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

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(10 (1) over bar4) 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.