Dynamic atomic force microscopy is currently evolving from a single to a multifrequency instrument for nanoscale imaging often employing higher-order microcantilever eigenmodes for improved resolution and force spectroscopy. In this work the authors study the fundamentals of cantilever dynamics and energy dissipation when soft cantilevers are driven at their second flexural eigenmode and interact with samples in liquid environments. Contrary to the conventional first eigenmode operation, second eigenmode operation in liquids is often dominated by a subharmonic response (e.g., one tap every four drive cycles) and there is an energy transfer to the first eigenmode creating a new channel of energy dissipation and compositional contrast.

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Experiments were also performed with magnetic drive but the second eigenmode was hard to excite sufficiently thus subharmonics could not be seen as well compared to acoustic drive.
24.
At least two eigenmodes are needed to predict dynamics when driving the first eigenmode in liquids.6 We found three eigenmodes necessary while driving the second eigenmode.
25.
Under conditions relevant to typical biological AFM (high concentration buffer solutions with amplitudes >23nm) the forces due to adhesion, the electrical double layer, and solvation shells are relatively small and have little effect on the dynamics, justifying the use of Hertz model as opposed to more detailed models.
26.
The experimental time history was acquired in a separate measurement from the approach curves. Time history was acquired at a steady-state Z to reduce noise and comb filtered to multiples of Ωd/4 with a 1 kHz bandwidth.
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