Thermodynamic properties of nanotubes: zone-folding approach

Abstract

A zone-folding approach is applied for the estimation of phonon contributions to the thermodynamic properties of carbon nanotubes and nanotubes based on transition metal oxides (TiO₂, V₂O₅) and sulfides (TiS₂, ZrS₂) with different morphology and various chiralities. The results obtained are compared with those from the direct calculation of the thermodynamic properties of nanotubes in the harmonic approximation. All calculations have been made using the PBE0 hybrid exchange–correlation functional. It is found that the zone-folding approach allows a sufficiently accurate estimation of phonon contributions to internal energy and heat capacity and shows worse but acceptable results for Helmholtz free energy and entropy.