Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

This article is part of the Thematic Series "Noncontact atomic force microscopy".

Detalhes bibliográficos
Autores: Herruzo, Elena T., García García, Ricardo
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/135110
Acesso em linha:http://hdl.handle.net/10261/135110
Access Level:acceso abierto
Palavra-chave:AFM
Atomic force microscopy
Bimodal AFM
Frequency shift
Integral calculus applications
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spelling Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculusHerruzo, Elena T.García García, RicardoAFMAtomic force microscopyBimodal AFMFrequency shiftIntegral calculus applicationsThis article is part of the Thematic Series "Noncontact atomic force microscopy".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.This work was funded by the Spanish Ministry of Science (MICINN) (CSD2010-00024;MAT2009-08650), and the Comunidad de Madrid (S2009/MAT-1467).Peer reviewedBeilstein-Institut zur Förderung der Chemischen WissenschaftenMinisterio de Ciencia e Innovación (España)Comunidad de MadridConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]201620162012info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/135110reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#S2009/MAT-1467/NANOOBJETOS-CMhttp://dx.doi.org/10.3762/bjnano.3.22Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1351102026-05-22T06:33:51Z
dc.title.none.fl_str_mv Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
title Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
spellingShingle Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
Herruzo, Elena T.
AFM
Atomic force microscopy
Bimodal AFM
Frequency shift
Integral calculus applications
title_short Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
title_full Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
title_fullStr Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
title_full_unstemmed Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
title_sort Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus
dc.creator.none.fl_str_mv Herruzo, Elena T.
García García, Ricardo
author Herruzo, Elena T.
author_facet Herruzo, Elena T.
García García, Ricardo
author_role author
author2 García García, Ricardo
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Comunidad de Madrid
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv AFM
Atomic force microscopy
Bimodal AFM
Frequency shift
Integral calculus applications
topic AFM
Atomic force microscopy
Bimodal AFM
Frequency shift
Integral calculus applications
description This article is part of the Thematic Series "Noncontact atomic force microscopy".
publishDate 2012
dc.date.none.fl_str_mv 2012
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/135110
url http://hdl.handle.net/10261/135110
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
S2009/MAT-1467/NANOOBJETOS-CM
http://dx.doi.org/10.3762/bjnano.3.22
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Beilstein-Institut zur Förderung der Chemischen Wissenschaften
publisher.none.fl_str_mv Beilstein-Institut zur Förderung der Chemischen Wissenschaften
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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