Friction Enhancement and Autoparametric Resonance

Recent intriguing experimental observations of atomic scale friction enhancement, that takes place at scanning velocities correspondent with the cantilever frequency and/or its fractions (1/n, n = 1, 2, 3, …), can be explained as the manifestation of an autoparametric resonance. Taking explicitly into account high flexibility of AFM tips, the developed theory reveals the autoparametric resonance to be a natural consequence of the rich dynamics of the combined tip–cantilever system. Besides the explanation of the observed friction force peaks, the theory predicts a dense multiplicity of smaller peaks to appear when the washboard frequency coincides with a rational part (m/n, with integer m and n) of the cantilever frequency. An important conclusion is made that the resonance enhancement of friction is independent of frequency of excited phonons, and it should manifest itself for any possible mechanism of frictional energy dissipation in the substrate, phononic, electronic, or any other.