Determination and simulation of nanoscale energy dissipation processes in amplitude modulation AFM

We develop a theoretical framework that explains the use of amplitude modulation AFM to measure and identify energy dissipation processes at the nanoscale. The variation of the dissipated energy on a surface by a vibrating tip as a function of its amplitude has a shape that singles out the dissipative process. The method is illustrated by calculating the dynamic-dissipation curves for surface adhesion energy hysteresis, long-range interfacial interactions and viscoelastic processes. We also show that by diving the dissipated energy by its maximum value, the dynamic-dissipation curves become independent of the experimental parameters. In particular, for long-range dissipative processes we have derived an analytical relationship that shows the independence of the normalized dynamic-dissipation curves with respect the free amplitude, cantilever constant or quality factor.