Frequency-distance curves

Analyzing the measured frequency shift versus distance curves one can determine the distance dependence of the tip-sample force. The results of such analyzing demonstrate that not only non-contact, but also elastic contact forces can be quantitatively measured by dynamic force spectroscopy opening a new and direct way to the verification of contact mechanical models of nanoasperities [1].
Frequency-distance (f-d) curves show a similar overall shape. As one can see on the animated picture during the approach of the cantilever to the sample surface, the frequency shift decreases and reaches a minimum. With a further reduction of the nearest tip-sample distance, the frequency shift increases again and becomes positive. For smaller resonance amplitudes, the minimum of the Df(z) curves is deeper and the slope after the minimum is steeper than for larger amplitudes. Also f-d curves became deeper in area with increased adhesion force.
A comparative experimental and theoretical study of the frequency shift in dynamic force microscopy in dependence of the tip-sample distance and the resonance amplitude revealed that frequency shift versus distance curves obtained with different amplitudes scale with 1/A^3/2 and can therefore be condensed to a single normalized frequency shift curve [2].
This experimental force curve shows good agreement with specific force laws for long-range (van der Waals), short-range (Lennard-Jones), and contact (Hertz/DMT) forces [3].
 

   References

1. Phys. Rev. B 61, 12678 (2000). 
2. Phys. Rev. B 56, 16010 (1997). 
3. Appl. Phys. Lett. 75, 433 (1999).

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