Non-Linear Dynamics of Microcantilevers in Liquid Environment Atomic Force Microscopy When Operating at the Second Eigenmode: Subharmonics, Multiple Impacts, and Chaos

Many newer atomic force microscopy (AFM) methods aim to excite higher-order eigenmodes of the microcantilevers in multi-frequency excitation/detection schemes for improving compositional contrast in nanoscale imaging. Yet, before moving to multi-mode excitation schemes it is important to understand how, if at all, operating the microscope at eigenmodes beyond the fundamental is different from operating at the fundamental eigenmode. This question becomes particularly relevant for biological applications when cantilevers are operated in liquid environments, which is critical for studying biological processes under physiological “native” conditions. In this work, the dynamics of AFM cantilevers in liquids are investigated when the cantilever is driven at its second natural frequency — a situation, which from prior work in air or vacuum, ought not be essentially different from operating at the first natural frequency. The dynamics of cantilevers in liquids tapping on samples are in fact found to be surprisingly different when operating at the second eigenmode. A complex set of behaviors are found including sub-harmonic (e.g. only one impact every four drive cycles), drum-roll like multiple-impacts (e.g.two or three impacts every drive cycle) and chaotic. The subharmonic behaviors, in particular, have not been studied before in liquids and are not accounted for in any current method. These behaviors are demonstrated through numerical simulations and confirmed with experiments.