# Minimum atomic clearance permitting motion

Suppose you were to build the piston and cylinder in a car engine atom-by-atom. Let's just say carbon, since you can make a lot of different shapes due to it's high valence.

So assuming you make the most perfect piston possible, a perfect cylinder accurate to within an atom; and you make a perfect cylinder wall to go around the piston, again accurate to within an atom; and the diameter of piston has a single atom clearance from the cylinder wall.

What would happen if you tried to move the piston up and down inside the cylinder? Would there be significant force due to the Casimir effect? Would there be friction? The two objects aren't strictly touching, but then again the atoms in my fingers aren't strictly touching the atoms in the keys on my keyboard. It's all just the electro-magnetic force.

What is the minimum distance required between the piston and cylinder to allow smooth motion with no friction?

(Assume we have a way of moving the piston up and down perfectly along the common axis, and it's not "wobbling" about)

Since the electronic wave function around the cylinder as well as the piston decays exponentially, a few atom's diameters should be enough to totally eliminate interaction. The forces between unpolarized materials are called van der Waals or London forces, but the usually act at a distance smaller than 1 nm.

I'm not sure about one atom (2-2.5 Angström for carbon), but you should be on the same side with 1 nm.

The main problem is really the mechanical "wobbling": You can't move the piston inside the cylinder in a purely straight motion. You are bound to get off track and touch the cylinder. That way, you will destroy the surfaces and cause friction.

I'm more into solid-state physics, but I think you can completely forget about the Casimir effect here.

By the way, all interaction which qualifies as "touching" comes from the electrostatic force.