Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, 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.     

Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material,contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N →∞.For the finite size,thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain.For the present 1D diatomic chain,obtained value of power divergent exponent of thermal conductivity0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size,increases the thermal conductivity and existence of anomalous energy diffusion.Existing numerical data supports our findings.     

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 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.     

Carbon nanotube-epoxy composites: The role of acid treatment in thermal and electrical conductivity

Wet acid oxidation treatment methods have been widely reported as an effective method to purify and oxidize the surface of industrial multi-walled carbon nanotubes. This work examines the use of a concentrated HNO₃/H₂SO₄ mixture in an attempt to optimize the purification procedure of industrial multi-walled carbon nanotubes with diameter distribution statistics. It is shown that acid treatments of several hours are enough to purify the nanotubes. The electrical and thermal conductivities of epoxy composites containing 0.05–0.25 wt% of an acid-treated multi-walled carbon nanotube have been studied. The electrical conductivity of the composites decreases by more than three orders, whereas the thermal conductivity of the same specimen increases very modestly as a function of the filler content.     

Understanding length dependences of effective thermal conductivity of nanowires

We have studied the length dependence of effective thermal conductivity of silicon nanowires by a thermon gas model and MD simulations. After modifications of the force term by considering the resistance enhancements from thermon gas interactions with the confined surfaces and the ends (inlet and outlet), the theoretical predictions of effective thermal conductivity agree well with the results of MD simulations in the length range of 4 to 550 nm. The result suggests that the resistance enhancement effect by thermon–boundary interactions, instead of the heat inertia, plays the dominating role in the non-Fourier heat conduction in silicon nanowires.     

From compact point defects to extended structures in silicon

We show that in contrast to the 1d Frenkel-Kontorova (FK) chain known to obey the Fourier law of heat conduction and several 2d models which show logarithmic dependence of conductivity on system size, a scalar 2d FK lattice with commensurate structure exhibits anomalous heat conduction, whose thermal conductivity displays a power law behavior. The dependence of thermal gradient on bulk temperature and noise correlation is critically analyzed. A dynamical contribution to conductivity when the system attains a nonequilibrium steady state of thermal conduction has been identified.     

异质结碳纳米管的热整流效率

采用非平衡分子动力学方法, 通过分别控制异质结碳纳米管管径、手性和平均温度的方式研究了异质结碳纳米管的热整流效应. 研究表明, 随着异质结碳纳米管两端几何不对称性的增强, 其热整流效率会随之上升, 而异质结碳纳米管两端的手性的改变和夹角的大小都会对热整流效率产生一定的影响. 热整流效率会随着碳纳米管平均温度的上升而下降. 研究异质结碳纳米管热整流效率对于热二极管、碳纳米散热元器件等潜在应用价值有理论指导作用.     

基于热质运动概念的普适导热定律

根据爱因斯坦的质能等效关系式,热能具有的等效质量称为热质,从而在固态和气态介质中分别建立了声子气质量和热子气质量的概念.应用牛顿定律建立了含有驱动力、阻力和惯性力的热质(声子气或热子气)运动的动量守恒方程.由于热量在介质中的传递本质上就是热质(声子气和热子气)在介质中的运动,所以热质动量守恒方程就是普适的导热定律,能够统一描述各种条件下的导热规律.当热流密度不是很大从而热质惯性力可以忽略时,热质动量守恒方程就退化为傅里叶导热定律,这表明傅里叶导热定律是特殊条件下的导热定律,对于微纳尺度条件下的导热,热流密度可以极高,由速度空间变化引起的惯性力不能忽略,在稳态导热情况下也将出现非傅里叶导热,此时在计算或者实验中不能用热流密度除温度梯度求导热系数.在超快速加热条件下,必需考虑惯性力,与基于CV导热模型的波动方程相比,普适的导热定律增加了因速度空间变化引起的惯性力项,所以在介质中热波叠加时不会出现产生负温度的非物理现象,表明基于热质运动概念的普适导热定律更为合理. 关键词： 傅里叶导热定律 普适导热定律 热质运动 非傅里叶导热     

导热优化:热耗散与最优导热系数场

本文讨论了通过重新布置场内的导热系数分布来强化热传导的导热优化问题。针对边界上传热量一定的任意几何区域的稳态导热,在全场的导热系数积分为定值的条件下,以最小热耗散作为目标,利用变分方法导出了导热优化的基本准则;导热系数与局部热流密度成正比。该准则指导下的导热优化过程可获得热耗散最小的导热系数分布。实例证明了该方法是有效且合理的。     

剖面不变性与托卡马克放电中的

从通常的局部输运模型的角度分析,托卡马克等离子体中有相当多的输运现象会被视为“奇怪”的或“反常”的,即难于被正确的理解,也难于给出统一的描述方式。基于温度剖面不变性的－－这里称炎这相容模型的描述方法,在不涉及非局部输运任何具体物理机制的情况下,给出了包含非局部效应的热导系数及其与局部反常热导系数的关系。利用这种相容热导模型统一地描述并分析了一些看似奇怪或反常的输运现象。     

随机结构多孔介质等效热导率数值计算

本文对二维颗粒弥散多孔介质的辐射导热耦合等效热导率进行了数值计算研究。首先采用随机生成结构方法(Random generate-growth method,RGGM)生成实际多孔材料的复杂结构。在此基础上,采用离散坐标法及有限容积法求解了复杂结构内部辐射导热耦合换热,进而计算得到材料的等效热导率。根据建立的材料随机结构模型及等效热导率数值计算模型,分别研究了衰减系数、弥散相体积分数、温度等因素对材料等效热导率的影响,并将数值计算结果与理论计算结果进行对比,吻合较好,反映出模型用于预测实际多孔材料等效热导率的有效性。     

Thermal conductivity and thermal rectification in carbon nanotubes with geometric variations of doped nitrogen: Non-equilibrium molecular dynamics simulations

The thermal conductivity of carbon nanotubes with geometric variations of doped nitrogen is investigated. The phenomenon of thermal rectification shows that the heat transport is preferably in one direction. The asymmetric heat transport of the triangular single-nitrogen-doped carbon nanotubes (SNDCNTs) is larger than that of the parallel various-nitrogen-doped carbon nanotubes (VNDCNTs).     

Observation and measurement of anomalous responses in a differential mobility analyzer caused by ultrafine fibrous carbon aerosols

We observed anomalous instrument responses above certain voltages when characterizing aggregates of airborne carbon nanotubes or nanofibers using a differential mobility analyzer (DMA). These were associated with sudden increases in measured number concentrations at high voltages, fluctuations in DMA voltage and audible high-frequency sounds from the DMA column. Onset of the anomalies depended on the material forming the aerosol and DMA sampling flow rate. The low density of the nanotubes relative to the nanofibers is thought to be the main reason the anomalous responses occur more easily and strongly with the nanotubes. Two possible mechanisms are suggested to explain the observations. The results indicate that measurement of nanometer-diameter conducting fibrous material by electrical mobility analysis may present a unique challenge.     

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     

真空热流法测定不良导体的导热系数

以恒定导热原理为基础,选用由温度表和温差电偶组成的温度测量装置,在真空环境下测量试样上下压杆对称位置的温度、有效传热面积和试样的厚度,通过计算机计算试样的导热系数.与传统的稳态法比较,采用真空热流法测定导热系数,材料内部的温度分布很快达到稳定,可以减小测量过程中试样及上加热盘和下散热盘侧面散热产生的影响.     

板状激光振荡介质温度场和应力场的数值模拟

以非均匀内热源模型为基础,并考虑材料的导热系数和热膨胀系数的温度相关性,利用有限元方法,对板状激光振荡介质在不同功率和冷却强度下的温度和热应力分布进行了数值模拟及分析。根据计算结果提出了最大有效换热系数的概念,指出换热系数超过最大有效换热系数后,继续强化传热对减小高功率激光器的热效应已无明显效果。以此得出采用常规冷却技术所允许的最大泵浦加热功率。     

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.     

Surface and quantum-size effects on the specific heat of layered and nonlayered nanotubes

A detailed analysis of room temperature specific heat of unrelaxed layered and nonlayered nanotubes is presented. Our results exhibit a close interplay between surface and quantization contributions of specific heat, i.e. C_surface and C_quantum. The calculated specific heat of single-layer and multi-layer layered nanotubes increases with diameter regardless of the species. However, slowly increasing C_quantum and rapidly decreasing C_surface with diameter result in the decrease of specific heat of nonlayered nanotubes. Moreover, our theoretical results are compared with experimental observation and physical mechanisms are discussed. These results imply that the existence of surface in nonlayered nanotubes has an important influence on specific heat.