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.     

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     

单、双原子空位缺陷对扶手椅型单层碳纳米管屈曲性能的不同影响

采用分子动力学方法,对完善和含缺陷扶手椅型单层碳纳米管进行轴向压缩的数值模拟,对比研究三种不同的温度环境下单、双原子空位缺陷对碳纳米管轴压变形性能的特殊影响.研究结果表明管壁缺陷显著降低了纳米管低温时的承载能力,由于单原子空位缺陷造成的特殊应力集中效应会引发纳米管过早发生局部屈曲,单原子缺陷管的屈曲强度反而小于双原子管的屈曲强度. 关键词： 分子动力学 碳纳米管 屈曲 缺陷     

单壁氮化硼纳米管压缩特性的分子动力学模拟

采用分子动力学方法,分别模拟完好的和含有缺陷的(7,7)扶手椅型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.为验证结果的可靠性,同时针对(7,7)扶手椅型碳纳米管进行对比计算.结果表明,氮化硼纳米管的压缩失效模式同碳纳米管相同,均表现为管壁的局部屈曲.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.     

电子束诱导单壁碳纳米管不稳定的新观察

利用透射电镜在室温下对不同形态的单壁碳纳米管进行了原位电子束辐照研究.研究发现:在相同的辐照条件下随着辐照时间(或辐照剂量)的增加,两端固定的单壁碳纳米管径向收缩,且收缩速率越来越快;相同直径的轴向弯曲的单壁碳纳米管比平直的单壁碳纳米管更加不稳定;一端固定另端自由的单壁碳纳米管轴向收缩,但其直径基本不变.利用单壁碳纳米管纳米曲率效应和能量束诱导非热激活效应,对上述单壁碳纳米管不稳定性现象进行了新的、合理的解释.     

范德华力对双壁碳纳米管轴向压缩屈曲行为的影响

使用分子动力学方法研究几种不同半径尺寸的单壁碳纳米管组成的双壁碳管，预测了其初始稳定构型；分析了其自由弛豫阶段的特征；并模拟了它们在轴向压缩载荷作用下的屈曲行为；研究了不同层间距导致的范德华力变化对屈曲行为的影响.采用Tersoff-Brenner势描述单壁碳纳米管内原子间作用，Lennard-Jones势描述内外层间的范德华相互作用.计算结果表明：在通常意义下的双壁管间距(约0.34 nm)外还可以存在稳定的双壁碳管构型，并且这些新的稳定构型表现出了不同的力学性质. 关键词： 双壁碳纳米管 分子动力学 屈曲     

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.     

表面官能化碳纳米管^13C NMR参数的理论研究

碳纳米管表面化学修饰是当前研究的一大热点,修饰后由于极性基团的存在,碳纳米管在极性溶液环境中的分散度得到明显改善,这在很大程度上扩展了纳米管研究的应用范围.本文采用C80H20模型来表示(10,0)碳纳米管,基于此模型计算了一系列氮烯、卡宾和氟化的单壁纳米管的结构、偶极矩,以及核磁共振参数.研究表明高精度的密度泛函理论(DFT)计算能够用来预测纳米管的13C化学位移,理论研究的结果揭示了氮烯、卡宾以及1,2和1,4氟化的单壁纳米管的若干13C信号特征化学位移值,为实验NMR谱图的归属提供了一定的依据,并且可通过与实验相结合来监测表面官能化碳纳米管加成反应是否发生以及确认其加成方式.     

单壁碳纳米扶手椅、锯齿管声子色散关系的计算

引用石墨经验力常数计算碳纳米管声子色散关系时，必须处理由二维平面卷曲形成三维实体纳米管所引入的问题. 报道对一系列扶手椅和锯齿单壁碳纳米管计及卷曲效应的声子色散关系的计算结果. 基于实际的数值计算结果，以及对单壁碳纳米扶手椅、锯齿管结构的对称性分析，讨论了Brillouin区中心Γ点晶格振动模的分类. 关键词： 碳纳米管 声子色散关系     

表面官能化碳纳米管13C NMR参数的理论研究

碳纳米管表面化学修饰是当前研究的一大热点,修饰后由于极性基团的存在,碳纳米管在极性溶液环境中的分散度得到明显改善,这在很大程度上扩展了纳米管研究的应用范围. 本文采用C₈₀ H₂₀模型来表示（10,0）碳纳米管,基于此模型计算了一系列氮烯、卡宾和氟化的单壁纳米管的结构、偶极矩,以及核磁共振参数. 研究表明高精度的密度泛函理论（DFT）计算能够用来预测纳米管的¹³C化学位移,理论研究的结果揭示了氮烯、卡宾以及1,2和1,4氟化的单壁纳米管的若干¹³C信号特征化学位移值,为实验NMR谱图的归属提供了一定的依据,并且可通过与实验相结合来监测表面官能化碳纳米管加成反应是否发生以及确认其加成方式.     

Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure

A nonlocal multiple-shell model is developed for the elastic buckling of multi-walled carbon nanotubes under uniform external radial pressure on the basis of theory of nonlocal elasticity. The effect of small length scale is incorporated in the formulation. An explicit expression is derived for the critical buckling pressure for a double-walled carbon nanotube. The influence of the small length scale on the buckling pressure is examined. It is concluded that the critical buckling pressure for a carbon nanotube could be overestimated by the classic (local) shell model due to ignoring the effect of small length scale.     

热力耦合作用下双层碳纳米管的扭转屈曲

考虑碳纳米管周边弹性介质和层间范德瓦耳斯力的作用,利用连续介质力学的壳体理论,建立了热力耦合作用下碳纳米管屈曲问题的控制方程,给出了相应的临界屈曲扭矩的解析解.数值模拟结果表明,在低温和室温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而提高;在高温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而降低. 关键词： 碳纳米管 屈曲 热力耦合     

Influence of temperature change on column buckling of multiwalled carbon nanotubes

Based on theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. In this model, each of the nested concentric tubes is regarded as an individual column and the deflection of all the columns is coupled together through the van der Waals interactions between adjacent tubes. The thermal effect is incorporated in the formulation. Following this model, an explicit expression is derived for the critical buckling strain for a double-walled carbon nanotube. The influence of temperature change on the buckling strain is investigated. It is concluded that the effect of temperature change on the buckling strain is dependent on the temperature changes, the aspect ratios, and the buckling modes of carbon nanotubes.     

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.     

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.     

Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition

The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable s...     

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.     

Scale effects on thermal buckling properties of carbon nanotube

In this Letter, the thermal buckling properties of carbon nanotube with small scale effects are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equation is derived and the nondimensional critical buckling temperature is presented. The influences of the scale coefficients, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia are discussed. It can be observed that the small scale effects are significant and should be considered for thermal analysis of carbon nanotube. The nondimensional critical buckling temperature becomes higher with the ratio of length to diameter increasing. Furthermore, for smaller ratios of the length to the diameter and higher mode numbers, the transverse shear deformation and rotary inertia have remarkable influences on the thermal buckling behaviors.     

Prediction of compressive post-buckling behavior of single-walled carbon nanotubes in thermal environments

In the present investigation, the axial buckling and post-buckling configurations of single-walled carbon nanotubes (SWCNTs) are studied including the thermal environment effect. For this purpose, Eringen’s nonlocal elasticity continuum theory is implemented into the classical Euler–Bernoulli beam theory to represent the SWCNTs as a nonlocal elastic beam model. A closed-form analytical solution is carried out to analyze the static response of SWCNTs in their post-buckling state in which the axial buckling load is assumed to be beyond the critical axial buckling load. Common sets of boundary conditions, named simply supported–simply supported (SS–SS), clamped–clamped (C–C), and clamped–simply supported (C–SS), are considered in the investigation. Selected numerical results are given to represent the variation of the carbon nanotube’s mid-span deflection with the applied axial load corresponding to various nonlocal parameters, length-to-diameter aspect ratios, temperature changes, and end supports. Moreover, a comparison between the post-buckling behaviors of SWCNTs at low- and high-temperature environments is presented. It is found that the size effect leads to a decrease of the axial buckling load especially for SWCNTs with C–C boundary conditions. Also, it is revealed that the value of the temperature change plays different roles in the post-buckling response of SWCNTs at low- and high-temperature environments.