Generalized Hertz model for bimodal nanomechanical mapping

Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a...

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Main Authors:	Labuda, Aleksander, Kocuń, Marta, Meinhold, Waiman, Walters, Deron, Proksch, Roger
Format:	Online
Language:	English
Published:	Beilstein-Institut 2016
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4979904/

id	pubmed-4979904
recordtype	oai_dc
spelling	pubmed-49799042016-08-19 Generalized Hertz model for bimodal nanomechanical mapping Labuda, Aleksander Kocuń, Marta Meinhold, Waiman Walters, Deron Proksch, Roger Full Research Paper Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface. Beilstein-Institut 2016-07-05 /pmc/articles/PMC4979904/ /pubmed/27547614 http://dx.doi.org/10.3762/bjnano.7.89 Text en Copyright © 2016, Labuda et al.; licensee Beilstein-Institut. http://www.beilstein-journals.org/bjnano This is an Open Access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The license is subject to the Beilstein Journal of Nanotechnology terms and conditions: (http://www.beilstein-journals.org/bjnano)
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Labuda, Aleksander Kocuń, Marta Meinhold, Waiman Walters, Deron Proksch, Roger
spellingShingle	Labuda, Aleksander Kocuń, Marta Meinhold, Waiman Walters, Deron Proksch, Roger Generalized Hertz model for bimodal nanomechanical mapping
author_facet	Labuda, Aleksander Kocuń, Marta Meinhold, Waiman Walters, Deron Proksch, Roger
author_sort	Labuda, Aleksander
title	Generalized Hertz model for bimodal nanomechanical mapping
title_short	Generalized Hertz model for bimodal nanomechanical mapping
title_full	Generalized Hertz model for bimodal nanomechanical mapping
title_fullStr	Generalized Hertz model for bimodal nanomechanical mapping
title_full_unstemmed	Generalized Hertz model for bimodal nanomechanical mapping
title_sort	generalized hertz model for bimodal nanomechanical mapping
description	Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four independent observables that are sensitive to the tip–sample nanomechanical interaction parameters. To demonstrate this, a generalized theoretical framework for extracting nanomechanical sample properties from bimodal experiments is presented based on Hertzian contact mechanics. Three modes of operation for measuring cantilever parameters are considered: amplitude, phase, and frequency modulation. The experimental equivalence of all three modes is demonstrated on measurements of the second eigenmode parameters. The contact mechanics theory is then extended to power-law tip shape geometries, which is applied to analyze the experimental data and extract a shape and size of the tip interacting with a polystyrene surface.
publisher	Beilstein-Institut
publishDate	2016
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4979904/
_version_	1613625108183646208

Generalized Hertz model for bimodal nanomechanical mapping

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