Near-Grazing Dynamics in Tapping-Mode Atomic Force Microscopy

In tapping-mode atomic force microscopy, nonlinear e¤ects due to large variations in the force …eld on the probe tip over very small length scales and the intermittency of contact may induce strong dynamical instabilities. In this paper, a discontinuity-mapping-based analysis is employed to investigate the destabilizing e¤ects of low-velocity contact on a lumped-mass model of an oscillating atomic-force-microscope cantilever tip interacting with a typical sample surface. As illustrated using two tip-sample force models, the analysis qualitatively captures the potential loss of stability and disappearance of a low-contact-velocity steady-state response. The quantitative agreement of the predictions of the discontinuity-mapping-based analysis with direct numerical simulations, at least for su¢ciently low-velocity contact, supports its use in the passive redesign or active control of the tip-sample mechanism for purposes of preventing such a loss of stability