In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon’s approximation (2000, “General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load,” J. Colloid Interface Sci., 226(1), pp. 166–171) of the Maugis–Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement–Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young’s modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young’s modulus close to those obtained with Hertzian models for the extension curves. The Pietrement–Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis–Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon’s empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young’s moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.
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e-mail: lindavid@mail.nih.gov
e-mail: dimitria@helix.nih.gov
e-mail: horkay@helix.nih.gov
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December 2007
Research Papers
Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials
David C. Lin,
David C. Lin
Laboratory of Integrative and Medical Biophysics,
e-mail: lindavid@mail.nih.gov
National Institutes of Health
, 9 Memorial Drive, Building 9, Room 1E118, Bethesda, MD 20892
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Emilios K. Dimitriadis,
Emilios K. Dimitriadis
National Institute of Biomedical Imaging and Bioengineering,
e-mail: dimitria@helix.nih.gov
National Institutes of Health
, 13 South Drive, Building 13, Room 3N17, Bethesda, MD 20892
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Ferenc Horkay
Ferenc Horkay
Laboratory of Integrative and Medical Biophysics,
e-mail: horkay@helix.nih.gov
National Institutes of Health
, 13 South Drive, Building 13, Room 3W16, Bethesda, MD 20892
Search for other works by this author on:
David C. Lin
Laboratory of Integrative and Medical Biophysics,
National Institutes of Health
, 9 Memorial Drive, Building 9, Room 1E118, Bethesda, MD 20892e-mail: lindavid@mail.nih.gov
Emilios K. Dimitriadis
National Institute of Biomedical Imaging and Bioengineering,
National Institutes of Health
, 13 South Drive, Building 13, Room 3N17, Bethesda, MD 20892e-mail: dimitria@helix.nih.gov
Ferenc Horkay
Laboratory of Integrative and Medical Biophysics,
National Institutes of Health
, 13 South Drive, Building 13, Room 3W16, Bethesda, MD 20892e-mail: horkay@helix.nih.gov
J Biomech Eng. Dec 2007, 129(6): 904-912 (9 pages)
Published Online: April 6, 2007
Article history
Received:
October 19, 2006
Revised:
April 6, 2007
Citation
Lin, D. C., Dimitriadis, E. K., and Horkay, F. (April 6, 2007). "Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials." ASME. J Biomech Eng. December 2007; 129(6): 904–912. https://doi.org/10.1115/1.2800826
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