Power transfer in bimodal amplitude modulation atomic force microscopy in liquids: A numerical investigation

Bimodal amplitude modulation atomic force microscopy (AM-AFM) is an emerging technique for compositional imaging in liquids. In this work, we investigate the power transfer in bimodal AM-AFM in liquids by a numerical analysis. Power items are calculated by direct numerical integral and the corresponding amplitude and phase response is presented. Results show power balance is satisfied for each mode. The power transfer in each mode is significantly small compared to the external input power and most of the power is dissipated into the surrounding medium, especially for a large setpoint or cantilever-sample separation. The power transfer among different modes is complex and strongly depends on the cantilever and imaging parameters. Power transfer between different modes goes up with increasing free amplitude of the second mode. In addition, a stiffer sample will produce a more complex force spectra, which perturbs the cantilever oscillation more heavily compared to a compliant sample. Besides, the non-driven higher mode of a softer cantilever is more likely to be momentarily excited. The power items and cantilever response during imaging are also provided, revealing the phases in bimodal AFM in liquids may not be utilized to characterize the sample elasticity due to the non-monotonic trends. Instead, the amplitude of the second mode could be used to characterize the elasticity of the sample with moderate to high moduli.