Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory

Theoretical predictions are presented for wave propagation in nonlinear curved single-walled carbon nanotubes (SWCNTs). Based on the nonlocal theory of elasticity, the computational model is established, combined with the effects of geometrical nonlinearity and imperfection. In order to use the wave analysis method on this topic, a linearization method is employed. Thus, the analytical expresses of the shear frequency and flexural frequency are obtained. The effects of the geometrical nonlinearity, the initial geometrical imperfection, temperature change and magnetic field on the flexural and shear wave frequencies are investigated. Numerical results indicate that the contribution of the higher-order small scale effect on the shear deformation and the rotary inertia can lead to a reduction in the frequencies compared with results reported in the published literature. The theoretical model derived in this study should be useful for characterizing the mechanical properties of carbon nanotubes and applications of nano-devices.     

Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

In the present work, nonlocal Euler–Bernoulli beam theory is used to investigate the wave propagation in zigzag double-walled carbon nanotube (DWCNT) embedded in an elastic medium. Winkler-type foundation model is employed to simulate the interaction of the DWCNT with the surrounding elastic medium. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is noticed in the presented study that the equivalent Young’s modulus for zigzag DWCNT is derived using an energy-equivalent model. Influences of nonlocal effects, the chirality of zigzag DWCNT, Winkler modulus parameter, and aspect ratio on the frequency of DWCNT are analyzed and discussed. The new features of the vibration behavior of zigzag DWCNTs embedded in an elastic medium and some meaningful results in this paper are helpful for the application and the design of nanostructures in which zigzag DWCNTs act as basic elements.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.     

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.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

Wave dispersion in viscoelastic single walled carbon nanotubes based on the nonlocal strain gradient Timoshenko beam model

Based on the nonlocal strain gradient theory and Timoshenko beam model, the properties of wave propagation in a viscoelastic single-walled carbon nanotube (SWCNT) are investigated. The characteristic equations for flexural and shear waves in visco-SWCNTs are established. The influence of the tube size on the wave dispersion is clarified. For a low damping coefficient, threshold diameter for shear wave (SW) is observed, below which the phase velocity of SW is equal to zero, whilst flexural wave (FW) always exists. For a high damping coefficient, SW is absolutely constrained, and blocking diameter for FW is observed, above which the wave propagation is blocked. The effects of the wave number, nonlocal and strain gradient length scale parameters on the threshold and blocking diameters are discussed in detail.     

Interwall conductance in double-walled armchair carbon nanotubes

The dependence of the interwall conductance on distance between walls and relative positions of walls are calculated at the low voltage by Bardeen method for (n,n)@(2n,2n) double-walled carbon nanotubes (DWCNTs) with n=5,6,…,10. The calculations show that interwall conductance does not depend on temperature (for T?500 K) and current-voltage characteristic is linear. The conductance decreases by 6 orders of magnitude when the interwall distance is doubled. Thus, depending on the interwall distance, DWCNTs can be used as temperature stable nanoresistors or nanocapacitors.     

Dispersion of dilatation wave propagation in single-wall carbon nanotubes using nonlocal scale effects

Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This paper investigates a model of wave propagation in single-wall carbon nanotubes (SWCNTs) with small scale effects are studied. The equation of motion of the dilatation wave is obtained using the nonlocal elastic theory. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture of a local and a nonlocal strain. The SWCNTs structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The SWCNT was the (40,0) zigzag tube with an effective diameter of 3.13 nm. Nonlinear frequency equations of wave propagation in SWCNTs are described through the effect of small scale. The phase velocity and the group velocity are derived, respectively. The nonlinear dispersion relation is analyzed with different wave numbers versus scale coefficient. It can be observed from the results that the dispersion properties of the dilatation wave are induced by the small scale effects, which will disappear in local continuous models. The dispersion degree can be strengthened by increasing the scale coefficient and the wave number. Furthermore, the characteristics for the group velocity of the dilatation wave in carbon nanotubes can also be tuned by these factors.     

Third-order nonlinear optical response in double-walled carbon nanotubes

Resonant behavior and magnitudes of third-order nonlinear optical susceptibilities in double-walled carbon nanotubes (DWNTs) have been investigated by means of femtosecond pump-probe spectroscopy with different pump-photon energies. With the selective excitation of the E₂₂ exciton transition of the inner tubes labeled by the chiral vector indices (7,5) and (7,6), the imaginary part of nonlinear susceptibility Imχ⁽³⁾ has shown the resonant enhancement compared with the case of the nonresonant excitation of the specific tube. The nonlinear response signal at the E₂₂ transition energy of the (8,7) tube has been also enhanced for the excitation of the G-band phonon sideband of its E₂₂ transition. This result is consistent with the phonon-mediated nonlinear optical process observed for the E₂₂ transitions in single-walled carbon nanotubes (SWNTs). It has been also found that the values of the figure of merit Im χ⁽³⁾/α (α: absorption coefficient) of the inner tubes in DWNTs are smaller than those of the corresponding SWNTs, which is interpreted in terms of decay time shortening due to the energy relaxation between the inner and outer tubes.     

Rotational dynamics and friction in double-walled carbon nanotubes

We report a study of the rotational dynamics in double-walled nanotubes using molecular dynamics simulations and a simple analytical model that reproduces the observations very well. We show that the dynamic friction is linear in the angular velocity for a wide range of values. The molecular dynamics simulations show that for large enough systems the relaxation time takes a constant value depending only on the interlayer spacing and temperature. Moreover, the friction force increases linearly with contact area and the relaxation time decreases with the temperature with a power law of exponent -1.53+/-0.04.     

Electrical conductivity of double-walled carbon nanotubes in the framework of the Hubbard model

The electrical conductivity of double-walled carbon nanotubes of the “armchair” type with the ABAB packing of layers is investigated theoretically. The temperature dependences of the longitudinal electrical conductivity σ(T) for a number of double-walled carbon nanotubes, such as the (3, 3)@(8, 8), (5, 5)@(10, 10), (8, 8)@(13, 13), (10, 10)@(15, 15), and (15, 15)@(20, 20) nanotubes, are obtained in the framework of the Hubbard model with the use of the Green’s function method. It is revealed that the dependences of the electrical conductivity for single-walled and double-walled carbon nanotubes exhibit different behavior in the temperature range from 30 to 60 K. In particular, the dependence of the electrical conductivity for the double-walled carbon nanotubes flattens out in this temperature range.     

Viscoelastic wave propagation in the viscoelastic single walled carbon nanotubes based on nonlocal strain gradient theory

In this paper, the viscoelastic wave propagation in an embedded viscoelastic single-walled carbon nanotube (SWCNT) is studied based on the nonlocal strain gradient theory. The characteristic equation for the viscoelastic wave in SWCNTs is derived. The emphasis is placed on the influence of the tube diameter on the viscoelastic wave dispersion. A blocking diameter is observed, above which the wave could not propagate in SWCNTs. The results show that the blocking diameter is greatly dependent on the damping coefficient, the nonlocal and the strain gradient length scale parameters, as well as the Winkler modulus of the surrounding elastic medium. These findings may provide a prospective application of SWCNTs in nanodevices and nanocomposites.     

双壁碳纳米管电浸润现象的分子动力学模拟

在单壁碳纳米管电浸润现象原子模拟的基础上,对双壁碳纳米管的电浸润现象进行了计算机模拟.运用经典分子动力学方法结合一个宏观的电毛细管模型模拟了双壁碳纳米管在水银中的电浸润过程,对不同内管尺寸情况下的浸润现象作了研究和比较.计算结果表明双壁碳管和单壁碳管的电浸润过程存在很大的不同,双壁碳管的内管在电浸润过程中起到重要的作用：当改变双壁碳管中内管的尺寸时,浸润现象会产生很大的改变. 关键词： 双壁碳纳米管 电浸润 分子动力学     

Wave propagation in double walled carbon nanotubes by using doublet mechanics theory

Flexural and axial wave propagation in double walled carbon nanotubes embedded in an elastic medium and axial wave propagation in single walled carbon nanotubes are investigated. A length scale dependent theory which is called doublet mechanics is used in the analysis. Governing equations are obtained by using Hamilton principle. Doublet mechanics results are compared with classical elasticity and other size dependent continuum theories such as strain gradient theory, nonlocal theory and lattice dynamics. In addition, experimental wave frequencies of graphite are compared with the doublet mechanics theory. It is obtained that doublet mechanics gives accurate results for flexural and axial wave propagation in nanotubes. Thus, doublet mechanics can be used for the design of electro-mechanical nano-devices such as nanomotors, nanosensors and oscillators.     

Molecular dynamics simulations of electrowetting in double-walled carbon nanotubes

On the basis of the atomistic simulations of electrowetting in single-walled carbon nanotubes, electrowetting of double-walled carbon nanotubes by mercury is studied using classical molecular dynamics simulations. Wetting of double-walled carbon nanotubes by mercury occurs above a threshold size of inner tube when the voltage is applied on the outer tube, but no wetting phenomenon appears when the voltage is applied on the inner tube. The filling rate increases greatly with enlarging the inner tube size. The space between the two walls of double-walled carbon nanotubes cannot be filled by mercury during electrowetting process.     

Curvature-induced metallization of double-walled semiconducting zigzag carbon nanotubes

We report total-energy electronic-structure calculations that provide energetics and electronic structures of double-walled carbon nanotubes consisting of semiconducting (n,0) nanotubes. We find that optimum spacing between the walls of the nanotubes is slightly larger than the interlayer spacing of the graphite. We also find that the electronic structures of the double-walled nanotubes with the inner (7,0) nanotube are metallic with multicarrier characters in which electrons and holes exist on inner and outer nanotubes, respectively. Interwall spacing and curvature difference are found to be essential for the electron states around the Fermi level.     

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.     

Transport of liquid mercury under pressure in double-walled carbon nanotubes

In this paper, transport of liquid mercury under pressure through double-walled carbon nanotubes is studied using classical molecular dynamics simulations in conjunction with a pressure control model. The results indicate that wetting of double-walled carbon nanotubes by mercury occurs above a threshold pressure of liquid mercury. Liquid mercury can be transported through the inner tube of double-walled carbon nanotubes with the continuous increase of its pressure. The threshold pressure of liquid mercury decreases and the transport efficiency increases greatly with enlarging the inner tube size. The space between the two walls of double-walled carbon nanotubes can also transport the liquid mercury while the distance between the two walls is much larger than the radius of the inner tube. Transport efficiency of double-walled carbon nanotubes is a little lower than that of single-walled carbon nanotubes while double-walled carbon nanotubes transport liquid more steadily than single-walled carbon nanotubes.     

有限长双壁碳纳米管的电子输运性质

基于Landauer公式，研究了有限长的非公度和公度双壁碳纳米管的电子输运性顾，结果表明 ，双壁管的几何结构对其电子输运性质有显著的影响：非公度的双壁碳管的电导随能量的不 同，既可以是弹道型的，也可以是非弹道型的；由armchair管组成的公度的双壁碳管的电导 随能量变化呈现快速的电导振荡，并且此快速振荡叠加在背景慢振荡上，而zigzag管组成的 公度双壁管的电导随能量变化只有快速振荡、没有规则的慢振荡背景. 关键词： 碳纳米管 电子输运性质