Frequency response of an atomic force microscope in liquids and air: Magnetic versus acoustic excitation

Abstract

We discuss the dynamics of an amplitude modulation atomic force microscope in different environments such as water and air. Experiments, analytical expressions, and numerical simulations show that the resonance curves depend on the excitation method used to drive the cantilever, either mechanical or magnetic. This dependence is magnified for small force constants and quality factors, i.e., below 1 N / m and 10, respectively. We show that the equation for the observable, the cantilever deflection, depends on the excitation method. Under mechanical excitation, the deflection involves the base and tip displacements, while in magnetic excitation, the cantilever deflection and tip displacement coincide.

Quantitative Analysis of Scanning Force Microscopy Data Using Harmonic Models

“…It can be shown numerically and experimentally that both methods are equivalent for the case of small damping. 21 Using eq 1 to interpret AFM measurements requires a relation between the tip-sample forces F ts and the quantities usually measured in an AFM, namely amplitude and phase of the cantilever oscillation at the driving frequency. The interaction forces F ts are highly nonlinear functions of the tip position z(t) and possibly the velocity ż(t).…”

Viscoelastic Drag Forces and Crossover from No-Slip to Slip Boundary Conditions for Flow near Air-Water Interfaces

“…with the effective mass of the cantilever In the standard dynamic AFM where the driving force is induced by the cantilever base displacement [23][24], the measured signal is the oscillation of the cantilever deflection (2) gives rise to a linear relation between the tip velocity z  and the hydrodynamic force,…”

Role of the driving laser position on atomic force microscopy cantilevers excited by photothermal and radiation pressure effects

“…The resonance frequency, i.e., the position of the peak of the frequency response of the system, is mainly determined by the mechanical transfer function, strictly dependent on the geometrical and physical properties of the cantilever, but it can be influenced by the frequency behavior of the external driving force. 15,24 The radiation pressure does not depend on the frequency and it is not expected to influence in any way the resonance of the system. Differently, the photothermal effect has a frequency decay that induces a shift in the resonant frequency depending on the position of the laser spot on the cantilever, 12 and thus we should observe a decrease in the resonant frequency 1 ͑x͒ near the base of the cantilever, where this effect dominates.…”

“…1, a theoretical model of the physical phenomenon has been exploited. The dynamics of a micrometric cantilever subject to a viscous drag and external forces has been treated in several conditions 14,15 and explicitly solved for the homogeneous case ͑no external forces͒, 16 obtaining a set of normal modes n ͑x͒, where x indicates the coordinate along the cantilever length and n is the mode. Because these functions constitute a complete and orthonormal set, the dynamics induced by the presence of a sinusoidally intensity modulated external laser can be described by projection on this base as follows: a͒ Electronic mail: massimo.vassalli@cnr.it.…”