Mechanical properties of single- and double-walled carbon nanotubes under hydrostatic pressure

Based on a molecular mechanics coupled with atomistic-based continuum theory, a closed-form formula is presented to examine the elastic properties of single- and double-walled carbon nanotubes subjected to hydrostatic pressure. Following the present model, the effects of the armchair and zigzag CNT structures on the pressure behavior are theoretically investigated. The computational result indicates that the bulk modulus is less sensitive to the chiral structures except for very small tube diameters. Moreover, closed-end nanotubes under hydrostatic pressure exhibit a larger bulking modulus than open ended nanotubes. The cap of the zigzag tubes has a larger effect on the bulk modulus when compared to the armchair tubes, especially in small diameter nanotubes. The predicted strain and the bulk modulus are in good agreement with existing theoretical results. PACS 61.46.+w; 62.20.Dc; 62.20.-x; 62.25.+g     

Radial breathing vibration of double-walled carbon nanotubes subjected to pressure

A theoretical vibrational analysis of the radial breathing mode (RBM) of double-walled carbon nanotubes (DWCNTs) subjected to pressure is presented based on an elastic continuum model. The results agree with reported experimental results obtained under different conditions. Frequencies of the RBM in DWCNTs subjected to increasing pressure depend strongly on circumferential wave numbers, but weakly on the aspect ratio and axial half-wave numbers. For the inner and outer tubes of DWCNTs, the frequency of the RBM increases obviously as the pressure increases under different conditions. The range of variation is smaller for the inner tube than the outer tube.     

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.     

Tomonaga-Luttinger liquid and Coulomb blockade in multiwall carbon nanotubes under pressure

We report that the conductance of macroscopic multiwall nanotube (MWNT) bundles under pressure shows power laws in temperature and voltage, as corresponding to a network of bulk-bulk connected Tomonaga-Luttinger liquids (LLs). Contrary to individual MWNTs, where the observed power laws are attributed to Coulomb blockade, the measured ratio for the end and bulk obtained exponents, approximately 2.4, can be accounted for only by LL theory. At temperatures characteristic of interband separation, it increases due to thermal population of the conducting sheets unoccupied bands.     

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.     

拉伸条件下双壁碳纳米管弹性性能的原子模拟

利用分子动力学方法，对双壁碳纳米管在拉伸条件下的弹性性能进行模拟，研究了直径在1 nm以上的4根双壁碳纳米管，模拟了它们的应力-应变关系以及泊松比.计算结果表明，在弹性范围内，双壁碳纳米管的应力与应变呈非线性关系，切线弹性模量大致从720 GPa减小至570 GPa，出现软化现象；随着拉伸应变的增大，泊松比从0.3变化到0.17，但结构尺寸对泊松比的影响不大. 关键词： 双壁碳纳米管 分子动力学 弹性模量 泊松比     

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.     

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.     

液体水银在碳纳米管中传输的压力控制模型

碳纳米管在纳米技术中有一个很重要的应用,就是它可以作为纳米管道传输液体. 本文用分子动力学模拟方法,结合一个液体压力控制模型,对液体水银由于外部压力作用在碳纳米管中传输的现象进行研究. 研究结果表明,当液体水银的内部压强超过一个临界值时,液体水银能够浸入到碳纳米管内部;不断增大液体内部的压强,碳纳米管可以连续地传输液体;而当对液体水银进行循环加压时,碳纳米管可以间断地传输液体水银. 关键词： 碳纳米管 流体传输 分子动力学     

液体水银在碳纳米管中传输的压力控制模型

碳纳米管在纳米技术中有一个很重要的应用，就是它可以作为纳米管道传输液体. 本文用分子动力学模拟方法，结合一个液体压力控制模型，对液体水银由于外部压力作用在碳纳米管中传输的现象进行研究. 研究结果表明，当液体水银的内部压强超过一个临界值时，液体水银能够浸入到碳纳米管内部；不断增大液体内部的压强，碳纳米管可以连续地传输液体；而当对液体水银进行循环加压时，碳纳米管可以间断地传输液体水银.     

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.     

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.     

Probing structural stability of double-walled carbon nanotubes at high non-hydrostatic pressure by Raman spectroscopy

Theoretical calculations predict that the collapse pressure for double-walled carbon nanotubes (DWCNTs) is proportional to 1/R ³, where R is the effective or average radius of a DWCNT. In order to address the problem of CNT stability at high pressure and stress, we performed a resonance Raman study of DWCNTs dispersed in sodium cholate using 532 and 633 nm laser excitation. Raman spectra of the recovered samples show minor versus irreversible changes with increasing I _D/I _G ratio after exposure to high non-hydrostatic pressure of 23 and 35 GPa, respectively. The system exhibits nearly 70% pressure hysteresis in radial breathing vibrational mode signals recovery on pressure release which is twice that predicted by theory.     

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     

Coupling analysis of screwing motion of double-walled carbon nanotubes

As the inner tube is excited from a rotation frequency at a separation distance, the inner tube will generate a reciprocating screwing motion. In this work, this coupling effect is investigated theoretically. The van der Waals force between two carbon nanotubes is expressed in a simple form of Fourier series so that the coupled nonlinear differential equations can be quickly solved. The proposed approach is thousands of times faster than the traditional method, which makes it possible to fit the coupling coefficients. As a result, expressions for the coefficients of the coupled equations are given. It is observed that a larger initial rotation frequency excitation will result in a higher dissipation rate of the axial oscillation, and vice versa.     

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     

Torsion induced by axial strain of double-walled carbon nanotubes

Axial-strain-induced torsions of chiral double-walled carbon nanotubes are studied. Effects of interlayer van der Waals interaction, chirality and curvature of inner and outer tubes are investigated. Results show that the van der Waals interactions change dramatically the induced torsion, while the chirality and curvature dependences are rather weak.     

Structural transformations in single-wall carbon nanotubes under high pressure

Single-wall carbon nanotubes (SWNTs) under high pressure exhibit high structural stability and a series of structural transitions up to 35 GPa. As theoretically predicted, the irreversible transformation of SWNTs in the pressure range of 10–30 GPa can be attributed to the polymerization of nanotubes. The electrical conductivity of SWNTs is studied at high pressures up to 35 GPa using a diamond anvil cell (DAC) with electrically conductive anvils of the “rounded cone-plane” type made of synthetic carbonado-type diamonds. SWNTs are studied before and after the application of high pressure using the Raman confocal microscopy technique. Analysis of Raman spectra and pressure dependences of the SWNT resistance shows that the observed structural changes in SWNTs are reversible and no polymerization or collapse are observed.     

Observation of fluid layering and reverse motion in double-walled carbon nanotubes

Most modelling-based research in the field of carbon nanotube-related nano-fluidics has been concerned with the fluid flow in single-walled carbon nanotubes (SWCNTs), showing that the dynamics of the channel affect the structure and behaviour of the fluid. We have extended this work by modelling the flow of Ar in a double-walled carbon nanotube, and have modelled the flow in both the inner shell and the outer annular region of such a nanotube. We have found that the flows in these channels are strongly correlated, such that the fluid moves in opposite directions in these two regions. This phenomenon can give rise to a circulatory motion which can be exploited in nano-fluidic devices. Fluid layering phenomenon, that is usually associated with the flow of fluids in nano-scale channels, is also observed. Furthermore, we have also found that the fluid velocity in dynamic channels is smaller than in static channels, in line with the findings reported for single-walled carbon nanotubes.     

Linking chiral indices and transport properties of double-walled carbon nanotubes

We performed in situ transport measurements in a transmission-electron microscope (TEM) on individual double-walled carbon nanotubes (DWNT). Using selected-area electron diffraction, the chiral indices of the two tubes constituting the DWNTs were determined through careful comparison with theory. We discuss the case of a DWNT whose two tubes have a gap at half filling and show a finite density of delocalized state at the Fermi level. The exact determination of chiral indices should be reachable in any transport-measurement experiment with samples that allow TEM characterization.