Size and temperature dependence of the specific heat capacity of carbon nanotubes

The specific heat capacity (Cv) of carbon nanotubes for different temperatures and radii is calculated and presented. These calculations are based upon the continuum model of Zhang et al. The change in dimensionality behaviour (from quasi-1D to quasi-2D) as a function of temperature for tubes of different radii is investigated. It is found that for a range of radii the changeover occurs between 180 K and 400 K. Thicker nanotubes have intrinsically stronger quasi-2D behaviour beyond this temperature range than thinner nanotubes. The present numerical results confirm a qualitative discussion of this behaviour presented earlier by Benedict et al. For a given temperature, the variation of Cv as a function of radius is also discussed. An expression has been obtained to show the linear variation of Cv in the appropriate low temperature region.