Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review

TL;DR

This review discusses atomistic modeling of carbon nanotubes using Molecular Mechanics, focusing on energy minimization, stability, and elastic behavior under tension, with emphasis on the Cauchy-Born rule and short-range potentials.

Contribution

It provides a comprehensive overview of atomistic potentials and the application of the Cauchy-Born rule to carbon nanotubes, highlighting stability and elastic properties.

Findings

Local energy minimizers indicate stability of nanotube structures.

Periodic configurations remain optimal under moderate tension.

Elastic behavior is justified in axial traction regime.

Abstract

Carbon nanotubes are modeled as point particle configurations in the framework of Molecular Mechanics, where interactions are described by means of short range attractive-repulsive potentials. The identification of local energy minimizers yields a variational description for the stability of rolled-up hexagonal-lattice structures. Optimality of periodic configurations is preserved under moderate tension, hence justifying the elastic behavior of carbon nanotubes in the axial traction regime.