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I remember reading that it was impossible to theoretically estimate the coefficient of friction between materials even if their structure was known. The book where I've read this was The Feynman Lectures on Physics, volume I, in the chapter where he speaks about the force of friction.

But this book was written some time ago, and Physics changes with time.

My question is: given two materials whose structures (and compositions) are known, is there a way to estimate the coefficient of friction (static or kinetic) between them without having to do experiments? Perhaps computers could somehow do this.

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    $\begingroup$ Clean metals in vacuum will stick together and form a cold weld. That is what one could calculate. In air, everything is covered by a layer of crud - all kinds of molecules. $\endgroup$
    – user137289
    Commented Nov 25, 2018 at 22:18

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There still isn't, and here is why.

Coefficients of friction are extremely sensitive, to among other things, 1) the surface roughness of the parts across many orders of magnitude of length scales, 2) the exact chemical state of the surfaces, and 3) the shear strength of the materials from which the surfaces are formed.

To successfully predict from first principles the coefficient of friction between any two sliding surfaces would require accurate analytical models of each of these characteristics, which then become inputs to the friction model.

Those models continue to be extremely difficult to write down, which means the friction model which would contain them still cannot be written down.

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