Stability analysis of double-walled carbon nanotubes as AFM probes based on a continuum model

The instability of single-walled carbon nanotubes (SWCNTs) under compressive loading has been observed experimentally by TEM and may limit their performance and structural integrity as atomic force microscopy (AFM) tips. Double-walled carbon nanotubes (DWCNTs) with inner and outer nanotubes of different lengths are proposed as AFM probes, and a theoretical approach based on a nanobeam model is developed for investigating the critical buckling stress of the DWCNTs under an axial compressive load. The influence of structural parameters on the buckling stress of DWCNT AFM probes are analyzed using this approach. The results show that the influence of the length mismatch between inner and outer nanotubes, as well as buckling modes on the buckling stress of DWCNTs was significant.     

Effect of strain rate on the buckling behavior of single- and double-walled carbon nanotubes

Molecular dynamics simulations are performed on single- (SWCNTs) and double-walled carbon nanotubes (DWCNTs) to investigate the effects of strain rate on their buckling behavior. The Brenner’s second-generation reactive empirical bond order and Lennard-Jones 12-6 potentials are used to describe the short range bonding and long range van der Waals atomic (vdW) interaction within the carbon nanotubes, respectively. The sensitivity of the buckling behavior with respect to the strain rate is investigated by prescribing different axial velocities to the ends of the SWCNTs and DWCNTs in the compression simulations. In addition, the effects of vdW interaction between the walls of the DWCNTs on their buckling behavior are also examined. The simulation results show that higher strain rates lead to higher buckling loads and buckling strains for both SWCNTs and DWCNTs. A distinguishing characteristic between SWCNTs and DWCNTs is that the former experiences an abrupt drop in axial load whereas the axial load in latter decreases over a finite, albeit small, range of strain after buckling initiates. The buckling capability of DWCNT is enhanced in the presence of vdW interaction. DWCNTs can sustain a higher strain before buckling than SWCNTs of similar diameter under otherwise identical conditions.     

Analysis of the vibration characteristics of double-walled carbon nanotubes

The induced electric-field has been applied to measure the elastic modulus of carbon nanotubes. However, the vibrational modes of the multi-walled carbon nanotubes are quite different from those of the single-walled carbon nanotubes. Analysis of the vibration characteristics of double-walled carbon nanotubes (DWCNTs) with simply supported boundary condition are carried out based on Euler–Bernoulli beam theory. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is found that the vibrational modes of DWCNTs are noncoaxial intertube vibrations, and the deflections of the inner and outer nanotubes can occur in the same or in opposite deflections. In the same vibrational mode, the resonant frequencies of DWCNTs with deflections between the inner and outer nanotubes in the same direction are smaller than those of DWCNTs with the opposite deflections.     

Torsional buckling of double-walled carbon nanotubes

The mechanical instability of doubled-walled carbon nanotubes subject to torsion motion is investigated through molecular dynamics. A newly revealed buckling mode with one or three thin, local rims on the outer tube was discovered while the inner tube shows a helically aligned buckling mode in three dimensions. The distinct buckling modes of the two tubes imply the inapplicability of continuum mechanics modeling in which it is postulated that the buckling modes of the constituent tubes have the same shape. In view of this problem, a new concept of the equivalent thickness of double-walled carbon nanotubes is introduced, which enables the Kromm shell model to be applied to the derivation of the torsional buckling angle without the restraint of the two tubes having identical shapes.     

Radial breathing mode of carbon nanotubes subjected to axial pressure

In this paper, a theoretical analysis of the radial breathing mode (RBM) of carbon nanotubes (CNTs) subjected to axial pressure is presented based on an elastic continuum model. Single-walled carbon nanotubes (SWCNTs) are described as an individual elastic shell and double-walled carbon nanotubes (DWCNTs) are considered to be two shells coupled through the van der Waals force. The effects of axial pressure, wave numbers and nanotube diameter on the RBM frequency are investigated in detail. The validity of these theoretical results is confirmed through the comparison of the experiment, calculation and simulation. Our results show that the RBM frequency is linearly dependent on the axial pressure and is affected by the wave numbers. We concluded that RBM frequency can be used to characterize the axial pressure acting on both ends of a CNT.     

Torsional instability of carbon nanotubes encapsulating C60 fullerenes

The torsional instability of a single-walled carbon nanotube containing C60 fullerenes is investigated using molecular dynamics. A newly revealed observation of a reduction of the shear stiffness of the carbon nanotube filled with C60 fullerenes during torsion shows an unusual local buckling nature of the material instead of a global buckling of an unfilled carbon nanotube at a critical torsional angle. Such local buckling largely increases the critical torsional angle for the instability of the material, and hence enhances its stability. Simulations show that the local buckling of the material is a result of the van der Waals interaction between the nanotube and the encapsulated C60 fullerenes.     

The effect of carbon nanotube aspect ratio and loading on the elastic modulus of electrospun poly(vinyl alcohol)-carbon nanotube hybrid fibers

The reinforcement effect of carbon nanotubes (CNTs) has been examined as a function of their loading and aspect ratio in poly(vinyl alcohol) (PVA) based hybird fibers. Lignosulfonic acid sodium salt (LSA) was used to disperse CNTs to produce consistently high CNT loaded PVA-LSA-CNT hybrid fibers using an electrospinning process. The elastic modulus of individual fibers was measured using atomic force microscopy. The presence of CNTs significantly increased the average elastic modulus of PVA-LSA-CNT fibers compared to PVA-LSA fibers. The elastic modulus, however, exhibited no fiber diameter dependency. Transmission electron microscopy (TEM) was used to determine the loading and the aspect ratio of CNTs in each hybrid fiber. The CNT loading in PVA-LSA-CNT fibers varied widely due to non-uniform CNT dispersion and displayed no relationship with the elastic modulus. Our results also demonstrated that the average value of CNT aspect ratio significantly affected the elastic modulus of the hybrid fibers. Such a result was in agreement with theoretical prediction in which the stress transfer efficiency in a composite matrix is strongly dependent on the CNT aspect ratio.     

Elastic buckling of circular annular plate reinforced with carbon nanotubes

The buckling analysis of circular annular plate reinforced by carbon nanotubes (CNTs) subjected to compressive and torsional loads with various axially symmetric boundary conditions are studied in this paper. The developed model is based on the classical laminated plate theory (CLPT). The Mori‐Tanaka method is employed to calculate the effective elastic modulus of composites having aligned oriented straight CNTs. The eigenvalues of the problem are obtained by means of an analytical approach based on the optimized Rayleigh‐Ritz method. The effects of CNTs orientation angles, edge conditions, geometric ratio of plate and agglomeration of the randomly oriented straight CNTs are investigated on the critical buckling loads. Extensive studies validity of the results based on available data have been carried out prior to the presentation of salient results of this analysis. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

The confined growth of double-walled carbon nanotubes in porous catalysts by chemical vapor deposition

Double-walled carbon nanotubes (DWCNTs) were prepared from methane using a Fe/MgO porous catalyst. A series of catalyst powders with different pore size distributions were obtained by compression at pressures of 0-233 MPa. These were used to decompose methane and synthesize DWCNTs which differed in activity, purity, yield and degree of perfection. Characterization by transmission electron microscopy, scanning electron microscopy, Raman spectroscopy, thermo-gravimetric analysis, N₂ adsorption measurement (Brunauer-Emmett-Teller (BET)) and Hg penetration provided direct evidence that a compact catalyst structure is not good for the nucleation and growth of DWCNTs, e.g., a catalyst with a compact structure that did not have pores larger than 30-50 nm mostly produced multi-walled carbon nanotubes. The confined growth and buckling model of DWCNTs inside the porous catalysts are proposed to explain the growth behavior. These results suggest that a porous catalyst for DWCNT synthesis should have a large pore size distribution or loose stacked structure, which provides new guidelines for catalyst design.     

Torsional buckling of carbon nanopeapods

Torsional buckling of carbon nanopeapods (carbon nanotubes filled with fullerenes) is studied using a continuum-based multi-layered shell model. The model takes into account non-bonded van der Waals interactions between nested fullerenes and the innermost layer of host nanotube. For nanopeapods with linearly arranged nested fullerenes, equivalent pressure distribution is proposed to model these interactions. Deriving explicit equations governing the torsional stability, it is concluded that the critical torsional load of a carbon nanopeapod is less than that of a carbon nanotube under otherwise identical geometric and mechanical conditions. Performing numerical calculations, it is also shown that increasing the number of layers of the host carbon nanotube decreases the weakening effect of encapsulated fullerenes on torsional stability of the nanopeapod.     

Differentiation of chemical reaction activity of various carbon nanotubes using redox potential: Classification by physical and chemical structures

The present study systematically examined the kinetics of a hydroxyl radical scavenging reaction of various carbon nanotubes (CNTs) including double-walled and multi-walled carbon nanotubes (DWCNTs and MWCNTs), and carbon nano peapods (AuCl₃@DWCNT). The theoretical model that we recently proposed based on the redox potential of CNTs was used to analyze the experimental results. The reaction kinetics for DWCNTs and thin MWCNTs agreed well with the theoretical model and was consistent with each other. On the other hand, thin and thick MWCNTs behaved differently, which was consistent with the theory. Additionally, surface morphology of CNTs substantially influenced the reaction kinetics, while the doped particles in the center hollow parts of CNTs (AuCl₃@DWCNT) shifted the redox potential in a different direction. These findings make it possible to predict the chemical and biological reactivity of CNTs based on the structural and chemical nature and their influence on the redox potential.     

Dispersion of a bundle of carbon nanotubes by mechanical torsional energy

Dispersion of a bundle of carbon nanotubes by applying torsional energy is realized by molecular dynamics simulations. The torsional energy applied on the two ends of the bundle leads to a local buckling of the tube structures. The impulse between carbon nano-tubes owing to the local buckling of the tubes forms the driving force through a process of releasing the energy for a successful dispersion. The critical dispersion energy between two carbon nanotubes in a bundle in different solutions and the critical torsional energy for a successful dispersion are calculated by molecular dynamics simulations, and thus the dispersion efficiency is obtained. Effects of different parameters, such as the length and the diameter of the carbon nano-tubes and the temperature of the solution, on the dispersion efficiency are discussed. The dispersion of a bundle of five carbon nano-tubes in an aqueous solution is realized to further prove the feasibility of the proposed dispersion method by torsional energy. This paper provides an effective mechanical approach for dispersion of carbon nano-tubes from their bundle structure.     

碳纳米管材料导热性能的实验研究

本文对碳纳米管与环氧树脂(Epoxy-EP)复合材料的导热性能进行了定量的研究,探索了CNTs/EP复合材料的制备方法,运用Hotdisk热常数分析仪研究了CNTs/EP复合材料的导热系数;利用CNTs/EP两相复合材料的导热理论模型得到了室温下单壁碳纳米管(Single-Wall Carbon Nanotubes-SWCNTs)的导热系数为3980 W/(m.K),双壁碳纳米管的导热系数(Double-Wall Carbon Nanotubes-DWCNTs)为3580 W/(m.K),以及多壁碳纳米管(Multi-Wall Carbon Nanotubes-MWCNTs)的导热系数为2860 W/(m.K)。     

Phenomenological model of interfacial stress transfer in carbon nanotube reinforced composites with van der Waals effects

A pullout model is presented to analyze interfacial stress transfer in the double‐walled carbon nanotube (DWCNT) reinforced composites. The effects of the van der Waals (vdW) interaction between two layers of DWCNT and the Poisson's effects of DWCNT and matrix are taken into account in the model. Based on the equilibrium of the interfacial shear stress and the DWCNT axial stress as well the continuous condition of the displacement and stress on the interface of DWCNT and matrix, normalized interfacial shear stress, DWCNT axial stress and matrix axial stress are derived, respectively. Moreover, the effects of DWCNT aspect ratio, DWCNT volume fraction and relative modulus between the DWCNT and matrix are analyzed in details. Finally, the maximum normalized interfacial shear stress with vdW effect is compared with that without vdW effects. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

TEM observations of buckling and fracture modes for compressed thick multiwall carbon nanotubes

The buckling and fracture modes of thick (diameter >20 nm) multiwall carbon nanotubes (MWCNTs) under compressive stress were examined using in situ transmission electron microscopy. The overall dynamic deformation processes of the MWCNTs as well as the force/distance curves can be obtained. The buckling behavior of MWCNTs under compression falls into two categories, the first is non-axial buckling and subsequently complex Yoshimura patterns can be induced on the compressive side of the MWCNTs. The second is axial buckling followed by catastrophic failure. We find the buckling mode of thick MWCNTs is highly dependent on the diameter and length of the MWCNTs. A continuum mechanics model is employed to determine the buckling mode criterion for the MWCNTs. Moreover, the shell by shell fracture mode and planar fracture mode of MWCNTs are directly observed in our experiments.     

Elastic axial buckling of carbon nanotubes via a molecular mechanics model

Based on a molecular mechanics model, analytical solutions for the critical buckling strain of single-walled achiral carbon nanotubes under axial compression are obtained. The results show that zigzag tubes are more stable than armchair tubes with the same diameter. Comparison with the results given by continuum mechanics model shows that the continuum mechanics model underestimates the critical buckling strain for smaller tubes if a Young’s modulus for larger tubes (or for graphene sheets) is adopted. The effect of intertube van der Waals interaction from the inner tube of multi-walled carbon nanotubes on the buckling of the outermost tube is also qualitatively discussed and it is found that the van der Waals interaction has little effect on the critical buckling strain for double-walled carbon nanotubes.     

Nonlinear vibration of embedded smart composite microtube conveying fluid based on modified couple stress theory

Electro‐thermo‐mechanical nonlinear vibration and instability of a fluid conveying smart composite microtube made of polyvinylidene fluoride (PVDF) are investigated in this article based on the modified couple stress theory and Timoshenko beam model. The composite matrix is reinforced by double‐walled boron nitride nanotubes (BNNTs). Mechanical, electrical, and thermal characteristics of equivalent composite are determined based on micromechanical model. The surrounded elastic medium is taken into account using Winkler and Pasternak models. Considering the small‐size effects and slip boundary conditions of microflow through Knudsen number and applying Hamilton's principle, the coupled differential equations, containing displacement and electric potential terms, are obtained. The differential quadrature method is applied to discretize the coupled governing equations and boundary conditions, which are then solved to obtain the nonlinear frequency and critical fluid velocity of the fluid‐conveying microtube. The detailed parametric study is conducted, focusing on the combined effects of the Knudsen number, nonlocal parameter, BNNT volume percent, temperature change, elastic medium, and aspect ratio on the nonlinear frequency and critical fluid velocity. Results indicate that the natural frequency and the critical fluid velocity of the smart composite microtube increase with increasing the small‐scale parameter. POLYM. COMPOS., 36:1314–1324, 2015. © 2014 Society of Plastics Engineers     

Transportation of hydrogen molecules using carbon nanotubes in torsion

The transportation of hydrogen molecules using carbon nanotubes subjected to torsion is studied with molecular dynamics. Molecular dynamics simulations reveal that the transportation in a (10, 0) carbon nanotube is a result of the van der Waals effect through the propagation of the kink initiated at the onset of the tube torsional buckling. In addition, the applied torsional loading rate has an obvious effect on the orientation of the molecular transportation. On the other hand, the motion of the molecules in a (10, 10) carbon nanotube is found to be less oriented. The mechanism of the transportation in the larger carbon nanotube is investigated through the transform of the collapsed wall of the tube in the dynamic process of the torsional buckling.     

Comparison of double-walled with single-walled carbon nanotube electrodes by electrochemistry

Double-walled carbon nanotubes (DWCNTs) were selectively functionalised by treatment with concentrated nitric and sulphuric acid, resulting in carboxylated outer and pristine inner tube constituents. The functionalised DWCNTs were then incorporated into two types of pre-existing carbon nanotube (CNT) electrode platforms, and the performance of each was compared to single-walled carbon nanotubes (SWCNTs). To make the CNT electrode platforms DWCNTs were covalently bound to fluorinated tin oxide glass (FTO) or electrografted aminophenyl tether layers on silicon. The performance of single- compared to double-walled CNTs on FTO or silicon supported electrodes was then determined through electrochemical methods, using the redox probes, ferrocene and ruthenium hexaamine, respectively. The DWCNTs showed an improved heterogeneous rate constant. This improvement was attributed to the protection of the electronic properties of the inner wall of the DWCNT during the chemical modification and suggests that DWCNTs may offer a useful alternative to SWCNTs in future electronic devices.     

Transport properties of double-walled carbon nanotubes and carbon boronitride heteronanotubes

Using the density functional theory combined with the nonequilibrium Green's function, the transport properties of double-walled carbon nanotubes (DWCNTs) and carbon boronitride (CBN) heteronanotubes were investigated. As the hopping length increases, the conductance of DWCNTs shows a dramatic variation that is independent of the intertube space. The transport of the CBN heterojunctions also displays abnormal behavior when the hopping length is changed, which is very different from the behavior of DWCNTs. The currents of the forward in the CBN heterojunctions are about 3–15 times as large as those of the back under lower bias voltages. The negative differential resistance (NDR) effect occurs in the CBN heterojunctions, and the peak-to-valley ratio in the additional NDR regions is about 2–4 for the current–voltage relationship. The hopping length and BN parts have a great influence on the transport of the double-walled nanodevices.