Analysis of the effect of mechanical properties of liquid and geometrical parameters of cantilever on the frequency response function of AFM

The dynamic behavior of atomic force microscopy (AFM) cantilevers in liquid is completely different from its behavior in air due to the applied hydrodynamic force. Exciting cantilever with frequencies close to resonance frequency and primary position alignment are two critical issues that should be considered in deriving frequency response function (FRF). In this paper, the hydrodynamic force has been modeled with string of spheres and the effect of the damping and the added mass on the model has been analyzed. Afterward, this force is applied to the dynamic equation so that the dynamic behavior of AFM cantilevers is studied in liquids by analyzing the effect of some important parameters such as added mass, internal, and fluid damping. By simulations of the dynamic equations for a silicon cantilever, FRF is determined in both air and liquid. In addition, the effects of two significant parameters of liquid mechanical properties (liquid viscosity and density) and geometrical parameters of cantilever on FRF are studied. The results for string of spheres model are compared with the other hydrodynamic model and the experimental data. When length/width ratio decreases, it is found that string of spheres model has a better agreement than the other hydrodynamic model with experimental data.