Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves

Kunio TAKAHASHI; Nancy A. BURNHAM; Hubert M. POLLOCK; Tadao ONZAWA

Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves

Kunio TAKAHASHI, Nancy A. BURNHAM, Hubert M. POLLOCK, Tadao ONZAWA

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Force curves obtained from an elastic contact theory are shown and compared with experimental results. In the elastic contact theory, a pin-on-disk contact is assumed and the following interaction are taken into consideration; (i) elastic deformation, (ii) the specific energy of adhesion in the area of the contact, which is expressed as the difference between the surface energies and the interface energy, (iii) the long-range interaction outside the area of contact, assuming the additivity of the Lennard-Jones type potential, and (iv) another elastic term for the measurement system such as the cantilever stiffness of an atomic force microscope (AFM). In the limit when the stiffness is infinite, the theory conforms to Muller-Yushchenko-Derjaguin (MYD) theory. In the limit when the surface-surface interaction is negligible, the theory conforms to the analytical theory by Takahashi-Mizuno-Onzawa. In the limit when the stiffness is infinite and the long-range interaction outside the area of contact is negligible, the theory conforms to Johnson-Kendall-Roberts (JKR) theory. All parameters and all equations are normalized and the normalized force curve is obtained as the functional of only two parameters; (1) the normalized stiffness of the measurement system, and (2) the normalized distance which is used in the expression of the Lennard-Jones potential. The force-displacement plots are converted into force-penetration plots.

Publication: IEICE TRANSACTIONS on Electronics Vol.E80-C No.2 pp.255-262

Publication Date: 1997/02/25

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Type of Manuscript: Special Section PAPER (Special Issue on Micromachine Technology)

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Kunio TAKAHASHI, Nancy A. BURNHAM, Hubert M. POLLOCK, Tadao ONZAWA, "Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves" in IEICE TRANSACTIONS on Electronics, vol. E80-C, no. 2, pp. 255-262, February 1997, doi: .
Abstract: Force curves obtained from an elastic contact theory are shown and compared with experimental results. In the elastic contact theory, a pin-on-disk contact is assumed and the following interaction are taken into consideration; (i) elastic deformation, (ii) the specific energy of adhesion in the area of the contact, which is expressed as the difference between the surface energies and the interface energy, (iii) the long-range interaction outside the area of contact, assuming the additivity of the Lennard-Jones type potential, and (iv) another elastic term for the measurement system such as the cantilever stiffness of an atomic force microscope (AFM). In the limit when the stiffness is infinite, the theory conforms to Muller-Yushchenko-Derjaguin (MYD) theory. In the limit when the surface-surface interaction is negligible, the theory conforms to the analytical theory by Takahashi-Mizuno-Onzawa. In the limit when the stiffness is infinite and the long-range interaction outside the area of contact is negligible, the theory conforms to Johnson-Kendall-Roberts (JKR) theory. All parameters and all equations are normalized and the normalized force curve is obtained as the functional of only two parameters; (1) the normalized stiffness of the measurement system, and (2) the normalized distance which is used in the expression of the Lennard-Jones potential. The force-displacement plots are converted into force-penetration plots.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e80-c_2_255/_p

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@ARTICLE{e80-c_2_255,
author={Kunio TAKAHASHI, Nancy A. BURNHAM, Hubert M. POLLOCK, Tadao ONZAWA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves},
year={1997},
volume={E80-C},
number={2},
pages={255-262},
abstract={Force curves obtained from an elastic contact theory are shown and compared with experimental results. In the elastic contact theory, a pin-on-disk contact is assumed and the following interaction are taken into consideration; (i) elastic deformation, (ii) the specific energy of adhesion in the area of the contact, which is expressed as the difference between the surface energies and the interface energy, (iii) the long-range interaction outside the area of contact, assuming the additivity of the Lennard-Jones type potential, and (iv) another elastic term for the measurement system such as the cantilever stiffness of an atomic force microscope (AFM). In the limit when the stiffness is infinite, the theory conforms to Muller-Yushchenko-Derjaguin (MYD) theory. In the limit when the surface-surface interaction is negligible, the theory conforms to the analytical theory by Takahashi-Mizuno-Onzawa. In the limit when the stiffness is infinite and the long-range interaction outside the area of contact is negligible, the theory conforms to Johnson-Kendall-Roberts (JKR) theory. All parameters and all equations are normalized and the normalized force curve is obtained as the functional of only two parameters; (1) the normalized stiffness of the measurement system, and (2) the normalized distance which is used in the expression of the Lennard-Jones potential. The force-displacement plots are converted into force-penetration plots.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves
T2 - IEICE TRANSACTIONS on Electronics
SP - 255
EP - 262
AU - Kunio TAKAHASHI
AU - Nancy A. BURNHAM
AU - Hubert M. POLLOCK
AU - Tadao ONZAWA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E80-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 1997
AB - Force curves obtained from an elastic contact theory are shown and compared with experimental results. In the elastic contact theory, a pin-on-disk contact is assumed and the following interaction are taken into consideration; (i) elastic deformation, (ii) the specific energy of adhesion in the area of the contact, which is expressed as the difference between the surface energies and the interface energy, (iii) the long-range interaction outside the area of contact, assuming the additivity of the Lennard-Jones type potential, and (iv) another elastic term for the measurement system such as the cantilever stiffness of an atomic force microscope (AFM). In the limit when the stiffness is infinite, the theory conforms to Muller-Yushchenko-Derjaguin (MYD) theory. In the limit when the surface-surface interaction is negligible, the theory conforms to the analytical theory by Takahashi-Mizuno-Onzawa. In the limit when the stiffness is infinite and the long-range interaction outside the area of contact is negligible, the theory conforms to Johnson-Kendall-Roberts (JKR) theory. All parameters and all equations are normalized and the normalized force curve is obtained as the functional of only two parameters; (1) the normalized stiffness of the measurement system, and (2) the normalized distance which is used in the expression of the Lennard-Jones potential. The force-displacement plots are converted into force-penetration plots.
ER -