Axial and radial thermal expansions of single-walled carbon nanotubes

This paper examines the thermal expansion of single-walled carbon nanotubes. The vibrational frequencies of carbon atoms are calculated by applying the molecular structural mechanics approach. The entropy of a nanotube is obtained by the quantization of vibrational frequencies. The coefficients of thermal expansion (CTE) of single-walled carbon nanotubes in the axial and radial directions are then obtained by the differential of entropy with respect to the applied pressure. The computational results indicate that both the axial and radial CTEs are positive and increase with increasing temperature. The nanotube diameter has an insignificant effect on the axial thermal expansion. But the radial thermal expansion increases significantly with increasing tube diameter. The effect of nanotube length on radial CTE is larger than that on axial CTE and becomes more pronounced at high temperatures. The nanotube chirality has a slight effect on both of the axial and radial CTEs.