Thermal fluctuations and dynamic modeling of a dAFM cantilever

The Brownian thermal noise which affects the cantilever dynamics of a dynamic atomic force microscope (dAFM) is discussed, both when it works in air and in presence of water. The relationship between the cantilever thermal fluctuations and its interactions with the surrounding liquid is investigated, and an analytical model to describe the interaction forces is presented. The novelty of this approach is that a very simple integral expression to describe fluid-cantilever interactions is found. More specifically, besides including fluid inertia and viscosity, an additional diffusivity term needs to be considered, whose crucial influence for the correct evaluation of the cantilever response to the thermal excitation is shown. The coefficients of the model are obtained by using numerical results for a 2D fluid flow around a vibrating rectangular cross section, so that the dynamics of a dAFM cantilever can be characterized when it also operates in tilted conditions. The analytical model is validated by comparison with numerical and experimental data previously presented in literature, and with experiments carried out by the authors. It is shown that the present model can provide an extremely accurate prediction of the beam response up and beyond the second resonant peak.