# Can the coefficient of friction be derived from fundamentals?

It is common to want to derive macroscopic laws from what we know microscopically - after all, given a (correct) microscopic description, everything larger should follow.

Has it ever been done to calculate a coefficient of static/kinetic friction simply from fundamental properties of materials? (say, the crystal structure or intermolecular forces). I searched for some time on the internet and found nothing (although my results were saturated by classical physics problems).

If it has been done, what was the general strategy?

• No. Friction is a thermodynamic force, so it depends on the thermodynamics of the process that causes it, and that's not universal. One can make friction forces so large by simple patterning of the surface that the materials will break or abrade before the surfaces will start moving against each other. That's how tools like a file work. – CuriousOne May 1 '15 at 19:25
• The coefficient of friction $\mu$ is not for a specific material. It is a combined property for the two surfaces touching - a property of the current system. If you wish to look at roughness of one material alone, have a look at the $R_a$ value e.g., which is most commen, or any of the other mathematical means of describing that. – Steeven May 1 '15 at 19:52
• @CuriousOne I thought there were only four fundamental forces. 'Thermodynamic Force' is a new one to me. I would have guessed friction is fundamentally an electromagnetic force. And there is another option over breaking or shearing - you can have elastic yielding. – docscience May 1 '15 at 20:15
• I'll bet that if you thought long and hard enough about it there might be a an approach to derive a model that would lead to a statistical result. The 'coefficient of friction' comes from a highly idealized, linear model. There are nonlinear models that provide much better predictions of frictional forces, such as the Dahl Model addressed among others in the paper here: mate.tue.nl/mate/pdfs/11194.pdf . But these models were not derived from the fundamentals. – docscience May 1 '15 at 20:21
• Yes, it has been done. See First-principles theory of atomic-scale friction Phys. Rev. Lett. 64, pg. 3054 – Published 18 June 1990 – pentane May 1 '15 at 20:31