Effective stick-slip parameter for structurally lubric 2D 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 = 2π^2 U_0/K_p a^2, where U_0 is the potential magnitude, a the lattice spacing, and K_p the pulling spring constant. Here we show, supported by a repertoire of graphene flake/graphene sliding simulations, that a similar stick-slip predictor η_eff can be defined with the same form but suitably defined U_eff, a_eff and K_eff. Remarkably, simulations show that a_eff = a of the substrate remains an excellent approximation, while K_eff is an effective stiffness parameter, combining equipment and internal elasticity. Only the effective energy barrier U_eff 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 U_eff, whose magnitude for a micrometer size diameter is of order 1 eV, scales as A^1/4, thus increasing very gently with size. The PT-like parameter η_eff is therefore proposed as a valuable tool in 2D layer sliding.