Quantitative analysis of the frictional properties of solid materials at low loads. I. Carbon compounds

Abstract

Load-dependent studies of the frictional properties of the carbon compounds graphite, diamond, amorphous carbon, and C${}_{60}$ were performed by friction force spectroscopy in air and dry argon. During the experiments, the surface was profiled at low loads without wear or plastic deformation. The tips used for profiling were fabricated according to a special production procedure in order to obtain apexes with a well-defined spherical shape and known apex radius. The data obtained were compared with a theoretical model based on the contact mechanical analysis of a Hertzian-type tip/sample contact with small tip radius, low surface energies, but not too low elastic moduli of the tip and sample material. Our experimental results are in excellent agreement with a $F_{\mathrm{f}}\sim F_{\mathrm{n}}^{2/3}$ dependence of the frictional force $F_{\mathrm{f}}$ on the normal force $F_{\mathrm{n}}$ as predicted for this case. These findings suggest that contact mechanical models, in spite of being based on continuum elasticity theory, are valid for tip radii down to a few nanometers and that the shear stress is constant within the elastic regime. Additionally, it was shown that the friction coefficient $\mu {=F}_{\mathrm{f}}{/F}_{\mathrm{n}}$ is not well suited for comparing the tribological behavior of different materials in the case of single-asperity friction. Therefore, an effective friction coefficient for point-contact-like single-asperity friction was introduced for the classification of the microscopic frictional properties of materials. As quantitative results, high microscopic friction was found for C${}_{60}$ thin films, medium friction for amorphous carbon and diamond, and very low friction for graphite.