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?
 A: Fundamentally, this is no different from computing the friction in a fluid (shear viscosity). The theory of viscosity goes back to Maxwell and Boltzmann, and microscopic calculations are possible for many fluids. Solid friction is more complicated, because the exact preparation of the surface obviously matters. First principles theories therefore concentrate on idealized crystalline surfaces, see for example these two papers. These days, systems like this can be studied, and theories tested, using nano-scale devices. This is field is known as nano-tribology.
A: In general, yes. But it has been done only for static friction coefficients. 
The manner of which two surfaces in contact interact is highly investigated by the Tribology community.In particular, the field exploring the mechanics of the interaction is called contact mechanics.
Tackling problems of contact mechanics analytically/numerically is often done by solving the elasticity equations. By predicting quantitatively the forces and deformation of the bodies in contact, the coefficient of friction can be calculated. Much research has been carried on the subject: starting from Hertz's groundbreaking work, to more contemporary papers such as
A Static Friction Model for
Elastic-Plastic Contacting Rough
Surfaces, and Static Friction Coefficient Model for Metallic Rough Surfaces.
