Shortcomings of the Derjaguin–Muller–Toporov model in dynamic atomic force microscopy

Force–distance curves recorded by frequency modulated atomic force microscopy (FM AFM) provide insight into the tip–sample mechanics. For quantitative analysis, FM AFM is able to separate conservative from dissipative forces by simultaneously measuring amplitude–distance and frequency–distance curves. Here, we report on the conservative forces in the gentle tip–sample contact of mesoscopic tips at low Tabor parameters. We introduce an analytical expression for the frequency shift based on the Derjaguin–Muller–Toporov (DMT) contact model to simplify the comparison between the experiment and theory. From the analytical formulas, a scaling law between the tip radius and minimal frequency shift is found, which is supported by experimental data. Although excellent fits for full frequency–distance curves are possible, the resulting material properties do not match the accepted literature values. We suspect that these flaws are a consequence of the incomplete treatment of attractive forces and DMT’s strain-stiffness approximation, rendering DMT-based models inappropriate to measure material properties by dynamic AFM in gentle contact.