Frequency response of atomic force microscopy microcantilevers oscillating in a viscous liquid: A comparison of various methods

Operating an Atomic Force Microscopy (AFM) with the cantilever and sample immersed in a liquid has many advantages, including the elimination of capillary forces and reduction of van der Waals forces in the study of liquid–solid interactions. Accurately identifying the maximum of the amplitude–frequency curves at which resonances occur is a challenging issue. The frequency response of a cantilever beam in a viscous liquid near a surface depends on the hydrodynamic loadings. First, in this paper, there is a comparison of predicted resonant frequencies from five different theoretical models, with measurements for the case of an ambient liquid of infinite extent. The precision of each method is indicated. Then, the motion of microcantilevers of variable widths close to a solid surface is simulated. When the cantilever tip approaches the sample surface gradually, the effect of squeezed film damping causes the resonance frequencies to shift toward lower values at lower amplitudes, and subsequently as the tip-sample separation becomes smaller, the resonance peaks seem to vanish completely. The results demonstrate that any changes in the geometrical dimensions of the cantilever and in the fluid properties may influence the accuracy of the model. Furthermore, due to the considerable effect of tip-sample separation on the resonance, some models are restricted to be applicable only in the circumstances of free liquid