Experimental and theoretical characterization of a dAFM cantilever dynamics

In this paper we accurately describe the dynamics of a dAFM (dynamic atomic force microscope), by deeply investigating the relationship between the cantilever thermal fluctuations and its interactions with the surrounding liquid. To this end, we discuss the Brownian thermal noise, which affects the cantilever dynamics, both when it works in air and in presence of water. We present an analytical model of the drag of the liquid on the cantilever, which takes into account both the fluid inertia and diffusivity terms, whose crucial influence for the correct evaluation of the cantilever response to the thermal excitation is widely discussed. By fitting our analytical model with experimental or numerical data, the coefficients of the liquid response can be calculated, as a function of the distance of the beam from the substrate. Our analytical model is assessed by comparison with numerical and experimental results previously presented in literature, and with our experiments conducted with a dAFM working in air.