Time-frequency analysis of the tip motion in liquids using the wavelet transform in dynamic atomic force microscopy

Area of Science:

• Physics
• Materials Science
• Nanotechnology

Background:

• Dynamic atomic force microscopy (AFM) in liquids presents challenges in analyzing complex tip-sample interactions.
• Low stiffness cantilevers exhibit transient behaviors, including momentary excitation of the second flexural mode and multiple impacts per oscillation cycle.
• Traditional Fourier transform methods lack the time-resolution necessary to capture these transient dynamics.

Purpose of the Study:

• To introduce and validate the wavelet transform for time-frequency analysis of dynamic AFM tip motion in liquids.
• To overcome the limitations of Fourier analysis in characterizing transient behaviors.
• To quantitatively assess the excitation of the second flexural mode and multiple impact events.

Main Methods:

• Application of wavelet transform for time-frequency analysis of dynamic AFM tip motion.
• Utilizing wavelet scalograms to visualize transient phenomena like second mode excitation and multiple impacts.
• Employing wavelet ridge analysis to extract instantaneous frequencies and magnitudes of the second mode.

Main Results:

• Wavelet scalograms clearly depict the momentary excitation of the second flexural mode and multiple tip-sample impacts.
• Wavelet ridge analysis enables quantitative estimation of the second mode's instantaneous frequencies and magnitudes.
• The maximum instantaneous magnitude (MIM) was found to correlate with the amplitude setpoint and sample Young's modulus.

Conclusions:

• Wavelet transform analysis provides superior time-frequency insights into dynamic AFM tip motion in liquids compared to Fourier methods.
• The study demonstrates the capability of wavelet analysis to identify and quantify complex transient events.
• Maximum instantaneous magnitude (MIM) shows potential as a metric for characterizing nanomechanical properties of sample surfaces, particularly at high amplitude setpoints.