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, $\ensuremath{\eta}$, does exist in the ideal (Prandtl-Tomlinson) problem of a point particle sliding across a 1D periodic lattice potential. In that case $\ensuremath{\eta}>1$ implies mechanical instability, generally leading to stick-slip, with $\ensuremath{\eta}=\frac{2{\ensuremath{\pi}}²{U}₀}{{K}_{\mathrm{p}}{a}²}$, where ${U}₀$ is the potential magnitude, $a$ the lattice spacing, and ${K}_{\mathrm{p}}$ the pulling spring constant. Here we show, supported by a repertoire of graphene flake/graphene sliding simulations, that a similar stick-slip predictor ${\ensuremath{\eta}}_{\mathrm{eff}}$ can be defined with the same form but suitably defined ${U}_{\mathrm{eff}}$, ${a}_{\mathrm{eff}}$, and ${K}_{\mathrm{eff}}$. Remarkably, simulations show that ${a}_{\mathrm{eff}}=a$ of the substrate remains an excellent approximation, while ${K}_{\mathrm{eff}}$ is an effective stiffness parameter, combining equipment and internal elasticity. Only the effective energy barrier ${U}_{\mathrm{eff}}$ 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 ${U}_{\mathrm{eff}}$, 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 ${\ensuremath{\eta}}_{\mathrm{eff}}$ is therefore proposed as a valuable tool in 2D layer sliding.