A generalization of the Coulomb's friction law: from graphene to macroscale

At the nanoscale, differently to what happens at the macroscale, friction even without an applied normal pressure and spontaneous adhesion take place. In particular, the nanotribology between two layers of graphene, or other two-dimensional nanomaterials (even curved, such as nanotube walls), remains controversial. It is sufficient to say that friction between two graphene layers or nanotube walls is described in the current literature giving as material property a constant friction force or a constant friction shear strength, even if such views are obviously mutually exclusive. Is friction dominated by a strength, by a force or by an energy? Coupling elasticity and energy balance we solve this paradox deriving a generalization of the celebrated Coulomb's friction law, reconciling the two current views. Molecular dynamics simulations on graphene are conducted to verify its validity at the nanoscale whereas statistical simulations confirm its validity even at the macroscale.