Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves (Special Issue on Micromachine Technology)

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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. When the long-range interaction is negligible, the normalized force-penetration (F-P) plots superimpose each other. When the long-range interaction is NOT negligible, and before contact (or after separation), the F-P plots also superimpose. When the long-range interaction is NOT negligible, and during the contact, they do not superimpose, although during the first stage of contact the F-P plots are very similar, forming a narrow band. Stiffness of measurement system such as cantilever of AFM and significant figures of measured displacement are important to interpret adhesional force curves. The stiffness and the significant figures of displacement which are required to interpret force curves are deduced and the relation between them are discussed. A stiffer cantilever is more suitable for the interpretation of surface forces. The experimental force-displacement plot obtained from AFM with an Au-coated tip and a Si (100) wafer, is converted into a force-penetration plot. The influence of the nano-scopic shape of the tip or the sample on the force curve could be shown using both the force-penetration plot and the contact theory.
社団法人電子情報通信学会の論文
1997-02-25

Stiffness of Measurement System and Significant Figures of Displacement which are Required to Interpret Adhesional Force Curves (Special Issue on Micromachine Technology)

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