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, $\eta$, does exist in the ideal (Prandtl-Tomlinson) problem of a point particle sliding across a 1D periodic lattice potential. In that case $\eta >1$ implies mechanical instability, generally leading to stick-slip, with $\eta =\frac{2{\pi }^2{U}_0}{K_{\mathrm{p}}{a}^2}$, 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 ${\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ can be defined with the same form but suitably defined $U_{\mathrm{e}\mathrm{f}\mathrm{f}}$, $a_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and $K_{\mathrm{e}\mathrm{f}\mathrm{f}}$. Remarkably, simulations show that $a_{\mathrm{e}\mathrm{f}\mathrm{f}}=a$ of the substrate remains an excellent approximation, while $K_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is an effective stiffness parameter, combining equipment and internal elasticity. Only the effective energy barrier $U_{\mathrm{e}\mathrm{f}\mathrm{f}}$ 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 $U_{\mathrm{e}\mathrm{f}\mathrm{f}}$, whose magnitude for a micrometer size diameter is of order 1 eV, scales as $A^{1\mathrm{/}4}$, thus increasing very gently with size. The PT-like parameter ${\eta }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is therefore proposed as a valuable tool in 2D layer sliding.