Length-dependent thermal conductivity of an individual single-wall carbon nanotube

Wang, Zhao Liang; Tang, Da Wei; Li, Xiao Bo; Zheng, Xing; Zhang, Wei Gang; Li, Zheng; Zhu, Yuntian; Jin, Ai Zi; Yang, He; Gu, Chen

doi:10.1063/1.2779850

Cited by 91 publications

(40 citation statements)

References 17 publications

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“…There seems to be rapid progress in the direction of making this possible. The first indication of length dependence was reported by Wang et al [200], for the case of a SWCNT placed on a silicon substrate. They measured samples of lengths between 0.5 − 7µm at room temperature and found a slow increase of the conductance.…”

Section: Methodsmentioning

confidence: 93%

Heat transport in low-dimensional systems

Dhar

2008

Advances in Physics

906

1,114

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Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard particle and hard disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green-Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ, diverges with system size L, as κ ∼ L α . For one dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given. IntroductionIt is now about two hundred years since Fourier first proposed the law of heat conduction that goes by his name. Consider a macroscopic system subjected to different temperatures at its boundaries. One assumes that it is possible to have a * Corresponding author. Email: dabhi@rri.res.in November 19, 2008 19:56 Advances in Physics reva 2 coarse-grained description with a clear separation between microscopic and macroscopic scales. If this is achieved, it is then possible to define, at any spatial point x in the system and at time t, a local temperature field T (x, t) which varies slowly both in space and time (compared to microscopic scales). One then expects heat currents to flow inside the system and Fourier argued that the local heat current density J(x, t) is given bywhere κ is the thermal conductivity of the system. If u(x, t) represents the local energy density then this satisfies the continuity equation ∂u/∂t + ∇.J = 0. Using the relation ∂u/∂T = c, where c is the specific heat per unit volume, leads to the heat diffusion equation:Thus, Fourier's law implies diffusive transfer of energy. In terms of a microscopic picture, this can be understood in terms of the motion of the heat carriers, i.e. , molecules, electrons, lattice vibrations(phonons), etc., which suffer random collisions and hence move diffusively. Fourier's law is a phenomological law and has been enormously succesful in providing an accurate description of heat transport phenomena as observed in experimental systems. However there is no rigorous derivation of this law starting from a microscopic Hamiltonian description and this basic question has motivated a large number of studies on heat conduction in model systems. One important and somewhat surprising conclusion that emerges from these studies is that Fourier's law is probably not valid in one and two dimensional systems, except when the ...

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Section: Methodsmentioning

confidence: 93%

Heat transport in low-dimensional systems

Dhar

2008

Advances in Physics

906

1,114

View full text Add to dashboard Cite

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“…Some other researches focused on room temperature behavior, which showed obvious diversities as well. Measurements on individual CNT varied from 300 to 3294W/m · K, 11,12 while values of aligned CNT film varied from 27 to 200 W/m · K. [13][14][15] Molecular dynamics and phonon analysis have been widely used in this field too, offering more systematic insights that yet cannot be achieved through experiments. However, modeling and theoretical methods were not able to produce consistent results either.…”

Section: Introductionmentioning

confidence: 99%

A practical dimensionless equation for the thermal conductivity of carbon nanotubes and CNT arrays

Chen

Huang

2014

AIP Advances

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Experimental results reported in the last decade on the thermal conductivity of carbon nanotubes (CNTs) have shown a fairly divergent behavior. An underlying intrinsic consistency was believed to exist in spite of the divergence in the thermal conductivity data of various CNTs. A dimenisonless equation that describes the temperature dependence of thermal conductivity was derived by introducing reduced forms relative to a chosen reference point. This equation can serve as a practical approximation to characterize the conductivity of individual CNT with different structural parameters as well as bulk CNT arrays with different bundle configurations. Comparison of predictions by the equation and historical measurements showed good agreements within their uncertainties.

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“…However, this kind of modification inevitably destroys the structure of CNTs, resulting in the corrosions of graphite crystal layer and the decrease of high aspect ratio. It is well acknowledged that the integrity of CNTs' structure is the precondition of its thermal performances [14]. So the properties of CNTs modified by these methods may not be as good as the original ones.…”

mentioning

confidence: 99%

Preparation and properties of natural rubber reinforced with polydopamine-coating modified carbon nanotubes

Lu¹,

Ma²,

Xu³

et al. 2017

Express Polym. Lett.

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IntroductionNR is one of the most important nature polymers, which is widely used as the elastomeric matrix of various materials, including conveyor belts, sealing rings, tires, etc. In order to meet the requirements of the use of tires, NR composites must have the following two properties: (1) good mechanical properties, in order to undergo cyclic loading and strains in actual use, (2) good thermal conductivity and electrical conductivity, in order to export the heat or static electricity effectively and timely. However, traditional fillers (such as carbon black, silica, alumina, etc.) cannot improve both aspects simultaneously, though the high surface carbon blacks may improve both mechanical properties and electrical conductivity, but the precondition is that a relative large amount of high surface carbon black must be added, this may adversely affect the processing performance of the composites. Recently, the carbon nanotubes (CNTs) have become a hot spot in various research fields for their unique structure and outstanding performances [1,2]. High mechanical properties (tensile strength is 50 GPa, Young modulus is ~5 TPa) and good conductivity (electrical conductivity is ~10 7 s/m, thermal Abstract. Multi-walled carbon nanotubes (MWCNTs) were functionalized by polydopamine (PDA)-coating and mixed with natural rubber (NR) via latex compounding. Compared with pristine MWCNTs, the surface of MWCNT-PDA was covered by an amorphous and nanometer-scale PDA layer which had a large amount of oxygenic and nitric functional groups. So the MWCNT-PDA showed a perfect dispersion in NR matrix. The tensile strength of NR/MWCNT-PDA (5 phr) composites is 28.6 MPa, compared with the pure NR, which increased by 42%. For the electrical properties, when the content of MWCNT-PDA or MWCNTs is 2 phr, the volume resistivity of NR/MWCNT-PDA composites falls to about 2.7·10 9 Ω·cm, compared with 3.3·1013 Ω·cm of NR/MWCNT composites. The thermal conductivity of NR composites increased only by 28.2% when 5 phr MWCNT-PDA was added. A model proposed by Nan was used to calculate the thermal conductivity of NR/MWCNT composites, and the calculated values were compared with the experimental values, the results showed that the interface thermal resistance is the main reason why MWCNTs could not significantly increase the thermal conductivity of natural rubber.

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Length-dependent thermal conductivity of an individual single-wall carbon nanotube

Cited by 91 publications

References 17 publications

Heat transport in low-dimensional systems

Heat transport in low-dimensional systems

A practical dimensionless equation for the thermal conductivity of carbon nanotubes and CNT arrays

Preparation and properties of natural rubber reinforced with polydopamine-coating modified carbon nanotubes

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