Abstract
This paper presents computational simulations of single-mode and bimodal atomic force microscopy (AFM) with particular focus on the viscoelastic interactions occurring during tip–sample impact. The surface is modeled by using a standard linear solid model, which is the simplest system that can reproduce creep compliance and stress relaxation, which are fundamental behaviors exhibited by viscoelastic surfaces. The relaxation of the surface in combination with the complexities of bimodal tip–sample impacts gives rise to unique dynamic behaviors that have important consequences with regards to the acquisition of quantitative relationships between the sample properties and the AFM observables. The physics of the tip–sample interactions and its effect on the observables are illustrated and discussed, and a brief research outlook on viscoelasticity measurement with intermittent-contact AFM is provided.
Highlights
Atomic force microscopy (AFM) has developed considerably since its introduction in the mid-1980s, and today constitutes one of the most powerful and versatile tools in nanotechnology [1,2,3]
The first subsection provides an analysis of the tip–sample interaction physics for ideal and numerically computed trajectories of the tip, both for single-mode and bimodal AFM
For some cantilever frequencies certain regions may not exhibit a measurable viscous behavior, and for other frequencies, regions of different properties may exhibit similar dissipation behaviors. As it can be inferred from the results presented here, it is not possible to express the tip–sample force curve analytically, since it depends on the sample deformation timescale as well as on the previous history of the surface
Summary
Atomic force microscopy (AFM) has developed considerably since its introduction in the mid-1980s, and today constitutes one of the most powerful and versatile tools in nanotechnology [1,2,3]. For soft samples the contrast is often associated with viscoelasticity for which measurements are most commonly carried out by using contact resonance techniques [4,5,6,7,8], whereby classical properties are approximated by using contact models under small-amplitude oscillatory deformations Such characterization is much more challenging to carry out by using. Multi-frequency AFM [13] is a family of techniques in which the cantilever probe is driven simultaneously at more than one frequency with the purpose of expanding the amount and type of information that can be acquired during each scan Most commonly this is accomplished by driving simultaneously more than one cantilever eigenmode (multimodal characterization), such that the contrast signals from each eigenmode serve different purposes. Most of the discussion in this paper is based on the AM-OL method of Rodriguez and Garcia [11,12], which is the most common, but some of the discussion is applicable to bimodal methods involving frequency-modulation
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