By Ricardo Garcia
Filling a niche within the literature, this publication positive aspects in-depth discussions on amplitude modulation AFM, offering an outline of the idea, instrumental concerns and functions of the process in either academia and undefined. As such, it contains examples from fabric technological know-how, gentle condensed topic, molecular biology, and biophysics, between others. The textual content is written in this type of method as to permit readers from varied backgrounds and degrees of workmanship to discover the data compatible for his or her wishes.
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However, the use of continuum mechanics models to describe nanoscale mechanical properties has some limitations [14, 22 24]. To determine the deformation of two elastic objects in contact, here tip and sample, requires to establish and solve the relationship between the stress C and the strain e tensors. This functional relationship is called the constitutive equation. For an isotropic material, it is deduced Cij ¼ lell dij þ Geij ; ð3:4Þ where l is the Lame coefﬁcient and G is the shear modulus.
11 Amplitude and phase distance curves obtained in air with a silicon tip on a mica surface. 12 Scheme of the relevant distances in amplitude modulation AFM; d is the instantaneous tip surface separation, z is the instantaneous tip deflection, zc is the average x tip surface separation, x is the spatial coordinate along the longitudinal axis of the cantilever, and w(x,t) is the cantilever bending. the cantilever is excited by a mechanical force, the amplitude of the displacement of the cantilever base is Ad.
The ultimate goal of any theory of dynamic AFM is to provide the mathematical link between the AFM observables, namely, the amplitude, the phase shift, and the resonant frequency, and the sample properties. The theory should also explain the dependence of the observables with respect to the tip surface separation. From these dependencies, it should be possible to establish the optimum imaging conditions and to determine the forces exerted on the sample surface. At present, several theoretical formalisms compete to describe the various aspects of amplitude modulation AFM.