Explicit solution of the radial breathing mode frequency of single-wailed carbon nanotubes

On the basis of a molecular mechanics model, an analytical solution of the radial breathing mode （RBM） frequency of single-walled carbon nanotubes （SWCNTs） is obtained. The effects of tube chirality and tube diameter on the RBM frequency are investigated and good agreement between the present results and existing data is found. The present analytical formula indicates that the chirality and size dependent elastic properties are responsible for the effects of the chirality and small size on the RBM frequency of an SWCNT.

A semi-analytical approach for calculating the equilibrium structure and radial breathing mode frequency of single-walled carbon nanotubes

A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent variables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium configuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilibrium structure and radial breathing mode frequency of CNTs.

A glance on the effects of temperature on axisymmetric dynamic behavior of multiwall carbon nanotubes

In this paper the effects of temperature on the radial breathing modes （RBMs） and radial wave propaga- tion in multiwall carbon nanotubes （MWCNTs） are inves- tigated using a continuum model of multiple elastic isotropic shells. The van der Waals forces between tubes are simulated as a nonlinear function of interlayer spacing of MWCNTs. The governing equations are solved using a finite element method. A wide range of innermost radius-to-thickness ratio of MWCNTs is considered to enhance the investigation. The presented solution is verified by comparing the results with those reported in the literature. The effects of temperature on the van der Waals interaction coefficient between layers of MWCNTs are examined. It is found that the variation of the van der Waals interaction coefficient at high temperature is sensible. Subsequently, variations of RBM frequencies and radial wave propagation in MWCNTs with temperatures up to 1 600 K are illustrated. It is shown that the thick MWC- NTs are more sensible to temperature than the thin ones.

Radial breathing modes of multi-walled carbon nanotubes by an atomic beam-spring model

Based on molecular force fields,a new finite element model is constructed for multi-walled carbon nanotubes where the interlayer interactions and C--C bonds are simulated by the elements of piece-wise linear spring and rectangular cross section beam,respectively.For high computation efficiency and atomic reification,the radial breathing modes of multi-walled carbon nanotubes are studied systemically using this model.The results show the correspondence between carbon nanotube structures and vibrational modes,which provide unequivocal data for the experimental characterization of carbon nanotubes.An empirical relationship of radial breathing modes frequencies with the nanotube radius are also obtained for two-layer carbon nanotubes.

单壁碳纳米管RBM的拉曼光谱研究

在室温下首次观察到碳纳米管的27条径向呼吸振动拉曼峰,并且通过与理论值对照,对其进行了初步标定。所观测到的径向呼吸振动模数目是迄今最多的。

径向载荷下单壁碳纳米管振动频率分析

碳纳米管的基频对外载荷非常敏感。将碳纳米管作为微纳米应变/力传感器敏感元件时要求对基频和外载荷之间的关系进行深入的研究。在单壁碳纳米管分子结构力学模型的基础上,研究了径向载荷和单壁碳纳米管基频之间的关系。结果表明:基频随着径向拉力载荷的增加而线性增加,随着径向压力载荷的增加而线性减小,并且基频对压力载荷更加敏感。

CVD生长多壁碳纳米管的拉曼光谱径向呼吸振动模式观察(英文)

采用拉曼光谱仪、透射电镜、俄歇能谱仪、X射线光电子能谱仪等研究在Si O2/Si基底上化学沉积的多壁碳纳米管(MWCNTs)经390℃的空气中热处理120 min前后与HCl溶液化学处理前后的结构变化情况。拉曼光谱集中测试低频(250-300 cm-1)带。结果表明,经热处理和化学处理后,在250-300 cm-1形成的拉曼带在峰位和半宽几乎没变。由透射电镜可知,小直径碳纳米管的内径值与拉曼光谱测试结果一致。这些结果表明,低频带产生于小直径碳纳米管的内壁中碳原子的径向呼吸振动。

利用径向呼吸模及其倍频模的共振特性精确测定单壁碳纳米管的电子跃迁能量

提出一个根据拉曼基频模及其倍频模的斯托克斯和反斯托克斯拉曼成分的不同共振行为来探测样品与激光共振的系统能级的方法.此方法被应用到不均匀单壁碳纳米管束样品中某一径向呼吸模频率为219波数的金属型碳纳米管.通过分析呼吸模及其倍频模和切向模的共振行为,获得了该碳纳米管的电子跃迁能量,并获得纳米管C-C最近邻重叠积分因子为2.80eV.此数值可以很好的解释单壁碳纳米管径向呼吸模的共振行为.