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Yes, there are. They result from the splitting of a large correlated contact into many small patches. When the lubricant consists of thin solid sheets, like graphene, the patches are expected to act independently from each other. Crude estimates for the friction forces between hard, stiff solids with randomly rough surfaces are given, which apply to surfaces with Hurst roughness exponents H > 0.5. The estimates are obtained by combining realistic contact-patch-size distributions with friction-load relations deduced for isolated contact patches. The analysis reveals that load is carried predominantly by large patches, while most frictional forces stem from small contact patches. Low friction is favored when the root-mean-square height gradients are small, while a large roll-off wavelength and thus large root-mean-square roughness is predicted to lead to small friction. Moreover, friction is found to increase sublinearly with load in a nominally flat, structurally lubric contact.

Are There Limits to Superlubricity of Graphene in Hard, Rough Contacts?