  Traditional laws of friction believe that the friction coefficient of two
specific solids takes constant value. However, molecular simulations revealed
that the friction coefficient of nanosized asperity depends strongly on contact
size and asperity radius. Since contacting surfaces are always rough consisting
of asperities varying dramatically in geometric size, a theoretical model is
developed to predict the friction behavior of fractal rough surfaces in this
work. The result of atomic-scale simulations of sphere-on-flat friction is
summarized into a uniform expression. Then, the size dependent feature of
friction at nanoscale is incorporated into the analysis of fractal rough
surfaces. The obtained results display the dependence of friction coefficient
on roughness, material properties and load. It is revealed that the friction
coefficient decreases with increasing contact area or external load. This model
gives a theoretical guideline for the prediction of friction coefficient and
the design of friction pairs.
