Effective stick-slip parameter for structurally lubric two-dimensional interface friction

The wear-free sliding of layers or flakes of graphene-like 2D materials, important in many experimental systems, may occur either smoothly or through stick-slip, depending on driving conditions, corrugation, twist angles, as well as edges and defects. No single parameter has been so far identified to discriminate a priori between the two sliding regimes. Such a parameter, η, does exist in the ideal (Prandtl-Tomlinson) problem of a point particle sliding across a 1D periodic lattice potential. In that case η>1 implies mechanical instability, generally leading to stick-slip, with η=2π²U₀Kₚa², where U₀ is the potential magnitude, a the lattice spacing, and Kₚ the pulling spring constant. Here we show, supported by a repertoire of graphene flake/graphene sliding simulations, that a similar stick-slip predictor ηeff can be defined with the same form but suitably defined Ueff, aeff, and Keff. Remarkably, simulations show that aeff=a of the substrate remains an excellent approximation, while Keff is an effective stiffness parameter, combining equipment and internal elasticity. Only the effective energy barrier Ueff needs to be estimated in order to predict whether stick-slip sliding of a 2D island or extended layer is expected or not. In a misaligned defect-free circular graphene sliding island of contact area A, we show that Ueff, whose magnitude for a micrometer size diameter is of order 1 eV, scales as A1/4, thus increasing very gently with size. The PT-like parameter ηeff is therefore proposed as a valuable tool in 2D layer sliding.