Investigation of the normal load and contact stiffness effect on kinetic friction in the Prandtl-Tomlinson model

Simona Skuratovsky, Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
Ronen Berkovich, Department Of Chemical Engineering, Ben-gurion University Of The Negev, Beer Sheva, Israel

Friction Force Microscopy (FFM) explores the interaction between two sliding surfaces on the nanoscale, providing information on the frictional dynamics and contact stiffness with lattice resolution. Incorporating load dependency of the surface corrugation energy, U₀, measured for NaCl in ethanol into the Prandtl-Tomlinson (PT) model, we study the effect of varying normal load and the effective contact stiffness, K_eff, on kinetic friction for symmetric 1-d and 2-d potentials, as well as for an asymmetric 1-d potentials. While the lateral force and the corrugation energy scales with the applied load for all potentials, K_eff display an unexpected behavior. When K_eff is taken to be constant, its simulated value asymptotically approaches its nominal value with increasing of the normal load. However, since U₀ increases with the applied load, multiple slips in the friction stick-slip pattern begin to occur. This can be explained via the PT parameter, which is a dimensionless number determined by the ratio between the stiffness of the surface potential and o the contact, that monotonously grow for K_eff = const. On the other hand, when K_eff is set to scale with the applied load, the PT parameter reaches an extremum point, as the friction pattern maintain regular single stick-slip events, in agreement with the experimental measurements.