Comparison of frequency response of atomic force microscopy cantilevers under tip-sample interaction in air and liquids

The frequency response behavior of Atomic Force Microscopy (AFM) cantilevers in liquids is completely different from that in air, due to changes in the applied hydrodynamic forces and squeeze forces. In this paper, a finite-element method is used to explore the dynamic behavior of AFM cantilevers in air and in liquids. Furthermore, the frequency response of the tapping mode AFM under acoustic excitation force is studied. In the theoretical model, hydrodynamic forces exerted by the liquid on the AFM cantilever are approximated by additional mass and hydrodynamic damping. The results show that the microcantilever operating in liquids is an intensively damped system, with a relatively large shift in its resonant frequencies from its natural frequencies, along with a considerable reduction in vibration amplitudes. The simulation results are compared with experimental results, showing very good agreement between the two. In addition, the effects of liquid viscosity and liquid density on the frequency response function are studied. Finally, the dynamic behavior of the AFM cantilever under tip-sample interactions is analysed in both repulsive and attractive regimes. The paper shows further that the frequency response in liquid environments close to the surface depends on two important parameters: squeeze force and tip-sample interaction.