Nanoscale Viscoelastic Characterization Using Tapping Mode AFM
The tapping mode atomic force microscopy (AFM) has been widely used as a tool to image sample surfaces [1–3]. It has been modeled as a single degree-of-freedom nonlinear oscillator [4–11], In this model, the tip-sample interactions are described by contact theory with adhesion (Johnson-Kendall-Roberts (JKR) theory) [12–14]. The viscoelasticity is considered as a friction force by adding a damping constant. Magonov and Elings  presented experimental results which show different phase sensitivity for stiff and soft samples. Anczykowski et al. presented results on amplitude vs. tip-sample separation and showed the existence of hysteresis due to nonlinearity and the transition between attractive and repulsive forces. Kuhle et al  demonstrated experimentally the frequency response hysteresis and pointed out the effect of attractive force on this hysteresis using a linear interaction force approximation.
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