Surface mechanical instabilities and dissipation under the action of an oscillating tip

We analyze the mechanical response of a surface under the action of an oscillating tip in non-contact situations. The surface behavior is modelled as a simple viscoelastic material. In particular, special attention is paid to the surface displacement due to the attractive interaction between the tip and the surface. Analytical expressions describing the oscillation behavior of the tip at the proximity of the surface are obtained by considering two asymptotic regimes. The two asymptotic regimes are controlled by the characteristic relaxation time of the surface. Fast relaxation times correspond to time shorter than that of the residence time, e.g. the time during which the oscillating tip is at the proximity of the surface. Slow surface relaxation processes correspond to time larger than that of the oscillation period. The results allow the calculation of the non-contact dissipation as a function of the surface mechanical properties. Also, two criterions are derived that give the threshold values of the surface mechanical instability. The threshold values are shown to be strongly dependent of the characteristic time scale of the surface relaxation, thus of its dissipative properties.