Predicting mechanical properties of single-walled carbon nanocones using a higher-order gradient continuum computational framework

The higher-order gradient continuum theory is employed to study the structural parameters and elastic properties of single-walled carbon nanocones (SWCNCs), where the higher-order Cauchy–Born rule is used to link the deformation of the carbon atomic structure to that of the continuum level. Unlike single-walled carbon nanotubes (SWCNTs), mechanical properties of SWCNCs vary along its side edge’s direction, owing to the monotonically increasing radius. In the constitutive model, a representative cell in an initial graphite sheet is selected to study the mechanical property of this domain of SWCNCs. By minimizing the potential energy of the representative cell in the undeformed SWCNC, structural parameters and elastic properties of the domain are obtained. The varying chiralities seem to have a large impact on mechanical properties of SWCNCs. Five kinds of SWCNCs are chosen in our study to test the influence of the apex angle on mechanical properties. The computational results demonstrate that mechanical properties of SWCNCs trend to the constant of graphite sheet when the radius is extremely large but this trend becomes mild as the apex angle increases.     

Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh–Ritz technique

Axial buckling characteristics of single-walled carbon nanotubes (SWCNTs) including thermal environment effect are studied in this paper. Eringen’s nonlocal elasticity equations are incorporated into the classical Donnell shell theory to establish a nonlocal elastic shell model which takes small-scale effects into account. The Rayleigh–Ritz technique is implemented in conjunction with the set of beam functions as modal displacement functions to consider the four commonly used boundary conditions namely as simply supported–simply supported, clamped–clamped, clamped–simply supported, and clamped-free in the buckling analysis. Selected numerical results are presented to demonstrate the influences of small scale effect, aspect ratio, thermal environment effects and boundary conditions in detail. It is found that the value of aspect ratio has different effects on the critical axial buckling loads of SWCNTs in low and high temperature environments. Also, it is observed that the difference between the thermal axial buckling responses of SWCNTs relevant to various boundary conditions is more prominent for higher values of nonlocal elasticity constant.     

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.     

Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM

In the present work differential transformation method (DTM) is used to predict the buckling behaviour of single walled carbon nanotube (SWCNT) on Winkler foundation under various boundary conditions. Four different boundary conditions namely clamped–clamped, simply supported, clamped hinged and clamped free are used to study the critical buckling loads. Effects of (i) size of SWCNT (ii) nonlocal parameter and (iii) Winkler elastic modulus on nonlocal critical buckling loads are being investigated and discussed. The DTM is implemented for the nonlocal SWCNT analyses and this yields results with high degree of accuracy. Further, present method can be applied to linear and nonlinear problems.     

Nonlocal and shear effects on column buckling of single-layered membranes from stocky single-walled carbon nanotubes

Axial buckling behavior of single-layered membranes from vertically aligned single-walled carbon nanotubes is studied in the context of the nonlocal continuum theory of Eringen. To this end, useful discrete models based on the nonlocal Rayleigh, Timoshenko, and higher-order beam theories are developed to evaluate critical buckling loads associated with both in-plane and out-of-plane buckling modes. In discrete models, the size of the eigenvalue equations to be solved drastically magnifies for highly populated membranes. Thereby, development of models whose computational efforts do not affected by the population of the membrane is of great advantageous. To bridge this scientific gap, appropriate nonlocal continuous models are established based on the developed discrete models. The accuracy of the proposed discrete and continuous models is checked and remarkable results are achieved. Subsequently, the roles of the influential factors on both in-plane and out-of-plane axial buckling loads are addressed. The obtained results can be regarded as a basic step in examining of axial buckling mechanisms of more complex systems consist of multi-layered membranes from parallel or even orthogonal single-walled carbon nanotubes.     

Nonlocal continuum model and molecular dynamics for free vibration of single-walled carbon nanotubes

Free transverse, longitudinal and torsional vibrations of single-walled carbon nanotubes (SWCNTs) are investigated through nonlocal beam model, nonlocal rod model and verified by molecular dynamics (MD) simulations. The nonlocal Timoshenko beam model offers a better prediction of the fundamental frequencies of shorter SWCNTs, such as a (5, 5) SWCNT shorter than 3.5 nm, than local beam models. The nonlocal rod model is employed to study the longitudinal and torsional vibrations of SWCNT and found to enable a good prediction of the MD results for shorter SWCNTs. Nonlocal and local continuum models provide a good agreement with MD results for relatively longer SWCNTs, such as (5, 5) SWCNTs longer than 3.5 nm. The scale parameter in nonlocal beam and rod models is estimated by calibrations from MD results.     

基于非局部应变梯度欧拉梁模型的充流单壁碳纳米管波动分析

将非局部弹性理论和应变梯度理论结合,再根据流体滑移边界理论,建立了考虑流体和固体小尺度效应的充流单壁碳纳米管(SWCNT)流固耦合动力学模型,分别以非局部应力效应、应变梯度效应和流体滑移边界效应模拟微观小尺度效应对系统的影响,推导得出充流单壁碳纳米管的Euler-Bernoulli梁波动控制方程。通过对控制方程的求解,分析材料不同类型尺度效应对充流碳纳米管的振动和波动特性影响。结果显示,应变梯度效应和流体边界效应对低频波动起促进作用,对高频波动起阻尼作用,应力非局部效应则对波动始终产生阻尼作用。三种尺度效应对低流速系统的振动有促进作用,而对高流速系统产生阻尼作用。     

A structural mechanics study of single-walled carbon nanotubes generalized from atomistic simulation

A new structural mechanics model is developed to closely duplicate the atomic configuration and behaviours of single-walled carbon nanotubes (SWCNTs). The SWCNTs are effectively represented by a space frame, where primary and secondary beams are used to bridge the nearest and next-nearest carbon atoms, to mimic energies associated with bond stretching and angle variation, respectively. The elastic properties of the frame components are generalized from molecular dynamics (MD) simulation based on an accurate ab initio force field, and numerical analyses of tension, bending, and torsion are carried out on nine different SWCNTs. The space-frame model also closely duplicates the buckling behaviours of SWCNTs in torsion and bending. In addition, by repeating the same process with continuum shell and beam models, new elastic and section parameters are fitted from the MD benchmark experiments. As an application, all three models are employed to study the thermal vibration behaviours of SWCNTs, and excellent agreements with MD analyses are found. The present analysis is a systematic structural mechanics attempt to fit SWCNT properties for several basic deformation modes and applicable to a variety of SWCNTs. The continuum models and fitted parameters may be used to effectively simulate the overall deformation behaviours of SWCNTs at much larger length-?and timescales than pure MD analysis.     

Fabrication and electrochemical behavior of single-walled carbon nanotube/graphite-based electrode

An electrochemical method for determining the dihydroxybenzene derivatives on glassy carbon (GC) has been developed. In this method, the performance of a single-walled carbon nanotube (SWCNT)/graphite-based electrode, prepared by mixing SWCNTs and graphite powder, was described. The resulting electrode shows an excellent behavior for redox of 3,4-dihydroxybenzoic acid (DBA). SWCNT/graphite-based electrode presents a significant decrease in the overvoltage for DBA oxidation as well as a dramatic improvement in the reversibility of DBA redox behavior in comparison with graphite-based and glassy carbon (GC) electrodes. In addition, scanning electron microscopy (SEM) and atomic force microscopy (AFM) procedures performed for used SWCNTs.     

Polydiacetylene single-walled carbon nanotubes nano-hybrid for cellular imaging applications

The functionalization of single-walled carbon nanotubes (SWCNTs) by forming self-assembled supramolecular structure of 10,12-pentacosadiynoic acid (PCDA) on the carbon nanotube wall is reported. PCDA assemblies on SWCNTs (PCDA/SWCNTs) were polymerized by UV irradiation to extensively conjugated polydiacetylene (PDA). PDA/SWCNT was identified by absorption and emission spectroscopy, scanning and transmission electron microscopies (SEM and TEM) and atomic force microscopy (AFM). PDA/SCWNTs showed strong near-infrared (NIR) fluorescence caused by fluorescence resonance energy transfer (FRET) between PDA network and semiconducting SWCNT core. The micro-patterning of biotinylated PDA/SWCNT with FITC-avidin on biotinylated glass surface demonstrated the potential application for a bio-sensing device. Furthermore, the biocompatibility for mammalian cancer cells was tested by viability experiments, which revealed that the PDA/SWCNTs had very low toxicity below 31.3 mg/L in terms of pristine SWCNTs concentration. Also, PDA/SWCNTs inside the cells can be observed by NIR microscopy. This unique modular method of preparation can contribute to diverse functionalities for practical applications in various non-invasive cellular imaging.     

Modal analysis of carbon nanotubes and nanocones using FEM

Modal analysis of single-walled carbon nanotubes (SWCNTs) and nanocones (SWCNCs) was performed using a finite element method (FEM) with ANSYS. The vibrational behaviors of fixed beam and cantilever SWCNTs with different section types of a circle and an ellipse were modeled using three-dimensional elastic beams of carbon bonds and point masses. Also, the vibrational behaviors of fixed beam and cantilever SWCNCs with different disclination angles of 120°, 180°, and 240° were modeled using the same method. The beam element natural frequencies were calculated by considering the mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. Each mass element of the carbon atoms was assigned as a point mass at the nodes of the FEM elements. The natural frequencies of zigzag and armchair SWCNTs and SWCNCs were also computed. There were some differences between the findings obtained in this study and the molecular structural mechanics data available in the literature. The natural frequencies of SWCNCs were estimated depending on the geometrical type and disclination angle with different boundary conditions. The natural frequencies of the SWCNCs with disclination angles of 120°, 180°, and 240° increased significantly at higher modes of vibration.     

Manipulation of single-walled carbon nanotubes with a tweezers tip

We demonstrate that a tweezers tip can be directly used to manipulate single-walled carbon nanotube (SWCNT) films and individual SWCNTs (or bundles). Specifically, we can align, bend, and even cut SWCNTs on the substrates where they are grown. With this manipulation technique, we are able to control the position, direction, and length of SWCNTs and fabricate complex patterns. Because of the large size of the tweezers tip, long SWCNTs (hundreds of micrometers in length) are found to be critical for the realization of such manipulations. This finding would contribute to the property studies on nanotubes and the fabrication of nanodevices.     

Oligodeoxyribonucleotide association with single-walled carbon nanotubes studied by SPM

Studies have been performed on both as-received and chemically oxidized single-walled carbon nanotubes (SWCNTs) grown by two different growth methods to better understand the preferential association of the oligodeoxyribonucleotide T30 (ODN) with SWCNTs. Samples of T30 ODN:SWCNT were examined under ambient conditions using non-contact scanning probe microscope (SPM) techniques. The resulting images show different morphologies ranging from tangled networks of SWCNTs to individual, well-dispersed isolated SWCNTs as the sonication time is increased. SPM images of well-dispersed, as-received SWCNTs reveal isolated features that are 1.4 to 2.8 nm higher than the bare SWCNT itself. X-ray photoemission spectroscopy (XPS) confirmed these features to be T30 ODN in nature. Chemically oxidizing the SWCNTs before sonication is found to be an effective way to increase the number of T30 ODN features.     

Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes

Axial, torsional and radial breathing mode (RBM) vibrations of free–free unstressed (i.e., relaxed) single-walled carbon nanotubes (SWCNTs) of different helicities having aspect ratio (length/diameter) of about 15 have been studied using the MM3 potential. It is found that for axial and torsional vibrations, frequencies of the second and the third modes of SWCNTs equal, respectively, twice and three times that of the corresponding first mode. A similar relation also holds for axial and torsional vibrations of a homogeneous linear elastic prismatic body. The RBM frequencies are also used to validate computed frequencies of SWCNTs.Equivalent continuum structures (ECSs) whose frequencies in axial, torsional and radial breathing modes are equal to those of the SWCNTs are identified. The consideration of free ends eliminates the effect of boundary conditions and avoids resolving equivalence between boundary conditions in the analysis of SWCNTs and their ECSs. It is found that the ECS made of a linear elastic homogeneous material is a cylindrical tube of mean radius and length equal to those of the SWCNT. Poisson’s ratio of the ECS (and hence of the SWCNT) computed without assuming any value for the wall thickness converges with an increase in the diameter of the SWCNT to 0.20 for armchair, 0.23 for zigzag, and 0.21 for chiral tubes. For a wall thickness of the ECS equal to 3.4 Å, Young’s modulus of the material of the ECS (and hence of the SWCNT) equals 1 TPa and is independent of the helicity and the diameter of the SWCNT. However, the shear modulus varies with the diameter and the helicity of the underlying SWCNT. In the more common terminology, normal modes of vibrations of a SWCNT give Young’s modulus of 1 TPa in the axial and the circumferential directions, and the shear modulus of 0.4 TPa. Whereas Young’s modulus of a SWCNT is found to be independent of its diameter and helicity, the shear modulus depends weakly upon them.     

Magnetophoretic continuous purification of single-walled carbon nanotubes from catalytic impurities in a microfluidic device

A magnetophoretic continuous purification method is presented of single-walled carbon nanotubes (SWCNTs) from the superparamagnetic iron-catalyst impurities in a microfluidic device without any influence on inherent SWCNT properties. By employing microfluidics and a magnetic-field-induced saw-tooth nickel microstructure, a highly enhanced magnetic force in adjoining microchannels is exploited. The iron impurities of SWCNTs are attracted towards areas of higher magnetic-flux density in the microchannels where magnetic field was asymmetrically generated perpendicularly to the streamline. We obtained highly purified SWCNTs at a rate of 0.36 mg h(-1) and that are estimated to be about 99% purity.     

Functionalization of single-walled carbon nanotubes by citric acid/oxygen plasma treatment

A safe and simple method of functionalizing single-walled carbon nanotubes (SWCNTs) has been developed, that significantly increases their dispersibility in water. SWCNTs in pure ethanol are treated with a supersonic homogenizer and dried. Then they are wetted with weak citric acid solution. Finally an RF (13.56 MHz) citric acid/oxygen plasma reaction is carried out under optimum conditions. As a result, hydrophilic functional groups attach onto the SWCNT surfaces, which enhance their dispersibility in water. The attachment of functional groups is identified by the FT-IR spectroscopy, X-ray photoelectron spectroscopy and thermogravimetric analysis. The dispersibility and dispersion stability are studied by the precipitation tests, UV-visible spectroscopy, and transmission electron microscopy. These functionalized SWCNTs are expected to be used in various applications.     

Enhanced critical pressure for buckling of carbon nanotubes due to an inserted linear carbon chain

Recent findings of linear carbon-atom chains (C-chains) inside carbon nanotubes have stimulated considerable interest. In this work, molecular dynamics (MD) simulation and an elastic string-elastic shell model is adopted to study radial pressure-induced buckling of single-walled carbon nanotubes (SWCNT) filled with a C-chain. The continuum model predicts that the C-chain increases critical buckling pressure considerably (about 40%-160%) for SWCNTs of diameters ranging from 0.68 to 0.72?nm, in reasonable quantitative agreement with the prediction of MD simulation. In particular, the MD simulation confirms that the originally circular cross section of filled SWNTs becomes elliptical after buckling, as predicted by the continuum model.     

Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality

A nonlocal anisotropic elastic shell model is developed to study the effect of small scale on shell-like vibration of single-walled carbon nanotubes (SWCNTs) with arbitrary chirality. Anisotropic elastic shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion are derived and analytical solution for the vibration of anisotropic SWCNTs is presented by using the Flügge shell theory and complex method. The suggested model is justified by a good agreement between the results given by the present model and available data in literature. Furthermore, the model is used to elucidate the effect of small scale on the vibration of zigzag, armchair and chiral SWCNTs. Our results show that small scale is essential for vibration of SWCNTs when the axial wave-length is not extremely long. Moreover, the results show that local model substantially overestimates vibrational frequencies of almost all modes.     

Energetic trends of single-walled carbon nanotube ab initio calculations

Hartree–Fock (HF) calculations for a variety of single-walled carbon nanotube (SWCNT) systems indicate linear relationships between electronic energies and changes in length and circumference for both armchair and zigzag type nanotubes. A simple protocol to predict energies for large SWCNT (C atoms >500) is developed through a set of structural parameters and AM1 optimized geometries from small SWCNTs. The energetic trends shown by the calculations are used to support the theory of SWCNT nucleation from a preformed carbon, or graphene with six 5-member rings, cap.