Atomic force microscopy cantilever oscillation

Using the FM mode in vacuum improved the resolution dramatically and atomic resolution was obtained even on chemically reactive samples. In this article we focus on FM mode atomic force microscopy. In FM-AFM, a cantilever with eigenfrequency /o and spring constant k is subject to controlled feedback such that it oscillates with a constant amplitude A as illustrated in Fig. 9. 

Figure 5.13 The dynamic non-contact mode. The frequency shift of the cantilever oscillation is used to operate the feedback loop. (Reproduced with permission from P.C. Braga and D. Ricci (eds), Atomic Force Microscopy, Humana Press. 2004 Humana Press.)...

The following section describes the use of the two-timing approximation for the analysis of QCM data. The same formalism is also used in the field of non-contact atomic force microscopy [28,29]. In the latter context, the tip-sample interaction perturbs the oscillation of the cantilever. As long as the tip-sample force is weak compared to the force needed to bend the cantilever, the interaction potential can be reconstructed from the frequency of the cantilever as a function of amplitude and mean vertical distance. 

In 1991, Albrecht et al. invented frequency modulation atomic force microscopy (FM-AFM) for operating d3mamic-mode AFM in vacuum environments. Before this invention, it was common to operate d3mamic-mode AFM with the amplitude detection method, which is referred to as amplitude modulation AFM (AM-AFM). In AM-AFM, the tip-sample distance is regulated such that the oscillation amplitude of the cantilever (A) is kept constant. 

This article presents recent progress in high-speed atomic force microscopy for dynamic imaging of biomolecular processes, including the theoretical basis for the highest possible imaging rate, instrumentation, hydrodynamic effects on cantilever oscillation, and various visualization studies on the dynamic molecular process and structure of proteins. 

Many techniques have been developed to measure the Young s modulus and the stress of the mesoscopic systems [12, 13]. Besides the traditional Vickers microhardness test, techniques mostly used for nanostructures are tensile test using an atomic force microscope (AFM) cantilever, a nanotensile tester, a transmission electron microscopy (TEM)-based tensile tester, an AFM nanoindenter, an AFM three-point bending tester, an AFM wire free-end displacement tester, an AFM elastic-plastic indentation tester, and a nanoindentation tester. Surface acoustic waves (SAWs), ultrasonic waves, atomic force acoustic microscopy (AFAM), and electric field-induced oscillations in AFM and in TEM are also used. Comparatively, the methods of SAWs, ultrasonic waves, field-induced oscillations, and an AFAM could minimize the artifacts because of their nondestructive nature though these techniques collect statistic information from responses of all the chemical bonds involved [14]. 

Yuya et al. [243] extracted the elastic modulus of single electrospun PAN nanofibre dynamically through the natural frequencies of a pair of AFM microcantilevers linked by a nanofibre segment (Fig. 4.24b). The theory of this technique is based on the dynamic relationship between the fibre stiffness (i.e. spring constant) and the resonance frequencies of cantilever vibration mode. On the other hand, Liu et al. [244] used atomic force acoustic microscopy (AFAM) based on ultrasonic frequency oscillations to excite an AFM cantilever when the tip was in contact with a sample. A different approach based on a model of the resonant frequency that is dependent on the bob s free flight was employed to measure the elastic modulus of as-spun nylon 6, 6. A ball was glued to a nanofibre and suspended from a cantilever beam that was attached to a piezoelectric-actuated base [245]. 

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