Calculations of the threshold force and threshold power to move adsorbed nanoparticles

We propose and analyze a simple model for the calculation of the power P* necessary to depin an essentially rigid cluster or nanoparticle on a surface with a scanning force microscope tip in tapping mode. The model contains the coupling between the particle's lateral and normal motion. We show that there are two important limiting regimes. (i) If momentum transfer occurs gradually between tip and particle, P* depends mainly on the viscous-type drag between particle and surface. (ii) If momentum transfer occurs instantaneously once per oscillation, P* is dominated by the minimum energy barrier necessary to move the cluster by one lattice constant. In the quasistatic driving mode (i), a critical impact angle αₜ* is identified below which depinning cannot be achieved due to lateral-normal coupling.