Nonlinear dynamics of tapping-mode atomic force microscopy in liquid

Abstract

One problem in imaging is due to coexistence of double stable responses which can reduce the precision of the images. Our target is comparing coexistence of double responses in liquid with responses obtained in air. Contact forces have some differences in liquid in comparison to air in magnitude and in the formulation. Hydrodynamic forces are also applied on the cantilever. This may change the nonlinear dynamics of tapping-mode Atomic Force Microscopy (AFM) in liquid in comparison to air. In this paper, we have simulated a tapping-mode AFM (TMAFM) cantilever in liquid environment and explored the existence of multi responses in amplitude and phase diagrams. For modeling we have used a continuous beam model with its first mode and forward-time simulation method for the solution of its hybrid dynamics. Frequency response results of the simulation show a good agreement with experiments. The results for studying the nonlinear dynamics of an AFM microcantilever show that while there are two stable responses in air, in liquid just one response exists. Amplitude diagrams show that there is not any shift from low amplitude to high amplitude and both diagrams of sweeping up and down of the driving frequency coincide on each other. Average force diagrams show that in liquid there is not any repulsive regime and the magnitude of attractive force is small too. Sensitivity analysis for studying the effect of the free amplitude shows that in common setpoints double responses do not occur in liquid. Frequency response results show that just in driving frequencies larger than the resonance frequency of the microcantilever in liquid double responses can occur.