Abstract
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.
Highlights
Multifrequency atomic force microscopy (MF-AFM) is an emerging technique involving excitation at multiple frequencies.1,2 MF-AFM provides topography information and yields quantitative elastic, viscoelastic or magnetic properties with a low force and a high sensitivity in a single scan
Power balance is satisfied for each mode of the cantilever, as expected, i.e., the power input is equal to the sum of the power dissipated into the medium and the power transferred into the sample and/or other modes
Power transfer in bimodal amplitude modulation atomic force microscopy (AM-AFM) in liquid environments were investigated by numerical simulations
Summary
Multifrequency atomic force microscopy (MF-AFM) is an emerging technique involving excitation at multiple frequencies. MF-AFM provides topography information and yields quantitative elastic, viscoelastic or magnetic properties with a low force and a high sensitivity in a single scan. Bimodal AM-AFM was first proposed by Rodriguez and Garcia through numerical simulations.. Bimodal AM-AFM was first proposed by Rodriguez and Garcia through numerical simulations.3 It was applied in experimental imaging and showed a higher sensitivity for the second mode in both attractive and repulsive regimes.. Kiracofe et al have shown contrast reversal is directly related to the relative magnitude of modal free kinetic energy.. Chakraborty et al have shown the amplitude and phase contrast inversion, respectively, depends on the modal kinetic energy ratio and free air drive energy ratio of the two modes on different domains in a copolymer.. Modal virial and energy dissipation have been mapped in tetramodal and scitation.org/journal/adv pentamodal AM-AFM by An et al, showing the energy dissipation in each mode could be negative or positive, depending on energy influx or efflux among different modes Kiracofe et al have shown contrast reversal is directly related to the relative magnitude of modal free kinetic energy. Chakraborty et al have shown the amplitude and phase contrast inversion, respectively, depends on the modal kinetic energy ratio and free air drive energy ratio of the two modes on different domains in a copolymer. Modal virial and energy dissipation have been mapped in tetramodal and scitation.org/journal/adv pentamodal AM-AFM by An et al, showing the energy dissipation in each mode could be negative or positive, depending on energy influx or efflux among different modes
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