Modeling of cylindrically tapered cantilevers for transverse dynamic force microscopy (TDFM)

In transverse dynamic force microscopy a cylindrically tapered cantilever is mounted perpendicularly to the sample surface and set into transversal oscillation. The dynamics of the cantilever has been studied using the continuum mechanical model with discrete element analysis. A viscoelastic model has been used to describe the tip-sample interaction. In this way an in-phase and an out-of-phase component of the force has been extracted from the experimental data. Two different techniques, involving two experimental setups and two corresponding data analysis routines, have been developed to calculate the two components of the force at different tip-sample separations. In one case the change in resonant frequency and corresponding oscillation amplitude is measured whereas in the second case the usual way of recording amplitude and phase signal at a fixed driving frequency is applied. The results from these two methods are shown to be completely consistent and produce almost identical force curves.