ArticleBeilstein journal of nanotechnology2012
Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus.
Article in Beilstein journal of nanotechnology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- Nanoscale Rheology: Dynamic Mechanical Analysis over a Broad and Continuous Frequency Range Using Photothermal Actuation Atomic Force Microscopy.Macromolecules · 2024Article
- Light-induced modulation of viscoelastic properties in azobenzene polymers.Nanophotonics (Berlin, Germany) · 2024Article
- Fast and high-resolution mapping of elastic properties of biomolecules and polymers with bimodal AFM.Nature protocols · 2018Article
- A robust AFM-based method for locally measuring the elasticity of samples.Beilstein journal of nanotechnology · 2018Article
- Generalized Hertz model for bimodal nanomechanical mapping.Beilstein journal of nanotechnology · 2016Article
- Unlocking higher harmonics in atomic force microscopy with gentle interactions.Beilstein journal of nanotechnology · 2014Article
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2 authors.
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Abstract
Bimodal atomic force microscopy is a force-microscopy method that requires the simultaneous excitation of two eigenmodes of the cantilever. This method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We show that this approximation is valid for situations in which the amplitude of the first mode is larger than the length of scale of the force, corresponding to the most common experimental case. We also show that this approximation is valid for very different types of tip-surface forces such as the Lennard-Jones and Derjaguin-Muller-Toporov forces.
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