Wavelet transforms to probe long- and short-range forces by thermally excited dynamic force spectroscopy.

The use of wavelet transforms in thermally excited dynamic force spectroscopy allows us to gain insight into the fundamental thermodynamical properties of a cantilever's Brownian motion as well as giving a meaningful and intuitive representation of the cantilever dynamics in time and frequency caused by the interaction with long- and short-range forces. The possibility of carrying out measurements across the jump-to-contact transition without interruption, providing information on both van der Waals forces and short-range adhesion surface forces, is remarkable.

Tip-sample interactions on graphite studied using the wavelet transform.

Wavelet transform analysis is applied to a thermally excited cantilever to get insights into fundamental thermodynamical properties of its motion. The shortcomings of the widely used Fourier analysis are briefly discussed to put into perspective the wavelet transform analysis, used to describe the temporal evolution of the spectral content of the thermal oscillations of a cantilever with an interacting tip. This analysis allows to retrieve the force gradients, the forces and the Hamaker constant in a measurement time of less than 40 ms.