Friction laws for elastic nanoscale contacts

The effect of surface curvature on the law relating frictional forces F with normal load L is investigated by molecular dynamics simulations as a function of surface symmetry, adhesion, and contamination. Curved, on-adhering, dry, commensurate surfaces show a linear dependence, F proportional to L, similar to dry at commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to L-2/3 similar to friction force microscopes. Curved lubricated or contaminated surfaces show again different behaviour; details depend on how much of the contaminant gets squeezed out of the contact. The shear stress distribution in the contact is highly on-uniform in all cases, i.e. it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.