Load- and Size Effects of the Diamond Friction Coefficient at the Nanoscale

The friction coefficient, an important parameter to evaluate the dynamic properties of friction pairs, has been widely used in macro engineering fields. However, it is probably inappropriate to characterize the tribological properties at the nanoscale due to the strong size effect, and the conventional formula cannot reveal its determinants owing to its oversimple form. Therefore, in the present work, a new formula is deduced to overcome these shortcomings. The established formula for the friction coefficient considers the adhesion and discloses the relationship between the friction coefficient and the material properties of diamond. It effectively suppresses the dependency of the friction coefficient on the load, although such a dependency cannot be eliminated completely. Therefore, another new formula, independent of the loading force, is derived. Interestingly, the results indicate that the size effect is invariably observed in the friction coefficients derived from the three formulas due to different accumulation effects of debris atoms, which is verified by molecular dynamics simulations. Graphic Abstract