Thermal conductivity of multi-walled carbon nanotubes:Molecular dynamics simulations

Heat conduction in single-walled carbon nanotubes(SWCNTs) has been investigated by using various methods, while less work has been focused on multi-walled carbon nanotubes(MWCNTs). The thermal conductivities of the double-walled carbon nanotubes(DWCNTs) with two different temperature control methods are studied by using molecular dynamics(MD) simulations. One case is that the heat baths(HBs) are imposed only on the outer wall, while the other is that the HBs are imposed on both the two walls. The results show that the ratio of the thermal conductivity of DWCNTs in the first case to that in the second case is inversely proportional to the ratio of the cross-sectional area of the DWCNT to that of its outer wall. In order to interpret the results and explore the heat conduction mechanisms, the inter-wall thermal transport of DWCNTs is simulated. Analyses of the temperature profiles of a DWCNT and its two walls in the two cases and the interwall thermal resistance show that in the first case heat is almost transported only along the outer wall, while in the second case a DWCNT behaves like parallel heat transport channels in which heat is transported along each wall independently.This gives a good explanation of our results and presents the heat conduction mechanisms of MWCNTs.     

Nanotube phonon waveguide

We find that the high thermal conductivity of carbon nanotubes remains intact under severe structural deformations while the corresponding electrical resistance and thermoelectric power show compromised responses. Similar robust thermal transport against bending is found for boron nitride nanotubes. Surprisingly, for both systems the phonon mean free path exceeds the characteristic length of structural ripples induced by bending and approaches the theoretical limit set by the radius of curvature. The robustness of heat conduction in nanotubes refines the ultimate limit that is far beyond the reach of ordinary materials.     

Carbon nanotubes as heat dissipaters in microelectronics

We review our recent modelling work of carbon nanotubes as potential candidates for heat dissipation in microelectronics cooling. In the first part, we analyze the impact of nanotube defects on their thermal transport properties. In the second part, we investigate the loss of thermal properties of nanotubes in presence of an interface with various substances, including air and water. Comparison with previous works is established whenever is possible.     

Optimization of the parameters of a carbon nanotube-based field-emission cathode

A procedure for optimizing a field-emission cathode based on carbon nanotubes (CNTs) is developed. An array of identical equidistant vertical CNTs is considered. The optimization procedure takes into account the effect of screening of an electric field by neighboring nanotubes by solving a Laplace equation and the thermal instability of nanotubes, which limits the emission current density of a nanotube, by solving a heat conduction equation. The relation between the emission current and the applied voltage is described by the Fowler-Nordheim relationship containing the CNT tip temperature as a parameter. Upon optimization, the optimum distance between CNTs that ensures the maximum emission current density is calculated. The calculation results demonstrate that this parameter depends substantially on both the applied voltage and the nanotube geometry. These dependences are weakly sensitive to the choice of the transport coefficients (thermal conductivity, electrical conductivity) of nanotubes.     

Nonlinear transport and heat dissipation in metallic carbon nanotubes

We show that the local temperature dependence of thermalized electron and phonon populations along metallic carbon nanotubes is the main reason behind the nonlinear transport characteristics in the high bias regime. Our model is based on the solution of the Boltzmann transport equation considering both optical and zone boundary phonon emission as well as absorption by charge carriers. It also assumes a local temperature along the nanotube, determined self-consistently with the heat transport equation. By using realistic transport parameters, our results not only reproduce experimental data for electronic transport but also provide a coherent interpretation of thermal breakdown under electric stress. In particular, electron and phonon thermalization prohibits ballistic transport in short nanotubes.     

Ballistic phonon thermal transport in multiwalled carbon nanotubes

We report electrical transport experiments, using the phenomenon of electrical breakdown to perform thermometry, that probe the thermal properties of individual multiwalled carbon nanotubes. Our results show that nanotubes can readily conduct heat by ballistic phonon propagation. We determine the thermal conductance quantum, the ultimate limit to thermal conductance for a single phonon channel, and find good agreement with theoretical calculations. Moreover, our results suggest a breakdown mechanism of thermally activated C-C bond breaking coupled with the electrical stress of carrying approximately 10(12) A/m2. We also demonstrate a current-driven self-heating technique to improve the conductance of nanotube devices dramatically.     

碳纳米管包裹的硅纳米线复合结构的热稳定性研究

采用经典分子动力学方法模拟一定直径[111]晶向的硅纳米线填充不同扶手椅型单壁碳纳米管复合结构的加热过程, 通过可视化和能量分析的方法判断复合结构中硅纳米线和碳纳米管的热稳定性. 通过讨论碳纳米管的空间限制作用和分子间相互作用力的关系, 对碳纳米管和硅纳米线的热稳定性变化进行初步解释. 研究发现碳纳米管中硅纳米线的热稳定性和碳纳米管的直径关系密切: 当管径较小时, 硅纳米线的热稳定性有所提高, 当管径增大到一定大小时, 硅纳米线的热稳定性会突然显著地下降, 直到硅纳米线与管壁不存在分子间相互作用力, 硅纳米线的热稳定性才会恢复. 而硅纳米线填充到碳纳米管中对碳纳米管的热稳定性有着明显的降低作用.     

Mesoscopic thermal and thermoelectric measurements of individual carbon nanotubes

We discuss the mesoscopic experimental measurements of electron energy dissipation, phonon thermal transport, and thermoelectric phenomena in individual carbon nanotubes. The temperature distributions in electrically heated individual multiwalled carbon nanotubes have been measured with a scanning thermal microscope. The temperature profiles along the tube axis in nanotubes indicate the bulk dissipation of electronic energy to phonons. In addition, thermal conductivity of an individual multiwalled nanotube has been measured using a microfabricated suspended device. The observed thermal conductivity is two orders of magnitude higher than the estimation from previous experiments that used macroscopic mat samples. Finally, we present thermoelectric power (TEP) of individual single walled carbon nanotubes using a novel mesoscopic device. A strong modulation of TEP as a function of the gate electrode was observed.     

Nonequilibrium Green's function approach to phonon transport in defective carbon nanotubes

We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident phonons are scattered by localized phonons around the defects. We find a remarkable change from quantum to classical features for the thermal transport through defective carbon nanotubes with increasing temperature.     

Understanding of temperature and size dependences of effective thermal conductivity of nanotubes

The anomalous thermal transport properties of nanotubes may lead to many important applications, but the mechanisms are still unclear. In this work, we present new governing equations for non-Fourier heat conduction in nanomaterials based on the concept of thermomass. The effective thermal conductivities of nanotubes are therefore predicted which agree very well with the available experimental data. Analysis suggests that the inertial effect of heat and the confined heat flux by nanostructured surfaces are two key mechanisms causing the anomalous temperature and size dependences of effective thermal conductivity of nanotubes.     

Universal features of quantized thermal conductance of carbon nanotubes

The universal features of quantized thermal conductance of carbon nanotubes (CNTs) are revealed through a theoretical analysis based on the Landauer theory of heat transport. The phonon-derived thermal conductance of semiconducting CNTs exhibits a universal quantization in the low-temperature limit, independent of the radius or atomic geometry. The temperature dependence follows a single curve given in terms of temperature scaled by the phonon energy gap. The thermal conductance of metallic CNTs has an additional contribution from electronic states, which also exhibits quantized behavior up to room temperature.     

碳纳米管中点缺陷对热导率影响的正交试验模拟分析

在碳纳米管的制备过程中, 各种点缺陷不可避免地存在于其晶格结构中, 对于碳管的热输运性质造成不可忽视的影响. 使用非平衡分子动力学方法, 选用反应经验键序势能, 模拟计算含有缺陷的碳纳米管的热导率. 尝试采用正交试验方法设计算例, 不但减少了计算量, 并且利于分析缺陷类型、 管长和管径三种结构因素对缺陷造成的热导率下降影响的主次和趋势. 重点研究了掺杂、 吸附和空位三类点缺陷的影响, 与无缺陷完整碳纳米管进行比较, 开展缺陷效应分析, 并进一步考察了环境温度等因素的影响. 模拟结果表明, 相对完整无缺陷碳管, 含有点缺陷的碳管热导率显着下降; 在有缺陷存在的情况下, 缺陷的类型对碳管热导率的影响最大, 管径次之, 管长影响相对最小; 缺陷类型对热导率影响力从大到小依次为: 空位 > 掺杂 > 吸附; 不同环境温度下, 点缺陷对碳管热导率的影响不尽相同.     

碳纳米管的热导率:从弹道到扩散输运

采用非平衡分子动力学方法研究了300 K和1000 K时（5,5）碳纳米管热导率随长度的变化.在室温下,碳纳米管长度小于40 nm时热导率与长度呈线性关系,此时导热处于弹道输运阶段,单位面积弹道热导为5.88×10⁹ Wm^-2K^-1．随着碳纳米管长度的增加,其热导率逐渐增加,但增加速度随长度逐渐减小,此时导热处于弹道—扩散输运阶段,并随长度的增加从以弹道输运为主向以扩散输运为主转变．长度大于10 μm时由于弹道输运可以忽略,导热近似达到完全 关键词： 碳纳米管 热导率 弹道输运 低维导热     

碳纳米管电缆式复合材料的热导率

通过非平衡分子动力学方法, 对单壁碳管填充金纳米线的碳纳米管电缆式复合材料开展热导率的模拟分析. 采用Tersoff势函数描述碳-碳原子间的相互作用, Lennard-Jones长程作用势描述碳-金原子间的相互作用, 嵌入原子势函数描述金-金原子间相互作用. 研究结果表明: 相同尺寸下, 金纳米线的电子热导率相较于空碳管以及电缆式复合材料的声子热导率小很多, 对复合材料总热导率的贡献可以忽略; 由于管内金纳米线的存在, 其与碳管的相互作用使得碳管碳原子倾向于沿着轴向振动, 声子间U散射随之减少, 声子平均自由程增加, 导致复合材料热导率明显大于空碳管, 在100–500 K温度范围内高出约20%–45%, 但增大幅度随温升呈降低趋势; 复合材料热导率随着管长增加而增大, 变化趋势和空碳管相似, 但其增长幅度更大; 复合材料和空碳管的热导率随管径增大而减小, 且变化幅度基本一致. 关键词： 碳纳米管 纳米线 电缆式复合材料 导热     

Thermal properties of carbon nanotubes and nanotube-based materials

The thermal properties of carbon nanotubes are directly related to their unique structure and small size. Because of these properties, nanotubes may prove to be an ideal material for the study of low-dimensional phonon physics, and for thermal management, both on the macro- and the micro-scale. We have begun to explore the thermal properties of nanotubes by measuring the specific heat and thermal conductivity of bulk SWNT samples. In addition, we have synthesized nanotube-based composite materials and measured their thermal conductivity. The measured specific heat of single-walled nanotubes differs from that of both 2D graphene and 3D graphite, especially at low temperatures, where 1D quantization of the phonon bandstructure is observed. The measured specific heat shows only weak effects of intertube coupling in nanotube bundling, suggesting that this coupling is weaker than expected. The thermal conductivity of nanotubes is large, even in bulk samples: aligned bundles of SWNTs show a thermal conductivity of >200 W/m K at room temperature. A linear K(T) up to approximately 40 K may be due to 1D quantization; measurement of K(T) of samples with different average nanotube diameters supports this interpretation. Nanotube–epoxy blends show significantly enhanced thermal conductivity, showing that nanotube-based composites may be useful not only for their potentially high strength, but also for their potentially high thermal conductivity. Received: 17 October 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

Carbon nanotube ballistic thermal conductance and its limits

Calculations of the quantum-mechanical ballistic thermal conductance of single-walled carbon nanotubes, graphene, and graphite are presented, which explain previous experimental results, and directly disprove earlier theoretical calculations. The ballistic thermal conductances are smaller than had been previously thought, whereas the maximum sample lengths in which phonon transport remains ballistic are orders of magnitude larger than previously suggested. Good agreement with previous experiments is obtained, which shows that measured lower bounds to the thermal conductance of multiwalled carbon nanotubes are very close to the upper theoretical bounds for graphite. The bounds shown here draw a line between what is physical and unphysical in any measurements or calculations of carbon nanotube thermal conductance, and constitute a necessary test to their validity.     

Transport of liquid mercury under pressure in double-walled carbon nanotubes

In this paper, transport of liquid mercury under pressure through double-walled carbon nanotubes is studied using classical molecular dynamics simulations in conjunction with a pressure control model. The results indicate that wetting of double-walled carbon nanotubes by mercury occurs above a threshold pressure of liquid mercury. Liquid mercury can be transported through the inner tube of double-walled carbon nanotubes with the continuous increase of its pressure. The threshold pressure of liquid mercury decreases and the transport efficiency increases greatly with enlarging the inner tube size. The space between the two walls of double-walled carbon nanotubes can also transport the liquid mercury while the distance between the two walls is much larger than the radius of the inner tube. Transport efficiency of double-walled carbon nanotubes is a little lower than that of single-walled carbon nanotubes while double-walled carbon nanotubes transport liquid more steadily than single-walled carbon nanotubes.     

Thermal transport of oil and polymer composites filled with carbon nanotubes

We studied the thermal transport properties of multi-walled carbon nanotubes (MWNTs) in polymer and oil matrices. The thermal conductivity of the oils and polymers increased linearly when adding tubes. We observe a particularly high increase in the thermal diffusivity of carbon-nanotube-loaded liquid crystal polymers (6×10⁻⁵ cm²/s wt%), which is due to a spontaneous alignment of the MWNTs. Carbon nanotubes increased the thermal conductivity of oil by a factor of three for 20 wt% loading. We found little or no dependence of the thermal enhancement on the specific flavor of multiwall nanotubes used in the composites. Carbon nanotubes are excellent nanoscale fillers for composites in thermal management application.     

形变碳纳米管中水的输运行为研究

水分子通过碳纳米管的运输行为对认识生命的新陈代谢活动、海水淡化和纳米运输器件有着重要的参考作用.本文通过分子动力学的方法研究了水分子通过形变碳纳米管的运输行为,即椭圆柱状碳纳米管的离心率e对管内水分子输运的影响.结果发现椭圆柱状碳纳米管的离心率对管内水分子的偶极矩概率分布、径向函数分布和流量有重要的影响作用.分析认为碳纳米管的形变使管内水分子的偶极矩态及其运输状态发生变化;同时也发现在一定范围内通过改变碳纳米管的形状能起到分子开关的作用.     

形变碳纳米管中水的输运行为研究

水分子通过碳纳米管的运输行为对认识生命的新陈代谢活动、海水淡化和纳米运输器件有着重要的参考作用. 本文通过分子动力学的方法研究了水分子通过形变碳纳米管的运输行为, 即椭圆柱状碳纳米管的离心率e对管内水分子输运的影响. 结果发现椭圆柱状碳纳米管的离心率对管内水分子的偶极矩概率分布、径向函数分布和流量有重要的影响作用. 分析认为碳纳米管的形变使管内水分子的偶极矩态及其运输状态发生变化; 同时也发现在一定范围内通过改变碳纳米管的形状能起到分子开关的作用.