Contact mechanics and friction of fractal surfaces probed by atomic force microscopy

We investigated the contact mechanics and friction forces between atomic force microscope (AFM) probes and self-affine fractal carbon films. We studied single-asperity contacts by means of conventional nanometric conical tips whilst custom-designed micrometric flat tips were adopted to form multiple junctions between the probe and the sample. By varying the externally applied load we found that the average frictional force follows a power-law behavior in the single-asperity regime and a linear behavior in the multi-asperity regime. The friction coefficient was the same for carbon specimens having different fractality. We also acquired quasi-static load-displacement curves on micrometric scale, revealing a strong dependence of the average indentation depth on the values of fractal parameters. A comparison of experimental data with contact theories for randomly rough surfaces is provided.