The diversity of friction behavior between bi-layer graphenes

For relative sliding between two rigid graphene sheets that are interacted on by a van der Waals force, we show that the friction behavior is significantly dependent on the interlayer separation distance h. Around the equilibrium interlayer distance he, the friction behavior exactly obeys a linear law. When h is far smaller than he, the linear friction behavior transforms to overlinear behavior. On the other hand, when h is larger than he, there is another critical value of the interlayer distance, hc; when h is larger than he and smaller than hc, the friction behavior transforms from linear to sublinear behavior; however, when h is larger than hc, the coefficient of friction becomes negative. Further, the different friction behaviors are found to be well described by a universal power law, τ = μ*(σ + σ0)(n).