• Z. P. Popović NanoLab, Faculty of Physics, University of Belgrade, Serbia
  • M. Damnjanović NanoLab, Faculty of Physics, University of Belgrade, Serbia
  • I. Milošević NanoLab, Faculty of Physics, University of Belgrade, Serbia



We have constructed a model of single-wall helically coiled carbon nanotubes by means of graph theory and topological coordinates method.  After obtaining three-dimensional coordinates of the atoms we proceed with the relaxation by successive application of the following methods: 1) harmonic approximation; 2) molecular mechanics based on the Brenner potential; and 3) density functional tight binding (DFTB). Finally, by DFTB and line group symmetry implemented POLSym code, we calculate total and cohesive energy of the obtained fully relaxed structures of CNCs.


[1] S. Itoh, S. Ihara, J. Kitakami, Toroidal form of carbon C360, Phys. Rev. B 47 (1993) 1703-1704.

[2] X. B. Zhang, X. F. Zhang, D. Bernaerts, G. Van Tendeloo, S. Amelinckx, J. Van Landuyt, V. Ivanov, J. B. Nagy, Ph. Lambin, and A. A. Lucas, The texture of catalytically grown coil-shaped carbon nanotubules, Europhys. Lett. 27 (1994) 141−147.

[3] D. Fejes and K. Hernadi, Review of the Properties and CVD Synthesis of Coiled Carbon Nanotubes, Materials 3 (2010) 2618−2642.

[4] L.P. Biro, S. D. Lazarescu, P. A. Thiry, A. Fonseca, J. B Nagy, A. A. Lucas and Ph. Lambin, Scanning tunneling microscopy observation of tightly wound, single-wall coiled carbon nanotubes, Europhys. Lett. 50 (4) (2000) 494−500.

[5] M. Damnjanović and I. Milošević, Line Groups in Physics (Springer-Verlag, Berlin, 2010).

[6] M. Damnjanović and I. Milošević, Helically coiled carbon nanotubes, Contemporary Materials, I−1, (2010) 1−3.

[7] I. Laszlo, A. Rassat, The geometric structure of deformed nanotubes and the topological coordinates, J.Chem. Comput. Sci. 43 (2) (2003) 519−524.

[8] I. Laszlo, A. Rassat, P. W. Fowler, A. Graovac, Topological coordinates for toroidal structures, Chemical Physics Letters 342 (2001) 369−374.

[9] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni and S. B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys. Condens. Matter 14 (2002) 783−802.

[10] Li Zhao Liu, Hai Li Gao, Ji Jun Zhao, Jian Ping Lu, Superelasticity of Carbon Nanocoils from Atomistic Quantum Simulations, Nanoscale Res. Lett 5 (2010) 478−483.