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.     

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.     

Torsional elastic instability of double-walled carbon nanotubes

In this paper, a theoretical analysis of the torsional buckling instability of double-walled carbon nanotubes (DWCNTs) and the DWCNTs embedded in an elastic medium is presented based on the continuum elastic shell model and Winkler spring model. Using the proposed theoretical approach, the influences of the aspect ratio, the buckling modes and the surrounding medium on the torsional stability are examined in detail. The simulation results show that the torsional instability of DWCNTs can occur in different buckling modes according to the aspect ratio. The van der Waals (vdW) interaction force between nanotubes reinforces the stiffness of nanoshells. Thus, the DWCNTs possess higher buckling stability than the SWCNTs without considering vdW interaction force.     

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.     

Multi-Stable Conductance States in Metallic Double-Walled Carbon Nanotubes

Electrical transport properties of individual metallic double-walled carbon nanotubes (DWCNTs) were measured down to liquid helium temperature, and multi-stable conductance states were found in DWCNTs. At a certain temperature, DWCNTs can switch continuously between two or more electronic states, but below certain temperature, DWCNTs are stable only at one of them. The temperature for switching is always different from tube to tube, and even different from thermal cycle to cycle for the same tube. In addition to thermal activation, gate voltage scanning can also realize such switching among different electronic states. The multi-stable conductance states in metallic DWCNTs can be attributed to different Fermi level or occasional scattering centers induced by different configurations between their inner and outer tubes.     

Atomically resolved Moiré-type superstructures in double-walled carbon nanotubes

Double-wall carbon nanotubes (DWCNTs) are investigated with high resolution by scanning tunneling electron microscopy at 78 and 4.5 K. Besides the atomic structure of the DWCNT surface, an additional honeycomb-type superstructure is revealed at these low temperatures. This periodic structure can be interpreted in terms of a Moiré pattern resulting from a rotation between the rolled up graphene sheets that constitute the DWCNT. Deviations of the observed Moiré patterns from the perfect hexagonal Moiré patterns that are commonly resolved for multi-graphene layer surfaces are found to be related to the intrinsic different curvature of the inner and outer tube of the DWCNT. Investigation of such Moiré patterns in the surface of DWCNTs allows one to gain more insight into the structure and chirality of the otherwise inaccessible inner shell of the DWCNTs.     

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.     

Synthesis of boron-doped double-walled carbon nanotubes by the catalytic decomposition of tetrahydrofuran and triisopropyl borate

Boron-doped double-walled carbon nanotubes (DWCNTs) were produced by the catalytic decomposition of tetrahydrofuran and triisopropyl borate over a Fe–Mo/MgO catalyst at 900 °C. The synthesized B-doped DWCNTs had average outer and inner diameters in the range of 1.6–2.4 nm and 0.8–1.6 nm within the bundle, respectively. They had a larger interlayer spacing in the range of 0.36–0.39 nm, than did undoped DWCNTs. The B-C bonding evident from the B 1s signals in the X-ray photoelectron spectroscopy results indicated that highly coordinated boron atoms replaced the carbon atoms within the graphene sheet. As the triisopropyl borate concentration was increased from 0 to 2.5 M, the substituted boron concentration increased from 0.8 to 3.1 at.%. The results demonstrate that the substituted boron concentration in the hexagonal carbon lattices can be easily controlled by regulating the triisopropyl borate concentration.     

Pressure dependence of Raman modes in double wall carbon nanotubes filled with 1D Tellurium

The preparation of highly anisotropic one-dimensional (1D) structures confined into carbon nanotubes (CNTs) in general is a key objective in nanoscience. In this work, capillary effect was used to fill double wall carbon nanotubes (DWCNTs) with trigonal Tellurium. The samples are characterized by high resolution transmission electronic microscopy and Raman spectroscopy. In order to investigate their structural stability and unravel the differences induced by intershell interactions, unpolarized Raman spectra of radial and tangential modes of DWCNTs filled with 1D nanocrystalline Te excited with 514 nm were studied at room temperature and high pressure. Up to 11 GPa we found a pressure coefficient of 3.7 cm⁻¹ GPa⁻¹ for the internal tube and 7 cm⁻¹ GPa⁻¹ for the external tube. In addition, the tangential band of the external and internal tubes broaden and decrease in amplitude. All findings lead to the conclusion that the outer tube acts as a protection shield for the inner tube (at least up 11 GPa). No pressure-induced structural phase transition was observed in the studied range.     

Stability comparison of simulated double-walled carbon nanotube structures

The focus of this research is to systematically study and classify electronic energy trends in different double-walled carbon nanotube (DWCNT) structures through ab initio simulations. Simulations comparing the stability of DWCNTs with different interwall spacings, tube types (armchair or zigzag), lengths, diameters, and endcaps were performed at a variety of computational levels. These simulations showed that DWCNTs nucleate from end caps and become energetically more stable as length and diameter increase. Another finding of this research was that the interwall spacing is dependent on which type of tube is in the outer position of the DWCNT. High stability configurations occurred when the interwall spacing was approximately 3.3 Å and a zigzag tube was in the outer position or when the interwall spacing was approximately 3.5 Å and an armchair tube was in the outer position. It was also seen that endcaps affected which tube combinations were more stable; the armchair@armchair DWCNT was the most energetically stable combination for capped tubes, while the armchair@zigzag DWCNT had the highest stability of uncapped tubes. Understanding if there is a preferred structural motif for DWCNTs and clarifying which nucleation and growth paths are favored by nanotubes will elucidate if controlled fabrication can be achieved.     

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.     

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.     

Effect of H2O adsorption on the electrical transport properties of double-walled carbon nanotubes

Water molecules adsorbed on a double-walled carbon nanotube (DWCNT) serve as charge trapping centers when present in low density and as electron donors when present in high density. There is a discontinuous change between the low- and high-density regions. H₂O molecules are apt to be adsorbed on the outer surface of DWCNTs, and in this case the electrical transport properties are extremely sensitive to environment, which suggests that DWCNTs are hole doped and act as an electric dipole with the inner tube.     

The effects of confinement inside carbon nanotubes on catalysis

The unique tubular morphology of carbon nanotubes (CNTs) has triggered wide research interest. These structures can be used as nanoreactors and to create novel composites through the encapsulation of guest materials in their well-defined channels. The rigid nanotubes restrict the size of the encapsulated materials down to the nanometer and even the sub-nanometer scale. In addition, interactions may develop between the encapsulated molecules and nanomaterials and the CNT surfaces. The curvature of CNT walls causes the π electron density of the graphene layers to shift from the concave inner to the convex outer surface, which results in an electric potential difference. As a result, the molecules and nanomaterials on the exterior walls of CNTs likely display different properties and chemical reactivities from those confined within CNTs. Catalysis that utilizes the interior surface of CNTs was only explored recently. An increasing number of studies have demonstrated that confining metal or metal oxide nanoparticles inside CNTs often leads to a different catalytic activity with respect to the same metals deposited on the CNT exterior surface. Furthermore, this inside and outside activity difference varies based on the metals used and the reactions catalyzed. In this Account, we describe the efforts toward understanding the fundamental effects of confining metal nanoparticles inside the CNT channels. This research may provide a novel approach to modulate their catalytic performance and promote rational design of catalysts. To achieve this, we have developed strategies for homogeneous dispersion of nanoparticles inside nanotubes. Because researchers have previously demonstrated the insertion of nanoparticles within larger nanotubes, we focused specifically on multiwalled carbon nanotubes (MWCNTs) with an inner diameter (i.d.) smaller than 10 nm and double-walled carbon nanotubes (DWCNTs) with 1.0-1.5 nm i.d. The results show that CNTs with well-defined morphology and unique electronic structure of CNTs provide an intriguing confinement environment for catalysis.     

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.     

Controllable synthesis of single- and double-walled carbon nanotubes from petroleum coke and their application to solar cells

Single- and double-walled carbon nanotubes (SWCNTs and DWCNTs) have been controllably synthesized by an arc discharge in different atmosphere using petroleum coke as carbon source. The morphology and properties of two kinds of carbon nanotubes (CNTs) synthesized with Fe as catalyst were characterized by scanning electron microscopy, high-resolution transmission electron microscopy, Raman spectroscopy, energy dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, UV–visible spectroscopy, inductively coupled plasma optical emission spectrometer, thermogravimetric analysis and infrared spectroscopy. In the He gas atmosphere only SWCNTs were found to be synthesized by arc discharge in contrast to the case in Ar gas atmosphere in which only DWCNTs were formed, In addition, properties of solar cells based on both kinds of CNTs and n-type Si are examined under illumination of light emission diode (LED). It is found that the performance of solar cells depends significantly on the type of CNTs, i.e., SWCNTs-based solar cells show better performance under LED illumination with wavelengths in the range of 400–940 nm than the case of DWCNTs which exhibit high performance under illumination of the 1310 nm infrared light.     

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.     

Buckling and axially compressive properties of perfect and defective single-walled carbon nanotubes

Molecular dynamics simulation is employed for the axial compression of both perfect and defective single-walled carbon nanotubes (SWCNTs). Morse potential, harmonic angle potential, a proper dihedral potential and the Lennard-Jones potential are used to simulate the interactions among carbon atoms. It is revealed that the buckling and axially compressive properties of SWCNTs obviously lie on the length, the chirality, the temperature and the initial structural defects of the tube. Especially at normal temperature, the Euler formula could be adopted to predict the axially critical buckling loads of SWCNTs with large aspect ratio.     

Nanocarbon aerogel complexes inspired by the leaf structure

Inspired by the structure of a leaf, which is constituted of veins, midribs and laminas, we report the synthesis of aerogels based on nanocarbon complexes that exhibit good electrical conductivity, large internal surface area and stable structural integrity upon cyclic compression. These materials are prepared as monolithic solids from suspensions of unzipped and partially exfoliated multi-walled carbon nanotubes. Under optimized oxidation conditions, all the walls of the multi-walled carbon nanotubes are unzipped but only the outer tubes are exfoliated, creating nanoscale multi-layered graphene oxide sheets attached to inner trench-like structures. The exfoliated parts provide high surface area and functional groups, while the inner trench-like structures remain relatively intact and thus retain their electrical conductivity and mechanical properties, which facilitates charge transport and structural stability for the aerogel. The hydrophilic functional groups on the graphene oxide nanosheets make these structures highly soluble, and as a result, the density and mechanical properties can be adjusted to a large extent without sacrificing the porosity or cell wall uniformity. These nanocarbon aerogel complexes exhibit high damping capability with no significant change in piezoresistive properties after more than 4500 compressive cycles, and its original shape can be recovered quickly after compression release.