ITT we post funny pictures...

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It depends on where we think most of the friction actually occurs in this case - between whole molecules or on the outskirts of individual atoms that make these molecules.

Irrelevant, just freeze water into a solid enough sheet with a big staple already in it with both upper and lower parts outside the water and gently staple it into the tree with a hammer. It would work with a nail too (and better). Ice is still water just in a different state.
 
It depends on where we think most of the friction actually occurs in this case - between whole molecules or on the outskirts of individual atoms that make these molecules.
Actually, it would depend on the point of contact being a small section of the hydrogen bonded lattice that is somewhat present in water in it's liquid form, or the molecule of water being trapped by the surface of the staple. By saying it is on a sub-atomic level you are talking about the staple separating the nucleus of the individual hydrogen and oxygen atoms, splitting an atom... and that definitely doesn't happen.