Is friction a function of surface area? What is the microscopic workings of friction? I know the friction is given by the following equation
$$\mu F_N=F_f$$
which tells me friction is independent of surface area, but how do I characterize it as such if I want to add surface area into my equation what would the equation be?
We all know friction is a function of the normal reaction exerted on the body and the coefficient of friction. How is this coefficient derived, any equation? Or is it all experimental? Any quantum mechanical explanation for friction?
 A: The most common model for dry friction is the Coulomb Friction, which results in the friction equation you give.
The model is based on considering the asperities (roughness) of the two surfaces and the force required to lift asperities on one surface over the other. If assume that the contact points/area is approximately constant why find that the fiction is independent of the contact area as the increase in contact area is countered by a decrease in the load each point must lift (assuming constant total mass).
Also note that $\mu$ is an experimental value for two particular surfaces. Coulomb friction is a fairly macroscopic model and does not consider the real interaction between the surfaces, which would be very difficult to measure over a large area. 
In many cases Coulomb's model doesn't hold and friction is proportional to contact area. This is particularly true for lubricated contacts and sometimes when there is significant deformation of the surface.
A: Friction coefficients are experimental... For a friendly discussion of microscopic friction, I refer you to chapter 12 section 1,2,3 of Feynman Lectures on Physics. Here is a link:
http://www.feynmanlectures.caltech.edu/I_12.html#Ch12-S2
Hope that helps
