Quantized molecular structural mechanics modeling for studying the specific heat of single-walled carbon nanotubes

We extend the molecular structural mechanics approach to the study of the specific heat of carbon nanotubes. The vibrational modes of the nanotube are quantized according to the theory of quantum mechanics. The partition function is directly expressed by the vibrational frequencies of carbon atoms. The specific heat of finite-length individual single-walled carbon nanotubes is calculated and the temperature dependence of the specific heat is demonstrated. The specific heat is shown to increase with increasing tube diameter, but the effect mainly exists at the temperature range of $25–350\mathrm{K}$. The tube chirality has a slight influence on the specific heat at high temperature. The specific heat is also shown to increase with increasing tube length when the nanotube length/diameter ratio is less than 20, and the effect is more distinguishable at higher temperature. The computational predictions are compared with available experimental as well as theoretical results of the specific heat of carbon nanotubes.

Figure 1

(Color online) Vibrational frequencies of armchair and zigzag SWNT’s.

Figure 2

(Color online) The variation of specific heat of $2.4\text{−}\mathrm{nm}$-diam SWNT’s with temperature.

Figure 3

(Color online) Comparison of specific heat for single-walled carbon nanotubes at low temperatures with experimental results on nanotube ropes.

Figure 4

(Color online) Comparison of specific heat for single-walled carbon nanotubes at low temperatures with other theoretical results.

Figure 5

(Color online) The effect of tube diameter on (a) zigzag and (b) armchair SWNT specific heat.

Figure 6

(Color online) The effect of tube length on the specific heat of SWNT’s.