Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part II: parametric study

The capabilities of the proposed nonlocal beam models in the companion paper in capturing the critical velocity of a moving nanoparticle as well as the dynamic response of double-walled carbon nanotubes (DWCNTs) under a moving nanoparticle are scrutinized in some detail. The role of the small-scale effect parameter, slenderness of DWCNTs and velocity of the moving nanoparticle on dynamic deflections and nonlocal bending moments of the innermost and outermost tubes as well as their maximum values are then investigated. The results reveal that the critical velocity increases with the slenderness of DWCNTs and the magnitude of the van der Waals interaction force. Nevertheless, the critical velocity generally decreases with the small-scale effect as well as the ratio of the mean diameter to the thickness of the innermost tube. Additionally, the predicted maximum dynamic deflections and nonlocal bending moments of the innermost and outermost tubes by using the nonlocal Euler?CBernoulli and Timoshenko beam theories are generally the lower and upper bounds of those obtained by the nonlocal higher-order beam theory (NHOBT). In the case of ??₁?<?20, the use of the NHOBT is highly recommended for more realistic prediction of dynamic response of DWCNTs under a moving nanoparticle.     

Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part I: theoretical formulations

The current work suggests mathematical models for the vibration of double-walled carbon nanotubes (DWCNTs) subjected to a moving nanoparticle by using nonlocal classical and shear deformable beam theories. The van der Waals interaction forces between atoms of the innermost and outermost tubes are modeled by an elastic layer. The equations of motion are derived for the nonlocal double body Euler?CBernoulli, Timoshenko and higher-order beams connected by a flexible layer under excitation of a moving nanoparticle. Analytical solutions of the problem are provided for the aforementioned nonlocal beam models with simply supported boundary conditions. The dynamical deflections and nonlocal bending moments of the innermost and outermost tubes are then obtained during the courses of excitation and free vibration. Finally, the critical velocities of the moving nanoparticle associated with the nonlocal beam theories are expressed in terms of small-scale effect parameter, geometry, and material properties of DWCNTs.     

Stochastic FEM on nonlinear vibration of fluid-loaded double-walled carbon nanotubes subjected to a moving load based on nonlocal elasticity theory

This paper adopts stochastic FEM to study the statistical dynamic behaviors of nonlinear vibration of the fluid-conveying double-walled carbon nanotubes (DWCNTs) under a moving load by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The Young’s modulus of elasticity of the DWCNTs is considered as stochastic with respect to the position to actually characterize the random material properties of the DWCNTs. Besides, the small scale effects of the nonlinear vibration of the DWCNTs are studied by using the theory of nonlocal elasticity. Based on the Hamilton’s principle, the nonlinear governing equations of the fluid-conveying double-walled carbon nanotubes under a moving load are formulated. The stochastic finite element method along with the perturbation technique is adopted to study the statistical dynamic response of the DWCNTs. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the non-dimensional dynamic deflections are computed and checked by the Monte Carlo Simulation, meanwhile the effects of the nonlocal parameter, aspect ratio and the flow velocity on the statistical dynamic response of the DWCNTs are investigated. It can be concluded that the nonlocal solutions of the dynamic deflections get larger with the increase of the nonlocal parameters due to the small scale effect, and as the flow velocity increases, the maxima non-dimensional dynamic deflections of the DWCNTs get larger.     

Filling double-walled carbon nanotubes with WO3 and W nanowires via confined chemical reactions

Carbon nanotubes filled with metals and semiconductors have been regarded as one of the most promising materials for nanodevices. Here, we demonstrate a simple and effective method to produce tungsten trioxide (WO3) and tungsten (W) nanowires with diameters of below 4 nm inside double-walled carbon nanotubes (DWCNTs). First, the precursors, i.e., phosphotungstic acid (HPW, H3PW12O40) molecules, are successfully introduced into DWCNTs. Subsequent decomposition and reduction lead to the formation of WO3 and W nanowires inside DWCNTs. The products were carefully characterized by high-resolution transmission electron microscopy (HRTEM), Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy. FTIR spectra provide a direct proof that the HPW molecules enter the DWCNTs as an ionic state, i.e., PW12O40(3-) and H+, instead of the molecular state. HRTEM analysis shows that the diameter of the WO3 nanowires inside DWCNTs is 1.1-2.4 nm with the average length of 16-18 nm, and that for W nanowires is 1.2-3.4 nm with the average length of 15-17 nm. Meanwhile, DWCNTs are doped by the encapsulated WO3 and W nanowires. Tangential band shift in Raman spectra revealed the charge transfer between the nanowires and carbon nanotubes.     

Fabrication of flexible transparent conductive films from long double-walled carbon nanotubes

The fabrication of flexible transparent conducting films (TCFs) is important for the development of the next-generation flexible devices. In this study, we used double-walled carbon nanotubes (DWCNTs) as the starting material and described a fabrication method of flexible TCFs. We have determined in a quantitative way that the key factors are the length and the dispersion states of the DWCNTs as well as the weight-ratios of dispersant polymer/DWCNTs. By controlling such factors, we have readily fabricated a flexible highly transparent (94% transmittance) and conductive (surface resistivity = 320 Ω sq⁻¹) DWCNT film without adding any chemical doping that is often used to reduce the surface resistivity. By applying a wet coating, we have succeeded in the fabrication of large-scale conducting transparent DWCNT films based on the role-to-role method.     

Controlled doping of double walled carbon nanotubes and conducting polymers in a composite: An in situ Raman spectroelectrochemical study

The interaction of double wall carbon nanotubes (DWCNTs) and the conducting polymer poly(3,4-ethylenedioxythiphene)/polystyrenesulfonate (PEDOT/PSS) was studied by in-situ Raman spectroelectrochemistry. The mixing of DWCNTs with PEDOT/PSS caused a partial doping of the outer tube of DWCNTs, which was indicated by the relative change of the Raman intensity of the DWCNTs features. On the other hand, the bands corresponding to inner tubes of DWCNTs and to the polymer were almost untouched by assembling both species into a composite. The in-situ Raman spectroelectrochemical experiments have shown that the changes in electronic structure of inner tubes of DWCNTs embedded in PEDOT/PSS matrix are dependent on the doping level. While at the low doping level of the composite, the Raman features of inner tubes of DWCNTs do not change significantly, at high doping level they reflect the changes caused by the applied electrochemical potential similar to those observed in the polymer-free DWCNTs.     

Characterization of free vibration of elastically supported double-walled carbon nanotubes subjected to a longitudinally varying magnetic field

Free transverse vibrations of elastically supported double-walled carbon nanotubes (DWCNTs) subjected to axially varying magnetic fields are examined. Using nonlocal Rayleigh beam theory, the explicit expressions of the governing equations are obtained and then numerically solved via an efficient numerical scheme. For magnetically affected DWCNTs with simply supported, fully clamped, simple-clamped, and clamped-free ends, the flexural frequencies as well as the corresponding vibration modes are evaluated for different varying magnetic fields. The influences of the small-scale parameter and the magnetic field strength on the dominant flexural frequencies of the DWCNTs are explained and discussed. The results indicate that the vibration characteristics of DWCNTs can be significantly affected by the axially varying magnetic field. The role of variation of the axial magnetic field on the vibrational mode patterns of both the innermost and outermost tubes is also revealed. For a special applied magnetic field, the alteration from coaxial to noncoaxial vibration pattern is also reported. The obtained results display that the flexural frequencies magnify with the magnetic field strength. Generally, the variation of the magnetic field strength has more influence on the variation of the frequencies of DWCNTs with higher small-scale parameters. This matter is mainly attributed to the incorporation of the size effect into the nonlocal Lorentz forces.     

Surface energy heterogeneity and heterogeneous adsorption of benzene on double-walled carbon nanotubes

We examined the adsorption properties of double walled carbon nanotubes (DWCNTs) synthesized by using a catalytic chemical decomposition vapor method. To analyze the structural and energetical surface characteristics of the DWCNTs, nitrogen and benzene adsorption isotherms were measured. The Toth isotherm equation was used to correlate the adsorption data and evaluate the thermodynamic properties such as Henry's constant and the adsorption second virial coefficient. The existence of heterogeneous surface in DWCNTs was confirmed by the analysis of pore size distribution, the isosteric heat of adsorption, and the adsorption energy distribution determined for nitrogen and benzene.     

Ultra-thin double-walled carbon nanotubes: A novel nanocontainer for preparing atomic wires

Double-walled carbon nanotubes (DWCNTs) with high graphitization have been synthesized by hydrogen arc discharge. The obtained DWCNTs have a narrow distribution of diameters of both the inner and outer tubes, and more than half of the DWCNTs have inner diameters in the range 0.6–1.0 nm. Field electron emission from a DWCNT cathode to an anode has been measured, and the emission current density of DWCNTs reached 1 A/cm² at an applied field of about 4.3 V/μm. After high-temperature treatment of DWCNTs, long linear carbon chains (C-chains) can be grown inside the ultra-thin DWCNTs to form a novel C-chain@DWCNT nanostructure, showing that these ultra-thin DWCNTs are an appropriate nanocontainer for preparing truly one-dimensional nanostructures with one-atom-diameter.      

Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method

This research deals with the dynamic instability analysis of double-walled carbon nanotubes (DWCNTs) conveying pulsating fluid under 2D magnetic fields based on the sinusoidal shear deformation beam theory (SSDBT). In order to present a realistic model, the material properties of DWCNTs are assumed viscoelastic using Kelvin–Voigt model. Considering the strain gradient theory for small scale effects, a new formulation of the SSDBT is developed through the Gurtin–Murdoch elasticity theory in which the effects of surface stress are incorporated. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The van der Waals interactions between the adjacent walls of the nanotubes are taken into account. The size dependent motion equations and corresponding boundary conditions are derived based on the Hamilton’s principle. The differential quadrature method in conjunction with Bolotin method is applied for obtaining the dynamic instability region. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of DWCNTs. The results depict that the surface stress effects on the dynamic instability of visco-DWCNTs are very significant. Numerical results of the present study are compared with available exact solutions in the literature. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems in advanced biomechanics applications with magnetic field as a parametric controller.     

Characterizing load transfer efficiency in double-walled carbon nanotubes using multiscale finite element modeling

Load transfer efficiency from matrix to carbon nanotubes (CNTs) plays an important role in the mechanical response of CNTs nanocomposites as it may affect the effectiveness of the nano-reinforcements. For double-walled carbon nanotubes (DWCNTs), the outer graphene layer as well as the inner layer may be responsible for the load bearing capacity. In this study, the load transfer efficiency within DWCNTs was investigated using a multiscale simulation scheme. The multiscale simulation consists of two steps. First, the atomistic behaviors between the adjacent graphite layers in DWCNTs were characterized using molecular dynamic (MD) simulation, from which a cylindrical equivalent continuum solid of DWCNTs with embedded spring elements was proposed to describe the interactions of neighboring graphene layers. Two kinds of interatomistic properties in DWCNTs, i.e., van der Walls (vdW) interactions and artificial build-up covalent bonds, were considered in the equivalent solid. Subsequently, the equivalent solid was implemented as reinforcement in the micromechanical model of CNTs nanocomposites for evaluating the load transfer efficiency. Results indicated that the DWCNTs with covalent bonds exhibit superior load transfer efficiency than those with only vdW interactions. In addition, when the DWCNTs get long, the load transfer efficiency of DWCNTs increases accordingly.     

Synthesis,characterization, and its photocatalytic activity of double-walled carbon nanotubes-TiO2 hybrid

Double-walled carbon nanotube (DWCNT)-TiO₂ hybrid was prepared by hydrothermal method and characterized by X-ray diffraction, electron microscopy, N₂-adsorption analysis, Raman spectroscopy, Fourier transform infrared spectroscopy, and UV–vis diffuse reflectance spectroscopy. The photocatalytic activity of DWCNT-TiO₂ hybrid was tested by the photocatalytic degradation of sulfathiazole. The experimental results showed that the introduction of the DWCNTs provides DWCNT-TiO₂ hybrid with visible light-induced photoactivity and a large surface area. The DWCNTs were coated with TiO₂ nanoparticles, which generated an intimate contact between the DWCNTs and TiO₂. The DWCNT-TiO₂ hybrid showed an excellent visible-light-induced activity, compared with multi-walled carbon nanotube-TiO₂ and single-walled carbon nanotube-TiO₂ hybrids, which can be attributed to the unique electronic structure of the DWCNTs that can work well as not only a photosensitizer but also an electron conductor. In addition, DWCNT-TiO₂ hybrid with the DWCNTs of long length showed higher degradation efficiency than that with the short length.     

Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle

This study presents an analytical method for the forced vibration of an elastically connected double-carbon nanotube system (DCNTS) carrying a moving nanoparticle based on the nonlocal elasticity theory. The two nanotubes are identical and are connected with each other continuously by elastic springs. The problem is also solved numerically by using the Galerkin method and the time integration method of Newmark to establish the reliability of the analytical method. Two sets of critical velocity exist for DCNTS. The closed-form solutions for the dynamic deflections of the two nanotubes are derived for these two sets of critical velocity for the first time in this study. The influences of the nonlocal parameter, aspect ratio, velocity of the moving nanoparticle and the elastic layer between the nanotubes on the dynamic responses are discussed. The study shows that the dynamic behavior of the double-carbon nanotube system is greatly influenced by the nonlocal effects. The dynamic deflections predicted by the classical theory are always smaller than those predicted by the nonlocal theory due to the nonlocal effects. Thus, the classical beam models are not suitable in modeling carbon nanotubes with small aspect ratio, and nonlocal effects should be taken into account. Furthermore, the velocity of the nanoparticle and the stiffness of the elastic layer have significant effects on the dynamic behavior of DCNTS.     

双壁碳纳米管研究进展

单壁碳纳米管和多壁碳纳米管的合成和应用研究得到广泛的关注和重视，并已取得了许多令人鼓舞的成果。双壁碳纳米管(DWCNTs)作为介于单壁碳纳米管和多壁碳纳米管之间的一种特殊结构碳纳米管，由于潜在的应用价值及作为研究碳纳米管层间作用最简单和理想的模型开始得到高度重视。介绍了双壁碳纳米管合成方法及理论和应用研究取得的进展。     

Buckling of defective single-walled and double-walled carbon nanotubes under axial compression by molecular dynamics simulation

Buckling of defective single-walled and double-walled carbon nanotubes (SWCNTs and DWCNTs, respectively) due to axial compressive loads has been studied by molecular dynamics simulations, and results compared with those of the perfect structures. It is found that single vacancy defect greatly weakens the carrying capacity of SWCNTs and DWCNTs, though it does slight harm to the effective elastic modulus of the tubes. The influence of defects on the buckling properties of nanotubes is related to the density of the defects, and the relative position of defects also plays an important role in buckling of DWCNTs. The van der Waals force among atoms in the inner and the outer tubes of short defective DWCNTs makes the critical buckling strain of DWCNTs greater than that of the inner tube.     

Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model

Double-walled carbon nanotubes (DWCNTs) are being investigated for use as latent materials for drug carriers. However, the surface effects cannot be ignored when drugs or other functional materials, such as nickel or silver, adhere to the surface of the outer tube of a DWCNT. In this paper, the vibrational frequency of DWCNTs, while accounting for surface effects, is studied using the nonlocal Timoshenko beam model. The influence of the surface elasticity modulus, residual surface stress, nonlocal parameter, axial half-wave number and aspect ratio are investigated in detail. The results show that the vibrational frequency is significantly affected by the surface material, nonlocal parameter, vibration mode and aspect ratio. In short DWCNTs on condition of higher vibrational modes, the influences of the surface and nonlocal effects on vibration are more pronounced.     

Torsional vibration analysis of double walled carbon nanotubes using nonlocal elasticity

In the present study, the torsional vibration behavior of double walled carbon nanotubes (DWCNTs) is investigated using nonlocal elasticity theory. The effects of van der Waals Force interaction, nanotube length and nonlocal parameter are studied in detail. Two frequency set are obtained for DWCNTs for a given half wave number. It is also shown that some mode shapes are anti-phase and some of them are in-phase. The present results can be useful in design of nano electromechanical systems like nanobearings and rotary servomotors.     

The Identification of Inner Tube Defects in Double‐Wall Carbon Nanotubes

The precise atomic structure and relative atomic conformation of the individual carbon nanotubes comprising a double wall carbon nanotube (DWCNT) is determined. The DWCNTs are imaged using an aberration corrected high resolution transmission electron microscope (HRTEM) operating at 80 kV. Using processing in Fourier space images of the inner and outer tube of a double‐wall carbon nanotube (DWCNT) are analysed. Comparisons of these results with simulated HRTEM images enable the chiral indices and relative atomic correlation of the component tubes of non‐commensurate DWCNTs to be determined. This technique is used to reveal the presence of a defect in the inner tube of a (6, 6)@(18, 2) DWCNT.     

In situ Raman spectroelectrochemical study of 13C-labeled fullerene peapods and carbon nanotubes

C60 fullerene peapods and double-walled carbon nanotubes (DWCNTs) containing highly 13C enriched C60 and inner tubes, respectively, are studied using Raman spectroscopy and in situ Raman spectroelectrochemistry in order to follow the influence of 13C enrichment on the vibrational pattern of these carbon nanostructures. The Raman response of 13C60 after encapsulation in fullerene peapods differs from that of isotope-natural species, (Nat)C60. The Raman A(g)(2) mode of encapsulated 13C60 is upshifted in frequency compared to that of the (Nat)C60 peapods with the same filling factor. The chemical doping of 13C60 peapods (peapod = C(60)@SWCNT) with K-vapor leads to the downshift of the A(g)(2) mode, similar to the case of (Nat)C60 peapods. The 13C60 peapods were successfully transformed into DWCNTs, which confirms high filling of single-walled (SW) CNTs with 13C60. The DWCNTs exhibited distinctly downshifted G and D Raman modes for inner tubes, which proves that only inner tubes were enriched by 13C. The in situ Raman spectroelectrochemistry of (Nat)C60 exhibits strong anodic enhancement, while for 13C60 peapods the enhancement is only weak. On the other hand, the electrochemical charging of the inner-tube-labeled DWCNTs (13C(i)-DWCNTs) followed the behavior of ordinary (Nat)C(i)-DWCNTs as indicated by in situ Raman spectroelectrochemistry. In addition, the spectroelectrochemical behavior of the G mode of inner tubes in 13C(i)-DWCNTs is followed from the start of the electrochemical doping, which was not feasible for (Nat)C(i)-DWCNTs.     

纳米碳管结构差异对树脂炭包覆硅/纳米碳管复合材料电化学性能的影响

采用聚乙烯醇（PVA）树脂炭化的方法，制备了PVA树脂炭包覆硅／不同纳米碳管复合材料，通过X-射线、高分辩电镜观察和电化学性能测试等手段比较研究了单壁、双壁和多壁纳米碳管作为弹性导电网络缓解硅在充放电过程中体积变化方面的效果。结果表明，单壁纳米碳管和双壁纳米碳管比多壁纳米碳管能够更好地缓解硅在循环过程中产生的结构和体积变化，这主要是因为其长径比大，缠裹效果更好。单壁纳米碳管和双壁纳米碳管具有相近的直径、长径比及宏观分布形式，但在循环过程中，双壁纳米碳管的结构稳定性好于单壁纳米碳管，进而其缓解硅结构变化的效果更好。