A precise model to predict the structural and elastic properties of single-walled carbon nanotubes

This paper presents a continuum analysis for the structural and elastic properties of single-walled carbon nanotubes (SWCNTs). An SWCNT is viewed as a rolled-up graphite sheet, and the transformation is appropriately written into a set of equations with three geometrical parameters. The microscale bond deformation in a representative cell is calculated exactly, and the atomic energy is evaluated with the Brenner potential. The structural properties of SWCNTs are determined by minimizing the atomic energy, and the elastic constants are calculated from the second-order derivatives of the strain energy density with respect to the set geometrical parameters. The dependence of the elastic constants on the chirality and tube radius is discussed. The paper also investigates the precision of the Cauchy-Born rule and the higher-order Cauchy-Born rule, which have previously been used to derive the continuum constitutive model of SWCNTs. Copyright © 2010 American Scientific Publishers.