Refined force-velocity relation in atomic friction experiments

The stick slip motion of an atomic-force-microscopy tip in contact with a uniformly moving surface consists of the stick phases when the tip is confined to one of the moving surface sites and thermally activated slips of the tip from one site to the next. The stick phase is associated with the increase of the elastic deformation of the cantilever spring, the tip apex, and the surface in the contact region. The corresponding spring constant is experimentally determined from the rate of increase of the elastic force. By taking into account the effect of the tip-surface interaction potential, we refine the expression for the experimentally measured spring constant and show that it weakly depends on the pulling velocity. We incorporate this expression into the force-velocity relation obtained previously within the rate theory and demonstrate that such a refinement leads to a notable improvement of the accuracy of this relation.