Scale Dependence of Friction: How Elasticity Destroys Superlubricity

The talk will discuss friction in single-asperity contacts as a function of contact radius a, substrate stiffness, atomic structure and adhesive strength. The friction between bare, rigid surfaces can be obtained by a simple sum over atomic forces. When surfaces are aligned and have the same periodicity, the forces add in phase and the friction force F rises linearly with area A. When the two surfaces are misaligned or disordered, so that there is no common periodicity, forces add out of phase and F∝A^x with x≤0.5. This is known as structural superubricity and implies that friction vanishes in the limit of large contact sizes. Most surfaces do not share a common period but friction is almost always observed at macroscopic scales. We use an efficient Greens function technique to study contacts with dimensions of micrometers while resolving atomistic interactions at the surface. For small tips and high loads the contact area follows predictions for contact of rigid surfaces, x=1 for identical aligned surfaces, x=1/2 for random surfaces and x=1/4 for incommensurate crystals. Elasticity becomes important when a exceeds the core width b_core of interfacial dislocations. For a>b_core parts of the contact can advance independently. The friction for identical aligned surfaces drops as a power law and then saturates at the Peierls stress for moving edge dislocations. The friction on large incommensurate¹ and disordered surfaces saturates at nearly the same value. Thus for all geometries x=1 in large contacts. While this means that elasticity destroys superlubricity, the friction drops exponentially with the ratio of substrate stiffness to local interfacial shear stress. This ratio is expected to be particularly large for common solid lubricants that have weak interfacial interactions and large in-plane stiffness.
¹Sharp, Pastewka, Robbins, Phys. Rev. B93, 121402(R) (2016)