Revealing Subsurface Vibrational Modes by Atomic-Resolution Damping Force Spectroscopy

Abstract

Damping of the oscillating cantilever in dynamic atomic force microscopy contains valuable information about the local vibrational structure and elastic compliance of the substrate. We review Damping Force Spectroscopy which has successfully visualized atomically-resolved damping in supramolecular assemblies, capable of identifying the location and packing of inner molecules as well as local excitations of vibrational modes, dependent on outer molecules with specific geometry. We introduce the physical origin of damping in a microscopic model and quantitative interpretation of the practical observations by calculating the vibrational spectrum and damping of inner metallofullerene Dy@C$_{82}$ molecules inside carbon nanotubes with different diameters using ab initio total energy and molecular dynamics calculations.