Mapping Electrostatic Forces Using Higher Harmonics Tapping Mode Atomic Force Microscopy in Liquid

A simple model of a damped, harmonic oscillator is used to describe the motion of an atomic force microscope cantilever tapping in fluid. By use of experimentally obtained parameters, excellent agreement is found between theory and experimental results. From the model we estimate that the force applied on the sample can range up to 100 nN, depending on the surface charge density. Detailed analysis of the cantilever deflection reveals subtle differences in the oscillatory motion, as a result of differences in the tip-sample interaction, which can conveniently be visualized by spectral analysis. The amplitudes of the higher harmonic frequencies are shown to be sensitive for electrostatic interactions. Mapping of higher harmonic amplitudes is applied to qualitatively map the surface charge density of DNA molecules on poly-L-lysine coated mica.