Thermal conductivity of zigzag single-walled carbon nanotubes: Role of the umklapp process

Abstract

Considering the three-phonon process, we calculate the thermal conductivity of zigzag tubes. It is found that thermal conductivity of an isolated ͑6, 0͒ single-walled carbon nanotube increases with the increase of temperature at low temperature, and would show a peak behavior at about 85 K before falling off at high temperature. Moreover, thermal conductivity is high for single-walled carbon nanotubes with small diameters as compared to the tubes with large diameters. The thermal conductivity at 300 K is approximately inversely proportional to the tube's diameter.Potential applications of carbon-nanotube-based devices, such as diodes, 1 field-effect transistors, 2 single-electron transistors, 3 as well as elementary logic circuits 4 rely on an effective way of removing high density of excess heat from the device active regime. 5-7 Removal of heat, actually, depends on the thermal conductivity of carbon nanotubes and the related compounds. 8 Thermal conductivity of singlewalled carbon nanotubes ͑SWCN's͒ is predicted to be unusually high by molecular-dynamics simulations at room temperature. 9-11 The measurement on ropes of SWCN's indicates a linear temperature dependence up to 30 K and an upward bend near 30 K on the curve of thermal conductivity (T). 12 In contrast to that of SWCN's, for multiwall carbon nanotube ͑MWNT͒ ropes increases with temperature in a parabolic fashion at low temperature up to ϳ120 K. 13 In order to reveal temperature dependence behavior of , Kim 14 performed scanning electron microscopy technique on individual MWNT. It is found that at low temperature (8 KϽT Ͻ50 K), increases following a power law with an exponent 2.50, and then increases quadratically when T Ͻ150 K. Although there is a vast literature concerning thermal transport in SWCN's, it is necessary to describe phonon characteristics for understanding the physical essence of the various experimental observations. In this paper, considering the three-phonon umklapp process, we analyze the physical mechanics of the thermal transport in a perfect isolated SWCN.As heat in SWCN's is mostly carried by acoustic phonons, it is reasonable to neglect the electronic component of thermal conductivity. The expression for lattice thermal conductivity at a given temperature T can be written as 15,16where , C , and V are phonon relaxation time, specific heat, and phonon group velocity of phonon mode , respectively. In a perfect isolated SWCN, phonon relaxation time is mainly controlled by boundary scattering and three-phonon umklapp scattering process. So, the total phonon relaxation time is usually given by the Matthiessen rule as 17with the relaxation-time parameters for boundary scattering B and for three-phonon umklapp scattering process U . Here, we choose B ϭ50 ps to be independent of temperature and phonon energy. 12,14,[19][20][21] From the first-order perturbation theory, the relaxation time U in the three-phonon umklapp process for thermal modes q is given by 18where ␥ is the Gruneisen parameter, ប is the Planck constant, M is atomic mas...

Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene

“…Numerous theoretical investigations of the thermal transport properties of carbon based materials such as diamond [1][2][3], graphite [4][5], graphene [6][7][8][9] and carbon nanotubes [10][11][12][13][14][15][16][17][18][19][20][21] have been performed in recent years partly because these materials possess the highest known thermal conductivities [22][23][24][25][26][27][28][29][30]. Theoretical investigations of phonon thermal transport in materials commonly employ either molecular dynamics (MD) simulations or Boltzmann transport approaches.…”

Frequency-dependent phonon mean free path in carbon nanotubes from nonequilibrium molecular dynamics

“…The effective MFP in CNTs has been experimentally estimated to be in the range 500-750 nm at room temperature 8,9 . These estimates are based, however, on a kinetic formula, which is known to underestimate the true MFP 19 and cannot account for the strong dependence of MFP on the phonon frequency [20][21][22][23][24] . The frequency-dependence is visible, e.g., in the thermal conductivity accumulation function 25,26 , whose experimental measurement has been recently enabled by advanced spectroscopic techniques [27][28][29][30] .…”

“…The frequency-dependence is visible, e.g., in the thermal conductivity accumulation function 25,26 , whose experimental measurement has been recently enabled by advanced spectroscopic techniques [27][28][29][30] . The frequency-dependent MFPs have been previously determined theoretically either from the decay of the mode energy correlation function 31,32 in equilibrium molecular dynamics (EMD) simulations 5,33 or by calculating the phonon-phonon scattering rates from first principles [21][22][23][24]34,35 . While it is known that only the Umklapp scattering processes can directly generate thermal resistance due to the change in crystal momentum 36,37 , both normal and Umklapp scattering processes contribute to redistributing the mode energy.…”

Les excitations dans la matière condensée : vibrations et phonons

“…Que la chaîne à constantes de forces alternées puisse constituer aussi le modèle le plus simple pour un cristal moléculaire peut servir de motivation supplémentaire. 50 La molécule est associée aux paires d'atomes liés par la constante de force la plus forte. L'interaction entre les molécules est prise en compte par des ressorts plus faibles.…”

“…50 Dans la réalité, les atomes qui forment une molécule sont beaucoup plus proches les uns des autres que les molécules ellesmêmes. Nous devrions par conséquent construire une chaîne avec deux atomes par maille primitive, de positions à l'équilibre na et na + d, avec d < a/2.…”