Rate description of the stick-slip motion in friction force microscopy experiments

During the stick-slip motion of an atomic force microscope tip contacting with a uniformly moving atomically clean surface, the force developed in the cantilever spring performs random sawtoothlike oscillations resulting from the thermally activated transitions of the tip from one surface site to the next. Using escape rate theory, the probability distribution of forces is calculated numerically to deduce the time-average lateral force as a function of pulling velocity. A transcendental equation for the average force is proposed and its approximate solution is obtained. The accuracy of this analytic approximation is demonstrated via comparison with the numerical results. The analogous force-velocity relations existing in the literature are shown to be the limiting cases of low and high cantilever spring constants of our analytic approximation.