Abstract

In attempting to perform frequency modulation atomic force microscopy (FM-AFM) in liquids, a non-flat phase transfer function in the self-excitation system prevents proper tracking of the cantilever natural frequency. This results in frequency-and-phase modulation atomic force microscopy (FPM-AFM) which lies in between phase modulation atomic force microscopy (PM-AFM) and FM-AFM. We derive the theory necessary to recover the conservative force and damping in such a situation, where standard FM-AFM theory no longer applies. Although our recovery procedure applies to all cantilever excitation methods in principle, its practical implementation may be difficult, or even impossible, if the cantilever is driven piezoacoustically. Specifically, we contrast the piezoacoustic excitation method to the photothermal method in the context of force spectroscopy of hydration structures at the mica-water interface. The results clearly demonstrate that photothermal excitation is superior to piezoacoustic excitation, as it allows for accurate quantitative interpretation of the acquired data.

Highlights

  • The benefits of frequency modulation atomic force microscopy[1] (FM-AFM) over amplitude modulation atomic force microscopy[2] (AM-AFM) in vacuum are clear: is the response time greatly improved, but the conservative and dissipative forces are decoupled because the cantilever is always driven at its natural frequency, which maintains the signal-to-noise ratio (SNR) at its maximum throughout the experiment

  • We refer to this mode of AFM operation as frequency-and-phase modulation atomic force microscopy (FPM-AFM), which lies in between phase modulation atomic force microscopy[5,6] (PM-AFM) and FM-AFM

  • We extend our conclusions to topography imaging, and present potential benefits that can be exploited by deliberately tuning the ratio of frequency-to-phase modulation in Frequency-and-phase modulation (FPM)-AFM

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Summary

INTRODUCTION

The benefits of frequency modulation atomic force microscopy[1] (FM-AFM) over amplitude modulation atomic force microscopy[2] (AM-AFM) in vacuum are clear: is the response time greatly improved, but the conservative and dissipative forces are decoupled because the cantilever is always driven at its natural frequency, which maintains the signal-to-noise ratio (SNR) at its maximum throughout the experiment In this ideal situation, the interpretation of the acquired FM-AFM data is straightforward: the conservative interaction between the cantilever tip and the sample is directly related to the shift in the self-excitation frequency, while the interaction damping is directly related to the drive amplitude of an automatic-gain-controller (AGC) which maintains a constant cantilever amplitude. We summarize our findings and extend our conclusions to topography imaging

Hydration spectroscopy experiment
AFM characterization
THEORY AND SIGNAL RECOVERY
Recovery of the conservative interaction
Recovery of the dissipative interaction
Practical limitations to damping recovery for piezoacoustic excitation
DISCUSSION
FPM-AFM in topography imaging
Outlook for FPM-AFM
CONCLUSION
Determining the cantilever transfer function from a thermal power spectrum
Full Text
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