Dynamic behavior of triple-walled carbon nanotubes conveying fluid

In this study, the instability of triple-walled carbon nanotubes (TWCNTs) conveying fluid is studied based on an Euler–Bernoulli beam model. The van der Waals (vdW) interactions between different carbon nanotubes (CNTs) are taken into account in the analysis, and the Galerkin discretization approach is used to solve the coupled equations of the motions. Numerical simulations show that the interlayer vdW interactions play a significant role in the natural frequencies and the stability of TWCNTs. The critical flow velocities—associated with divergence, restabilization and flutter—are determined. The effects of different inner radius and the value of mode N used in Galerkin discretization on the dynamical behaviors of the fluid-conveyed TWCNTs are also examined in detail. Results reveal that the internal moving fluid plays an important role in the instability of TWCNTs.     

Vibrations of double-nanotube systems with mislocation via a newly developed van der Waals model

This study deals with transverse vibrations of two adjacent-parallel-mislocated single-walled carbon nanotubes (SWCNTs) under various end conditions. These tubes interact with each other and their surrounding medium through the intertube van der Waals (vdW) forces, and existing bonds between their atoms and those of the elastic medium. The elastic energy of such forces due to the deflections of nanotubes is appropriately modeled by defining a vdW force density function. In the previous works, vdW forces between two identical tubes were idealized by a uniform form of this function. The newly introduced function enables us to investigate the influences of both intertube free distance and longitudinal mislocation on the natural transverse frequencies of the nanosystem which consists of two dissimilar tubes. Such crucial issues have not been addressed yet, even for simply supported tubes. Using nonlocal Timoshenko and higher-order beam theories as well as Hamilton's principle, the strong form of the equations of motion is established. Seeking for an explicit solution to these integro-partial differential equations is a very problematic task. Thereby, an energy-based method in conjunction with an efficient meshfree method is proposed and the nonlocal frequencies of the elastically embedded nanosystem are determined. For simply supported nanosystems, the predicted first five frequencies of the proposed model are checked with those of assumed mode method, and a reasonably good agreement is achieved. Through various studies, the roles of the tube's length ratio, intertube free space, mislocation, small-scale effect, slenderness ratio, radius of SWCNTs, and elastic constants of the elastic matrix on the natural frequencies of the nanosystem with various end conditions are explained. The limitations of the nonlocal Timoshenko beam theory are also addressed. This work can be considered as a vital step towards better realizing of a more complex system that consists of vertically aligned SWCNTs of various lengths.     

The effect of Fe and Ni catalysts on the growth of multiwalled carbon nanotubes using chemical vapor deposition

The effect of Fe and Ni catalysts on the synthesis of carbon nanotubes (CNTs) using atmospheric pressure chemical vapor deposition (APCVD) was investigated. Field emission scanning electron microscopy (FESEM) analysis suggests that the samples grow through a tip growth mechanism. High-resolution transmission electron microscopy (HRTEM) measurements show multiwalled carbon nanotubes (MWCNTs) with bamboo structure for Ni catalyst while iron filled straight tubes were obtained with the Fe catalyst. The X-ray diffraction (XRD) pattern indicates that nanotubes are graphitic in nature and there is no trace of carbide phases in both the cases. Low frequency Raman analysis of the bamboo-like and filled CNTs confirms the presence of radial breathing modes (RBM). The degree of graphitization of CNTs synthesized from Fe catalyst is higher than that from Ni catalyst as demonstrated by the high frequency Raman analysis. Simple models for the growth of bamboo-like and tubular catalyst filled nanotubes are proposed.     

Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix

In the current work, the nonlinear vibration of an embedded double-walled carbon nanotube (DWCNT) aroused by nonlinear van der Waals (vdW) interaction forces from both surrounding medium and adjacent tubes is studied. Using both Euler–Bernoulli and Timoshenko beam models, the relation between deflection amplitudes and resonant frequencies of the DWCNT is derived through harmonic balance method. It is found that the nonlinear vdW forces from the surrounding medium result in noncoaxial vibration of the embedded DWCNT. The noncoaxial vibration includes both uni-directional and bi-directional vibration modes. It is found that the surrounding matrix has more prominent effect on the uni-directional vibration in comparison to the bi-directional vibration. The axial load effect on the vibrational behavior of the embedded DWCNT is also discussed. Due to the influence of the surrounding polymer, the prediction on the resonant frequencies of embedded CNTs is quite different from that for free-standing CNTs. A softening behavior for the deflection amplitude-resonant frequency relation is observed for the first time in the bi-directional vibration of the embedded DWCNT, which can only be obtained using the Timoshenko beam theory.     

Structural dependence of nonlinear elastic properties for carbon nanotubes using a continuum analysis

Based on molecular mechanics coupled with the atomistic-based continuum theory, a structural mechanics approach is presented to examine the nonlinear elastic properties of carbon nanotubes (CNTs) subjected to large axial deformations. According to molecular mechanics, the interaction force between atoms is modeled using the Morse potential. The nanoscale continuum theory is established to directly incorporate the Morse potential function into the constitutive model of CNTs. In this paper, we simulate and examine the influence of CNT structures on the stress–strain response. The linear elastic property of CNTs is independent of the helicity of the hexagonal carbon lattice along the tubes, while their nonlinear elastic behavior shows a larger chirality dependence. The present theoretical approach supplies a set of very simple formulas and is able to serve as a good approximation of the mechanical properties of CNTs. PACS 62.20.-x; 62.20.Dc; 62.25.+g     

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.     

Nonlinear finite-element modeling of graphene and single- and multi-walled carbon nanotubes under axial tension

An effective finite-element (FE) approach for modeling the structure and the deformation of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) is presented. An individual tube was modeled using a frame-like structure with beam elements. The effect of van der Waals forces, crucial in MWCNTs, was modeled by spring elements. The success of this new carbon nanotube (CNT) modeling approach was verified by comparing the simulation results for single- and multi-walled nanotubes and graphene with other experimental and computational results available in the literature. Simulations of final deformed configurations were in excellent agreement with the atomistic models for various deformations. The proposed approach successfully predicts the experimentally observed values for mechanical behavior of SWCNTs and MWCNTs. The results demonstrated that the proposed FE technique could provide a valuable tool for studying the mechanical behavior of different types of nanotubes, as well as their effectiveness as load-bearing entities in nanocomposite materials.     

Radial breathing vibration of double-walled carbon nanotubes subjected to pressure

A theoretical vibrational analysis of the radial breathing mode (RBM) of double-walled carbon nanotubes (DWCNTs) subjected to pressure is presented based on an elastic continuum model. The results agree with reported experimental results obtained under different conditions. Frequencies of the RBM in DWCNTs subjected to increasing pressure depend strongly on circumferential wave numbers, but weakly on the aspect ratio and axial half-wave numbers. For the inner and outer tubes of DWCNTs, the frequency of the RBM increases obviously as the pressure increases under different conditions. The range of variation is smaller for the inner tube than the outer tube.     

Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure

Radial buckling stresses of carbon nanotubes (CNTs) need to be studied in high-pressure resonance Raman scattering spectrum. In this work, the closed-form expression of the critical buckling stress of multi-walled carbon nanotubes (MWCNTs) under hydrostatic pressure is derived that can be conveniently employed. Using the derived formulae, the critical buckling stresses of single-walled carbon nanotubes and double-walled carbon nanotubes with different diameters are calculated. The results are in good agreement with other reported literatures. In addition, the critical buckling stresses of each layer of a quintuple-walled CNT in different buckling modes are predicted, showing that the buckling instability can occur not only in the outermost rolled layer, but also in other rolled layer of MWCNTs by considering different diameters and buckling modes.     

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.     

Elastic properties of single-wall nanotubes

3 , BC₂N, and C₃N₄. These studies have been carried out using a total-energy, non-orthogonal, tight-binding parametrisation which is shown to provide results in good agreement both with calculations using higher levels of theory and the available experimental data. Our results predict that of all types of nanotubes considered, carbon nanotubes have the highest Young’s modulus. We have considered tubes of different diameters, ranging from 0.5 to 2 nm, and find that in the limit of large diameters the mechanical properties of nanotubes approach those of the corresponding flat graphene-like sheets. Received: 30 November 1998 / Accepted: 14 December 1998     

Vibrations of carbon nanotube-reinforced composites

This work deals with a study of the vibrational properties of carbon nanotube-reinforced composites by employing an equivalent continuum model based on the Eshelby-Mori-Tanaka approach. The theory allows the calculation of the effective constitutive law of the elastic isotropic medium (matrix) with dispersed elastic inhomogeneities (carbon nanotubes). The devised computational approach is shown to yield predictions in good agreement with the experimentally obtained elastic moduli of composites reinforced with uniformly aligned single-walled carbon nanotubes (CNTs). The primary contribution of the present work deals with the global elastic modal properties of nano-structured composite plates. The investigated composite plates are made of a purely isotropic elastic hosting matrix of three different types (epoxy, rubber, and concrete) with embedded single-walled CNTs. The computations are carried out via a finite element (FE) discretization of the composite plates. The effects of the CNT alignment and volume fraction are studied in depth to assess how the modal properties are influenced both globally and locally. As a major outcome, the lowest natural frequencies of CNT-reinforced rubber composites are shown to increase up to 500 percent.     

In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium

The effect of the induced vibrations in the carbon nanotubes (CNTs) arising from the internal fluid flow is a critical issue in the design of CNT-based fluidic devices. In this study, in-plane vibration analysis of curved CNTs conveying fluid embedded in viscoelastic medium is investigated. The CNT is modeled as a linear elastic cylindrical tube where the internal moving fluid is characterized by steady flow velocity and mass density of fluid. A modified-inextensible theory is used in formulation and the steady-state initial forces due to the centrifugal and pressure forces of the internal fluid are also taken into account. The finite element method is used to discretize the equation of motion and the frequencies are obtained by solving a quadratic eigenvalue problem. The effects of CNT opening angle, the elastic modulus and the damping factor of the viscoelastic surrounded medium and fluid velocity on the resonance frequencies are elucidated. It is shown that curved CNTs are unconditionally stable even for a system with sufficiently high flow velocity. The most results presented in this investigation have been absent from the literature for fluid-induced vibration of curved CNTs embedded in viscoelastic foundations.     

Vibrational analysis of carbon nanotubes using molecular mechanics and artificial neural network

This paper presents the molecular mechanics based finite element modeling of carbon nanotubes (CNTs) and their applications as mass sensors. The beam element with elastic behavior is considered as the bond between the carbon atoms and its properties are obtained using equating continuum and molecular characteristics. The first five natural frequencies of CNTs in cantilever and doubly clamped boundary conditions (BCs) and their corresponding mode shapes are studied in detail. Furthermore, a multilayer perceptron neural network is used to predict the fundamental vibration frequencies of the CNTs with different diameters and lengths. In addition, variations of the natural frequencies of the CNTs with distorted cross sections are investigated. Moreover, the effects of some attached masses with various values on the first three natural frequencies of a considered CNT are studied here.     

A Comprehensive Numerical Investigation on the Mechanical Properties of Hetero-Junction Carbon Nanotubes

A set of forty-three hetero-junction CNTs, made of forty-four homogeneous carbon nanotubes of different chiralities and configurations with all possible hetero-connection types, were numerically simulated, based on the finite element method in a commercial finite element software and their Young's and shear moduli, and critical buckling loads were obtained and evaluated under the tensile, torsional and buckling loads with an assumption of linear elastic deformation and also compared with each other. The comparison of the linear elastic behavior of hetero-junction CNTs and their corresponding fundamental tubes revealed that the size, type of the connection, and the bending angle in the structure of hetero-junction CNTs considerably influences the mechanical properties of these hetero-structures. It was also discovered that the Stone-Wales defect leads to lower elastic and torsional strength of hetero-junction CNTs when compared to homogeneous CNTs. However, the buckling strength of the hetero-junction CNTs was found to lie in the range of the buckling strength of their corresponding fundamental tubes. It was also determined that the shear modulus of hetero-junction carbon nanotubes generally tends to be closer to the shear modulus of their wider fundamental tubes while critical buckling loads of these heterostructures seem to be closer to critical buckling loads of their thinner fundamental tubes. The evaluation of the elastic properties of hetero-junction carbon nanotubes showed that among the hetero-junction models, those with armchair-armchair and zigzag-zigzag kinks have the highest elastic modulus while the models with armchair-zigzag connections show the lowest elastic stiffness. The results from torsion tests also revealed the fact that zigzag-zigzag and armchair-zigzag hetero-junction carbon nanotubes have the highest and the lowest shear modulus, respectively. Finally, it was observed that the highest critical buckling loads belong to armchair-armchair hetero-junction carbon nanotubes and the lowest buckling strength was found with the hetero-junction models with armchair-zigzag connection.     

Interaction of Methane with Single-Walled Carbon Nanotubes： Role of Defects,Curvature and Nanotubes Type

We investigate the interaction of single-walled carbon nanotubes （SWCNTs） and methane molecule from the first principles. Adsorption energies are calculated, and methane affinities for the typical semiconducting and metallic nanotubes are compared. We also discuss role of the structural defects and nanotube curvature on the adsorption capability of the SWCNTs. We could observe larger adsorption energies for the metallic CNTs in comparison with the semiconducting CNTs. The obtained results for the zig zag nanotubes with various diameters reveal that the adsorption energy is higher for nanotubes with larger diameters. For defected tubes the adsorption energies are calculated for various configurations such as methane molecule approaching to the defect sites pentagon, hexagon, and heptagon in the tube surface. The results show that the introduce defects have an important contribution to the adsorption mechanism of the methane on SWNTs.     

A Simple and Facile Approach to Synthesize Water-Soluble Multiwalled Carbon Nanotubes Wrapped by Poly(4-Vinylpyridine)

By simple grinding, water-soluble linear polymers poly(4-vinylpyridine) (PVP) wrapped around multiwalled carbon nanotubes (MWCNTs) and thus rendered them reversibly soluble in water, ethanol, and DMF. The structure and properties of the resulting nanocomposite, CNTs wrapped by PVP, were evaluated by SEM, AFM, TGA, and FTIR spectroscopy. Individual tubes are clearly observed after PVP-wrapped nanotubes were spin-coated onto a silicon wafer as determined by SEM and AFM. Subsequently, a novel and facile approach to attach high-density and uniform size gold nanoparticles on individual multiwalled carbon nanotubes was achieved by in situ reduction of HAuCl₄ in the homogeneous aqueous solution of MWCNTs–PVP.     

Nonlinear dynamics of bi-layered graphene sheet,double-walled carbon nanotube and nanotube bundle

Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff–Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6–12 potential function. The equivalent nonlinear material model of carbon–carbon bond is used to model it based on its force–deflection relation. Newmark’s algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.     

多壁碳纳米管储氢的物理吸附特性

采用巨正则蒙特卡罗方法 ,模拟常温、1 0MPa下氢在扶手椅型多壁壁碳纳米管中的物理吸附过程 .氢分子之间、氢分子与碳原子之间的相互作用采用Lennard Jones势能模型 .研究了双壁碳纳米管外 (内 )径固定而内 (外 )径改变时的物理吸附储氢情况 ,发现氢分子主要储存在双壁碳纳米管的管壁附近 ,当双壁碳纳米管的内外管壁间距由 0 .34nm增大到 0 .6 1或 0 .88nm时可有效增加物理吸附储氢量 ,并给出了相应的理论解释 .在此基础上 ,计算了管壁间距为 0 .34、0 .6 1和 0 .88nm时的三壁碳纳米管的物理吸附储氢量 ,并与相同条件下单壁和双壁碳纳米管的物理吸附储氢量作了比较 ,发现多壁碳纳米管的物理吸附储氢量随碳管层数的增加而减小 .     

Natural Frequencies of Bending Vibrations of Carbon Nanotubes

Technical Physics - Using a molecular-dynamics model with a reduced number of degrees of freedom, the natural frequencies of bending vibrations of carbon nanotubes (CNTs) of various diameters are...