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     

基于非局部弹性理论的单壁碳纳米管轴向受压屈曲研究

基于非局部弹性理论，在考虑小尺度效应影响的情况下，建立了单壁碳纳米管在均匀轴向外 部压力下的壳体模型. 得到了单壁碳纳米管的轴向受压屈曲的临界条件，验证了小尺度效应 对纳米管轴向受压屈曲的影响. 经典的壳体模型理论由于没有考虑小尺度效应影响而导致碳 纳米管轴向屈曲临界压力值偏高. 关键词： 非局部弹性理论 碳钠米管 小尺度效应 轴向受压     

Nonlinear structural mechanics based modeling of carbon nanotube deformation

A nonlinear structural mechanics based approach for modeling the structure and the deformation of single-wall and multiwall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell finite elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The effects of van der Waals forces are simulated with special interaction elements. This new CNT modeling approach is verified by comparison with molecular dynamics simulations and high-resolution micrographs available in the literature. The mechanics of wrinkling of multiwall CNTs are studied, demonstrating the role of the multiwalled shell structure and interwall van der Waals interactions in governing buckling and postbuckling behavior.     

Closed-form internal impedance model and characterization of mixed carbon nanotube bundles for three-dimensional integrated circuits

Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube(CNT) bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles.The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover,by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.     

Vibration and buckling of a double-beam system under compressive axial loading

On the basis of the Bernoulli–Euler beam theory, the properties of free transverse vibration and buckling of a double-beam system under compressive axial loading are investigated in this paper. It is assumed that the two beams of the system are simply supported and continuously joined by a Winkler elastic layer. Explicit expressions are derived for the natural frequencies and the associated amplitude ratios of the two beams, and the analytical solution of the critical buckling load is obtained. The influences of the compressive axial loading on the responses of the double-beam system are discussed. It is shown that the critical buckling load of the system is related to the axial compression ratio of the two beams and the Winkler elastic layer, and the properties of free transverse vibration of the system greatly depend on the axial compressions.     

Raman G‐mode of single‐wall carbon nanotube bundles under pressure

Raman studies of nanotubes under pressure have been a lively area of research. However, the results are not always as expected and at times have not been adequately explained. One example of the diversity of the results is the higher energy Raman mode (the graphitic mode, GM) shift to higher wavenumber under pressure. Here we report a new high‐pressure Raman study showing that the effects of the variation in the tube diameters and the pressure transmitting medium are both crucial for understanding the outcomes of such high‐pressure experiments. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamics and damping of electromagnetic solitons in the carbon nanotube bundles

The possible existence of the electromagnetic solitons in carbon nanotubes is analyzed. Solitons appear as a result of a simultaneous change in the classical electron distribution function and the electric field produced by the nonequilibrium electrons in carbon nanotube. The effective equations are obtained for the dynamics of electromagnetic field with allowance for the interband transitions causing soliton damping. The numerical results are presented evidencing the existence of solitons in carbon nanotubes. The propagation dynamics is studied for the periodic electromagnetic waves in the bundles of carbon nanotubes. The shape of electromagnetic wave is found to change during its propagation.     

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.     

Growth of patterned and aligned carbon nanotube bundles on micro-structured substrate

Microstructures are used as inducement for growth of patterned and aligned carbon nanotube (CNT) bundles by pyrolysis of iron phthalocyanine (FePc) under H₂/Ar. The flow of mixture gas can be influenced by geometry profile of microstructure, and the distribution density of catalyst will be different related to the different microstructure. Many types of substrates with different microstructures are used in this study, and several different profiles of CNT bundles are achieved under different process conditions, especially an apical dominance like plant growth is observed under specific H₂/Ar flow rate. Through using appropriate microstructures and controlling the flow rate, the density of CNT bundles can be adjusted, which is very important for weakening electric field shielding effect.     

Nonlinear vibration and stability analysis of a double-walled carbon nanotube under electrostatic actuation

In this paper, forced vibrations of a double-walled clamped–clamped carbon nanotube (DWNT) are studied. Two Euler–Bernoulli beams are used to model the inner and outer layers of the DWNT. An electrostatic actuation, which is comprised of DC and AC voltages is applied between the nanotubes and the electrode. In the system model, the nonlinear form of the interlayer van der Waals (vdW) force, and also, the mid-plane stretching are considered. The obtained equations are solved through Galerkin and multiple scales methods for primary and secondary resonances. The frequency response of the system is obtained as a function of some of the system parameters. A stability analysis of the response is conducted and bifurcation points are determined. The results demonstrate that the DWNT shows different behavior by changing the value of DC voltage. It is also observed that both layers of the DWNT vibrate with the same frequency under the primary and secondary resonance conditions.     

碳纳米管阵列、捆束的三步升温工艺制备及其形貌与结构

使用结构简单的单温炉设备，通过三步升温热解二茂铁、三聚氰氨混合物方法，在二氧化硅、多晶陶瓷基底上分别合成了碳纳米管阵列、碳纳米管捆束.使用扫描电子显微镜、透射电子显微镜、电子能量损失谱和x射线光电子能谱对合成样品进行了结构和成分分析.结果显示：两种基底上合成的纳米管均为多壁纯碳管；生长于光滑二氧化硅表面的碳纳米管具有高度取向性和一致的外径，长度为10—40μm.碳纳米管采取催化剂顶端生长模式并展示出类杯状形貌；生长于粗糙多晶陶瓷表面的碳纳米管捆束随机取向，碳纳米管直径为15—80nm，长度在几百微米，展示 关键词： 碳纳米管 热解法 三步升温工艺     

MD investigation of the collective carbon atom behavior of a (17, 0) zigzag single wall carbon nanotube under axial tensile strain

The collective dynamic behavior of carbon atoms of a (17, 0) zigzag single wall carbon nanotube is investigated under tensile strains by molecular dynamics (MD) simulations. The “slip vector” parameter is used to study the collective motion of a group of atoms and the deformation behavior in three different directions (axial, radial, and tangential) of a (17, 0) carbon nanotube. The variations of radial slip vectors indicate almost all carbon atoms of the (17, 0) carbon nanotube will stay on the cylindrical surface before the yielding of the single wall carbon nanotube (SWNT). Furthermore, the tangential vectors show kinking deformation for the (17, 0) zigzag tube only rarely appears when the crack occurs. Non-symmetrical deformation around a carbon atom along the axial direction also can be found. The variations in the slip vector values of each atom display a symmetrical crack along the horizontal direction and normal to the tube axis. Chain-like structures with 3–4 atoms can be observed, with the number of chain-like structures decreasing before the breakage of the SWNT. The mechanical properties and dynamic behavior of a (17, 0) zigzag SWNT under tensile strain are also compared with that of a (10, 10) armchair tube in our previous study (Weng et al. 2009).     

Fabrication of carbon nanotube bundles and measurement of field electron emission properties

Carbon nanotube (CNT) bundles are synthesized on rough polycrystalline ceramic wafers by pyrolyzing ferrocene/melamine mixtures through a three-step process in a single stage furnace in an Ar atmosphere. The CNTs are multi-walled and have outer diameters from 10 to 90 nm and lengths from 20 to 100 microns. These CNTs display a bamboo-like structure with open graphite layers and defects at the outer surfaces. Field electron emission (FEE) measurements show that the turn-on electrical field is 2.9 V/m and the field enhancement factor is 2700. PACS 61.46.+w; 82.30.Lp; 79.70.+q     

Electronic structure model of a metal-filled carbon nanotube

Carbon monolayer nanotubes filled with K, Rb, and Cs atoms, in which every ten carbon atoms captures an electron from the doping atoms, are considered. It is assumed that a positive charge in the bulk of the nanotube and a negative charge on its surface are distributed uniformly so that the potential energy of a conduction electron inside the nanotube is proportional to the square of the distance to its center. The dependences of the Fermi quasi-momentum for conduction electrons inside the nanotube on their volume density and the tube radius are obtained in the one-electron approximation for an arbitrary number of subbands of transverse motion. The Landauer formula is used for calculating the dependence of the conductivity of the metallic subsystem of the nanotube on its radius.     

A hybrid continuum and molecular mechanics model for the axial buckling of chiral single-walled carbon nanotubes

The purpose of this study is to describe the axial buckling behavior of chiral single-walled carbon nanotubes (SWCNTs) using a combined continuum-atomistic approach. To this end, the nonlocal Flugge shell theory is implemented into which the nonlocal elasticity of Eringen incorporated. Molecular mechanics is used in conjunction with density functional theory (DFT) to precisely extract the effective in-plane and bending stiffnesses and Poisson's ratio used in the developed nonlocal Flugge shell model. The Rayleigh-Ritz procedure is employed to analytically solve the problem in the context of calculus of variation. The results generated from the present hybrid model are compared with those from molecular dynamics simulations as a benchmark of good accuracy and excellent agreement is achieved. The influences of small scale factor, commonly used boundary conditions and chirality on the critical buckling load are fully explored. It is indicated that the importance of the small length scale is affected by the type of boundary conditions considered.     

Electron diffraction and microscopy of single-wall carbon nanotube bundles produced by different methods

The atomic structure of single-wall carbon nanotube bundles produced by three different techniques (laser ablation, electric arc discharge and catalytic chemical vapor deposition (CCVD)) has been characterized by electron diffraction and microscopy. Information on the helicity and the lattice packing has been obtained. Concerning the helicity, small bundles produced by CCVD exhibit only one or two tube helicities within a single bundle. The diffraction patterns of laser-ablation produced bundles also present well-defined but more diversified chiralities within a single bundle. By contrast the data acquired on bundles formed by arc discharge show a more diffuse pattern, characteristic of a random chirality dispersion within a single bundle. Concerning the lattice packing, informations are obtained via a detailed study of the equatorial line of the diffraction pattern for bundles produced by the three techniques. This electron diffraction study is completed by high-resolution electron microscopy. Received 8 August 2001 and Received in final form 14 March 2002     

External and internal coupling effects of rotor's bending and torsional vibrations under unbalances

External and internal bending–torsion coupling effects of a rotor system with comprehensive unbalances are studied by analytical analysis and numerical simulations. Based on Lagrangian approach, a full-degree-of-freedom dynamic model of a Jeffcott rotor is developed. The harmonic balance method and the Floquet theory are combined to analyze the stability of the system equations. Numerical simulations are conducted to observe the bending–torsion coupling effects. In the formulation of rotordynamic model, two bending–torsion coupling patterns, external coupling and internal coupling, are suggested. By analytical analysis, it is concluded that the periodic solution of the system is asymptotically stable. From numerical simulations, three bending–torsion coupling effects are observed in three cases. Under static unbalance, synchronous torsional response is observed, which is the result of external coupling under unbalanced force. Under dynamic unbalance, two-time synchronous frequency torsional response is observed, which is the result of internal coupling under unbalanced moment. Under comprehensive unbalance, synchronous and two-time synchronous frequency torsional components are observed, which are the results of both external and internal couplings under unbalanced force and moment. These observations agree with the analytical analysis. It is believed that these observed phenomena should make sense in the dynamical design and fault diagnostics of a rotor system.     

Modeling of stress transfer behavior in fiber-matrix composite under axial and transverse loadings

Interface between fiber and matrix as a stress transfer medium determines composite performances in load-bearing structures. For instance, failures in composite are most likely initiated by an accumulation of interfacial cracks allowing little or no stress transfer from the matrix to the fiber and vice versa. This paper studies stress transfer behaviors at the interface subject to axial and transverse loadings using the finite element method. Single fiber surrounded by matrix was modeled by introducing a cohesive zone model (CZM) at the interface taking into account the bonding mechanism. By the proposed technique, plastic deformation in the matrix and exerted friction at the interface was verified to govern the role of stress transfer at the interface. Further, the influence of other fibers in matrix surrounding the model was also discussed.