If we make the surfaces enough smooth that all asperities are removed then the two bodies in contact may act like a single body making frictional force infinte.
I know this is practically impossible but is this true theoretically? If not please tell where I am wrong.
As Feynman pointed out in his lectures:
If we try to get absolutely pure copper, if we clean and polish the surfaces, outgas the materials in a vacuum, and take every conceivable precaution, we still do not get μ. For if we tilt the apparatus even to a vertical position, the slider will not fall off—the two pieces of copper stick together! The coefficient μ, which is ordinarily less than unity for reasonably hard surfaces, becomes several times unity! The reason for this unexpected behavior is that when the atoms in contact are all of the same kind, there is no way for the atoms to “know” that they are in different pieces of copper. When there are other atoms, in the oxides and greases and more complicated thin surface layers of contaminants in between, the atoms “know” when they are not on the same part. When we consider that it is forces between atoms that hold the copper together as a solid, it should become clear that it is impossible to get the right coefficient of friction for pure metals.
http://www.feynmanlectures.caltech.edu/I_12.html
Also, it is how cold welding works.
The answer is yes.
Two smooth surfaces would appear to reduce friction, and that is caused because air particles will always be present within both planes.
So, in earth, two metals surfaces slide smoothly due to such effect. But in space, lacking the air molecules that prevent surfaces to reduce their distance, two smooth metallic surfaces can get sticked forever, because, paraphrasing Feynman, in such circumstance, the atoms on each surface don't know which surface they belong to.
That would precisely be equivalent to infinite friction.
to add another important observation: if you take two atomistically-smooth surfaces of the same material and rub them together hard enough, each will grab and tear material off the other and smear the result across the sliding surfaces by a mechanism known as galling. When galling occurs, the friction between the two surfaces jumps up suddenly and dramatically: the friction could start low but it will not stay there for very long at all.
