Strains in Axial and Lateral Directions in Carbon Nanotubes

TL;DR

This paper derives analytic expressions for strains and Poisson ratios in carbon nanotubes of all chiralities, revealing their dependence on chirality, bond flexibility, and initial stress, with implications for understanding their mechanical properties.

Contribution

It provides a generalized analytical framework for calculating Poisson ratios in all chiralities of carbon nanotubes considering bond flexibility and initial stress effects.

Findings

Poisson ratio is independent of nanotube diameter.

Poisson ratio depends on chirality and bond flexibility.

Poisson ratio varies significantly with initial stress.

Abstract

Analytic expressions for strains in carbon nanotubes of all chiralities in lateral and axial directions have been obtained. These expressions have been related to bond angle and bond length flexibilities. This finally results in obtaining very generalized results for Poisson ratio of all chirality and all diameter carbon nanotubes. It turns out that the Poisson ratio is always independent of carbon nanotube diameter, but depends on the their chirality. On the assumption of fixed bond lengths, (only flexible bond angle), the Poisson ratio of all chirality tubes is obtained to be 1.When realistic flexibility of bond lengths and bond angles is assumed, the Poisson ratio is between ~0 and 0.3, depending upon chirality. The present calculation of the Poisson ratio does not require any detail of molecular interactions under the assumption of either bond angle or bond length flexibility alone, but does depend on the interaction potential if both are assumed flexible. Further, it has been found that the Poisson ratio is sensitive to applied initial stress, varying significantly when obtained under different initial stress values. It is observed that Poisson ratio can be used to justify the interaction potential by finding out the bond length flexibility in comparison to bond angle flexibility.