Which mechanics or law is predominately seen on the nanoscale?
Its depence on the size of the system your are looking at. To understand spectroscopy of molecules, you usually use quantum mechanics. In molecular dynamics simulation, you'll need both: On the one hand, there is a potential needed based on QM-interactions, on the other hand, the classical equations of motion are good enought to move your atoms in a QM-force field. 

Based on your problem, you have to decide how much classical mechanics you can justify. But in the nanoscale everything is made up with quantum mechanics and classical mechanics are used to approach a problem, which is not solvable in quantum mechanic way in an accetable periode of time.