Calculus of Variations and Geometric Measure Theory

E. Mainini - H. Murakawa - P. Piovano - U. Stefanelli

Carbon-nanotube geometries as optimal configurations

created by mainini on 03 Aug 2016
modified on 27 Oct 2017


Published Paper

Inserted: 3 aug 2016
Last Updated: 27 oct 2017

Journal: Multiscale Model. Simul.
Volume: 15
Number: 4
Pages: 1448-1471
Year: 2017
Doi: 10.1137/16M1087862


The fine geometry of carbon nanotubes is investigated from the viewpoint of Molecular Mechanics. Actual nanotube configurations are characterized as being locally minimizing a given configurational energy, including both two- and three-body contributions. By focusing on so-called zigzag and armchair topologies, we prove that the configurational energy is strictly minimized within specific, one-parameter families of periodic configurations. Such optimal configurations are checked to be stable with respect to a large class of small nonperiodic perturbations and do not coincide with classical rolled-up nor polyhedral geometries.