STIFFNESS OF MEASUREMENT SYSTEM AND SIGNIFICANT FIGURES OF DISPLACEMENT WHICH ARE REQUIRED TO INTERPRET ADHESIONAL FORCE CURVES

Force curves obtained from an elastic contact theory are shown and com pared with experimental results. In the elastic contact theory, a pin- on-disk contact is assumed and the following interaction are taken int o consideration: (i) elastic deformation, (ii) the specific energy of adhesion in the area of the contact, which is expressed as the differe nce between the surface energies and the interface energy, (iii) the l ong-range interaction outside the area of contact, assuming the additi vity of the Lennard-Jones type potential, and (iv) another elastic ter m for the measurement system such as the cantilever stiffness of an at omic force microscope (AFM). In the limit when the stiffness is infini te, the theory conforms to Muller-Yushchenko-Derjaguin (MYD) theory. I n the limit when the surface-surface interaction is negligible, the th eory conforms to the analytical theory by Takahashi-Mizuno-Onzawa. In the limit when the stiffness is infinite and the long-range interactio n outside the area of contact is negligible, the theory conforms to Jo hnson-Kendall-Roberts (JKR) theory. All parameters and all equations a re normalized and the normalized force curve is obtained as the functi onal of only two parameters: (1) the normalized stiffness of the measu rement system, and (2) the normalized distance which is used in the ex pression of the Lennard-Jones potential. The force-displacement plots are converted into force-penetration plots. When the long-range intera ction is negligible, the normalized force-penetration (F-P) plots supe rimpose each other. When the long-range interaction is NOT negligible, and before contact (or after separation), the F-P plots also superimp ose. 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. Stiffne ss of measurement system such as cantilever of AFM and significant fig ures of measured displacement are important to interpret adhesional fo rce curves. The stiffness and the significant figures of displacement which are required to interpret force curves are deduced and the relat ion between them are discussed. A stiffer cantilever is more suitable for the interpretation of surface forces. The experimental force-displ acement plot obtained from AFM with an Au-coated tip and a Si (100) wa fer, 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.