Microcantilever dynamics: effect of Brownian excitation in liquids

Nowadays dynamic atomic force microscopes (dAFM) are being extensively investigated because of the so different and novel applications where dAFM are employed, e.g. to study biological targets as cells, proteins, DNA. In such cases the micro-cantilever tip often needs to operate in a liquid environment to extract the required information from the sample. However, tip dynamics is strongly affected by the presence of the liquid itself, so that understanding the actual microcantilever response in such conditions, has become one of the most challenging problems the researchers are trying to face. A deep knowledge of the degree of interaction between the cantilever dynamics and the fluid is extremely important to avoid misleading information. Because of the micro-scale size of the cantilever, thermal noise due to Brownian forcing of liquid particles cannot be neglected and therefore proper insights about this effect are required. This is why different numerical approaches have been presented in literature, which only approximatively describe the liquid - cantilever interaction. In this paper the authors provide a useful and relatively simple tool to describe the fluid-structure interaction. In particular we present an analytical heuristic formulation of the force the liquid exerts on the cantilever, which can be successfully utilized to investigate the AFM cantilever dynamics under the action of both linear and non linear forces. In particular we show that the liquid response consists of three terms: (i) a viscous term, (ii) a velocity-diffusive term, and (iii) an inertial term. The novelty of the model is mainly represented by the velocity-diffusive term, that to the best of our knowledge has never been taken into account before. We show indeed, that neglecting this term leads to large errors in the estimation of the cantilever response and , hence, of its thermal response, which is often used to calibrate the instrument.