Transient eigenmodes analysis of single-impact cantilever dynamics combining Fourier and wavelet transforms.

The transient eigenmode structure of an interacting cantilever during a single impact on different surfaces evidences the excitation of higher flexural modes and low frequency oscillations. The frequency shift of the fundamental mode after the tip comes into contact with the sample surface allows calculating the tip-sample interaction stiffness and evidences the role of capillary condensation and surface wettability on the cantilever dynamics. Wavelet transforms are used to trace the origin of spectral features in the cantilever spectra and calculate force gradients of the tip-sample interaction.

Energy dissipation in multifrequency atomic force microscopy.

The instantaneous displacement, velocity and acceleration of a cantilever tip impacting onto a graphite surface are reconstructed. The total dissipated energy and the dissipated energy per cycle of each excited flexural mode during the tip interaction is retrieved. The tip dynamics evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force microscopy, in a regime where few cantilever oscillation cycles characterize the tip-sample interaction.

Complex force dynamics in atomic force microscopy resolved by wavelet transforms.

The amplitude and phase evolution of the oscillations of a cantilever after a single tip-sample impact are investigated using a cross-correlation wavelet analysis. The excitation of multiple flexural modes is evidenced and the instantaneous amplitude and phase evolution is extracted from the experimental data at all frequencies simultaneously. The instantaneous total force acting on the tip during a single impact is reconstructed. This method has general relevance for the development of an atomic force spectroscopy of single tip-sample interactions, that develop in a few oscillation cycles of the interacting cantilever eigenmodes and their harmonics.