Some Notes on Boltzmann and Landauer Phonon Thermal Transport at Nanoscale

Author(s): Amelia Carolina Sparavigna

To evaluate the phonon thermal transport at the nanoscale of nanotubes and nanowires we can use Boltzmann and Landauer approaches. The Boltzmann equation is coming from a semiclassical formulation, whereas the Landauer equation is based on ballistic models. Here we show, for teaching purposes, a simple manner of linking these two approaches using dimensional equations.

Nanotubes, Nanowires, Nanostructures, Phonons, Thermal Transport, Relaxation Time Approximation, Boltzmann Equation, Landauer Formula

1. Yi, W., Lu, L., Dian-lin, Z., Pan, Z.W., and Xie, S.S. (1999). Linear specific heat of carbon nanotubes, Phys. Rev. B 59, R9015-R9018
2. Hone, J., Whitney, M., Piskoti, C., and Zettl, A. (1999). Thermal conductivity of single-walled carbon nanotubes, Phys. Rev. B 59, R2514-R2516
3. Kim, P., Shi, L., Majumdar, A., and McEuen, P.L. (2001). Thermal transport measurements of individual multiwalled nanotubes, Phys. Rev. Lett. 87, 215502 (5 pages)
4. Li, D., Wu, Y., Kim, P., Shi, L., Yang, P., and Majudar, A. (2003). Thermal conductivity of individual silicon nanowires, Appl. Phys. Lett. 83, 2934-2936
5. Dresselhaus, M.S., Dresselhaus, G., and Eklund, P.C. (1996). Science of fullerenes and carbon nanotubes, Academic Press, New York
6. Behabtu, N., Young, C.C., Tsentalovich, D.E., Kleinerman, O., Xuan Wang, X., Ma, A.W.K., Amram Bengio, E., ter Waarbeek, R.F., de Jong, J.J., Hoogerwerf, R.F., Fairchild, S.B., Ferguson, J.B., Maruyama, B., Kono, J., Talmon, Y., Cohen, Y., Otto, M.J., and Pasquali, M. (2013). Strong, light, multifunctional fibers of carbon nanotubes with ultrahigh conductivity, Science 339 (6116), 182-186
7. Salaway, R.N., and Zhigilei, L.V. (2014). Molecular dynamics simulations of thermal conductivity of carbon nanotubes: Resolving the effects of computational parameters, International Journal of Heat and Mass Transfer 70, 954-964
8. De Volder, M. F., Tawfick, S. H., Baughman, R. H., and Hart, A. J. (2013). Carbon nanotubes: present and future commercial applications, Science 339 (6119), 535-539
9. Ouyang, T., Chen, Y., Liu, L.-M., Xie, Y., Wei, X., and Zhong, J. (2012). Thermal transport in graphyne nanoribbons, Phys. Rev. B 85, 235436 (7 pages)
10. Zhong, W.-R., Zheng, D.-Q., and Hu, B. (2012). Thermal control in graphene nanoribbons: thermal valve, thermal switch and thermal amplifier, Nanoscale 4, 5217-5220
11. Sparavigna, A., and Ravetti A. (2005). Thermal conductivity in nanotubes and nanotube bundles, Recent Res. Devel. Physics 6, 173-184, S.G. Pandalai Ed., ISBN 81-7895-171-1
12. Sparavigna, A. (2008). Lattice specific heat of carbon nanotubes, Journal of Thermal Analysis and Calorimetry 93, 983-986
13. Ziman, J.M. (1960). Electrons and phonons: the theory of transport phenomena in solids, Clarendon, Oxford
14. Srivastava, G.P. (1990). The physics of phonons, Hilger, Bristol
15. Sparavigna, A. (2002). Influence of isotope scattering on the thermal conductivity of diamond, Phys. Rev. B 65, 064305 (5 pages)
16. Omini, M., and Sparavigna, A. (1997). Heat transport in dielectric solids with diamond structure, Nuovo Cim. D 19, 1537-1563
17. Omini, M., and Sparavigna, A. (1997). Beyond the isotropic-model approximation in the theory of thermal conductivity, Phys. Rev. B 53, 9064-9073
18. Sparavigna, A.C., and Galli, S. (2012). L'equazione di Boltzmann per la conducibilità termica fononica nell'approssimazione dei tempi di rilassamento, Lulu Enterprises, Raleigh, NC
19. Mahan, G.D., and Gun Sang Jeon, (2004). Flexure modes in carbon nanotubes, Phys. Rev. B, 70, 075405 (11pages)
20. Sparavigna, A. (2006). Lattice specific heat of carbon nanotubes, arXiv:cond-mat/0609139 [cond-mat.mtrl-sci]
21. Imry, J. (1997). Introduction to Mesoscopic Physics, Oxford University Press
22. Datta, A. (1995). Electronic transport in mesoscopic systems, Cambridge University Press
23. Rego, L.G.C., and Kirczenow, G. (1998). Quantized thermal conductance of dielectric quantum wires, Phys. Rev. Lett. 81, 232-235