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     

Effects of vacancy defects and axial strain on thermal conductivity of silicon nanowires: A reverse nonequilibrium molecular dynamics simulation

Thermal conductivity of silicon nanowires (SiNWs) is evaluated using the reverse nonequilibrium molecular dynamics simulation. The Stillinger–Weber (SW) and Tersoff interatomic potentials are employed to simulate thermal conductivity of SiNWs. In this work, the influence of random vacancy defects, axial strain, temperature and length on thermal conductivity and effective mean free path of SiNWs is investigated. It is found that by raising the percent of random vacancy defects, thermal conductivity of SiNWs decreases linearly for the results obtained form SW potential and nonlinearly for those obtained from Tersoff interatomic potential. Dependence of the thermal conductivity on axial strain is also studied. Results show that thermal conductivity increases as compressive strain increases and decreases as tensile strain increases. Influence of temperature is also predicted. It is found that the thermal conductivity of SiNWs decreases with increasing the mean temperature. Most of the simulations are performed for 4 UC×4 UC×40 UC silicon nanowires using ssp boundary condition.     

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 stability of silicon nanowires: atomistic simulation study

Using the Stillinger--Weber (SW) potential model, we investigate the thermal stability of pristine silicon nanowires based on classical molecular dynamics (MD) simulations. We explore the structural evolutions and the Lindemann indices of silicon nanowires at different temperatures in order to unveil atomic-level melting behaviour of silicon nanowires. The simulation results show that silicon nanowires with surface reconstructions have higher thermal stability than those without surface reconstructions, and that silicon nanowires with perpendicular dimmer rows on the two (100) surfaces have somewhat higher thermal stability than nanowires with parallel dimmer rows on the two (100) surfaces. Furthermore, the melting temperature of silicon nanowires increases as their diameter increases and reaches a saturation value close to the melting temperature of bulk silicon. The value of the Lindemann index for melting silicon nanowires is 0.037.     

热子动力学模拟方法

提出热子动力学模拟方法,以理想气体中的热质粒子即热子为模拟对象,建立热子间的碰撞模型,统计可获得热子气系统的热力学性质,实现对热质的直接模拟.基于该方法,对氩热子气的平衡态系统和非平衡态系统进行模拟计算,模拟计算的热子气的状态方程同理论表达式一致,准确得到了氩气热导率在微纳尺度下的变化规律,验证了热子动力学模拟方法的可行性.     

Thermal conductivity of periodic array of intermolecular junctions of silicon nanowires

Recent studies on intramolecular junctions of silicon nanowires and carbon nanotubes have revealed a wealth of intriguing phenomena. However, the thermal properties of the intramolecular junctions of silicon nanowires (SiNWs) are not yet well understood. In this study periodic arrays of intramolecular junctions with different lattice orientations are investigated, and their thermal conductivities are calculated using nonequilibrium molecular dynamics (NEMD) simulations. Different from the X-shaped and Y-shaped junctions of carbon nanotubes, no distinct jump is found in the temperature profile at the junctions. Compared with straight pristine SiNWs of the same length, the thermal conductivity of the periodic array of intramolecular junctions is reduced. The underlying mechanism of the observed behavior is analyzed by the phonon spectral density of the atomic velocities. The dependence of temperature on the thermal conductivity of this junction array structure is discussed.     

多约束纳米结构的声子热导率模型研究

纳米技术的快速发展使得对微纳尺度导热机理的深入研究变得至关重要. 理论和实验都表明, 在纳米尺度下声子热导率将表现出尺寸效应. 基于声子玻尔兹曼方程和修正声子平均自由程的方法得到了多约束纳米结构的声子热导率模型, 可以描述多个几何约束共同作用下热导率的尺寸效应. 不同几何约束对声子输运的限制作用可以分开计算, 总体影响则通过马西森定则进行耦合. 对于热流方向的约束, 采用扩散近似的方法求解声子玻尔兹曼方程; 对于侧面边界约束, 采用修正平均自由程的方法计算边界散射对热导率的影响. 得到的模型能够预测纳米薄膜(法向和面向)及有限长度方形纳米线的热导率随相应特征尺寸的变化. 与蒙特卡罗模拟及硅纳米结构热导率实验值的对比验证了模型的正确性.     

热质的运动和传递——热子气的守恒方程和傅立叶定律

本文在热质和热子气概念的基础上建立了热子气的质量、动量、能量守恒方程.基于傅立叶导热定律求得了热子气粘性系数和粘性力的近似表达式.分析了傅立叶定律的物理意义:傅立叶定律是在忽略惯性力的条件下对热子气动量方程的近似.在极低温度或极高热流密度条件下傅立叶定律不再适用.     

The effect of the electron-phonon coupling on the thermal conductivity of silicon nanowires

The thermal conductivity of free-standing silicon nanowires (SiNWs) with diameters from 1-3?nm has been studied by using the one-dimensional Boltzmann's transport equation. Our model explicitly accounts for the Umklapp scattering process and electron-phonon coupling effects in the calculation of the phonon scattering rates. The role of the electron-phonon coupling in the heat transport is relatively small for large silicon nanowires. It is found that the effect of the electron-phonon coupling on the thermal conduction is enhanced as the diameter of the silicon nanowires decreases. Electrons in the conduction band scatter low-energy phonons effectively where surface modes dominate, resulting in a smaller thermal conductivity. Neglecting the electron-phonon coupling leads to overestimation of the thermal transport for ultra-thin SiNWs. The detailed study of the phonon density of states from the surface atoms and central atoms shows a better understanding of the nontrivial size dependence of the heat transport in silicon nanowire.     

热质的运动与传递——热质和热子气

基于爱因斯坦的狭义相对论的质能关系建立了热质的概念。物体的热能所对应的动质量就是热质。提出了热子的概念和热子气模型。采用气体分子动理论导得了热子气的压力(热质压力)和热子气的状态方程。热子气中的热质压力梯度是热量(热子气)运动的推动力。     

硅纳米薄膜中声子弹道扩散导热的蒙特卡罗模拟

通过建立声子散射概率函数描述声子在输运过程中的散射,提出了一种模拟声子弹道扩散导热的蒙特卡罗方法,并将其应用于硅纳米薄膜中的稳态和瞬态弹道扩散导热过程的研究. 提出的蒙特卡罗方法对边界发射的声子束进行跟踪,根据散射概率函数模拟声子束在传播区域内经历的散射过程,并通过统计声子束的分布得到温度分布. 稳态导热过程的模拟发现,尺寸效应会引起边界温度跳跃,其值随着Knudsen数的增大而增大;计算的硅纳米薄膜的热导率随着厚度的增大而增大,与文献中的实验数据和理论模型相符. 通过瞬态导热过程的模拟得到了纳米薄膜内的温度分布随时间的变化,发现瞬态导热过程中的热波现象与空间尺度相关,材料尺寸越小,弹道输运越强,薄膜中的热波现象也越显著. 关键词： 纳米薄膜 弹道扩散导热 蒙特卡罗模拟 尺寸效应     

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。     

Tuning Thermal Conductivity in Si Nanowires with Patterned Structures

Tuning the thermal conductivity of silicon nanowires(Si-NWs)is essential for realization of future thermoelectric devices.The corresponding management of thermal transport is strongly related to the scattering of phonons,which are the primary heat carriers in Si-NWs.Using the molecular dynamics method,we find that the scattering of phonons from internal body defects is stronger than that from surface structures in the low-porosity range.Based on our simulations,we propose the concept of an exponential decay in thermal conductivity with porosity,specifically in the low-porosity range.In contrast,the thermal conductivity of Si-NWs with a higher porosity approaches the amorphous limit,and is insensitive to specific phonon scattering processes.Our findings contribute to a better understanding of the tuning of thermal conductivity in Si-NWs by means of patterned nanostructures,and may provide valuable insights into the optimal design of one-dimensional thermoelectric materials.     

Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

热质的运动与传递-热子气状态方程

基于相对论原理,提出能量的运动可以产生压强．在热质概念的基础上,针对理想气体,根据分子动理论建立了热子气状态方程,从而得到理想气体分子的热运动动能压强的表达式．基于硬球势能模型通过分子动力学模拟验证了热子气状态方程的正确性．     

Computing Raman and infrared wavenumbers of nanostructures: application to silicon nanowires

The characterization of nanostructures with spectroscopic methods is a fundamental tool in nanoscience. For novel nanostructures, the interpretation of spectral features is a challenging task. To address this issue, we present the “Symmetry‐Filtered Molecular Dynamics (SFMD)” method to calculate Raman and infrared wavenumbers from molecular dynamics (MD) simulations, employing only the symmetry of the atomic structure. Explicit and expensive calculations of the electric polarizability or the dipole moment are not required. Therefore, our method can be easily used with any standard MD software. On the basis of the density functional tight‐binding method for the MD simulations, we apply our method to bulk silicon and small‐diameter hydrogen‐passivated silicon nanowires. For bulk silicon, we study the wavenumber shift of the Raman peak with temperature and obtain results that are in good agreement with experiments. We further show that thermal lattice expansion is a minor effect (22%) and that temperature‐driven anharmonic effects (78%) are the main contributions to that wavenumber shift. By analyzing the bond lengths of different silicon nanowires, we found that surface stress manifests as a 0.37% shortening of bonds only in the outermost silicon layer. We further analyzed the diameter‐dependent wavenumber shift of a Raman peak in silicon nanowires. We found that the main contribution to the wavenumber shift comes from the phonon confinement effect and surface stress leads to an additional shift of 9–22%. Our results indicate that our method is able to produce quantitative results that can be compared with experiments. We propose our method to be used for the understanding of Raman and infrared spectra of novel bulk and nanostructures. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑接触热阻的纳米颗粒堆积热导率的分析

本文首先使用Callaway热导率模型对SiO₂纳米颗粒的热导率进行了近似计算,然后耦合堆积纳米孔隙内的导热和辐射、颗粒接触热阻,基于颗粒堆积单元结构模型的一维传热分析,最终推导得到了颗粒堆积有效热导率关于颗粒直径和温度、堆积孔隙率、颗粒热导率、气相热导率、辐射传热和接触热阻的关系式,并用该式进行了相关讨论。研究结果表明,对于纳米颗粒堆积,界面接触热阻不容忽略;在低孔隙率和颗粒不参与辐射的条件下,由于受到接触热阻的影响,存在最佳孔隙率（或密度）使得堆积热导率存在最大值。     

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.     

Effect of electrostatics techniques on the estimation of thermal conductivity via equilibrium molecular dynamics simulation: application to methane hydrate

Equilibrium molecular dynamics (MD) simulations for three system sizes of fully occupied methane hydrate have been performed at around 265 K to estimate the thermal conductivity using the Ewald, Lekner, reaction field, shifted-force and undamped Fennell–Gezelter methods. The TIP4P water model was used in conjunction with a fully atomistic methane potential with which it had been parameterized from quantum simulation. The thermal conductivity was evaluated by integration of the heat flux autocorrelation function (ACF) derived from the Green–Kubo formalism; this approach vas validated by estimation of the average phonon mean free path. The thermal conductivities predicted by non-periodic techniques were in reasonable agreement with the experimental results of 0.62 and 0.68 W/m K, although it was found that the estimates by the non-periodic techniques were up to 25% larger than those of Lekner and Ewald estimates, particularly for larger systems. The results for the Lekner method exhibited the least variation with respect to system size. A decomposition of the heat flux vector into its respective contributions revealed the importance of electrostatic interactions, and how different electrostatic treatments affect the contribution to the thermal conductivity.