Estimation of Young’s modulus of single-walled carbon nanotube using cellular automata

Properties of the carbon nanotube structure have been extensively examined in several analytical and numerical studies. The present paper, describes a cellular automata based numerical model to study the behavior of a single-walled carbon nanotube and to compute intrinsic properties such as an equivalent Young’s modulus. The cellular automata model derives from local rules of interaction among neighboring sites that evolve the state of each site locally. In the present approach, each site was occupied by a carbon atom, with its position representing the state variable for the site. The interaction rules were based on a minimization of the bonding energy between an atom and its three neighboring atoms, and from which a new position can be derived. The bonding energy was calculated using the empirical formulation suggested by Tersoff; a quasi-second order numerical approach was used to find a solution to the energy minimization problem. The Young’s modulus obtained from the proposed approach compares well against published results and those obtained from a molecular dynamics simulation. The computational cost of the cellular automata was also shown to be significantly lower than molecular dynamics. The proposed approach promises to be effective in computing other properties of such nanostructures, and can be extended to multi-wall configurations.