Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

Abstract

We present a combined theoretical and experimental study of the dependence of resonant higher harmonics of rectangular cantilevers of an atomic force microscope (AFM) as a function of relevant parameters such as the cantilever force constant, tip radius and free oscillation amplitude as well as the stiffness of the sample's surface. The simulations reveal a universal functional dependence of the amplitude of the 6th harmonic (in resonance with the 2nd flexural mode) on these parameters, which can be expressed in terms of a gun-shaped function. This analytical expression can be regarded as a practical tool for extracting qualitative information from AFM measurements and it can be extended to any resonant harmonics. The experiments confirm the predicted dependence in the explored 3-45 N/m force constant range and 2-345 GPa sample's stiffness range. For force constants around 25 N/m, the amplitude of the 6th harmonic exhibits the largest sensitivity for ultrasharp tips (tip radius below 10 nm) and polymers (Young's modulus below 20 GPa). 883

Quantification of nanomechanical properties of surfaces by higher harmonic monitoring in amplitude modulated AFM imaging

“…We have used the Derjaguin-Muller-Toporov (DMT) model to describe the tip-surface interaction [5] and the tip was approximated by a hemisphere with a well-defined radius R = 5 nm. For simplicity, neither viscoelastic nor capillary forces were considered [25].…”

“…In our case, we chose to detect the 6 th harmonic oscillation amplitude because it is in close proximity with the 2 nd flexural eigenmodes. Considerable theoretical effort has been made in the last few years to describe and understand the potential use of higher harmonics [21][22][23] and its functional dependence on relevant parameters such as cantilever force constant (kc), tip radius (R), free oscillation amplitudes (A0) and sample stiffness (E) [24,25]. It is well known that only a few amplitude signals are detectable when the tip-sample interaction is kept gentle i.e.…”

In situ characterization of nanoscale contaminations adsorbed in air using atomic force microscopy

“…Since the tip may change quite frequently during AFM operation, ex situ methods may be quite inadequate and unproductive for many AFM experiments. Some methods have been proposed to infer tip properties, in particular the radius, using AFM techniques, which in our opinion is the optimal approach [ 37 – 40 ].…”

Material discrimination and mixture ratio estimation in nanocomposites via harmonic atomic force microscopy

“…In addition, unlike force modulation and contact resonance techniques, the tip–sample contact time is dramatically reduced, which is suitable for imaging soft samples. In this regard, one of the most appealing characteristics of harmonic AFM is that it provides a method for fast, high-resolution and nondestructive mechanical mapping of numerous specimens [ 23 – 26 ].…”