear increase with velocity v0 and area AS, but never seriously addressed and calculated so far. Here we do that, exemplifying with a twisted graphene layer sliding on top of bulk graphite – a demonstration case that could easily be generalized to other systems. Neglecting quantum effects and assuming a classical Langevin dynamics, we derive friction expressions valid in two temperature regimes. At low temperatures the nonzero sliding friction velocity derivative dFk/dv0 is shown by Adelman–Doll–Kantorovich type approximations to be equivalent to that of a bilayer whose substrate is affected by an analytically derived effective damping parameter, replacing the semi-infinite substrate. At high temperatures, friction grows proportional to temperature as analytically required by fluctuation–dissipation. The theory is validated by non-equilibrium molecular dynamics simulations with different contact areas, velocities, twist angles and temperatures. Using 6°-twisted graphene on Bernal graphite as a prototype we find a shear stress of measurable magnitude, from 25kPa at low temperature to 260kPa at room temperature, yet only at high sliding velocities such as 100m/s. However, it will linearly drop many orders of magnitude below measurable values at common experimental velocities such as 1μm/s, a factor 10−8 lower. The low but not ultra-low “engineering superlubric” friction measured in existing experiments should therefore be attributed to defects and/or edges, whose contribution surpasses by far the negligible moiré contribution.