Revealing tip-surface interaction with dynamic force curves

The force between the AFM tip and the surface is conventionally studied using quasi-static deflection-approach curves. These must be converted into force-position curves by a transformation of coordinates, to be compared with models of the interaction, such as the Derjaguin-Muller-Toporov (DMT) model. For the transformation to be valid the motion has to be slow, as to not excite the resonance of the cantilever.

We instead excite the cantilever a two frequencies near its resonance, creating a beat that effectively approaches and retracts from the surface in what is called Intermodulation AFM. By measuring amplitude and phase during this beat, and using a transformation similar to that done for quasi-static curves (but now taking the full dynamics of the cantilever into account) we obtain two dynamic force curves. One conservative, Fi and one disipative, Fq.

Comparing theoretical Fi and Fq curves for standard models, such as the DMT, to experimental result reveal severe limitations of these models. They are typically not sufficient to explain the observed interaction between the tip and the surface. We show how a proposed new tip-surface model, which allow a dynamic surface, can overcome some of these limitations.