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.     

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.     

傅里叶变换系统的光线矩阵分析方法

本文应用光线矩阵方法,分析一般的非对称系统,导出了该系统的傅里叶变换条件;考虑到定位误差,文中给出了计算夫琅和费和傅里叶变换有效区域和物理焦深区的公式;并得出了在不同波面入射光波的情况下,谱面移动量的计算公式,最后给出了二个应用实例。     

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.     

A comparison between the mechanical and thermal properties of single-walled carbon nanotubes and boron nitride nanotubes

Carbon nanotubes (CNTs) are semimetallic while boron nitride nanotubes (BNNTs) are wide band gap insulators. Despite the discrepancy in their electrical properties, a comparison between the mechanical and thermal properties of CNTs and BNNTs has a significant research value for their potential applications. In this work, molecular dynamics simulations are performed to systematically investigate the mechanical and thermal properties of CNTs and BNNTs. The calculated Young’s modulus is about 1.1 TPa for CNTs and 0.72 TPa for BNNTs under axial compressions. The critical bucking strain and maximum stress are inversely proportional to both diameter and length-diameter ratio and CNTs are identified axially stiffer than BNNTs. Thermal conductivities of (10, 0) CNTs and (10, 0) BNNTs follow similar trends with respect to length and temperature and are lower than that of their two-dimensional counterparts, graphene nanoribbons (GNRs) and BN nanoribbons (BNNRs), respectively. As the temperature falls below 200 K (130 K) the thermal conductivity of BNNTs (BNNRs) is larger than that of CNTs (GNRs), while at higher temperature it is lower than the latter. In addition, thermal conductivities of a (10, 0) CNT and a (10, 0) BNNT are further studied and analyzed under various axial compressive strains. Low-frequency phonons which mainly come from flexure modes are believed to make dominant contribution to the thermal conductivity of CNTs and BNNTs.     

Impact of Mo and Ce on growth of single-walled carbon nanotubes by chemical vapour deposition using MgO-supported Fe catalysts

A series of nine catalysts containing Ce/Fe and Mo/Fe at various loadings on MgO supports have been studied as catalysts for chemical vapour deposition (CVD) of single-walled carbon nanotubes (SWCNTs) using a methane carbon source. Our results show that the Ce/Fe system is very suitable as a catalyst that favours SWCNT growth, and we question the special importance that has been attributed to Mo as an additive to Fe-based catalysts for SWCNT growth, as it appears that Ce is equally effective. Our results indicate that dehydroaromatization (DHA) is not a defining step for the growth mechanism, as has been suggested for Mo/Fe systems previously, and show that Ce and Mo do not seriously perturb the well-known Fe/MgO system for growth of high quality SWCNT. Using Raman spectroscopy, we have shown that the Ce/Fe/MgO catalyst system favours growth of SWCNTs with a different distribution of chiralities compared to the analogous Mo/Fe/MgO system.     

Prediction of reverberation time using the residual minimization method

In many practical situations the assumption of sound field dispersion needed for the application of the Sabine’s theory is not fulfilled. In general, sound field is sufficiently dispersed if there are no large differences in the dimensions of the room, limiting partitions are not parallel, or the sound absorbing material is uniformly distributed. In practice, very few of these requirements are satisfied. As a result, a number of other formulas describing reverberation time have been created, for example Fitzroy’s or Neubauer’s formulas. However, these methods in many cases differ significantly from the actual measurements. The paper presents a method used to estimate reverberation time as well as its applicability potential involving laboratory models and auditorium rooms. The proposed method can be classified into a group of learning methods and involves the use of statistical methods which allow for approximation with the use of the least squares method.     

Different mechanism of capacitance change for gas detection using semiconducting and metallic single-walled carbon nanotubes

Semiconducting single-walled carbon nanotubes (s-SWCNTs) with lower absorption energy of NO₂ gas exhibited higher sensitivity than metallic SWCNTs. The result originated from quantum capacitance of s-SWCNTs, which was readily affected by charge transfer, whereas that of m-SWCNTs showed no change with even more transferred charges. However, m-SWCNT that were aligned polarize adsorbed gases on the surface by a local field that contributed the capacitance changes of m-SWCNT networks. This is a newly introduced detection mechanism of gas sensing using m-SWCNTs.     

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     

Chemisorption of single fluorine atoms on the surface of zigzag single-walled carbon nanotubes: A model calculation

We report a model calculation of the chemisorption energies ΔE_ads of single fluorine atoms on the outer surface of zigzag single-walled carbon nanotubes (Z-SWCNTs) (p,0) with p ranging from 11 to 21. A simplified model based on an effective-mass theory is adopted to describe the electronic structure of the nanotubes. Chemisorption is treated within the Anderson–Newns approach, which takes account of Coulomb interaction between adsorbate electrons. Considering adsorption of an adatom directly on top of a surface carbon atom, we find that in the case of a fluorine atom bonded to the sidewall of the nanotubes, the absolute values of ΔE_ads are in the range for Z-SWCNTs with typical diameters of , larger |ΔE_ads| values being associated with semiconducting tubes. For the latter ones, |ΔE_ads| decreases rather significantly as the radius R of the tubes increases, tending towards the “infinite” radius graphene case, whereas for metallic tubes |ΔE_ads| slightly increases with increasing R. The localized acceptor states induced by a fluorine atom in the band gap of the semiconducting tubes are found to be responsible for such difference in the behaviour of ΔE_ads for the two above-mentioned types of tubes. The results obtained shed light on the possible mechanism of the atomic fluorine adsorption-induced hole-doping of the semiconducting tubes, which might significantly affect the transport properties of these tubes.     

Optimizing the manufacturing parameters of carbon nanotubes stiffened speaker diaphragm using Taguchi method

This study developed a thermal transfer printing (TTP) technique to fabricate a carbon nanotubes (CNTs) stiffened speaker diaphragm. The self-developed TTP stiffening technique does not require a high curing temperature that decreases the mechanical property of CNTs. Therefore, the inherent strength of CNTs was preserved. In addition to increasing the stiffness of diaphragm substrate, this technique alleviates the middle and high frequency attenuation associated with the sound pressure curve of a speaker, thereby smoothing the sound pressure curve and achieving a full sound range as well as reducing bass distortion and enhancing treble clarity. Furthermore, the TTP technique can stiffen a localized area on a diaphragm substrate, thus increasing diaphragm stiffness without markedly raising diaphragm weight. The Taguchi quality engineering method was applied to identify the optimal process parameters (i.e., transfer area, stiffening pattern, coating layers, and transfer temperature). Finally, the optimal process parameters were employed to fabricate a stiffened diaphragm, which was then assembled onto a speaker. The result indicated that the stiffened diaphragm improved the smoothness of the sound pressure curve for the speaker, which produced a mid-frequency dip difference (ΔdB) of 1.9 dB and an attenuation peak frequency (f_peak) of 4220 Hz.     

应用改进的矩阵束方法加速混响室时域仿真

为了减少混响室时域全波仿真的计算量,首次对混响室时域响应的预测做出探索研究。以改良矩阵束方法为基础,提出一种计算效率更高的矩阵束方法,并验证了该方法的正确性与稳定性。用复指数幂求和式对混响室的时域波形进行拟合,利用该方法能够高效求解出拟合式中的各极点,实现了对混响室时域响应的近似外推。由电场强度的前20 000步计算结果,可快速预测得到后20 000步响应,发现束参数比例取0.62左右时,对多个采样点的电场均可得到良好的预测效果,可保证仿真与预测相结合得到的结果与真实结果的频域相对误差小于15%。这种结合预测的仿真算法可节省计算量约50%。     

One-pot synthesis of one-dimensional array Pt nanoparticles on carbon nanotubes via a facile microwave polyol method

High-density attachment and one-dimensional array Pt nanoparticles (NPs) on carbon nanotubes (CNTs) to generate Pt/CNTs heterostructures are obtained via one-pot microwave polyol method. The morphology, composition of as-obtained Pt/CNTs heterostructures is characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD). The Raman spectrum and Fourier transform infrared (FTIR) spectrum show the introduction of defects or functional groups on CNTs surface, which are crucial factors to assist the nucleation and growth of Pt NPs along the skeleton of CNTs.     

Analysis of radial nonlocal effect on the structural response of carbon nanotubes

In this Letter, finite element model is developed to study the effect of nonlocal parameter in the radial structural response of carbon nanotubes. Timoshenko beam model is employed. The influence of nonlocal parameter in the radial direction due to interaction of atoms is defined as the radial nonlocal effect. It is found that there is significant influence of radial nonlocal effect on the structural response of the carbon nanotubes.     

Longitudinal waves in carbon nanotubes in the presence of transverse magnetic field and elastic medium

In the present paper, the coupling effect of transverse magnetic field and elastic medium on the longitudinal wave propagation along a carbon nanotube (CNT) is studied. Based on the nonlocal elasticity theory and Hamilton's principle, a unified nonlocal rod theory which takes into account the effects of small size scale, lateral inertia and radial deformation is proposed. The existing rod theories including the classic rod theory, the Rayleigh-Love theory and Rayleigh-Bishop theory for macro solids can be treated as the special cases of the present model. A two-parameter foundation model (Pasternak-type model) is used to represent the elastic medium. The influence of transverse magnetic field, Pasternak-type elastic medium and small size scale on the longitudinal wave propagation behavior of the CNT is investigated in detail. It is shown that the influences of lateral inertia and radial deformation cannot be neglected in analyzing the longitudinal wave propagation characteristics of the CNT. The results also show that the elastic medium and the transverse magnetic field will also affect the longitudinal wave dispersion behavior of the CNT significantly. The results obtained in this paper are helpful for understanding the mechanical behaviors of nanostructures embedded in an elastic medium.     

Effect of metal oxide and oxygen on the growth of single-walled carbon nanotubes by electric arc discharge

The effect of oxygen on the growth of single-walled carbon nanotubes was studied with Ni–Co alloy powder as catalyst under helium atmosphere of 500 Torr by electric arc discharge. The oxygen included in nickel or (and) cobalt oxides was added in catalyst. The content of oxygen in atmosphere was controlled by changing vacuum degree inside furnace before inputting buffer gas. The examinations of TEM and Raman scattering showed that oxygen in metal oxide as catalyst promotes the nucleation of SWCNT by taking effect on the metal catalyst particles. However, O₂ in atmosphere has the role of oxidizing amorphous particles along with nanotubes. When its molar proportion is higher than 0.22 ppm (Parts per million), the carbon nanotubes produced are oxidized and their purity decreases. The diameter of single-walled carbon nanotube obtained under different condition has a narrow distribution around 1.28 nm.     

Modeling and simulation for the field emission of carbon nanotubes array

To optimize the field emission of the infinite carbon nanotubes (CNTs) array on a planar cathode surface, the numerical simulation for the behavior of field emission with finite difference method was proposed. By solving the Laplace equation with computer, the influence of the intertube distance, the anode–cathode distance and the opened/capped CNT on the field emission of CNTs array were taken into account, and the results could accord well with the experiments. The simulated results proved that the field enhancement factor of individual CNT is largest, but the emission current density is little. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance. From the simulation the field emission can be optimized when the intertube distance is close to the tube height. The anode–cathode distance hardly influences the field enhancement factor of CNTs array, but can low the threshold voltage by decreasing the anode–cathode distance. Finally, the distribution of potential of the capped CNTs array and the opened CNTs array was simulated, which the results showed that the distribution of potential can be influenced to some extent by the anode–cathode distance, especially at the apex of the capped CNTs array and the brim of the opened CNTs array. The opened CNTs array has larger field enhancement factor and can emit more current than the capped one.     

高效循环电弧放电法制备大量单壁纳米碳管的研究

介绍一种利用电弧放电法高效率制备大量单壁纳米碳管的新方法.以钨代替传统的石墨棒作为放电阴极，采取循环式往返放电法.同时利用高分辨透射电子显微镜及拉曼光谱对制备的单壁纳米碳管进行了观察、表征.实验证明：以钨为阴极的循环电弧放电法可以初步实现单壁纳米碳管的高效率、大批量生产. 关键词： 单壁纳米碳管 钨电极 拉曼光谱     

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.     

Effects of composition of catalysts on the preparation of single-walled carbon nanotubes synthesized over W–Co–MgO catalysts

A series of W–Co–MgO catalysts were prepared for the first time by decomposing a mixture of magnesium nitrate, ammonium paratungstate, citric acid, and cobalt nitrate. Single-walled carbon nanotubes (SWCNTs) were synthesized over these W–Co–MgO catalysts and the effects of the quantity of metal in the catalysts on the synthesis of SWCNTs were investigated by Raman spectroscopy and transmission electron microscopy (TEM). The results show that, among W–Co–MgO catalysts, the W1–Co5 catalyst was found to be most effective for synthesizing SWCNTs. The diameter distribution of as-grown SWCNTs prepared over the W1–Co5 catalyst was estimated to range from 0.72–1.64 nm. When the molar ratios of W:MgO and Co:MgO in the catalysts are more than 2:100 and 5:100, respectively, the amorphous carbon content or defect concentration of SWCNTs may be increased with the increase of the quantity of metal in the catalysts. The dependence of the diameter distribution of SWCNTs on the quantity of W in the catalysts is small. However, the proportion of SWCNTs with larger diameter is increased as the quantity of Co in the catalysts is increased owing to the increase in the number of larger active sites.