In amplitude modulation atomic force microscopy the attractive and the repulsive force regimes induce phase shifts above and below 90°, respectively. In the more recent multifrequency approach, however, multiple operation regimes have been reported and the theory should be revisited. Here, a theory of phase contrast in multifrequency atomic force microscopy is developed and discussed in terms of energy transfer between modes, energy dissipation and the kinetic energy and energy transfer associated with externally driven harmonics. The single frequency virial that controls the phase shift might undergo transitions in sign while the average force (modal virial) remains positive (negative). © 2014 AIP Publishing LLC.

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