Molecular dynamic investigation of mechanical properties of armchair and zigzag double-walled carbon nanotubes under various loading conditions

Using molecular dynamic simulation (MDS), effects of chirality and Van der Waals interaction on Young's modulus, elastic compressive modulus, bending, tensile, and compressive stiffness, and critical axial force of double-walled carbon nanotube (DWCNT) and its inner and outer tubes are considered. Achieving the highest safety factor, mechanical properties have been investigated under applied load on both inner and outer tubes simultaneously and on each one of them separately. Results indicate that as a compressive element, DWCNT is more beneficial than single-walled carbon nanotube (SWCNT) since it carries two times higher compression before buckling. Except critical axial pressure and tensile stiffness, in other parameters zigzag DWCNT shows higher amounts than armchair type. Outer tube has lower strength than inner tube; therefore, most reliable design of nanostructures can be attained if the mechanical properties of outer tube taken as the properties of DWCNT.     

Effects of Radius and Orientation of Single-Walled Carbon Nanotubes on Their Nonlinear Tensile Deformation Behaviour

By capturing the atomic information and reflecting the behaviour governed by a nonlinear potential function, an analytical molecular mechanics approach is applied to establish the constitutive relation for single-walled carbon nanotubes （SWCNTs）. The nonlinear tensile deformation curves of zigzag and armchair nanotubes with different radii are predicted, and the elastic properties of these SWCNTs are obtained. A conclusion is made that the nanotube radius has little effect on the mechanical behaviour of SWCNTs subject to simple tension, while the nanotube orientation has larger influence.     

结构和变形对单壁碳纳米管力学性能的影响

使用分子动力学方法模拟了单壁碳纳米管的拉伸变形行为和泊松比,并从单壁碳纳米管晶胞单元的结构特征角度,系统分析了管径、螺旋性和应变对力学性能的影响．模拟结果显示,单臂性碳纳米管(8,8)-(22,22)和锯齿性碳纳米管(9,0)-(29,0)的拉伸弹性变形可以分别达到35％-38％和20％-27％,拉伸条件下这些碳纳米管的弹性模量随管径的增大从960 GPa下降到750 GPa,并且锯齿性碳纳米管的弹性模量比单臂性碳纳米管的弹性模量要高．通过对三根具有相同直径和不同螺旋性的碳纳米管(9,9),(12,6)和(16,0)分别在拉伸和压缩条件下的模拟发现,随着变形的增大,碳纳米管的泊松比将减小;在相同的拉伸应变下,碳纳米管的泊松比随其螺旋角的减小而减小,而在相同的压缩应变下,碳纳米管的泊松比随其螺旋角的减小而增大．     

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.     

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.     

轴压和扭转复合载荷作用下氮化硼纳米管屈曲行为的分子动力学模拟

采用分子动力学方法模拟了氮化硼纳米管在轴压和扭转复合荷载作用下的屈曲和后屈曲行为.在各加载比例下,给出了初始线性变形阶段和后屈曲阶段原子间相互作用力的变化,确定了屈曲临界荷载关系.通过对屈曲模态的细致研究,从微观变形机理上分析了纳米管对不同外荷载力学响应的差异.研究结果表明,扶手型和锯齿型纳米管均呈现出非线性的屈曲临界荷载关系,复合加载下的屈曲行为具有强烈的尺寸依赖性.温度升高将导致屈曲临界荷载的下降,且温度的影响随加载比例的变化而变化.无论在简单加载或复合加载中,同尺寸的碳纳米管均比氮化硼纳米管具有更强地抵抗屈曲荷载的能力.     

Derivation of a universal estimate for the stiffness of carbon nanotubes

An algorithm has been developed based on numerical simulation to relate physical geometry to the Young’s modulus of symmetric and asymmetric single-walled carbon nanotubes (SWCNTs). A large number of finite element results for the stiffness of SWCNTs has been categorized into three main classes (i.e., armchair, zigzag and chiral) and the best curve fitting function has been obtained to describe the relation between the geometry of SWCNTs and their stiffness. For two standard configurations of carbon nanotubes (i.e., armchair and zigzag), four equations referring to geometry parameters (n, m) and diameter (d) have been introduced. To find the size dependence of asymmetric nanotubes, three-dimensional surfaces of stiffness (E(n, m)) have been used. However, since the stiffness of asymmetric nanotubes depends upon n and m, it was impossible to define any diameter dependency. To account for the hidden mechanical behavior of asymmetric SWCNTs, a new physical factor (CF) was introduced as the major novelty in this work. The proposed CF converts any asymmetric geometry (n, m) into a value between 0 and 1. The CF for a chiral nanotube can imply the percentage of similarity in its mechanical properties to the two standard symmetric configurations. Based on the CF concept, a new equation is derived to predict the Young’s modulus of asymmetric carbon nanotubes based on the symmetric prediction of standard models. The new physical factor (CF) which is developed in this study can be useful for the characterization of SWCNTs and the selection of all configurations.     

温度、应变率和空位缺陷对氮化硼纳米管压缩性能的影响

采用分子动力学方法,分别模拟了完好的和含有缺陷的氮化硼纳米管的轴向压缩过程。原子间的相互作用采用Tersoff多体势函数来描述。结果表明,同尺寸的锯齿型氮化硼纳米管的临界轴向压缩强度高于扶手型氮化硼纳米管,这与碳纳米管的研究结果一致。发现纳米管的压缩强度,如临界轴向内力在低温下受温度影响明显,并且和应变率的大小有关。然而,应变率对纳米管的弹性变形没有影响。另外,还发现空位缺陷降低了纳米管的力学性能。与完好的纳米管相比,含有缺陷的纳米管轴向压缩强度对于温度的影响并不敏感。     

Effects of carbon nanotube structures on mechanical properties

This paper describes a structural mechanics approach to modelling the mechanical properties of carbon nanotubes (CNTs). Based on a model of truss structures linked by inter-atomic potentials, a closed-form elastic solution is obtained to predict the mechanical properties of single-walled carbon nanotubes (SWNTs). Moreover, the elastic modulus of multi-walled carbon nanotubes (MWNTs) is also predicted for a group of the above mentioned SWNTs with uniform interval spacing. Following the structural mechanics approach, the elastic modulus, Poissons ratio, and the deformation behaviors of SWNTs were investigated as a function of the nanotube size and structure. Poissons ratio of SWNTs shows a chirality dependence, while the elastic modulus is insensitive to the chirality. The disposition of the strain energy of bonds shows quite a difference between the zigzag and armchair tubes subjected to axial loading. A zigzag tube is predicted to have a lower elongation property than an armchair tube. PACS 62.20-x; 62.20.Dc; 62.25+g     

(n,n)-(2n, 0)碳纳米管异质结的扭转力学特性

相近直径的锯齿型和扶手椅型碳纳米管可以共轴组合形成5-7碳环交替出现的柱形对称异质结. 本文利用分子动力学方法研究了直径相近且等长锯齿型和扶手椅型碳纳米管形成的(n, n)-(2n, 0)结在扭转过程中的扭矩和轴向应力随扭转角度的变化规律以及应力传递过程. 研究发现, (n, n)-(2n, 0)结扭转应变在达弹性限度内不会产生轴向应力, 该效应对基于碳纳米管扭转特性的纳米振荡器件的设计具有重要意义.     

Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

Eringen's nonlocality is incorporated into the shell theory to include the small-scale effects on the axial buckling of single-walled carbon nanotubes (SWCNTs) with arbitrary boundary conditions. To this end, the Rayleigh-Ritz solution technique is implemented in conjunction with the set of beam functions as modal displacement functions. Then, molecular dynamics simulations are employed to obtain the critical buckling loads of armchair and zigzag SWCNTs, the results of which are matched with those of nonlocal shell model to extract the appropriate values of nonlocal parameter. It is found that in contrast to the chirality, boundary conditions have a considerable influence on the proper values of nonlocal parameter.     

Electromechanical buckling analysis of boron nitride nanotube using molecular dynamic simulation

In this paper, the effect of electric field on axial buckling of boron nitride nanotubes is investigated. For this purpose, molecular dynamics simulation and continuum mechanics are used for the first time simultaneously. In molecular dynamics simulation, the potential between boron nitride atoms is considered as Tersoff and Timoshenko beam theory is used in continuum mechanics. In this paper, buckling of zigzag and armchair boron nitride nanotubes are investigated. Here, the effects of the electric field and the length of the boron nitride nanotube on the critical load are investigated and it is shown that the effect of the electric field is different with respect to the arrangement of atoms in the boron nitride nanotubes. In fact, the electric field creates axial and torsional loads on the zigzag and armchair nanotube, respectively. Axial buckling of the zigzag nanotube is dependent on the electric field, whereas in the armchair nanotubes, the electric field changes have no effect on the axial buckling. To better understand the impact of the electric field on axial buckling, these results are compared with the continuum mechanics.     

Structure,Electronic, and Mechanical Properties of Three Fully Hydrogenation h-BN:Theoretical Investigations

The structural, electronic, elastic, mechanical properties and stress-strain relationship of chair, boat, and stirrup conformers of fully hydrogenated h-BN(fh-BN) are investigated in this work using the Perdew-Burke-Ernzerhof(PBE) function in the frame of density functional theory. The achieved results for the lattice parameters and band gaps of three conformers in this research are in good accordance with other theoretical results. The band structures of three conformers show that the chair, boat, and stirrup are direct band gap with a band gaps of(3.12, 4.95, and4.95 e V), respectively. To regulate the band structures of fh-BN, we employ a hybrid functional of Heyd-ScuseriaErnzerhof(HSE06) calculations and the band gaps are 3.84(chair), 6.12(boat), and 6.18 e V(stirrup), respectively.The boat and stirrup fh-BN exhibits varying degrees of mechanical anisotropic properties with respect to the Young's modulus and Poisson's ratio, while the chair fh-BN exhibits the mechanical isotropic properties. Furthermore, tensile strains are applied in the armchair and zigzag directions related to tensile deformation of zigzag and armchair nanotubes,respectively. We find that the ultimate strains in zigzag and armchair deformations in stirrup conformer are 0.34 and0.25, respectively, larger than the strains of zigzag(0.29) and armchair(0.18) deformations in h-BN although h-BN can surstain a surface tension up to the maximum stresses higher than those of three conformers of fh-BN. Furthermore, the band gap energies in three conformers can be modulated effectively with the biaxial tensile strain.     

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     

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     

A computational prediction of total carbo-merization on single-walled carbon nanotubes

The total carbo-mer of single-walled carbon nanotubes (C-SWCNTs) are constructed by inserting two sp carbon atoms into each C-C bond in pristine single-walled carbon nanotubes (SWCNTs). The geometric, mechanical and electronic properties for these novel structures are investigated by self-consistent-field crystal calculations. The calculated zigzag and chiral C-SWCNTs are all small gap semiconductors, whereas the metallic property is still kept in the armchair C-SWCNT. The calculated Young's moduli of C-SWCNTs are smaller than those of SWCNTs. Our calculations show that the zigzag C-SWCNTs have higher mobility than the corresponding SWCNTs. Moreover, the calculated mobility of the C-SWCNTs has a periodic change with the change of the tube diameters.     

Studying the buckling and vibration characteristics of single-walled zinc oxide nanotubes using a nanoscale finite element model

The free vibration and axial buckling of achiral zinc oxide nanotubes (ZnONTs) are studied in this paper based on a three-dimensional finite-element model in which bonds are modeled using beam elements and mass elements are placed at the joints of beams instead of atoms. To determine the mechanical properties of the nanotubes, a linkage is established between molecular mechanics and density functional theory. The fundamental frequency and critical buckling load of ZnONTs with different geometries, chiralities and boundary conditions are calculated. It is shown that zigzag nanotubes are more stable than armchair ones. Investigating the effect of aspect ratio on the critical force shows that longer nanotubes are less stable. Also, it is indicated that increasing the length of the nanotubes will result in decreasing the frequency. Moreover, as the aspect ratio increases, the effect of end conditions diminishes.     

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.