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

Abstract

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.

Compositional Contrast of Biological Materials in Liquids Using the Momentary Excitation of Higher Eigenmodes in Dynamic Atomic Force Microscopy

“…dAFM methods for compositional contrast (elasticity or chemistry) in such soft materials are limited by the low cantilever quality factor in liquids [1][2][3][4][5]. In what follows, we demonstrate a significant improvement in this capability.…”

“…The nonlinear tip-sample interaction in dAFM induces cantilever vibrations at higher harmonics of the drive frequency [1,[5][6][7][8][9][10] which can provide compositional contrast [1,[5][6][7]9,[11][12][13]. Under ambient or vacuum conditions, the higher harmonics are very small and need to be enhanced using special cantilevers [12] or bimodal excitation [14].…”

The dissipated power in atomic force microscopy due to interactions with a capillary fluid layer

“…It has been shown for AFM cantilevers that the higher harmonics of the fundamental mode of oscillation are often excited and this can be used to gain useful information about the sample. [25][26][27][28][29] The higher harmonics could be included in the analysis to yield a more accurate description of the dynamics and therefore an improvement in Eq. ͑8͒.…”

Quantitative biomolecular imaging by dynamic nanomechanical mapping

“…The nonlinear interaction force is able to be decoded from the spectrum of the higher harmonics. 83,114,115,[119][120][121] It has been demonstrated that the amplitude of the higher harmonics decreases with the order increasing; hence, when the amplitude decreases to the decay length of the short-range forces, the higher force gradients can be linked to the higher harmonics spectrum, which will increase the spatial resolution as well. 122,123 However, the rapid decay of the amplitude of higher eigenmodes and harmonics are often beneath the background noise, causing the information related to the material properties to stay hidden.…”