Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments

A mathematical model is presented to predict the oscillating dynamics of atomic force microscope cantilevers with nanoscale tips tapping on elastic samples in liquid environments. Theoretical simulations and experiments performed in liquids using low stiffness probes on hard and soft samples reveal that, unlike in air, the second flexural mode of the probe is momentarily excited near times of tip-sample contact. The model also predicts closely the tip amplitude and phase of the tip at different set points