Effects of geometrical dimensions and liquid properties on frequency response of resonating microcantilevers in the vicinity of a surface

• To observe specific behaviors and biological processes, accurate imaging techniques by using short cantilevers are studied.
• The frequency response of a rectangular (AFM) in liquid environment has been analyzed by using the Timoshenko beam model.
• The effects of physical and mechanical properties on the frequency response of system have been investigated.
• The frequency responses of the AFM cantilever immersed in various liquids have been compared with one another.
• The effect of geometrical parameters on the frequency response of the system has been studied.

Frequency response of an atomic force microscopy cantilever immersed in liquid near a surface strongly depends on the hydrodynamic forces specially the squeezed film damping, mechanical properties of the liquid including the dynamic viscosity and the density and the geometrical dimensions of the cantilever. For a slightly inclined magnetically oscillated cantilever with the approximate hydrodynamic forces acting on it, the analytical solution of the equation of motion has already been acquired. In this paper, the effects of geometrical dimensions of the cantilever on the resonance frequency, the motion amplitude and the quality factor are observed and then any increase in the kinematic viscosity of the liquid is studied through the simulation of the oscillatory motion of the cantilever. The acquired amplitude–frequency curves indicate that with an appropriate proportion between the cantilever dimensions, it is possible to optimize the quality factor for extremely small tip-sample separations. Also, if the thickness is increased and the width is reduced with the cross section area being held constant, the resonance will occur at higher frequency and the quality factor will be enhanced. Adding glycerol to water will result in the reduction of resonance frequency of the cantilever near the surface due to the viscous friction and squeezed film damping. Consequently the quality factor is decreased as a result of viscosity increase in the simulations.