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Title: Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

Abstract

We explore the contact problem of a flat-end indenter penetrating intermittently a generalized viscoelastic surface, containing multiple characteristic times. This problem is especially relevant for nanoprobing of viscoelastic surfaces with the highly popular tapping-mode AFM imaging technique. By focusing on the material perspective and employing a rigorous rheological approach, we deliver analytical closed-form solutions that provide physical insight into the viscoelastic sources of repulsive forces, tip-sample dissipation and virial of the interaction. We also offer a systematic comparison to the well-established standard harmonic excitation, which is the case relevant for dynamic mechanical analysis (DMA) and for AFM techniques where tip–sample sinusoidal interaction is permanent. This comparison highlights the substantial complexity added by the intermittent-contact nature of the interaction, which precludes the derivation of straightforward equations as is the case for the well-known harmonic excitations. The derivations offered have been thoroughly validated through numerical simulations. Despite the complexities inherent to the intermittent-con-tact nature of the technique, the analytical findings highlight the potential feasibility of extracting meaningful viscoelastic properties with this imaging method.

Authors:
 [1];  [1]
  1. George Washington Univ., Washington, DC (United States). Dept. of Mechanical and Aerospace Engineering
Publication Date:
Research Org.:
George Washington Univ., Washington, DC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1502935
Grant/Contract Number:  
[SC0011912]
Resource Type:
Accepted Manuscript
Journal Name:
Beilstein Journal of Nanotechnology
Additional Journal Information:
[ Journal Volume: 8]; Journal ID: ISSN 2190-4286
Publisher:
Beilstein Institute
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; atomic force microscopy; harmonic functions; tapping-mode AFM; viscoelasticity

Citation Formats

López-Guerra, Enrique A., and Solares, Santiago D. Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times. United States: N. p., 2017. Web. doi:10.3762/bjnano.8.223.
López-Guerra, Enrique A., & Solares, Santiago D. Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times. United States. doi:10.3762/bjnano.8.223.
López-Guerra, Enrique A., and Solares, Santiago D. Thu . "Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times". United States. doi:10.3762/bjnano.8.223. https://www.osti.gov/servlets/purl/1502935.
@article{osti_1502935,
title = {Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times},
author = {López-Guerra, Enrique A. and Solares, Santiago D.},
abstractNote = {We explore the contact problem of a flat-end indenter penetrating intermittently a generalized viscoelastic surface, containing multiple characteristic times. This problem is especially relevant for nanoprobing of viscoelastic surfaces with the highly popular tapping-mode AFM imaging technique. By focusing on the material perspective and employing a rigorous rheological approach, we deliver analytical closed-form solutions that provide physical insight into the viscoelastic sources of repulsive forces, tip-sample dissipation and virial of the interaction. We also offer a systematic comparison to the well-established standard harmonic excitation, which is the case relevant for dynamic mechanical analysis (DMA) and for AFM techniques where tip–sample sinusoidal interaction is permanent. This comparison highlights the substantial complexity added by the intermittent-contact nature of the interaction, which precludes the derivation of straightforward equations as is the case for the well-known harmonic excitations. The derivations offered have been thoroughly validated through numerical simulations. Despite the complexities inherent to the intermittent-con-tact nature of the technique, the analytical findings highlight the potential feasibility of extracting meaningful viscoelastic properties with this imaging method.},
doi = {10.3762/bjnano.8.223},
journal = {Beilstein Journal of Nanotechnology},
number = ,
volume = [8],
place = {United States},
year = {2017},
month = {10}
}

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    Works referencing / citing this record:

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    journal, January 1944

    • Alfrey, T.
    • Quarterly of Applied Mathematics, Vol. 2, Issue 2
    • DOI: 10.1090/qam/10499

    Settlement analysis of viscoelastic foundation under vertical line load using a fractional Kelvin-Voigt model
    journal, March 2012


    Rebound indentation problem for a viscoelastic half-space and axisymmetric indenter - Solution by the method of dimensionality reduction: Rebound indentation problem for a viscoelastic half-space and axisymmetric indenter
    journal, November 2015

    • Argatov, Ivan I.; Popov, Valentin L.
    • ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 96, Issue 8
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    Relationship between phase shift and energy dissipation in tapping-mode scanning force microscopy
    journal, November 1998

    • Tamayo, Javier; Garcı́a, Ricardo
    • Applied Physics Letters, Vol. 73, Issue 20
    • DOI: 10.1063/1.122632

    Selection of higher eigenmode amplitude based on dissipated power and virial contrast in bimodal atomic force microscopy
    journal, September 2014

    • Diaz, Alfredo J.; Eslami, Babak; López-Guerra, Enrique A.
    • Journal of Applied Physics, Vol. 116, Issue 10
    • DOI: 10.1063/1.4894837

    Dynamic mechanical analyses of Nafion®/organically modified silicate nanocomposites: Nafion®/Ormosil Nanocomposites
    journal, April 2001

    • Young, S. K.; Mauritz, K. A.
    • Journal of Polymer Science Part B: Polymer Physics, Vol. 39, Issue 12
    • DOI: 10.1002/polb.1102

    Constitutive modeling of the rate, temperature, and hydration dependent deformation response of Nafion to monotonic and cyclic loading
    journal, September 2010


    Measuring the loss tangent of polymer materials with atomic force microscopy based methods
    journal, March 2014


    Calculation of standard viscoelastic responses with multiple retardation times through analysis of static force spectroscopy AFM data
    journal, March 2017

    • López-Guerra, Enrique A.; Eslami, Babak; Solares, Santiago D.
    • Journal of Polymer Science Part B: Polymer Physics, Vol. 55, Issue 10
    • DOI: 10.1002/polb.24327

    Stress analysis in visco-elastic bodies
    journal, January 1955

    • Lee, E. H.
    • Quarterly of Applied Mathematics, Vol. 13, Issue 2
    • DOI: 10.1090/qam/69741

    Theory of Multifrequency Atomic Force Microscopy
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    • Eslami, Babak; López-Guerra, Enrique A.; Raftari, Maryam
    • Journal of Applied Physics, Vol. 119, Issue 16
    • DOI: 10.1063/1.4947264

    Confinement effects on glass forming liquids probed by dynamic mechanical analysis
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    Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy
    journal, January 2014

    • López-Guerra, Enrique A.; Solares, Santiago D.
    • Beilstein Journal of Nanotechnology, Vol. 5
    • DOI: 10.3762/bjnano.5.224

    Effect of contact deformations on the adhesion of particles
    journal, November 1975

    • Derjaguin, B. V.; Muller, V. M.; Toporov, Yu. P.
    • Journal of Colloid and Interface Science, Vol. 53, Issue 2
    • DOI: 10.1016/0021-9797(75)90018-1

    Stress-relaxation of polyisobutylene in the transition region (1, 2)
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    Contact-resonance atomic force microscopy for viscoelasticity
    journal, January 2008

    • Yuya, P. A.; Hurley, D. C.; Turner, J. A.
    • Journal of Applied Physics, Vol. 104, Issue 7
    • DOI: 10.1063/1.2996259

    Analysis and modification of defective surface aggregates on PCDTBT:PCBM solar cell blends using combined Kelvin probe, conductive and bimodal atomic force microscopy
    journal, January 2017

    • Noh, Hanaul; Diaz, Alfredo J.; Solares, Santiago D.
    • Beilstein Journal of Nanotechnology, Vol. 8
    • DOI: 10.3762/bjnano.8.62

    Energy dissipation in tapping-mode atomic force microscopy
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