双壁碳纳米管电浸润现象的分子动力学模拟

在单壁碳纳米管电浸润现象原子模拟的基础上,对双壁碳纳米管的电浸润现象进行了计算机模拟.运用经典分子动力学方法结合一个宏观的电毛细管模型模拟了双壁碳纳米管在水银中的电浸润过程,对不同内管尺寸情况下的浸润现象作了研究和比较.计算结果表明双壁碳管和单壁碳管的电浸润过程存在很大的不同,双壁碳管的内管在电浸润过程中起到重要的作用：当改变双壁碳管中内管的尺寸时,浸润现象会产生很大的改变. 关键词： 双壁碳纳米管 电浸润 分子动力学     

模拟研究碳纳米管的热稳定性质

运用分子动力学方法具体模拟研究单个碳纳米管（CNTs）在加热过程中的结构变化．选择多组不同结构的单壁碳纳米管（SWCNTs）和双壁碳纳米管（DWCNTs）作为研究对象,加热温度从室温开始到4000 K,压强保持为1 atm．结果表明单壁碳管中手性型结构热稳定性最好,其次是扶手椅型和锯齿型,当手性角相同时,直径大的热稳定性更高;对于双壁碳管,研究表明当双壁中至少之一为手性结构时其热稳定好,而内外壁均为锯齿结构的稳定性最差,该结果进一步支持了有关单壁碳管的结论;还从理论上探索了描述结构热稳定性的方式,并在键层 关键词： 单壁碳纳米管 双壁碳纳米管 分子动力学方法 热稳定性能     

温度对单壁碳纳米管端口结构的影响

利用紧束缚势分子动力学模拟方法，研究了温度在2000—3500 K之间单壁碳纳米管端口结构的变化趋势.研究表明，温度对整个管端口结构起关键作用，计算表明温度在3000K和3500K下碳管两端口在15ps时间尺度内依次闭合，温度高易于使理想单壁碳管端口封闭，且端口封闭导致碳管系统能量的降低.由于Armchair型碳纳米管与相同半径的Zigzag型碳纳米管相比有相对低的应力能，导致Armchair型碳纳米管更易形成端口封闭的结构. 关键词： 碳纳米管 紧束缚势     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形，并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响；单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化，合理地选择碳纳米管的弹性模量和壁厚，有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时，有限元方法将会成为更加准确、快捷的数值模拟方法.     

单壁碳纳米管轴向压缩变形的研究

采用Tersoff-Brenner势函数描述碳纳米管中碳原子间的相互作用，通过分子动力学方法对不同螺旋型的单壁碳纳米管的轴向压缩变形行为进行了研究.研究发现单臂碳纳米管的杨氏模量低于锯齿形碳纳米管，根据微观结构特征的差异对这一结果进行了分析.同时从能量和结构变化两方面对碳纳米管受压失稳进行了分析，揭示出碳纳米管失稳的微观特征. 关键词： 纳米管 分子动力学 杨氏模量 屈曲     

轴向冲击载荷作用下双壁碳纳米管的动力屈曲

应用改进的有限元方法,建立考虑层间范德华力作用的壳-弹簧非线性有限元模型,基于B-R运动准则,系统地研究了双壁碳纳米管的动力屈曲问题,得到了轴向冲击载荷作用下双壁碳纳米管的临界动力屈曲载荷和临界动力失效载荷. 研究结果表明,在动力屈曲过程中,双壁碳纳米管层间距的变化非常小,各管的变形相互协调;碳纳米管中应力波的传播导致碳纳米管出现非对称屈曲模态,可明显观测到四个环向波瓣,沿着碳纳米管的轴线方向,四个波瓣的波峰和波谷交替变化. 对碳纳米管动力屈曲问题的研究表明,冲击载荷的大小和持续时间对碳纳米管的动力屈曲有 关键词： 碳纳米管 动力屈曲 冲击载荷     

单壁碳纳米管端口结构的热稳定性

利用紧束缚势分子动力学模拟方法,研究了温度在1000 K-3000 K之间单壁碳纳米管端口结构的变化趋势.计算表明,温度对整个管端口结构有重要影响,温度升高容易使理想单壁碳管端口封闭.温度在3000 K下碳管端口达到封闭,而且端口封闭导致碳管系统能量的降低.碳纳米管长度越长,端口封闭越快,且扶手型碳纳米管比锯齿型碳纳米管更容易形成端口封闭的结构.     

功能化单壁碳纳米管的热导率

采用基于BrennerⅡ势的非平衡态分子动力学方法，模拟研究了300K温度下经氢化学修饰的(10,0)单壁碳纳米管的热导率.研究显示功能化后碳管的热导率有明显减小，当有一列碳原子被氢化后（功能化程度为5%），碳管的热导率减小了大约1/3，为了进一步解释这种功能化对碳纳米管热导率的影响，计算了不同功能化程度下碳纳米管的声子谱.     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形,并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响;单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化,合理地选择碳纳米管的弹性模量和壁厚,有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时,有限元方法将会成为更加准确、快捷的数值模拟方法. 关键词： 单壁碳纳米管 非线性力学行为 有限元     

单壁碳纳米管受压屈曲行为的数值模拟

采用以Tersoff Brenner势函数来描述碳纳米管中碳原子间的相互作用的分子动力学方法,模拟了单壁 碳纳米管(SWCNTs)的受压屈曲行为.计算结果表明,单壁碳纳米管的杨氏模量随着管径的增大而减小;碳纳米 管屈曲的临界应力和临界应变与碳纳米管细长比有关,不同的细长比决定了碳纳米管结构不同的屈曲模态;碳纳 米管的受压屈曲机理和连续介质力学中柱体壳的受压屈曲理论随细长比的不同而存在一些异同.     

Double-walled carbon nanotube with surrounding elastic medium under axial pressure

In this paper, the buckling behavior and critical axial pressure of double-walled carbon nanotubes (DWCNTs) with surrounding elastic medium are investigated. A double-shell (circular cylindrical shell) model is presented and the effects of surrounding elastic medium on the outer tube and the van der Waals forces between two adjacent tubes are taken into account. The analysis and the numerical solution method are based on the classical theory of plates and shells and the Galerkin method. Equations are derived for the critical axial forces and pressures of DWCNTs; the critical axial forces and pressures are calculated for different axial half sine wavenumbers and circumferential sine wavenumbers and compared with those for single-walled carbon nanotubes (SWCNTs).Results indicate that the critical axial force of a DWCNT is higher than that of an SWCNT, but the critical axial pressure of a DWCNT is lower than the critical axial pressure of a SWCNT. Although the critical axial force of a DWCNT decreases as the axial half sine wavenumbers increase, it rises as the circumferential sine wavenumbers increase.     

Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

In the present work, nonlocal Euler–Bernoulli beam theory is used to investigate the wave propagation in zigzag double-walled carbon nanotube (DWCNT) embedded in an elastic medium. Winkler-type foundation model is employed to simulate the interaction of the DWCNT with the surrounding elastic medium. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is noticed in the presented study that the equivalent Young’s modulus for zigzag DWCNT is derived using an energy-equivalent model. Influences of nonlocal effects, the chirality of zigzag DWCNT, Winkler modulus parameter, and aspect ratio on the frequency of DWCNT are analyzed and discussed. The new features of the vibration behavior of zigzag DWCNTs embedded in an elastic medium and some meaningful results in this paper are helpful for the application and the design of nanostructures in which zigzag DWCNTs act as basic elements.     

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.     

Nonlinear dynamics of bi-layered graphene sheet,double-walled carbon nanotube and nanotube bundle

Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff–Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6–12 potential function. The equivalent nonlinear material model of carbon–carbon bond is used to model it based on its force–deflection relation. Newmark’s algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.     

Influence of Intertube Additional Atoms on Sliding Behaviors of Double-Walled Carbon Nanotube

The effects of intertube additional atoms on the sliding behaviors of double-walled carbon nanotubes (DWCNTs) are investigated using molecular dynamics (MD) simulation method. The interaction between carbon atoms is modeled using the second-generation reactive empirical bond-order potential coupled with the Lennard-Jones potential. The simulations indicate that intertube additional atoms of DWCNT can significantly enhance the load transfer between neighboring tubes of DWCNT. The improvement in load transfer is guaranteed by the addition of intertube atoms which are covalently bonded to the inner and outer tubes of DWCNT. The results also show that the sliding behaviors of DWCNT are strongly dependent of additional atom numbers. The results presented here demonstrate that the superior mechanical properties of DWCNT can be realized by controlling intertube coupling. The general conclusions derived from this work may be of importance in devising high-performance CNT composites.     

Influence of Intertube Additional Atoms on Sliding Behaviors of Double-Walled Carbon Nanotube

The effects of intertube additional atoms on the sliding behaviors of double-walled carbon nanotubes(DWCNTs) are investigated using molecular dynamics(MD) simulation method.The interaction between carbon atoms is modeled using the second-generation reactive empirical bond-order potential coupled with the Lennard-Jones potential.The simulations indicate that intertube additional atoms of DWCNT can significantly enhance the load transfer between neighboring tubes of DWCNT.The improvement in load transfer is guaranteed by the addition of intertube atoms which are covalently bonded to the inner and outer tubes of DWCNT.The results also show that the sliding behaviors of DWCNT are strongly dependent of additional atom numbers.The results presented here demonstrate that the superior mechanical properties of DWCNT can be realized by controlling intertube coupling.The general conclusions derived from this work may be of importance in devising high-performance CNT composites.     

Finite element simulation for estimating the mechanical properties of multi-walled carbon nanotubes

A finite element simulation technique for estimating the mechanical properties of multi-walled carbon nanotubes is developed. In the present modeling concept, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam elements, the beam element properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics. As to the simulation of the interlayer van der Waals force which has intrinsic nonlinearity and complicated applying region, a simplifying method is proposed that the interlayer pressure caused by van der Waals force instead of the force itself is to be considered, and we make use of the linear part of the interlayer pressure near the equilibrium condition to avoid the nonlinearity in problem, then linear spring elements whose stiffness is determined by equivalent force concept can be utilized to simulate the interlayer van der Waals force such that significant modeling and computing effort is saved in performing the finite element analysis. Numerical examples for estimating the mechanical properties of nanotubes, such as axial and radial Young’s modulus, shear modulus, natural frequency, buckling load, etc., are presented to illustrate the accuracy of this simulation technique. By comparing to the results found in the literature and the possible analytical solutions, it shows that the obtained mechanical properties of nanotubes by the present method agree well with their comparable results. In addition, the relations between these mechanical properties and the nanotube size are also discussed.     

Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model

This paper is concerned with the characteristics of wave propagation in double-walled carbon nanotubes (DWCNTs). The DWCNTs is simulated with a Timoshenko beam model based on the nonlocal continuum elasticity theory, referred to as an analytically nonlocal Timoshenko-beam (ANT) model. The governing equations of the DWCNTs beam consist of a set of four equations that are derived from the variational principle of the beam with high-order boundary conditions at the both ends, in which the effects of the nano-scale nonlocality and the van der Waals interaction between inner and outer tubes are inclusive. The characteristics of the wave propagation in the DWCNTs beam were analyzed with the new ANT model proposed and the comparisons with the partially nonlocal Timoshenko-beam (PNT) models in publication were made in details. The results show that the nonlocal effects of the ANT model proposed in the present study on the wave propagations are more significant because it is in stronger stiffness enhancement to the DWCNTs beam.     

Analytical approaches for vibration analysis of multi-walled carbon nanotubes modeled as multiple nonlocal Euler beams

This paper concerns with the effect of small scale on the vibrational characteristics of multi-walled carbon nanotubes (MWCNTs) modeled as multiple nonlocal Euler beams. In this model, each nanotube interacts with its neighbors through the van der Waals force. Analytical approaches are expressed to solve coupled governing equations of the motion. Results for double- and five-walled carbon nanotubes (DWCNTs and FWCNTs), as two specific examples of MWCNTs, are presented for various boundary conditions. Then, effect of small scale on the natural and intertube resonant frequencies and their associated amplitude ratios are discussed. Besides the effect of small scale, the effect of end conditions on the vibrational properties and a comparison between the methods are provided. Natural and intertube frequencies reduce with the introduction of nonlocal parameter. However, reduction of intertube frequencies is less than the natural frequencies. Moreover, it is provided that the effect of small scale stiffens the van der Waals force and causes MWCNTs to behave similar to a single beam in high values of nonlocal parameter. Also, this study reveals that in high mode numbers, natural frequencies of a multiple classical Euler beams system tend to frequencies of its constituent beams.     

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.