Examination of the relationship between phase shift and energy dissipation in tapping mode atomic force microscopy by frequency-sweep and force-probe measurements

Abstract

The relationship between phase shift and energy dissipation in tapping mode atomic force microscopy was examined by performing frequency-sweep and force-probe experiments on polydimethylsiloxane (PDMS) samples of different cross-link densities. Phase shift is related to the reduced tip–sample energy dissipation, i.e. the fraction of the maximum energy of a tapping cantilever that is dissipated by the tip–sample interaction. The reduced tip–sample energy dissipation varies linearly with phase shift, and increases continuously as the tip–sample interaction increases. On a compliant polymer such as PDMS the tip–sample interaction dissipates only a small fraction of the power delivered to the tapping cantilever even under hard tapping conditions, so that the vibration of the tapping cantilever is well described in terms of the harmonic approximation.