 Solution

Four useful interactions are dispersion attraction, electrostatic interaction, capillary attraction and short-range repulsion. Their ranges are relative to atomic contact and depend on geometry and environment.

Van der Waals forces provide an attractive contribution extending beyond direct atomic overlap; for an ideal sphere and plane it scales as $F=-AR/(6z^2)$ in a simple nonretarded model. Electrostatic forces can also be long-ranged: biased conducting surfaces are commonly attractive, whereas charged insulating surfaces can attract or repel depending on their charge and screening.

A capillary meniscus in humid air can pull tip and sample together. It acts over the formation and rupture range of the liquid bridge and can greatly exceed atomically localized forces; it is not a universal interaction in a dry vacuum. At the shortest separations, overlap-related Pauli repulsion provides a steep repulsive contact contribution.

Atomic-scale contact contrast relies on strongly localized short-range tip–surface forces, especially the rapidly varying repulsive interaction in the simple contact-mode picture. Long-range attraction mainly adds a background. Real atomic-resolution imaging also depends on apex structure, stability and operating mode; a generic long-range force alone does not resolve individual surface atoms.