Short nanotubes or big molecules? The concept of minimal length

Abstract

We have studied the problem of what must be the minimal length of a nanotube with a given diameter to reasonably assert that its electronic properties can be extrapolated to longer structures. For this purpose the variation of the electronic chemical potential (ECP) was plotted against the number of units composing the nanotube for three systems: (5,5) armchair, (9,0) zigzag and (10,0) zigzag nanotubes. We found that the ECP curve defines a different minimal length for each system. This minimal length corresponds to the boundary between large molecules (short nanotubes) and nanotubes properly speaking. We suggest that this minimal length exists for at least all armchair and zigzag nanotubes.