Bond Lengths of Single-Walled Carbon Nanotubes

TL;DR

This study investigates the bond lengths of single-walled carbon nanotubes with various chiralities, revealing that two bond lengths are generally needed for energy minimization and that pressure can induce bond length equalization, aiding in nanotube characterization.

Contribution

It introduces a method using modified symmetries and Tersoff potential to accurately determine bond lengths, highlighting the importance of two bond lengths and their behavior under pressure for different chiralities.

Findings

Two bond lengths are generally required for minimum energy structures.

Bond lengths vary with chirality, radius, and pressure.

Pressure can equalize bond lengths, indicating potential for experimental chirality determination.

Abstract

Results of the bond lengths for various chiralities of single-wall carbon carbon nanotubes (SWNTs) (armchair, zigzag and chiral) are obtained. We use modified helical and rotational symmetries to describe the structure of SWNTs and Tersoff potential to minimize the energy of these tubes. It emerges that in general, two bond lengths are required for obtaining minimum energy structure, in contrast to one bond length commonly used. The difference in bond lengths depends on chirality and radius of achiral tubes. Significantly, even a small deviation from zigzag or armchair character leads to interesting behavior of bond lengths. A reduction in diameter is responsible for difference in the bond lengths of achiral nanotubes. We also calculate the bond lengths under hydrostatic pressure. The behavior of bond lengths for armchair single-wall nanotubes when calculated under pressure shows that the larger bond length decreases faster with pressure in comparison to the shorter bond length. At some critical pressure (depending upon the radius of the tube), the two bond lengths become equal to each other, reversing their difference above this critical pressure. We suggest that this behavior can be exploited to experimentally determine the chirality and radius of the carbon nanotubes, for example by observing the presence and disappearance of modes typical of two different bond lengths. This change occurs only within a few GPa of pressure.