Nanotubes vibrations, theory

Eklund et al. [38] provided a detailed theory of carbon nanotube vibrations. They started out with a two-dimensional graphene sheet and considered rolling it in three different ways. They called the resulting configuration armchair, zigzag, and chiral tubules and analyzed their modes of vibration. Figure 37 shows a Raman spectrum over the wide... 

VIBRATIONAL MODES OF CARBON NANOTUBES SPECTROSCOPY AND THEORY... 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

In the field of nanoscale materials, SIESTA has probably made its largest impact in the study of carbon nanotubes. This is a field which has captivated the attention of researchers for their unusual electronic and mechanical properties. Simulation and theory have played a major role, often providing predictions that have guided the way for experimental studies. Work done with SIESTA has spanned many aspects of nanotube science vibrational properties [239-241], electronic states [242-246] (including the effect of lattice distortions on the electronic states [247-250]), elastic and plastic properties [251-254], and interaction with other atomic and molecular species [255-259]. Boron nitride nanotubes have also received some attention [260, 261]. 

Natsuki Toshiaki, Ni Qing-Qing, Endo Morinobu. (2008). Analysis of the Vibration Characteristics of Double-Walled Carbon Nanotubes. Carbon, 46, 1570-1573. Aydogdu Metin. (2008). Vibration of Multi-Walled Carbon Nanotubes by Generalized Shear Deformation Theory. Int. J. Mech. Sci., 50, 837-844. 

Ansari, R., Gholami, R. Rouhi, H. (2012). Vibration Analysis of Single-Walled Carbon Nanotubes Using Different Gradient Elasticity Theories. Composites Part B, 43(8), 2985-2989. 

Figure 12 Zone center q = 0 modes for 3D graphite [38]. (Reproduced from Carbon, 33, Eklund, P. C., et al.. Vibrational modes of carbon nanotubes spectroscopy and theory, pp. 959-972. Copyright 1995, with permission from Elsevier Science.)...

P.C. Ekiund, J.M. Holden, and R.A. Jishi, Vibrational modes of carbon nanotubes spectroscopy and theory. Carbon 1995,959-972. 

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