Catalyst-free growth of amorphous silicon nanowires by laser ablation

Carbon nanotubes (CNTs) appear to be ideal tip materials of atomic force microscopy (AFM) due to their small diameter and high stiffness. In this study, double-walled carbon nanotube (DWCNT) structures with different lengths of inner and outer layers are proposed as AFM tips. Both the vibration response and mode shapes of the tipped nanotubes under axial compression are studied by a theoretical nanobeam model. The results show that the natural frequencies of DWCNTs are significantly affected by the compressive loads and the length difference between the inner and outer nanotubes. The natural frequency associated with certain vibrational modes decreases with increasing compressive loads. This research may provide a useful reference for practical design for AFM tips with CNTs.     

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.     

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.     

On the buckling behavior of connected carbon nanotubes with parallel longitudinal axes

The application of hetero-junction carbon nanotubes (CNTs) is increasing continuously due to their outstanding properties in nano-mechanical systems. Several investigations have been conducted to study the behavior of CNTs. In this paper, straight hetero-junctions and their constituent CNTs (armchair and zigzag) were simulated by a commercial finite element package. Then, the buckling behavior of CNTs was evaluated by comparing the critical buckling load of each straight hetero-junction and its constituent CNTs. Both obtained, i.e. analytical calculations and computational, results were compared. The investigations showed that, first, the behavior of homogeneous CNTs under cantilevered boundary conditions follows the assumption of the classical Euler equation. Second, the analytical solutions are in good agreement with the finite element simulation results. In addition, it was shown that the first critical buckling load of hetero-junctions lies within the value of the fundamental homogeneous CNT range. It was also concluded that the buckling load of straight hetero-junctions and their fundamental CNTs increases by increasing the chiral number of both armchair and zigzag CNTs. The current study provides a better insight towards the prediction of straight hetero-junction CNTs behavior.     

Predicting the nonlinear tensile behavior of carbon nanotubes using finite element simulation

Carbon nanotubes (CNTs) possess extremely high mechanical properties and could be the ultimate reinforcing materials for the development of nanocomposites. In this work, a Finite Element (FE) model based on the molecular mechanics theory was developed to evaluate tensile properties of single-walled carbon nanotubes (SWCNTs). The deformation and fracture of carbon nanotubes under tensile strain conditions were studied by common FE software, Ansys. In this model, individual carbon nanotube was simulated as a frame-like structure, and the primary bonds between two nearest-neighboring atoms were treated as beam elements. The beam element properties were determined via the concept of energy equivalence between molecular dynamics and structural mechanics. So far, several researches have studied the elastic behavior of CNTs, and its nonlinearity is not well understood. The novelty of the model lies on the use of nonlinear beam elements to evaluate SWNTs tensile failure. The obtained calculated mechanical properties show good agreement with existing numerical and experimental results.     

Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation

Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been an active research subject over the past few years. Despite the importance of the topic, robust knowledge is still missing in the understanding of the role of various physical parameters affecting the natural frequencies, such as the stretching of doubly clamped CNTs, the DC electrostatic force, and the initial curvature of slack CNTs. In this investigation, we use a 2D nonlinear curved beam model in the form of an arch to simulate the coupled in-plane and out-of-plane motions of a CNT with curvature. We calculate the variation of its natural frequencies and mode shapes with the level of slackness and the DC electrostatic load. Towards this end, we derive a reduced-order model using a multimode Galerkin procedure. We show various scenarios of mode crossing and mode veering as the levels of slackness and DC load are varied. Finally, we tackle the forced vibration problem of a curved CNT when actuated by small DC and AC loads. The results show the transfer of energy among the vibration modes involved in the veering phenomenon.     

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...     

Radial breathing mode frequencies of carbon nanotubes for determination of their diameters

In this paper, exact formulas are obtained for the radial breathing mode (RBM) frequencies of triple-walled carbon nanotubes (TWCNTs) using symbolic package in MAPLE software. For this purpose, TWCNT is considered as triple concentric elastic thin cylindrical shells, which are coupled through van der Waals (vdW) forces between two adjacent tubes. Lennard–Jones potential is used to calculate the vdW forces between adjacent tubes. Then, explicit formulas for RBM frequencies of single-walled (SW), and double-walled (DW) CNTs have been deduced from TWCNT formulas that show an excellent agreement with the available experimental results and the other theoretical model results. The advantage of this analytical approach is that the elastic shell model considers all degrees of freedom in the vibrational analysis of CNTs. To demonstrate the accuracy of this work, the RBM frequencies of different multi-walled carbon nanotubes (MWCNTs) are compared with the available experimental or atomistic results with relative errors of less than 1.5%. To illustrate the application of this approach, the diameters of DWCNTs are obtained from their RBM frequencies which show an excellent agreement with the available experimental results. Also, this approach can be used to determine the diameters of the TWCNTs and MWCNTs. The influence of changing the geometrical and mechanical parameters of a TWCNT on its RBM frequencies has been investigated, too.     

Investigating the effect of interphase and surrounding resin on carbon nanotube free vibration behavior

The free vibration analysis of a carbon nanotube (CNT) embedded in a volume element is performed using 3D finite element (FE) and analytical models. Three approaches consist of molecular and continuum mechanics FE methods and continuum analytical method are employed to simulate the CNT, interphase region and surrounding matrix. The bonding between CNT and polymer is treated as non-perfect bonding using van der Waals and triple phase material interaction in first and second approaches. In analytical approach a perfect bonding is assumed between nanotube and matrix. First, natural frequencies of CNT under different boundary conditions and aspect ratios are obtained by three approaches and the results are compared with published data. The results show the frequency response variations of CNT in GHz to THz range. Subsequently, vibration behaviors of CNT/polymer are evaluated and the results revealed the importance of interphase region role in the performance of nanocomposites. The results also showed the convergence of the natural frequencies for 1–2.5% of CNT volume in high aspect ratios using three methods, so that the interphase effects is negligible. In addition, it is observed that the molecular method due to interphase role has proper performance in vibration behavior investigation of volume elements.     

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.     

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

Based on the Mindlin's first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton's principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.     

模拟研究碳纳米管的热稳定性质

运用分子动力学方法具体模拟研究单个碳纳米管（CNTs）在加热过程中的结构变化．选择多组不同结构的单壁碳纳米管（SWCNTs）和双壁碳纳米管（DWCNTs）作为研究对象,加热温度从室温开始到4000 K,压强保持为1 atm．结果表明单壁碳管中手性型结构热稳定性最好,其次是扶手椅型和锯齿型,当手性角相同时,直径大的热稳定性更高;对于双壁碳管,研究表明当双壁中至少之一为手性结构时其热稳定好,而内外壁均为锯齿结构的稳定性最差,该结果进一步支持了有关单壁碳管的结论;还从理论上探索了描述结构热稳定性的方式,并在键层 关键词： 单壁碳纳米管 双壁碳纳米管 分子动力学方法 热稳定性能     

Estimation of mechanical properties of nanomaterials using artificial intelligence methods

Computational modeling tools such as molecular dynamics (MD), ab initio, finite element modeling or continuum mechanics models have been extensively applied to study the properties of carbon nanotubes (CNTs) based on given input variables such as temperature, geometry and defects. Artificial intelligence techniques can be used to further complement the application of numerical methods in characterizing the properties of CNTs. In this paper, we have introduced the application of multi-gene genetic programming (MGGP) and support vector regression to formulate the mathematical relationship between the compressive strength of CNTs and input variables such as temperature and diameter. The predictions of compressive strength of CNTs made by these models are compared to those generated using MD simulations. The results indicate that MGGP method can be deployed as a powerful method for predicting the compressive strength of the carbon nanotubes.     

碳纳米管对接成异质结器件的计算模拟

基于Stone-Wales缺陷演变理论与分子动力学、Monte Carlo计算方法, 进行了碳纳米管(CNTs)对接成异质结器件的计算模拟.首先, 提出了一种模拟CNTs端帽位置变化的新算法, 并计算模拟了单根CNT的端帽从开口到闭合的过程. Stone-Wales缺陷演变被设计模拟这些端帽变化的跃变过程, 以模拟C–C键的生成与断裂, 而分子动力学则作为跃变后构型弛豫的渐变模拟. 同时, 研究了不同管型CNTs的端帽打开并对接形成异质结的过程.研究结果显示, 对接初期在对接处先产生大量的缺陷, 以促进反应的发生. 这些缺陷趋向于演变成稳定的六元环结构, 或者五元环/七元环的结构, 使异质结趋于稳定. 关键词： 碳纳米管 Monte Carlo Stone-Wales缺陷 分子动力学     

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.     

Dynamic evolution of interacting carbon nanotubes suspended in a fluid using a dielectrophoretic framework

A theoretical investigation of the dynamic response of interacting carbon nanotubes (CNTs) dispersed in a liquid medium under alternating current electric fields is presented. The proposed modeling strategy is based on the dielectrophoretic theory and classical electrodynamics of rigid bodies, and considers the coupled rotation-translation motion of interacting CNTs represented as electrical dipoles. Based on experimental evidence, the parameters which are expected to cause a major contribution to the CNTs' motion are investigated for different initial configurations of CNTs. It is predicted that high electric field frequencies, long CNTs, high values of electrical permittivity and conductivity of the CNTs immersed in solvents of high polarity promote faster equilibrium conditions, achieved by CNT tip-to-tip contact and alignment along the electric field direction. For the majority of the scenarios, CNT alignment along the field direction is predicted as the first event, followed by the translation of aligned CNTs until the tip-to-tip contact condition is reached. For systems with interacting CNTs with different lengths, equilibrium of the shorter CNT is achieved faster. Predictions also show that the initial rotation angles and initial location of CNTs have a paramount influence on the evolution of the system towards the equilibrium configuration.     

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     

Mapping the intracellular distribution of carbon nanotubes after targeted delivery to carcinoma cells using confocal Raman imaging as a label-free technique

The uptake of carbon nanotubes (CNTs) by mammalian cells and their distribution within cells is being widely studied in recent years due to their increasing use for biomedical purposes. The two main imaging techniques used are confocal fluorescence microscopy and transmission electron microscopy (TEM). The former, however, requires labeling of the CNTs with fluorescent dyes, while the latter is a work-intensive technique that is unsuitable for in situ bio-imaging. Raman spectroscopy, on the other hand, presents a direct, straightforward and label-free alternative. Confocal Raman microscopy can be used to image the CNTs inside cells, exploiting the strong Raman signal connected to different vibrational modes of the nanotubes. In addition, cellular components, such as the endoplasmic reticulum and the nucleus, can be mapped. We first validate our method by showing that only when using the CNTs' G band for intracellular mapping accurate results can be obtained, as mapping of the radial breathing mode (RBM) only shows a small fraction of CNTs. We then take a closer look at the exact localization of the nanotubes inside cells after folate receptor-mediated endocytosis and show that, after 8-10 h incubation, the majority of CNTs are localized around the nucleus. In summary, Raman imaging has enormous potential for imaging CNTs inside cells, which is yet to be fully realized.     

Effect of electrochemical treatment on structural properties of conical carbon nanotubes

Interaction of multiwalled conical carbon nanotubes (CNTs) with hydrogen during their electrochemical treatment was studied by galvanostatic measurements and Raman spectroscopy. The structural changes occurring in the conical walls of the CNTs in consequence of the hydrogenation were investigated by using X-ray diffraction (XRD). The results obtained show that hydrogen sorption by conical CNTs is reversible. XRD studies revealed that the electrochemical hydrogenation leads to a change in the diffraction peak profile (2θ=26^°) and its position corresponding to the interplanar distance in conical CNTs. The results indicate structural changes occurring in the conical walls of the CNTs during hydrogenation. We assume that these structural changes can be caused by the hydrogen intercalation into the interplanar spaces of conical CNTs. Thus, the charge/discharge and structure data can be explained by the existence in this system of physically adsorbed molecular hydrogen and chemically bound atomic hydrogen.     

Compressive characteristics of single walled carbon nanotube with water interactions investigated by using molecular dynamics simulation

The elastic properties of single walled carbon nanotube (SWCNT) with surrounding water interactions are studied using molecular dynamics simulation technique. The compressive loading characteristic of carbon nanotubes (CNTs) in a fluidic medium such as water is critical for its role in determining the lifetime and stability of CNT based nano-fluidic devices. In this paper, we conducted a comprehensive analysis on the effect of geometry, chirality and density of encapsulated water on the elastic properties of SWCNT. Our studies show that defect density and distribution can strongly impact the compressive resistance of SWCNTs in water. Further studies were conducted on capped SWCNTs with varying densities of encapsulated water, which is necessary to understand the strength of CNT as a potential drug carrier. The results obtained from this paper will help determining the potential applications of CNTs in the field of nano-electromechanical systems (NEMS) such as nano-biological and nano-fluidic devices.