Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes

The measured drop of the effective bending stiffness of multiwalled carbon nanotubes (MWCNTs) with increasing diameter is investigated by a generalized local quasicontinuum method. The previous hypothesis that this reduction is due to a rippling mode is confirmed by the calculations. The observed ripples result from a complex three-dimensional deformation similar to the Yoshimura buckling pattern. It is found that thick MWCNTs exhibit a well-defined nonlinear moment-curvature relation, even for small deformations, governed by the interplay of strain energy relaxation and intertube interactions. Rippling deformations are also predicted for MWCNTs subject to torsion, resulting in an effective torsional modulus much smaller than that predicted by linear elasticity.     

空位结构缺陷对C纳米管弹性性质的影响

用分子动力学方法对不同空位缺陷的扶手椅型与锯齿型单壁C纳米管杨氏弹性模量进行了计算和分析. 结果表明：扶手椅型（5, 5）, （10,10）和锯齿型（9, 0）, （18, 0） 纳米管在无缺陷时其杨氏模量分别为948,901和804,860 GPa. 随管径的增大,扶手椅型和锯齿型单壁C纳米管弹性模量分别减小和增大,表现出完全不同的变化规律. 随着C纳米管中单点空位缺陷的均匀增加,杨氏模量下降,当缺陷比率增加到一定程度时,杨氏模量下降骤然趋缓,形成一下降平台;双空位缺陷对C纳米管杨氏模量的影响与其分布方向有关;随单点空位缺陷间原子数的增加,在轴向上,杨氏模量下降到某一值小幅波动,而在周向上杨氏模量先下降,然后上升到某一稳定值. 随两单点空位缺陷的空间距离进一步增大,杨氏模量又呈微降趋势. 通过分子间σ键与π键特征及缺陷间近程电子云耦合作用规律与空位缺陷内部5-1DB缺陷的形成特点等理论对上述规律进行了分析. 关键词： 空位缺陷 C纳米管 分子动力学 杨氏模量     

单壁纳米管的弹性性质

基于第一性原理计算了一系列单壁碳纳米管(椅型、锯齿型)和氮化硼锯齿型纳米管的杨氏模量.用实际的数值结果显示了杨氏模量与纳米管管径之间的依赖关系.还讨论了各类纳米管卷曲形变能以及平衡基矢长度a随管型的变化. 关键词： 单壁纳米管 平衡基矢长度 杨氏模量 形变能     

单壁碳纳米管杨氏模量的掺杂效应

用分子动力学方法研究了N,O,Si,P,S等5种杂质对扶手椅型(5，5)和锯齿型(9，0)单壁碳纳米管杨氏模量的影响.结果表明：直径为0.678和0.704 nm的扶手椅型(5，5)和锯齿型(9，0)碳纳米管在无掺杂时其杨氏模量分别为948和804 GPa.在掺杂浓度10％以下，碳纳米管的拉伸杨氏模量均随掺杂浓度增加近似呈线性下降规律，下降率以Si掺杂最大，N掺杂最小.对与C同周期的元素掺杂，随原子序数增加碳纳米管的杨氏模量下降率增大；与C不同周期的元素掺杂，碳纳米管的杨氏模量随掺杂浓度增加下降率更大，但 关键词： 碳纳米管 杂质 杨氏模量 分子动力学方法     

Transverse elasticity of multi-walled carbon nanotubes

A discrete shell model is proposed to describe the radial deformation of carbon nanotubes under a hydrostatic pressure and the radial Young's modulus of (single- or multi-walled) nanotubes is obtained. It is found that the radial modulus decreases with increasing tube diameter while increases with increasing number of layers. The computational results agree well with the previous results of SWNTs and indicate that the radial modulus of carbon nanotubes is independent of the Poisson's ratio.     

TiO2纳米管的力学和电子学性质

基于密度泛函理论研究了纤铁矿和锐钛矿型TiO₂纳米管的原子结构、稳定性、Young模量以及电子能带结构.计算结果显示：在纳米管直径较小时,锐钛矿型TiO₂纳米管的稳定性要好于纤铁矿型纳米管,随着管径的增大,纤铁矿型纳米管变得比锐钛矿型纳米管要更稳定.纤铁矿型TiO₂纳米管具有比锐钛矿型纳米管更大的Young模量,力学性能比较优异.另外,通过对电子能带结构的研究发现,手性对TiO₂纳米管的电子结构影响较大,纤铁矿（0,n）型和锐钛矿（n,0）型纳米管为间接带隙半导体,而纤铁矿（n,0）型和锐钛矿（0,n）型纳米管却具有直接带隙. 关键词： 2纳米管')" href="#">TiO₂纳米管 Young模量 间接带隙 直接带隙     

Effects of temperature and vacancy defects on tensile deformation of single-walled carbon nanotubes

This study adopts the Tersoff-Brenner interaction potential function in a series of molecular dynamic (MD) simulations which investigate the mechanical properties under tensile loading of (10,0) zigzag, (8,3) chiral and (6,6) armchair single-walled carbon nanotubes (SWCNTs) of similar radii. The Young's modulus values of the (10,0), (8,3) and (6,6) nanotubes are determined to be approximately 0.92, 0.95, and 1.03 TPa, respectively. Of these nanotubes, the results reveal that the (6,6) nanotube possesses the best tensile strength and toughness properties under tension. Although it is noted that under small tensions, the mechanical properties such as Young's modulus are essentially insensitive to helicity, under larger plastic deformations, they may be influenced by helicity effects. Finally, the simulations demonstrate that the values of the majority of the considered mechanical properties decrease with increasing temperature and increasing vacancy percentage.     

Effect of ending surface on energy and Young's modulus of single-walled carbon nanotubes studied using linear scaling quantum mechanical method

By using a linear scaling self-consistent charge, density functional tight-binding (SCC-DFTB) method and an ab intio Dmol3 calculation, the energy and Young's modulus as a function of tube length for (10, 0) single-walled carbon nanotubes (SWCNTs) are investigated. It was found that with increasing the length of SWCNTs the Young's modulus increases rapidly, then, there is a slow increase, which ultimately approaches a constant value after the length is increased to ~20 nm, whereas a reversed variation tendency was found for the average energy of atoms in SWCNTs with a change of the tube length. We found that the characters of the length-dependent energy and Young's modulus stem from the changed P_y-DOS of atoms in the ending region of the tube. Here one simple formula is proposed for quantitatively explaining the length-dependent energy and modulus.     

单壁碳纳米管弹性性质的羟基接枝效应

用分子动力学方法研究了端口接枝不同数量羟基对扶手椅型和锯齿型单壁碳纳米管弹性模量的影响.结果表明,未接枝的扶手椅型(5, 5),(10,10)管和锯齿型(9, 0),(18, 0)管杨氏模量分别为948,901和804,860GPa.在接枝2—8个羟基情况下,锯齿型单壁碳纳米管拉伸杨氏模量基本不随接枝数量增加发生变化,而扶手椅单壁碳纳米管则不同,接枝状态下的弹性模量比未接枝状态小很多,但接枝一定数量后,其杨氏模量又略增到某一稳定值.分别从接枝后碳纳米管变形电子密度等值线结构、C—C键长和系统结合能变化规律等方面,对单壁碳纳米管弹性模量的接枝效应进行了分析. 关键词： 碳纳米管 羟基 接枝效应 杨氏模量     

多壁碳纳米管弯曲导致的扭转

文章介绍了多壁碳纳米管弯曲的分子动力学模拟,从原子尺度上解释了由于屈曲失稳而导致的起皱现象,并发现多壁碳纳米管弯曲时会呈现出非线性的力学响应。同时,在模拟过程中,观察到了弯曲诱发扭转的现象,并揭示出扭转变形的内在起因是曲率诱导的晶格错配。     

Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

提出了一种纳米尺度的有限元方法,碳纳米管中的碳-碳化学键被模拟为键单元．按照平衡关系,根据有限元理论,作用于每个碳原子上的作用力可以写成键单元的刚度矩阵与每个碳原子位移的乘积．在分子力学的基本假设下,键单元刚度矩阵的每个元素可以写为分子力学中力场常数的函数,这样建立起了宏观力学方法(有限元)与纳米尺度力学方法(分子力学)之间的联系．应用该方法模拟了扶椅型与锯齿型单壁碳纳米管的力学行为从而验证了该方法的有效性．分析结果说明单壁碳纳米管的弹性模量与管厚度的选取直接相关．此外,弹性模量对所选取的分子力学中的力场常数非常敏感,管的弹性模量显示出对半径的尺度依赖性,但是管长度对弹性模量的影响小到可以被忽略．     

一种用于碳纳米管模拟的分子结构力学方法

提出一种基于分子力学的分子结构力学方法,该方法用分子力学中的力场势能函数表述系统的势能,从能量原理出发,在小变形假设的基础上建立系统方程．基于此方法,模拟了单壁碳纳米管的拉伸特性,得到碳纳米管弹性模量的尺度依赖性关系．在碳纳米管的弯曲分析中,将计算结果和材料力学中的理论结果进行了比较,发现随着碳纳米管半径的增大,计算结果与理论值趋于一致．     

氢对纯镍弹性模量的影响

用静电激发调频检测法对比测量了纯镍试样电解充氢和人为部分应力松弛后在室温时效过程中杨氏模量随时间的变化。结果表明:在人为部分应力松弛后的时效过程中,杨氏模量逐渐升高,其稳态值比初始值升高0.87％;而在充氢后的时效过程中,氢不断地从试样中逸出,同时杨氏模量也不断地降低,其稳态值比充氢后的瞬时值低2.87％;即,氢原子能明显地增高纯镍的弹性模量。 关键词：     

Processing dependence of Young's modulus of Ti-base nanostructured alloys

The cooling rate and heat treatment dependence of Young's modulus for Ti-base multicomponent nanostructure-dendrite composites exhibits a very different response compared with the monolithic nanostructured or normal grain-sized Ti alloys. With increasing cooling rate, the decrease in the volume fraction of the micrometer-sized β-phase dendrites induces a significant increase in Young's modulus for most of these composites. This increase can cover the decrease in Young's modulus induced by the reduction of grain size of the nanostructured matrix. Heat treatment induces a significant increase in Young's modulus due to the precipitation of intermetallics and/or α-phase in the nanostructured matrix.     

Mechanical properties of nanotubes of polyelectrolyte multilayers

The elastic properties of nanotubes fabricated by layer-by-layer (LbL) assembly of polyelectrolytes in the nanopores of polycarbonate track-etched membranes have been investigated by resonant contact Atomic Force Microscopy (AFM), for nanotube diameters in the range of 100 to 200 nm. The elastic modulus of the nanotubes was computed from the resonance frequencies of a cantilever resting on freely suspended LbL nanotubes. An average value of 115 MPa was found in air for Young's modulus of these nanostructures, well below the values reported for dry, flat multilayers, but in the range of values reported for water-swollen flat multilayers. These low values are most probably due to the lower degree of ionic cross-linking of LbL nanotubes and their consequently higher water content in air, resulting from the peculiar mode of growth of nanoconfined polyelectrolyte multilayers.     

Mechanical Properties of Single-Walled （5,5） Carbon Nanotubes with Vacancy Defects

First-principles simulation is used to investigate the structural and mechanical properties of vacancy defective single-walled （5,5） carbon nanotubes. The relations of the defect concentration, distribution and characteristic of defects to Young＇s modulus of nanotubes are quantitatively studied. It is found that each dangling-bond structure （per supercell） decreases Young＇s modulus of nanotube by 6.1% for symmetrical distribution cases. However the concentrative vacancy structure with saturated atoms has less influence on carbon nanotubes. It is suggested that the mechanical properties of carbon nanotubes depend strongly upon the structure and relative position of vacancies in a certain defect concentration.     

基于第一性原理研究单壁碳纳米管的力学性质

用基于第一性原理的Crysta103软件中的Hartree-Fock近似和密度泛函与Hartree-Fock混合近似两种方法计算一系列碳纳米管的杨氏模量,对两种近似方法的计算结果进行比较.Hatree-Fock近似计算的杨氏模量与实验和其它理论结果符合较好;密度泛函和Hartree-Fock混合近似计算的杨氏模量偏小,...     

Elastic properties of SWCNTs with curved morphology: Density functional tight binding based treatment

The self-consistent charge density functional based tight-binding method is used to calculate the effect of curvature on the structure, average energy of atoms and Young's modulus of armchair single-wall carbon nanotubes (SWCNTs) under axial strains. We found that as the amount of curvature increases, the average energy of atoms and the Young's modulus decrease and the equilibrium CC distance increases for (7,7) SWCNTs. However, we also found that the average energy of atoms and Young's modulus of (5,5) SWCNTs are weakly affected by increasing the amount of curvature. Our results also show that the average energy of atoms and Young's modulus of smaller diameter armchair nanotubes are smaller than that of the larger diameter ones.     

Mechanical properties of nickel-coated single-walled carbon nanotubes and their embedded gold matrix composites

The effects of nickel coating on the mechanical behaviors of armchair single-walled carbon nanotubes (SWCNTs) and their embedded gold matrix composites under axial tension are investigated using molecular dynamics (MD) simulation method. The results show that the Young's moduli and tensile strength of SWCNTs obviously decrease after nickel coating. For armchair SWCNTs, the decreased ratio of the Young's moduli of SWCNTs with smaller radius is larger than that of SWCNTs with larger radius. A comparison is made between the response to Young's modulus of a composite with parallel embedded nanotube and the response of a composite with vertically embedded nanotube. The results show that the uncoated SWCNT can enhance the Young's modulus of composite under the condition of parallel embedment, but such improvement disappears under the condition of vertical embedment because the interaction between SWCNT and gold matrix is too weak for effective load transfer. However, the nickel-coated SWCNT can indeed significantly improve the composite behavior.     

Bending induced rippling and twisting of multiwalled carbon nanotubes

We report that a twisting deformation mode emerges with the rippling in bent multiwalled carbon nanotubes via atomistic simulations. This mode arises from the curvature-induced lattice mismatch, and is energetically favorable. For the nanotubes with larger radii, twisting may enhance the local strain relaxation. Under the thermal fluctuation, the nucleation of defects involves bond breaking and reconstruction due to strain localization. The defective inner tubes undergo the cyclic torsion, resulting in unstable necking and even failure. Prior to fracture, a monatomic chain is formed under the combination of bending and twisting.