Characterization of distance-dependent damping in tapping-mode atomic force microscopy force measurements in liquid

We have used a spectral analysis method to characterize changes in the local damping coefficient for an acoustically driven cantilever as it approaches a hard surface in liquid. We show a significant distance dependence of the damping coefficient (and associated quality factor) that must be accounted for to achieve successful theoretical reproduction of experimental tapping-mode force curves. We model the cantilever dynamics using a forced damped harmonic oscillator model and solve the equation of motion using the method of finite differences. Experiments in solutions of differing viscosities show that bulk viscous damping is not the source of the system dissipation, while simulations of the cantilever dynamics including adhesion hysteresis also eliminate this as the origin of the dissipation. We conclude that frictional dissipation that occurs with the intermittent contact is the likely source of dissipation in the system. Our results identify a semiquantitative means of interpreting tapping-mode force curves on nondeformable surfaces in liquid.