Energy approach to the unstressed geometry of single-walled carbon nanotubes

In this paper, the geometry of single-walled carbon nanotubes without any external loading is analyzed via an energy procedure. The nanotube is assumed to be inscribed into a perfect cylinder of unknown diameter, which is estimated by minimizing the total interatomic potential involved into a basic cell with several carbon atoms and their corresponding bonds. In this step, two interatomic potentials have been adopted in order to compare their influence on the obtained results. Our calculations show that the widely used conformal mapping is not the most suitable option to reproduce the geometry of single-walled nanotubes in absence of external loading. Likewise, a more accurate method to estimate the initial diameter of the nanotube is developed, yielding higher differences with smaller nanotubes in comparison with other published works. The present analysis can be useful in the framework of molecular mechanics or continuum models as an alternative way to introduce initial stresses (due to the curvature of the cylinder) in the mechanical analysis, against other involved methods.