Buckling analysis of carbon nanotube bundles under axial compressive,bending and torsional loadings via a structural mechanics model

A structural mechanics model is employed for the investigation of the buckling behavior of carbon nanotube bundles of three single-walled carbon nanotubes (SWCNTs) under axial compressive, bending and torsional loadings. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element.The effects of different types of boundary conditions are studied for nanotubes with various aspect ratios. The results reveal that bundles comprising longer SWCNTs exhibit lower critical buckling load. Moreover, for the fixed-free boundary condition the rate of critical buckling load reduction is highest, while the lowest critical buckling load occurs. Simulations show good agreement between our model and molecular dynamics results.     

Dust acoustic wave oscillations in metallic carbon nanotubes

We present theoretical analysis of plasmon dispersion in single-walled metallic carbon nanotubes (SWCNTs) in the presence of low-frequency electromagnetic radiation, based on classical electrodynamic formulations and linearized hydrodynamic model. We assume that metallic carbon nanotubes (CNTs) are charged due to the field emission, and hence the metallic nanotubes can be regarded as charged dust rods surrounded by degenerate electrons and ions. Calculations are performed for the transverse electric (TE) and transverse magnetic (TM) waves, respectively, by solving the Maxwell and hydrodynamic equations with appropriate boundary conditions.     

Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates

The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.     

Assessment of Timoshenko Beam Models for Vibrational Behavior of Single-Walled Carbon Nanotubes Using Molecular Dynamics

In this paper, we study the flexural vibration behavior of single-walled carbon nanotubes (SWCNTs) for the assessment of Timoshenko beam models. Extensive molecular dynamics (MD) simulations based on second-generation reactive empirical bond-order (REBO) potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-to-diameter ratios, boundary conditions, chiral angles and initial strain. The effectiveness of the local and nonlocal Timoshenko beam models in the vibration analysis is assessed using the vibration frequencies of MD simulations as the benchmark. It is shown herein that the Timoshenko beam models with properly chosen parameters are applicable for the vibration analysis of SWCNTs. The simulation results show that the fundamental frequencies are independent of the chiral angles, but the chirality has an appreciable effect on higher vibration frequencies. The SWCNTs is very sensitive to the initial strain even if the strain is extremely small.     

Dispersion of dilatation wave propagation in single-wall carbon nanotubes using nonlocal scale effects

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This paper investigates a model of wave propagation in single-wall carbon nanotubes (SWCNTs) with small scale effects are studied. The equation of motion of the dilatation wave is obtained using the nonlocal elastic theory. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture of a local and a nonlocal strain. The SWCNTs structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The SWCNT was the (40,0) zigzag tube with an effective diameter of 3.13 nm. Nonlinear frequency equations of wave propagation in SWCNTs are described through the effect of small scale. The phase velocity and the group velocity are derived, respectively. The nonlinear dispersion relation is analyzed with different wave numbers versus scale coefficient. It can be observed from the results that the dispersion properties of the dilatation wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the dilatation wave in carbon nanotubes can also be tuned by these factors.     

On the merits of Raman spectroscopy and thermogravimetric analysis to asses carbon nanotube structural modifications

Raman spectroscopy, thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy, and transmission electron microscopy are used to assess structural changes generated on the surface of multi-walled (MWCNTs) and single-walled (SWCNTs) carbon nanotubes. Different levels of structural modifications are generated by the use of acidic oxidative treatments. It is found that Raman spectroscopy is a very powerful technique to assess structural modification of SWCNTs with initial low defect concentration. For MWCNTs grown by chemical vapor deposition, which already contain a high density of structural defects in their as-produced state, Raman spectroscopy is not a very sensitive tool to detect the generation of further defects or other structural modifications introduced through acidic treatments. For this later case, TGA is a sensitive technique to assess structural modifications on the nanotubes.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

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.     

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．     

Effects of gravity on single-wall carbon nanotubes synthesized by arc in water

The method using arc discharge in liquid is a simple and inexpensive route for synthesis of carbon nanotubes and other related nano-materials. In this study, we report the synthesis of single-wall carbon nanotubes (SWCNTs) by means of the arc-in-water method under extremely low gravity conditions. The strong heat convection caused by the arc plasma is suppressed under such conditions. Therefore, the boiling flow behavior and temperature distribution have been stabilized in low gravity. As a result, the possibility of the chirality control of SWCNTs by applying extremely low gravity was revealed; namely, the yield of semiconducting SWCNTs was increased and several SWCNTs of specific diameters turned out to be prominent under extremely low gravity conditions. PACS 52.80.Wq; 68.37.Lp; 81.07.De; 81.70.Ha; 82.80.Gk     

Effects of strain and higher order inertia gradients on wave propagation in single-walled carbon nanotubes

Dispersion relation of single-walled carbon nanotubes (SWCNTs) is investigated. The governing equations of motion of SWCNTs are derived on the basis of the gradient shell model, which involves one strain gradient and one higher order inertia parameters in addition to two Lamé constants. The present shell model can predict wave dispersion in good agreement with those of molecular dynamic (MD) simulations available in the literature. The effects of two small scale parameters on the angular frequency and phase velocity in the longitudinal, torsional and radial directions are studied in detail. The numerical results show that the angular frequency and phase velocity increase with the increase of strain gradient parameter, whereas decrease with inertia gradient parameter increases. In addition, analytical expressions of the cut-off frequencies and asymptotic phase velocities are given. It is found that the number of cut-off frequencies is dependent on the circumferential wave number, and two asymptotic phase velocities exist for nonzero value of strain gradient parameter, while only one exists when the strain gradient parameter is excluded.     

Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study

In the present work, the vibration characteristics of single- and double-walled carbon nanotubes under various layerwise boundary conditions at different lengths are investigated. This is accomplished by the use of molecular dynamics simulations based on the Tersoff-Brenner and Lennard-Jones potential energy functions. The effects of initial tensile and compressive strains on the resonant frequency of carbon nanotubes are also taken into consideration. From the results generated, it is observed that the natural frequency of carbon nanotubes is strongly dependent on their boundary conditions especially when tubes are shorter in length. The natural frequency and its dependence on tube end conditions reduce by increasing the tube length. The natural frequency of DWCNTs lies between those of the constituent inner and outer SWCNTs and is nearer to those of the outer one. It is further observed that the natural frequency is highly sensitive to tensile and compressive strains. The frequency shift occurring in the presence of small initial strains is positive for tensile strains and negative for compressive strains. The results obtained provide valuable information for calibrating the small scaling parameter of the nonlocal models for the vibration problem of carbon nanotubes.     

Non-covalent interaction of benzonitrile with single-walled carbon nanotubes

We have studied the interaction of benzonitrile with as-prepared and purified single-walled carbon nanotubes (SWCNTs). As-prepared SWCNTs, when suspended in benzonitrile, lead to a red colored dispersion which contains fragments composed mostly of amorphous carbon and carbon-coated catalyst, thus suggesting that benzonitrile is a solvent that can be used as one step of the purification process. Optical spectroscopic data (infrared, Raman, absorption) showed that purified carbon nanotubes interact weakly with benzonitrile. These experimental results are confirmed by first principles calculations that predict a very weak adsorption process through π–π interaction instead of through the free electron pair of the nitrile.     

光谱法研究水溶性羧基化碳纳米管与人血清白蛋白的相互作用

纳米材料与蛋白质等生物大分子的相互作用是纳米材料生物效应和安全性研究的重要基础。本实验利用荧光光谱、同步荧光光谱、圆二色谱(CD)等方法研究了四种结构特性不同的水溶性羧基化碳纳米管(long-SWCNTs-COOH,short-SWCNTs-COOH,DWCNTs-COOH,MWCNTs-COOH)与人血清白蛋白(human serum albumin, HSA)的相互作用。实验结果显示：四种水溶性羧基碳纳米管均能猝灭HSA的内源荧光,但猝灭能力有所不同,相同浓度下不同水溶性羧基化碳纳米管对HSA的荧光猝灭作用遵循如下规律：DWCNTs-COOH＜MWCNTs-COOH＜long-SWCTs-COOH＜short-SWCNTs-COOH;四种碳纳米管对HSA的同步荧光光谱影响表明,MWCNTs-COOH的作用位点更靠近色氨酸(Trp)残基,而DWCNTs-COOH的作用位点更靠近酪氨酸(Tyr)残基,而long-SWCNTs-COOH和short-SWCNTs-COOH对两种氨基酸残基的作用无明显差别;在碳纳米管作用下,HSA 的圆二色谱有微弱的变化,且与α-螺旋、β-折叠含量变化基本一致。结果表明,不同碳纳米管对HSA的荧光猝灭能力与它们的结构特性有关,两者作用过程中HSA构象基本不变,二级结构有微小变化,但无明显的剂量-效应关系。根据实验结果对可能的作用机制进行了讨论。     

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.     

Comparative study on modification of single wall carbon nanotubes by sodium dodecylbenzene sulfonate and melamine sulfonate superplasticiser

In this work, the results of synthesis and characterization of single wall carbon nanotubes (SWCNTs) functionalized by two surfactants (sodium dodecylbenzene sulfonate and melamine sulfonate superplasticiser) have been presented. The properties of pristine and modified SWCNTs have been compared by different techniques: Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR) and atomic force microscopy (AFM). Raman analysis reveals the changes in vibrational spectra of SWCNTs after modification by different surfactant molecules. FTIR analysis has shown the presence of sulfonate group which is strong evidence for nanotube modification. AFM analysis has shown separation of big single wall carbon nanotube bundles into thin bundles of them.     

Green luminescence from triphenylphosphine functionalized single-wall carbon nanotubes

In a simple wet chemical process, purified single-wall carbon nanotubes (SWCNTs) are treated with triphenylphosphine (Ph₃P) at room temperature. The functionalized material is characterized by scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM), Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy. HRTEM micrograph clearly reveals that triphenylphosphine nanocrystals of nearly uniform size are attached to the surfaces of SWCNTs. The hybrid structure shows remarkable green luminescence with peak emission at around 500 nm, under UV excitation. The photoluminescence may be attributed to charge transfer from the electron-donating phosphorous atoms to the carbon nanotubes.     

On the characterization of the elastic properties of asymmetric single-walled carbon nanotubes

In order to characterize asymmetric single-walled carbon nanotubes, an algorithm has been developed based on numerical simulation to relate the physical geometry to the elastic properties of asymmetric single-walled carbon nanotubes (SWCNTs). A large number of finite element results for the stiffness of asymmetric SWCNTs has been used to develop a best surface fitting function to define the relationship between the geometry of SWCNTs and their stiffness. However, since the stiffness of asymmetric nanotubes depends upon the configuration parameters, n and m, it was impossible to define any diameter dependency. Based on the maximum reaction force concept and in order to account for the hidden mechanical behavior of asymmetric SWCNTs, the chiral factor (CF) has been employed in this study. The proposed CF converts any asymmetric geometry (n and m) into a value between 0 and 1. A group of the SWCNTs with the same applied boundary condition (n+m=30) and different range of the CF was also used for studying of the shear contribution. The chiral factor dependency, which is developed in this study, is applicable for characterising and selecting asymmetric SWCNTs in the design of advanced nanomaterials. Furthermore, the equation which is calculated in this study can be useful for finding the best criteria for selecting asymmetric SWCNTs.     

Wave characteristics of single-walled fluid-conveying carbon nanotubes subjected to multi-physical fields

Wave propagation in single-walled carbon nanotubes (SWCNTs) conveying fluids and placed in multi-physical fields (including magnetic and temperature fields) is studied in this paper. The nanotubes are modelled as Timoshenko beams. Based on the nonlocal beam theory, the governing equations of motion are derived using Hamilton's principle, and then solved by Galerkin approach, leading to two second-order ordinary differential equations (ODEs). Numerical simulations are carried out to verify the analytical model proposed in the present study, and determine the influences of the nonlocal parameter, the fluid velocity and flow density, the temperature and magnetic field flux change, and the surrounding elastic medium on the wave behaviour of SWCNTs. The results show that the nonlocal parameter has a considerable influence on dynamic behaviour of the nanotube and the fluid flow inside it. The results also show that the magnetic and temperature fields play an important role on the wave propagation characteristics of SWCNTs.     

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