Static dielectric properties of carbon nanotubes from first principles

We characterize the response of isolated single-wall (SWNT) and multiwall (MWNT) carbon nanotubes and nanotube bundles to static electric fields using first-principles calculations and density-functional theory. The longitudinal polarizability of SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles it is given by the sum of the polarizabilities of the constituent tubes. The transverse polarizability of SWNTs is insensitive to band gaps and chiralities and is proportional to the square of the effective radius; in MWNTs, the outer layers dominate the response. The transverse response is intermediate between metallic and insulating, and a simple electrostatic model based on a scale-invariance relation captures accurately the first-principles results. The dielectric response of nonchiral SWNTs in both directions remains linear up to very high values of applied field.     

Forces and torque on a pair of uncharged conducting cylinders in an external electric field

Exact results are given for the forces per unit length acting on each of a pair of parallel conducting cylinders when polarized by an external electric field perpendicular to the cylinders. Simple analytic results are obtained at small and large separations of the cylinders. The torque on the cylinders (which acts to align them with the electric field) is proportional to the difference between the longitudinal and transverse polarizabilities. The forces acting on the cylinders (which are equal and opposite) are given by the derivatives of the polarizabilities with respect to their separation.     

Band gap tuning of defective silicon carbide nanotubes under external electric field: Density functional theory

We have theoretically investigated the effect of applying longitudinal and transverse electric field on silicon carbide nanotubes with different orientations of Stone Wales defects. We found that each type of Stone Wales defects maintained different formation energy. We have also successfully proved that the orientation of Stone Wales defects in silicon carbide nanotubes response quite differently upon applying external electric field, whereas, two important and interesting phenomena were observed. First, the semiconductor-metal phase transition occurred in silicon carbide nanotubes as well as the three types of Stone Wales defects. However, clear band gap variations were observed in all silicon carbide nanotubes under study. Second, the band gap variations in pristine silicon carbide nanotubes and nanotubes with different orientations of Stone Wales defects have the same trend, even though all silicon carbide nanotubes have clear band gap values under different strengths of the applied external electric field. However, band gap tuning under longitudinal electric field is less significant compared to band gap tuning under the transverse electric field.     

Dust acoustic wave oscillations in metallic carbon nanotubes

We present theoretical analysis of plasmon dispersion in single-walled metallic carbon nanotubes (SWCNTs) in the presence of low-frequency electromagnetic radiation, based on classical electrodynamic formulations and linearized hydrodynamic model. We assume that metallic carbon nanotubes (CNTs) are charged due to the field emission, and hence the metallic nanotubes can be regarded as charged dust rods surrounded by degenerate electrons and ions. Calculations are performed for the transverse electric (TE) and transverse magnetic (TM) waves, respectively, by solving the Maxwell and hydrodynamic equations with appropriate boundary conditions.     

The mechanical property of single-walled carbon nanotube under combined electromechanical loading

The mechanical properties and failure process of single-walled carbon nanotube (SWCNT) under combined electric field and tensile loading are investigated using the semi-empirical quantum mechanical method. The local and global structural deformation and variation of mechanical properties of SWCNT under different directions and intensity of external electric field are discussed systematically. It is shown that the electric field induced deformation in the radial and axial directions of the SWCNT are strongly dependent on the direction of electric field. The analysis of mechanical properties shows that the structure stiffness, tensile strength and failure strain of the SWCNT all decrease with the increase of the field intensity, which is particularly evident under the longitudinal electric field. The Young's modulus of SWCNTs vary with the tube diameter and are affected by the electric field. The increase of the length of the tubes intensifies the charge concentration at the tube ends under the electric field and lead to the decrease of mechanical properties of SWCNTs. The failure process of SWCNTs under the coupling effect of electric field and tensile loading is found to be controlled by the field strength and also affected by the electric charge accumulation.     

Electron transport in double-walled carbon nanotubes

The transport properties of finite length double-walled carbon nanotubes subject to the influences of a transverse electric field and a magnetic field with varying polar angles are investigated theoretically. The electrical conductance, thermal conductance and Peltier coefficient dependences on the external fields and symmetric configuration are studied in linear response regime. Prominent peak structures of the electrical conductance are predicted when varying the electric field strength. The features of the conductance peaks are found to be strongly dependent on the external fields and the intertube interactions. The heights of the electrical and thermal conductance peaks display the quantized behavior, while those of the Peltier coefficient do not. The conductance peaks are found to be broadened by the finite temperature.     

Heat conduction in extended X-junctions of single-walled carbon nanotubes

Non-equilibrium molecular dynamics (NEMD) simulations are employed to investigate the longitudinal thermal conductivity of non-orthogonal extended X-junction (EX-junction) of single-walled carbon nanotubes (SWCNTs). Different from standard junctions of SWCNTs, two distinct jumps in the temperature profile around the EX-junction are observed, which are responsible for the larger temperature gradient and reduction in thermal conductivity when compared to standard X-junction. Quantum corrected results show that the longitudinal thermal resistance of the X-junction and EX-junction decreases monotonically with increasing temperature which makes the longitudinal thermal conductivity of the tube with junction less sensitive to temperature above 400 K comparing with the individual pristine tube. The origin of the significant decrease of thermal conductivity of EX-junction is discussed through phonon spectra analysis.     

Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory

This Letter develops a model that analyzes the resonant frequency of the chiral single-walled carbon nanotubes (SWCNTs) subjected to a thermal vibration by using Timoshenko beam model, including the effect of rotary inertia and shear deformation. The analytical solution is derived and the frequency equation is obtained. The results based on the beam model show that the frequency increases with decreasing the nanotube aspect ratio of length to diameter. In addition, the frequency obtained by Timoshenko beam model is lower than that calculated by Euler beam model. As the nanotube aspect ratio of length to diameter decreased, the discrepancy is more obvious. Furthermore, as the effect of thermal vibration increases, the frequency for chiral SWCNTs decreases.     

Electronic properties of telescoping carbon nanotubes under external fields

In this work, we use the tight-binding model to study the low-energy electronic properties of telescoping double-walled carbon nanotubes subject to the influences of a transverse electric field and a parallel magnetic field. The state energy and energy spacings are found to oscillate significantly with the overlapping length. External fields would modify the state energies, alter the energy gaps, and destroy the state degeneracy. Complete energy gap modulations can be accomplished either by varying the overlapping length, or by applying an electric field or a magnetic field. The variations of state energies with the external fields will be directly reflected in the density of states. The numbers, heights, and frequencies of the density of states peaks are strongly dependent on the external fields.     

Analytical expression for the electric field enhancement between two closely-spaced conducting spheres

An external electric field applied to two conducting spheres in close approach is enhanced (by charge separation on the spheres) in the region between the spheres. For spheres of equal size, this enhancement is a universal function of the ratio of the separation of the spheres to their radius, and increases without limit as this ratio decreases. We calculate the enhancement factor analytically for perfectly conducting spheres, providing a simple formula valid when the spheres are close together, that is when the enhancement is large and the known series solution is difficult to evaluate. The same methods allow us to find the close-approach forms of the longitudinal and transverse polarizabilities of the two-sphere system.     

Polarizability of two parallel conducting circular cylinders

We give exact results for the polarizabilities, longitudinal and transverse, of two parallel cylinders of the same radius. The expressions are infinite sums, which converge rapidly if the cylinders are separated by a radius or more. In close approach the sums converge slowly, but are replaced by equivalent integral expressions, which give simple analytical results in this limit. The contact values of the longitudinal and transverse polarizabilities are π²/6 and π²/12 times the large-separation values. The longitudinal contact value is approached infinitely rapidly as the separation tends to zero, while the approach of the transverse polarizability to its contact value is regular.     

Fabrication of carbon nanotube-threephase organic photodetectors with high responsivity and wide spectrum and the underlying mechanisms

In this work, we incorporated single-walled carbon nanotubes (SWCNTs) into organic three-phase heterojunction active layer detectors, and systematically experimentally investigated the influences of single walled carbon nanotubes (SWCNTs) on the photoabsorption and photoelectric properties of the organic three-phase heterojunction detectors. Under -1 V bias voltage, the average photoresponsivity of three primary colors detector is 475 mA/W, about 2–3 times higher than that of similar devices that without SWCNTs. The average external quantum efficiency (EQE) increases to 111%. The results show that the incorporation of single-walled carbon nanotubes in the three-phase bulk heterojunction active layer maintains the original spectral morphology, while increases a higher degree of aggregation and crystallinity of the organic conjugated polymer, and further enhances a larger capacity of light absorption, regardless of the number of active layer's mixed phases. Under -1 V bias voltage, the average photoresponsivity of three primary colors detector is 475 mA/W, about 2–3 times higher than that of similar devices. The average external quantum efficiency (EQE) can be increased to 111%. In terms of carrier transport, SWCNT can increase the exciton dissociation area, dissociation rate of the film, and provide a fast transport channel for the charge, therefore improve the charge collection of the electrode. In a concentration range of 0.75–1.75 wt% and in high-energy photon excitation, single-walled carbon nanotubes can produce a multiple exciton generation.     

Effects of Radius and Orientation of Single-Walled Carbon Nanotubes on Their Nonlinear Tensile Deformation Behaviour

By capturing the atomic information and reflecting the behaviour governed by a nonlinear potential function, an analytical molecular mechanics approach is applied to establish the constitutive relation for single-walled carbon nanotubes （SWCNTs）. The nonlinear tensile deformation curves of zigzag and armchair nanotubes with different radii are predicted, and the elastic properties of these SWCNTs are obtained. A conclusion is made that the nanotube radius has little effect on the mechanical behaviour of SWCNTs subject to simple tension, while the nanotube orientation has larger influence.     

Longitudinal,transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes

Thanks to the brilliant mechanical properties of single-walled carbon nanotubes (SWCNTs), they are suggested as high speed nanoscale vehicles. To date, various aspects of vibrations of SWCNTs have been addressed; however, vibrations and instabilities of moving SWCNTs have not been thoroughly assessed. Herein, vibrational properties of an axially moving SWCNT with simply supported ends are studied using nonlocal Rayleigh beam theory. Employing assumed mode and Galerkin methods, the discrete governing equations pertinent to longitudinal, transverse, and torsional motions of the moving SWCNT are obtained. The resulting eigenvalue equations are then numerically solved. The speeds corresponding to the initiation of the instability within the moving nanostructure are calculated. The roles of the speed of the moving SWCNT, small-scale parameter, and aspect ratio on the characteristics of longitudinal, transverse, and torsional vibrations of axially moving SWCNTs are scrutinized. The obtained results show that the appearance of the small-scale parameter would result in the occurrence of both divergence and flutter instabilities at lower levels of the speed.     

Near-field effect in two-atom system

The self-consistent problem is solved for the interaction of two dipole atoms situated at arbitrary distance from one another with the field of quasiresonant light wave. Atoms are considered to be linear Lorenz oscillators. Polarizing fields inside the system include both Coulomb and retarding parts. The solutions obtained are investigated for the case when atoms have the same polarizabilities and interatomic distance is much less than external light wavelength. Formulas for electric fields inside and outside of small object are obtained. It is shown that longitudinal and transverse optical oscillations are possible to exist inside small two-atom object. Dispersion laws of these oscillations depend upon interatomic distance and upon angle between axis of the system and the direction of propagation of external wave. The field outside the small object in wave zone is linearly polarized with the choice of linear polarization of external field. However, the directions of polarization of these waves are different and depend essentially upon frequency. The amplitude of field outside small object in wave zone is shown to depend essentially on the frequency of external field and interatomic distance. The results obtained are treated as near-field effect in the optics of small objects making it possible to investigate the structure of small objects with optical radiation. Received 26 October 1998 and Received in final form 26 January 2000     

Energy anomaly and polarizability of carbon nanotubes

The energy of Fermi sea perturbed by an external potential is analyzed with the help of an energy anomaly. Using an example of massive Dirac fermions on a circle, we illustrate how the anomaly accounts for the contribution of the deep-lying states. The energy anomaly is a universal function of the applied field and is related to known field-theoretic anomalies. Applied to the transverse polarizability of carbon nanotubes, the anomaly reveals universality and scale invariance of the response dominated by electrons. The electron band transformation in a strong field-effect regime is predicted.     

Numerical study on the field emission properties of aligned carbon nanotubes using the hybrid field enhancement scheme

The magnitude of the local electric field and the electron emission current density for an array of aligned carbon nanotubes is estimated. For describing in detail the properties of the local electric field in the vicinity of the nanotube tips, a hybrid method allowing for the local determination of the field enhancement factor is introduced. The field factor consists of two parts: an internal factor which describes the structure of the carbon nanotubes and an external factor which represents the field screening effect due to neighboring nanotubes. The current density is obtained using the Fowler–Nordheim equation with the hybrid field enhancement scheme. As a result, the emission properties for an array of nanotubes with a given length are described satisfactorily, and an optimum value for the nanotube spacing is determined. PACS 85.45.Fd; 85.45.Db     

Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach

The magnetic properties of carbon nanotubes and their mechanical behaviour in a magnetic field have attracted considerable attention among the scientific and engineering communities. This paper reports an analytical approach to study the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive double-walled carbon nanotube (DWCNT). The study is based on nonlocal elasticity theory. Equivalent analytical nonlocal double-beam theory is utilised. Governing equations for nonlocal transverse vibration of the DWCNT under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell's relation. Numerical results from the model show that the longitudinal magnetic field increases the natural frequencies of the DWCNT. Both synchronous and asynchronous vibration phases of the tubes are studied in detail. Synchronous vibration phases of DWCNT are more affected by nonlocal effects than asynchronous vibration phases. The effects of a longitudinal magnetic field on higher natural frequencies are also presented. Vibration response of DWCNT with outer-wall stationary and single-walled carbon nanotube under the effect of longitudinal magnetic field are also discussed in the paper.     

Growth of aligned single-walled carbon nanotubes under ac electric fields through floating catalyst chemical vapour deposition

Through floating catalyst chemical vapour deposition(CVD) method,well-aligned isolated single-walled carbon nanotubes (SWCNTs) and their bundles were deposited on the metal electrodes patterned on the SiO₂/Si surface under ac electric fields at relatively low temperature(280℃). It was indicated that SWCNTs were effectively aligned under ac electric fields after they had just grown in the furnace.The time for a SWCNT to be aligned in the electric field and the effect of gas flow were estimated. Polarized Raman scattering was performed to characterize the aligned structure of SWCNTs. This method would be very useful for the controlled fabrication and preparation of SWCNTs in practical applications.     

一种平行背栅极碳纳米管阵列的场增强因子计算

建立一种平行背栅极碳纳米管阵列阴极,基于电场叠加原理,利用镜像电荷法对其进行计算,给出碳纳米管顶端表面电场增强因子。在此基础上,进一步分析器件各类参数对电场增强因子的影响。分析表明,碳纳米管阵列阴极具有最佳阵列密度,其对应碳纳米管间距大约为碳纳米管高度的两倍,靠阴极阵列边缘部位的碳纳米管发射电子能力比其中心部位的大。除了碳纳米管的长径比之外,栅极宽度、栅极厚度和栅极间距等也对电场增强因子有一定的影响:栅极越宽,场增强因子越大;而栅极厚度、栅极间距越大,场增强因子就越小。