Discriminating short-range from van der Waals forces using total force data in noncontact atomic force microscopy

Abstract

Noncontact atomic force microscopy (NC-AFM) features the measurement of forces with highest spatial resolution and sensitivity, resolving forces of the order of pico-Newtons with submolecular resolution. However, the measured total force is a mixture composed of various interactions. While some interactions such as electrostatic or magnetic forces can be excluded by a careful design of the experiment, the subtraction of van der Waals forces, which mainly originate from London dispersion interactions between the macroscopic tip shank and the bulk sample, remains a challenge. We present the determination of the inherently present van der Waals forces in total interaction force data from fitting a suitable model, allowing for extraction of the short-range force component. We compare the applicability of several van der Waals models based on experimental interaction data from the calcite$(1\phantom{\rule{0.59998pt}{0ex}}0\phantom{\rule{0.59998pt}{0ex}}\overline{1}\phantom{\rule{0.59998pt}{0ex}}4)$ surface. The feasibility to fit these models to experimental data is critically discussed. We furthermore introduce criteria to assess the transition point from pure long-range interaction to mixed short- and long-range forces based on the variance of lateral and vertical force data. This determination allows us to extract the short-range interaction forces, which remained a challenge so far in NC-AFM experiments.