[01] G. R. Ahmed Jamal, Department of Electrical and Electronic Engineering, University of Asia Pacific, Dhaka, Bangladesh. [02] S. M. Mominuzzaman, Department of Electrical and Electronic Engineering, Bangaldesh University of Engineering and Technology, Dhaka, Bangladesh.

Electronic and optical properties of single-wall carbon nanotubes (SWCNT) are directly associated with their geometrical structures which are uniquely specified by a pair of chiral index (n, m). Hence, determination of chirality of isolated or bundled SWCNTs is an important task to purify, identify, separate and sort nanotubes immediately after their synthesis. Knowing the chirality is also important for many applications of SWCNTs in device level so as to select the specific SWCNT with required electronic and optical properties suitable for that application. In this work, a review is presented on main existing theoretical and experimental methods for determination of chirality of SWCNTs. This review will give a summary of various new and old techniques proposed by different researchers for chirality assignment of metallic and semiconducting SWCNTs, including some most recent works. This review will also discuss the advantages and disadvantages of each technique for chirality assignment and will give an overall comparison between them.

Nanotube, SWCNT, Chiral Index, Optical Transition Energy, Diameter, Raman Spectroscopy

[01] V. N. Popov, “Carbon nanotubes: properties and application”, Materials Science and Engineering R, 43, pp. 61–102, 2004. [02] T. W. Odom, J. L. Huang, P. Kim, and C. M. Lieber, “Structure and Electronic Properties of Carbon Nanotubes”, J. Phys. Chem. B, 104, pp.2794-2809, 2000. [03] N. Hamada, S. Sawada, and A. Oshiyama, “New one-dimensional conductors: graphitic microtubules,” Phys. Rev. Lett., Vol.68, No.10, pp.1579-1581, 1992. [04] Y. Lim, K. Yee, J. Kim, E. H. Hároz, J. Shaver, J. Kono, S. K. Doorn , R. H. Hauge , R. E. Smalley, “Chirality Assignment of Micelle-Suspended Single-Walled Carbon Nanotubes Using Coherent Phonon Oscillations”, Journal of the Korean Physical Society, Vol. 51, No. 1, pp. 306-311, 2007. [05] C. Thomsen, H. Telg, J. Maultzsch and S. Reich, “Chirality assignments in carbon nanotubes based on resonant Raman scattering”, phys. stat. sol. (b) 242, No. 9, pp.1802–1806, 2005. [06] M. S. Strano, S. K. Doorn, E. H. Haroz, C. Kittrell, R. H. Hauge and R. E. Smalley, “Assignment of (n, m) Raman and Optical Features of Metallic Single-Walled Carbon Nanotubes”, Nano Lett., Vol.3, No.8, pp.1091-1096, 2003. [07] J. W. Mintmire and C. T. White, “Universal density of states for carbon nanotubes”, Phys. Rev. Lett., Vol. 81, No.12, 1998. [08] S. Reich and C. Thomsen, “Chirality dependence of the density-of-states singularities in carbon nanotubes”, Phys. Rev. B, Vol 62, No. 7, 2000. [09] M.S. Dresselhausa, G. Dresselhausc, A. Jorio, A.G. Souza Filho, R. Saito, “Raman spectroscopy on isolated single wall carbon nanotubes”, Carbon, 40, pp.2043–2061, 2002. [10] T. Tanaka, H. Jin, Y. Miyata, S. Fujii, H. Suga, Y. Naitoh, T. Minari, T. Miyadera, K. Tsukagoshi and H. Kataura, “Simple and Scalable Gel-Based Separation of Metallic and Semiconducting Carbon Nanotubes”, Nano Lett., 9 (4), pp 1497–1500, 2009. [11] R. Krupke, F. Hennrich, H. von Lohneysen and M. M. Kappes, “Separation of metallic from semiconducting single-walled carbon nanotubes”, Science, 301, pp.344–347, 2003. [12] R. Voggu, K. V. Rao, S. J. George and C. N. R. Rao, “A Simple Method of Separating Metallic and Semiconducting Single-Walled Carbon Nanotubes Based on Molecular Charge Transfer”, J. Am. Chem. Soc., 132 (16), pp 5560–5561, 2010. [13] S. Ghosh and C. N. R. Rao, “Separation of Metallic and Semiconducting Single-Walled Carbon Nanotubes Through Fluorous Chemistry”, Nano Res 2, pp.183-191, 2009. [14] M. Mattsson, A. Gromov, S. Dittmer, E. Eriksson, O. A. Nerushev, E. E. B. Campbell, “Dielectrophoresis-induced separation of metallic and semiconducting single-wall carbon nanotubes in a continuous flow microfluidic system”, Journal of nanoscience and nanotechnology, vol. 7, No. 10, pp.3431-3435, 2007 [15] F. Hennrich, K. Moshammer, M M Kappes, “Separation of metallic from semiconducting single walled carbon nanotubes by size exclusion chromatography”, Nature Nanotechnology, Vol. 344, Issue c, pp.76128-76128, 2009. [16] Feng Ye, “Metallic-semiconducting separation of single wall carbon nanotubes and their application to electronic devices”, Ph.D thesis in Materials Science, University of Tsukuba, Japan, February 2011. [17] H. Telg, J. Maultzsc, S. Reich, F. Hennrich, and C. Thomsen, “Raman intensities of the first optical transitions in carbon nanotubes”, Phys. stat. sol. (b) 243, No. 13, pp.3181–3185, 2006. [18] C. Qin and L.M. Peng, “Measurement accuracy of the diameter of a carbon nanotube from TEM images”, Phys. Rev. B 65, 155431, 2002. [19] M. Ge, and K. Sattler, “Scanning tunneling microscopy of single-shell nanotubes of carbon”, Appl. Phys. Lett., 65, 2284, 1994. [20] L. C. Venema, V. Meunier, Ph. Lambin, and C. Dekker, “Atomic structure of carbon nanotubes from scanning tunneling microscopy”, Phys. Rev. B 62, pp.2991-2996, 2000. [21] T. W. Odom, J. L. Huang and C. M. Lieber, “STM studies of single-walled carbon nanotubes”, J. Phys.: Condens. Matter 14, R145–R167, 2002. [22] J. E. Herrera, L. Balzano, F. Pompeo and D. E. Resasco, “Raman characterizatiuon of Single wall nanotubes of various diameters obtained by catalytic disproportionation of CO”, J. Nanosci. Nanotech, Vol. 3, No. 1, 2003. [23] R. B. Weisman and S. M. Bachilo, “Dependence of optical transition energies on structure for single-walled carbon nanotubes in aqueous suspension: an empirical kataura plot,” Nano Lett., Vol.3, No.9, pp.1235-1238, 2003. [24] Z. Wang, H. Zhao, and S. Mazumdar, “Quantitative calculations of the excitonic energy spectra of semiconducting single-walled carbon nanotubes within a π-electron model”, Phys. Rev. B 74, 195406, 2006. [25] J. Maultzsch, H. Telg, S. Reich, and C. Thomsen, “Radial breathing mode of single-walled carbon nanotubes Optical transition energies and chiral-index assignment”, Phys. Rev. B 72, 205438, 2005. [26] S.K. doorn, D.A. Heller, P.W. Barone, M.L. Usrey, M.S. Strano, “Resonant Raman excitation profiles of individually dispersed single walled carbon nanotubes in solution”, Appl. Phys. A 78, p.1147–1155, 2004. [27] Z. Yu and L. E. Brus, “(n, m) Structural Assignments and Chirality Dependence in Single-Wall Carbon Nanotube Raman Scattering”, J. Phys. Chem. B, 105, pp.6831-6837, 2001. [28] H. Telg, J. Maultzsch, S. Reich, F. Hennrich and C. Thomsen, “Chirality Distribution and Transition Energies of Carbon Nanotubes” Phys. Rev. Lett., Vol. 93, No. 17, 2004. [29] A. Jorio, A. P. Santos, H. B. Ribeiro, C. Fantini, M. Souza, J. P. M. Vieira, C. A. Furtado, J. Jiang, R. Saito, L. Balzano, D. E. Resasco and M. A. Pimenta, “Quantifying carbon-nanotube species with resonance Raman scattering” Phys. Rev. B 72, 075207, 2005. [30] H. Telg, J. Maultzsch, S. Reich, F. Hennrich and C. Thomsen, “Raman excitation profiles for the (n1, n2) assignment in carbon nanotubes” AIP Conf. Proceedings, Vol. 723, Issue 1, p.330, 2004. [31] C. Fantini, A. Jorio, M. Souza, M. S. Strano, M. S. Dresselhaus and M. A. Pimenta, “Optical Transition Energies for Carbon Nanotubes from Resonant Raman Spectroscopy: Environment and Temperature Effects”, Phys. Rev. B, Vol. 93, No. 14, 2004. [32] H. Telg, J. Maultzsch, S. Reich and C. Thomsen, “Resonant-Raman intensities and transition energies of the E11 transition in carbon nanotubes”, Phys. Rev. B 74, 115415, 2006. [33] Y. Lian, Y. Maeda, T. Wakahara, T. Akasaka, S. Kazaoui, N. Minami, N. Choi and H. Tokumoto, “Assignment of the Fine Structure in the Optical Absorption Spectra of Soluble Single-Walled Carbon Nanotubes”, J. Phys. Chem. B, 107, 12082-12087, 2003. [34] A. Hagen and T. Hertel, “Quantitative Analysis of Optical Spectra from Individual Single-Wall Carbon Nanotubes”, Nano letters, Vol. 3, No. 3, pp. 383-388, 2003. [35] M. Namkung, P. A. Williams, C. D.Mayweather, B. Wincheski, C. Park,; Namkung, S. Juock, “Chirality Characterization of Dispersed Single Wall Carbon Nanotubes” NASA, 2005 MRS Spring Meeting; San Francisco, CA; United States, 28 Mar. - 1 Apr. 2005. [36] S. Berciaud, L. Cognet, P. Poulin, R. Bruce Weisman, and B. Lounisa, “Absorption spectroscopy of individual single-walled carbon nanotubes”, Nano Lett., 7 (5), pp.1203–1207, 2007. [37] Bachilo S. M., Strano M. S., Kittrell C., Hauge R. H., Smalley R. E., Weisman R. B., “Structure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes”, Science, Vol 298 No. 5602, pp. 2361, 2002. [38] J. Lefebvre, S. Maruyama and P. Finnie, “Photoluminescence: science and applications”, Topics in Applied Physics, Vol. 111, pp.287-319, 2008. [39] R. B. Weisman, “Fluorimetric characterization of single-walled carbon nanotubes”, Anal. Bioanal. Chem. 396, 1015–1023, 2010. [40] M. J. O'Connell, S.M. Bachilo, C.B. Huffman, V.C. Moore, M.S. Strano, E.H. Haroz, K.L. Rialon, P.J. Boul, W.H. Noon, C. Kittrell, J. Ma, R.H. Hauge, R.B. Weisman, and R.E. Smalley, “Band Gap Fluorescence from Individual Single-Walled Carbon Nanotubes”, Science 297, pp.5581-5593, 2002. [41] D. A. Tsyboulski1, J. D. R. Rocha, S. M. Bachilo1, L. Cognet and R. B. Weisman,” Structure-Dependent Fluorescence Efficiencies of Individual Single-Walled Carbon Nanotubes”, Nano Lett., 7(10), pp.3080-5, 2007. [42] M. Jones, C. Engtrakul, W. K. Metzger, R. J. Ellingson, A. J. Nozik, M. J. Heben, and G. Rumbles, “Analysis of photoluminescence from solubilized single-walled carbon nanotubes”, Phys. Rev B, 71, 115426, 2005. [43] Y. Miyauchi, S. Chiashi, Y. Murakami, Y. Hayashida, S. Maruyama, “Fluorescence spectroscopy of single-walled carbon nanotubes synthesized from alcohol”, Chem. Phys. Lett., Vol. 387, Issues 1–3, pp.198–203, 2004. [44] T. S. Jespersen, “Raman Scattering in Carbon Nanotubes”, M.Sc. Thesis, Faculty of Science, University of Copenhagen, 2003. [45] J. Maultzsch, C. Thomsen , “Characterization of Carbon Nanotubes by Optical Spectroscopy, Advanced Micro and Nanosystems”, Carbon Nanotube Devices, Vol. 8., Edited by Christofer Hierold, Verlag GmbH and Co. KGaA, Weinheim, Berlin, Germany, 2008. [46] Z. Yu, L. E. Brus, “Rayleigh and Raman scattering from individual carbon nanotube bundles”, J. Phys. Chem. B, 105, p.1123, 2001. [47] M. Y Sfeir., T. Beetz, F Wang, L. Huang, X. M. H Huang., M. Huang, J. Hone, S. O’Brien, J. A Misewich, T. F. Heinz, L. Wu, Y. Zhu, L. E. Brus, “Optical Spectroscopy of Individual Single-Walled Carbon Nanotubes of Defined Chiral Structure”, Science, Vol. 312, April 2006. [48] W. Wu et al., “True-color real-time imaging and spectroscopy of carbon nanotubes on substrate by enhanced Rayleigh scattering”, Nano Res., Just Accepted Manuscript, DOI: 10.1007/s12274-015-0779-x, April 2015. [49] R. B. Weisman, “Fluorescence Spectroscopy of Single-Walled Carbon Nanotubes”, Applied Physics of Carbon Nanotubes, Editors: S. V. Rotkin, S. Subramoney, Chapter: NanoScience and Technology, pp. 183-202, 2005. [50] H. Telg, “Raman studies on individual nanotubes and nanotube ensembles –vibrational properties and scattering efficiencies”, Ph.d thesis, Physics, Institute für Festkörperphysik, Berlin, 2009. [51] J. L. Sauvajol, E. Anglaret, S. Rols, L. Alvarez, “Phonons in single wall carbon nanotube bundles”, Carbon, 40, 1697, 2002. [52] U. D. Venkateswaran, A. M. Rao, E. Richter, M. Menon, A. Rinzler and R. E. Smalley, “Probing the single-wall carbon nanotube bundle: Raman scattering under high pressure”, Phys. Rev. B, Vol. 59, No. 16, 1999. [53] L. J. Li, R. J. Nicholas, R. S. Deacon and P. A. Shields, “Chirality assignment of single-walled carbon nanotubes with strain”, Phys. Rev. Lett. 93(15):156104, 2004. [54] Y Ohno, S Kishimoto, T Mizutani, T Okazaki and H Shinohara, “Chirality assignment of individual single-walled carbon nanotubes in carbon nanotube field-effect transistors by micro-photocurrent spectroscopy”, App Phys Lett., Vol 84, No 8, 2004. [55] J. C. Meyer, M. Paillet, G. S. Duesberg, S. Roth, “Electron diffraction analysis of individual single - walled carbon nanotubes” Ultramicroscopy , 106, p.176, 2006. [56] M. Gao, J. M. Zuo, R. D. Twesten, I. Petrov, L. A. Nagahara, R. Zhang, “Structure determination of individual single - wall carbon nanotubes by nanoarea electron diffraction”, Appl. Phys. Lett. , 82, p.2703, 2003. [57] Kaihui Liu et al., “High-throughput optical imaging and spectroscopy of individual carbon nanotubes in devices”, Nature Nanotechnology 8, pp. 917–922, 2013. [58] A Roch, L Stepien, T Roch, I Dani, C Leyens, O Jost and A Leson, “Optical absorption spectroscopy and properties of single walled carbon nanotubes at high temperature”, Synthetic Metals 197, pp.182–187, 2014. [59] T. Inoue, D. Hasegawa, S. Chiashia and S. Maruyama, “Chirality analysis of horizontally aligned single walled carbon nanotubes: decoupling populations and lengths”, J. Mater. Chem. A, 3, 15119, 2015.