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 (TiO 2 , V 2 O 5 ) and sulfides (TiS 2 , ZrS 2 ) 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.

Phonon spectra, electronic, and thermodynamic properties of WS2 nanotubes

“…Obviously, folding a monolayer into a nanotube affects the electron and phonon band structures. Nevertheless, the relationship between layer and NT band structures can be estimated using the so‐called zone‐folding approach (ZFA). In this approach, the states of the nanotube with the fixed m are put into correspondence with so called cutting line in layer reciprocal space.…”

First‐Principles Calculations of Phonons and Thermodynamic Properties of Zr(Hf)S2‐Based Nanotubes

“…[5,6] Among the other transition metal dichalcogenides, the disulfides of Hf and Zr have attracted a significant attention because of their unique electronic features resulted in numerous applications in photocatalysis and electrochemical intercalation. The results of the first-principles calculations of phonons and thermodynamic properties are published only for ZrS 2 -based nanotubes [28,29] and absent for HfS 2 -based nanotubes. [6,9,10] The theoretical modeling was carried out in references [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] for bulk Zr(Hf) sulfides and their monolayers.…”

Application of zone‐folding approach to the first‐principles estimation of thermodynamic properties of carbon and ZrS2‐based nanotubes

“…The usefulness of the ZF approach is displayed more clearly when we compare the thermodynamic properties for systems with different chemical composition. In our recent work, [35] we reported the results of ZF calculations of the thermodynamic properties of some sulfide and oxide NTs. Here, in Figure 10 we give the temperature dependence of the internal energy and Helmholtz energy for the (4, 0) a-V 2 O 5 -based NT together with the (12, 12) carbon-and ZrS 2 -based NTs.…”

“…Figure 11. Temperature dependence of heat capacity (per 1 mole of atoms) of ZrS 2 -, a-V 2 O 5 -, [35] and Graphene-based SWNTs calculated directly and with ZF approximation. Dulong-Petit limit is shown by the straight dashed line (R is the gas constant).…”

“…Figure 10. Temperature dependence of internal energy a) and Helmholtz energy b) (per 1 formula unit) of ZrS 2 -, a-V 2 O 5 -, [35] and Graphene-based SWNTs calculated directly and with ZF approximation. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]…”