Solution (source code)

= Solution

Two useful properties are \b[<adhesion>] and \b[contact <elastic modulus>]. The <pull-off force>, the most negative <force> on retraction relative to the noncontact baseline, maps <adhesion>. Fit the contact part of the force-indentation relation using a suitable <contact mechanics> model to obtain a reduced <elastic modulus>; for example, the <DMT contact model> uses
$$
F-F_{\rm adh}=\frac43E^*\sqrt R\,\delta^{3/2},
$$
where $F_{\rm adh}<0$, $R$ is the calibrated tip radius and $\delta$ is indentation. Converting $E^*$ to a sample <Young's modulus> also requires the tip modulus and the two <Poisson's ratios>. The approach curve alone does not supply a retraction pull-off measurement. The loop area can additionally map dissipated energy; it is not automatically a purely viscous loss.<PeakForce QNM User Guide by Bruker>[Sections 2.5.1, 2.5.3 and 2.5.5: modulus, <adhesion> and dissipation]{ref}