Dynamic model of atomic force microscopy in tapping-mode

The theoretical model about energy dissipation of atomic force microscopy (AFM) in tapping-mode has great significance for the investigation of the dynamic response of AFM tip influenced by the adhesive force. Based on the Hamaker hypotheses and the Lennard-Jones potential and elastic theory, a novel elastic model is established for adhesive contact between a sphere and a plane. The model shows that the variation of the adhesive force with the distance in the loading process is different from that in the unloading process, i.e., an adhesive hysteresis, which is the indication of energy dissipation of AFM, is engendered in the tapping-mode. On the basis of the adhesive model, the dynamic model of AFM in tapping-mode is established to investigate the variations of the amplitude, phase shift and energy dissipation with the distance between AFM tip and the sample surface. The results obtained by the dynamic model are in agreement with the experimental results available.