Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data
Abstract
:1. Introduction
2. ModifiedTight Binding Model
MOD 1 Type | MOD 2 Type | |||
---|---|---|---|---|
Diameter, dt (nm) | Average | Average | Average | Average |
| Δ E | | % | Δ E | | | Δ E | | % | Δ E | | |
0.4 ≤ dt ≤ 3.0 | 0.0036 | 0.43% | 0.0033 | 0.32% |
1.0 ≤ dt ≤ 3.0 | 0.0023 | 0.36% | 0.0015 | 0.20% |
1.5 ≤ dt ≤ 3.0 | 0.0015 | 0.29% | 0.0006 | 0.11% |
MOD 1 Type | MOD 2 Type | |||
---|---|---|---|---|
Diameter, dt (nm) | Average | Average | Average | Average |
| ΔE | | % | ΔE | | | ΔE | | % | ΔE | | |
0.4 ≤ dt ≤ 3.0 | 0.0115 | 0.66% | 0.0083 | 0.57% |
1.0 ≤ dt ≤ 3.0 | 0.0052 | 0.46% | 0.0037 | 0.35% |
1.5 ≤ dt ≤ 3.0 | 0.0037 | 0.39% | 0.0031 | 0.33% |
3. Method
4. Results
RRS Data | (n, m) pair for mod 1a | (n, m) pair for mod 2b | Predicted chiralityc | Predi--ctedd | Assi--gnede | Re-assi--gnedf | Actual chiral | |||
ωrbm (cm−1) | E11 (ev) | (n, m) | Mod | Mod | Chirality | (n, m) | ||||
373.0 [50] | 1.488 [50] | 5.01 | 3.99 | 4.83 | 4.18 | (5, 4) | 1 | 1 | (5, 4) | |
335.2 [50] | 1.420 [50] | 5.28 | 4.79 | 6.03 | 3.97 | (6, 4) | 2 | 2 | (6, 4) | |
329.5 [43] | 1.249 [43] | 6.7 | 3.37 | 4.85 | 5.4 | (7, 3) | 1 | 1 | (7, 3) | |
309.0 [43] | 1.283 [43] | 6.04 | 4.9 | 5.97 | 4.98 | (6, 5) | 1 | 1 | (6, 5) | |
304.0 [34] | 1.362 [43] | 5.5 | 5.65 | 8.84 | 1.47 | (9, 1) | 2 | 2 | (9, 1) | |
297.0 [43] | 1.306 [43] | 5.78 | 5.64 | 7.78 | 3.36 | (8, 3) | 2 | 2 | (8, 3) | |
291.0 [38] | 1.100 [43] | 8.75 | 2.32 | 5.28 | 6.37 | (9, 2) | 1 | 1 | (9, 2) | |
283.0 [50] | 1.212 [50] | 6.39 | 5.62 | 7.01 | 4.95 | (7, 5) | 2 | 2 | (7, 5) | |
280.0 [42] | 1.110 [35] | 7.85 | 4.11 | 5.79 | 6.36 | (8, 4) | 1 | 1 | (8, 4) | |
263.0 [50] | 1.117 [50] | 6.49 | 6.48 | 9.75 | 2.54 | (10, 3) | 1 | 2 | (10, 2) | (10, 2) |
264.0 [43] | 1.110 [43] | 7.26 | 5.63 | 7.87 | 6.05 | (7, 6) | 1 | 1 | (7, 6) | |
256.0 [37] | 0.982 [50] | 11.23 | 0.63 | 5.91 | 7.42 | (11, 1) | 1 | 1 | (11, 1) | |
256.8 [43] | 1.140 [43] | 6.73 | 6.57 | 9.22 | 3.7 | (9, 4) | 2 | 2 | (9, 4) | |
251.0 [50] | 0.992 [50] | 9.85 | 3.24 | 6.23 | 7.38 | (10, 3) | 1 | 1 | (10, 3) | |
246.4 [39] | 1.060 [35] | 7.53 | 6.35 | 7.84 | 6.02 | (8, 6) | 2 | 2 | (8, 6) | |
242.0 [42] | 0.997 [50] | 8.77 | 5.25 | 6.91 | 7.25 | (9, 5) | 1 | 1 | (9, 5) | |
231.8 [42] | 1.036 [50] | 7.46 | 7.35 | 10.67 | 3.58 | (11, 4) | 1 | 2 | (11, 3) | (11, 3) |
229.0 [34] | 0.979 [50] | 8.41 | 6.57 | 8.04 | 6.96 | (8, 7) | 1 | 1 | (8, 7) | |
226.0 [42] | 0.901 [50] | 11.89 | 2.29 | 6.82 | 8.37 | (12, 2) | 1 | 1 | (12, 2) | |
221.8 [37] | 0.904 [50] | 10.74 | 4.34 | 7.19 | 8.32 | (11, 4) | 1 | 1 | (11, 4) | |
215.0 [50] | 0.937 [50] | 8.63 | 7.41 | 9.25 | 6.73 | (9, 7) | 2 | 2 | (9, 7) | |
213.4 [50] | 0.898 [50] | 9.81 | 6.24 | 8.01 | 8.17 | (10, 6) | 1 | 1 | (10, 6) | |
210.9 [50] | 0.949 [50] | 8.17 | 8.22 | 12.73 | 2.57 | (13, 3) | 1 | 2 | (13, 2) | (13, 2) |
206.0 [34] | 0.924 [50] | 8.43 | 8.37 | 12.47 | 3.51 | (12, 4) | 2 | 2 | (12, 4) | |
203.3 [39] | 0.828 [50] | 12.97 | 3.08 | 7.67 | 9.34 | (13, 3) | 1 | 1 | (13, 3) | |
198.5 [39] | 0.829 [50] | 11.43 | 5.73 | 8.27 | 9.2 | (11, 6) | 2 | 1 | (12, 5) | (12, 5) |
192.5 [50] | 0.841 [50] | 9.78 | 8.25 | 10.27 | 7.73 | (10, 8) | 2 | 2 | (10, 8) | |
187.2 [50] | 0.835 [50] | 9.49 | 9.12 | 12.82 | 5.26 | (13, 5) | 2 | 2 | (13, 5) |
RRS Data | (n, m) pair for mod 1a | (n, m) pair for mod 2b | Predicted chiralityc | Predi--ctedd | Assi--gnede | Re-assi--gnedf | Actual chiral | |||
ωrbm (cm−1) | E22 (ev) | (n, m) | Mod | Mod | Chirality | (n, m) | ||||
309.0 [38] | 2.180 [38] | 6.01 | 4.94 | 5.44 | 5.52 | (6, 5) | 1 | 1 | (6, 5) | |
304.0 [34] | 1.800 [42] | 5.07 | 6.07 | 9.22 | 0.83 | (9, 1) | 2 | 2 | (9, 1) | |
299.0 [38] | 1.860 [38] | 5.33 | 6.03 | 7.71 | 3.35 | (8, 3) | 2 | 2 | (8, 3) | |
283.0 [50] | 1.920 [42] | 6.01 | 6.01 | 6.69 | 5.34 | (7, 5) | 2 | 2 | (7, 5) | |
278.8 [43] | 2.110 [42] | 7.62 | 4.45 | 5.69 | 6.51 | (8, 4) | 1 | 1 | (8, 4) | |
264.6 [39] | 1.690 [39] | 5.93 | 6.95 | 9.98 | 2.09 | (10, 2) | 2 | 2 | (10, 2) | |
264.2 [37] | 1.910 [37] | 6.98 | 5.92 | 6.54 | 6.38 | (7, 6) | 1 | 1 | (7, 6) | |
257.5 [39] | 1.720 [39] | 6.31 | 6.95 | 8.55 | 4.51 | (9, 5) | 1 | 2 | (9, 4) | (9, 4) |
245.0 [42] | 1.720 [42] | 6.98 | 6.99 | 7.92 | 6.02 | (8, 6) | 2 | 2 | (8, 6) | |
242.0 [42] | 1.850 [42] | 8.66 | 5.37 | 6.69 | 7.46 | (9, 5) | 1 | 1 | (9, 5) | |
236.0 [50] | 1.556 [50] | 6.65 | 7.88 | 12.24 | 0.69 | (12, 1) | 2 | 2 | (12, 1) | |
233.0 [50] | 1.565 [50] | 6.84 | 7.89 | 11.04 | 2.95 | (11, 3) | 2 | 2 | (11, 3) | |
230.0 [42] | 1.700 [42] | 8.08 | 6.85 | 7.63 | 7.31 | (8, 7) | 1 | 1 | (8, 7) | |
227.0 [50] | 1.820 [37] | 11.88 | 2.21 | 6.76 | 8.37 | (12, 2) | 1 | 1 | (12, 2) | |
226.0 [46] | 1.570 [46] | 7.29 | 7.93 | 9.77 | 5.22 | (10, 5) | 2 | 2 | (10, 5) | |
221.8 [37] | 1.760 [37] | 11.16 | 3.77 | 7.04 | 8.47 | (11, 4) | 1 | 1 | (11, 4) | |
216.0 [39] | 1.564 [39] | 8.20 | 7.74 | 8.68 | 7.25 | (9, 7) | 2 | 2 | (9, 7) | |
212.0 [42] | 1.640 [50] | 9.98 | 6.16 | 7.74 | 8.55 | (10, 6) | 1 | 1 | (10, 6) | |
207.1 [46] | 1.447 [46] | 7.85 | 8.85 | 11.9 | 4.21 | (12, 4) | 2 | 2 | (12, 4) | |
204.0 [37] | 1.535 [37] | 9.36 | 7.65 | 8.64 | 8.39 | (9, 8) | 1 | 1 | (9, 8) | |
203.0 [42] | 1.620 [42] | 12.49 | 3.83 | 7.73 | 9.31 | (12, 4) | 2 | 1 | (13, 3) | (1, 3) |
200.0 [34] | 1.440 [34] | 8.45 | 8.88 | 10.66 | 6.51 | (11, 7) | 1 | 2 | (11, 6) | (11, 6) |
197.7 [46] | 1.560 [46] | 11.73 | 5.44 | 8.12 | 9.42 | (12, 5) | 1 | 1 | (12, 5) | |
192.5 [50] | 1.428 [50] | 9.28 | 8.78 | 9.94 | 8.08 | (10, 8) | 2 | 2 | (10, 8) | |
189.3 [46] | 1.479 [46] | 11.42 | 6.77 | 8.72 | 9.66 | (11, 7) | 1 | 1 | (11, 7) | |
183.0 [34] | 1.466 [34] | 14.14 | 4.00 | 8.63 | 10.40 | (14, 4) | 1 | 1 | (14, 4) | |
183.3 [50] | 1.390 [50] | 10.27 | 8.74 | 9.88 | 9.15 | (10, 9) | 1 | 1 | (10, 9) |
5. Conclusions
Appendix
A. Chirality Assignment from First Optical Transition Energy
B. Chirality assignment from Second Optical Transition Energy
References
- Chen, C.X.; Lu, Y.; Kong, E.S.; Zhang, Y.F.; Lee, S.T. Nanowelded carbon-nanotube-based solar microcells. Small 2008, 4, 1313–1318. [Google Scholar] [CrossRef]
- Lee, J.U. Photovoltaic effect in ideal carbon nanotube diodes. Appl. Phys. Lett. 2005, 87, 073101. [Google Scholar] [CrossRef]
- Lu, S.; Panchapakesan, B. Photoconductivity in single wall carbon nanotube sheets. Nanotechnology 2006, 17, 1843–1850. [Google Scholar] [CrossRef]
- Blackburn, J.L.; Barnes, T.M.; Beard, M.C.; Kim, Y.H.; Tenent, R.C.; McDonald, T.J.; To, B.; Coutts, T.J.; Heben, M.J. Transparent conductive single-walled carbon nanotube networks with precisely tunable ratios of semiconducting and metallic nanotubes. ACS Nano. 2008, 2, 1266–1274. [Google Scholar]
- Bindl, D.J.; Arnold, M.S. Semiconducting carbon nanotube photovoltaic photodetectors. Int. J. High Speed Electron. Syst. 2011, 20, 687. [Google Scholar] [CrossRef]
- Bindl, D.J.; Safron, N.S.; Arnold, M.S. Dissociating excitons photogenerated in semiconducting carbon nanotubes at polymeric photovoltaic heterojunction interfaces. ACS Nano. 2010, 4, 5657–5664. [Google Scholar] [CrossRef]
- Avouris, P.; Freitag, M.; Perebeinos, V. Carbon-nanotube photonics and optoelectronics. Nat. Photon. 2008, 2, 341–350. [Google Scholar] [CrossRef]
- Avouris, P.; Chen, J. Nanotube electronics and optoelectronics. Mater. Today 2006, 9, 46–54. [Google Scholar]
- Fuhrer, M.S.; Kim, B.M.; Dulrkop, T.; Brintlinger, T. High-mobility nanotube transistor memory. Nano Lett. 2002, 2, 755–759. [Google Scholar] [CrossRef]
- Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H.J. Ballistic carbon nanotube field-effect transistors. Nature 2003, 424, 654–657. [Google Scholar] [CrossRef]
- Barone, P.W.; Baik, S.; Heller, D.A.; Strano, M.S. Near-infrared optical sensors based on single-walled carbon nanotubes. Nat. Mater. 2005, 4, 86–92. [Google Scholar]
- Hamada, N.; Sawada, S.I.; Oshiyama, A. New one-dimensional conductors: Graphitic microtubules. Phys. Rev. Lett. 1992, 68, 1579–1581. [Google Scholar] [CrossRef]
- Zeng, H.; Hu, H.F.; Wei, J.W.; Wang, Z.Y.; Wang, L.; Peng, P. Curvature effects on electronic properties of small radius nanotube. Appl. Phys. Lett. 2007, 91, 033102. [Google Scholar]
- Lim, Y.; Yee, K.; Kim, J.; Hároz, E.H.; Shaver, J.; Kono, J.; Doorn, S.K.; Hauge, R.H.; Smalley, R.E. Chirality assignment of micelle-suspended single-walled carbon nanotubes using coherent phonon oscillations. J. Korean Phys. Soc. 2007, 51, 306–311. [Google Scholar] [CrossRef]
- Thomsen, C.; Telg, H.; Maultzsch, J.; Reich, S. Chirality assignments in carbon nanotubes based on resonant Raman scattering. Phys. Stat. Sol. B 2005, 242, 1802–1806. [Google Scholar]
- Strano, M.S.; Doorn, S.K.; Haroz, E.H.; Kittrell, C.; Hauge, R.H.; Smalley, R.E. Assignment of (n, m) Raman and optical features of metallic single-walled carbon nanotubes. Nano Lett. 2003, 3, 1091–1096. [Google Scholar] [CrossRef]
- Krupke, R.; Hennrich, F.; von Lohneysen, H.; Kappes, M.M. Separation of metallic from semiconducting single-walled carbon nanotubes. Science 2003, 301, 344–347. [Google Scholar] [CrossRef]
- Mattsson, M.; Gromov, A.; Dittmer, S.; Eriksson, E.; Nerushev, O.A.; Campbell, E.E.B. Dielectrophoresis-induced separation of metallic and semiconducting single-wall carbon nanotubes in a continuous flow microfluidic system. J. Nanosci. Nanotechnol. 2007, 7, 3431–3435. [Google Scholar] [CrossRef]
- Ghosh, S.; Bachilo, S.M.; Weisman, R.B. Advanced sorting of single-walled carbon nanotubes by nonlinear density-gradient ultracentrifugation. Nat. Nanotechnol. 2010, 5, 443–450. [Google Scholar]
- Arnold, M.S; Stupp, S.I.; Hersam, M.C. Enrichment of single-walled carbon nanotubes by diameter in density gradients. Nano Lett. 2005, 5, 713–718. [Google Scholar] [CrossRef]
- Hennrich, F.; Moshammer, K.; Kappes, M.M. Separation of metallic from semiconducting single walled carbon nanotubes by size exclusion chromatography. Nat. Nanotechnol. 2009, 344, 76128. [Google Scholar]
- Duesberg, G.S.; Muster, J.; Krstic, V.; Burghard, M.; Roth, S. Chromatographic size separation of single-walled carbon nanotubes. Appl. Phys. A 1998, 67, 117–119. [Google Scholar] [CrossRef]
- Tanaka, T.; Jin, H.; Miyata, Y.; Fujii, S.; Suga, H.; Naitoh, Y.; Minari, T.; Miyadera, T.; Tsukagoshi, K.; Kataura, H. Simple and scalable gel-based separation of metallic and semiconducting carbon nanotubes. Nano Lett. 2009, 9, 1497–1500. [Google Scholar] [CrossRef]
- Tu, X.; Manohar, S.; Jagota, A.; Zheng, M. DNA sequence motifs for structure-specific recognition and separation of carbon nanotubes. Nature 2009, 460, 250–253. [Google Scholar] [CrossRef]
- Hwang, J.Y.; Nish, A.; Doig, J.; Douven, S.; Chen, C.W.; Chen, L.C.; Nicholas, R.J. Polymer structure and solvent effects on the selective dispersion of single-walled carbon nanotubes. J. Am. Chem. Soc. 2008, 130, 3543–3553. [Google Scholar]
- Voggu, R.; Rao, K.V.; George, S.J.; Rao, C.N.R. A simple method of separating metallic and semiconducting single-walled carbon nanotubes based on molecular charge transfer. J. Am. Chem. Soc. 2010, 132, 5560–5561. [Google Scholar] [CrossRef]
- Dyke, C.A.; Tour, J.M. Covalent functionalization of single-walled carbon nanotubes for materials applications. J. Phys. Chem. A 2004, 108, 11151–11159. [Google Scholar] [CrossRef]
- Ghosh, S.; Rao, C.N.R. Separation of metallic and semiconducting single-walled carbon nanotubes through fluorous chemistry. Nano Res. 2009, 2, 183–191. [Google Scholar]
- Qin, C.; Peng, L.M. Measurement accuracy of the diameter of a carbon nanotube from TEM images. Phys. Rev. B 2002, 65, 155431. [Google Scholar] [CrossRef]
- Venema, L.C.; Meunier, V.; Lambin, Ph.; Dekker, C. Atomic structure of carbon nanotubes from scanning tunneling microscopy. Phys. Rev. B 2000, 61, 2991–2996. [Google Scholar] [CrossRef]
- Odom, T.W.; Huang, J.L.; Lieber, C.M. STM studies of single-walled carbon nanotubes. J. Phys. Condens. Matter 2002, 14, R145–R167. [Google Scholar]
- Herrera, J.E.; Balzano, L.; Pompeo, F.; Resasco, D.E. Raman characterizatiuon of single wall nanotubes of various diameters obtained by catalytic disproportionation of CO. J. Nanosci. Nanotech. 2003, 3, 133–138. [Google Scholar] [CrossRef]
- Yu, Z.; Brus, L.E. (n, m) structural assignments and chirality dependence in single-wall carbon nanotube Raman scattering. J. Phys. Chem. B 2001, 105, 6831–6837. [Google Scholar] [CrossRef]
- doorn, S.K.; Heller, D.A.; Barone, P.W.; Usrey, M.L.; Strano, M.S. Resonant Raman excitation profiles of individually dispersed single walled carbon nanotubes in solution. Appl. Phys. A 2004, 78, 1147–1155. [Google Scholar] [CrossRef]
- Wang, Z.; Zhao, H.; Mazumdar, S. Quantitative calculations of the excitonic energy spectra of semiconducting single-walled carbon nanotubes within a π-electron model. Phys. Rev. B 2006, 74, 195406. [Google Scholar] [CrossRef]
- Telg, H.; Maultzsch, J.; Reich, S.; Hennrich, F.; Thomsen, C. Chirality distribution and transition energies of carbon nanotubes. Phys. Rev. Lett. 2004, 93, 177401. [Google Scholar] [CrossRef]
- Maultzsch, J.; Telg, H.; Reich, S.; Thomsen, C. Radial breathing mode of single-walled carbon nanotubes optical transition energies and chiral-index assignment. Phys. Rev. B 2005, 72, 205438. [Google Scholar]
- Jorio, A.; Santos, A.P.; Ribeiro, H.B.; Fantini, C.; Souza, M.; Vieira, J.P.M.; Furtado, C.A.; Jiang, J.; Saito, R.; Balzano, L.; et al. Quantifying carbon-nanotube species with resonance Raman scattering. Phys. Rev. B 2005, 72, 075207. [Google Scholar]
- Telg, H.; Maultzsch, J.; Reich, S.; Hennrich, F.; Thomsen, C. Raman excitation profiles for the (n1, n2) assignment in carbon nanotubes. AIP Conf. Proc. 2004, 723, 330. [Google Scholar] [CrossRef]
- Weisman, R.B.; Bachilo, S.M. Dependence of optical transition energies on structure for single-walled carbon nanotubes in aqueous suspension: An empirical kataura plot. Nano Lett. 2003, 3, 1235–1238. [Google Scholar] [CrossRef]
- Dresselhausa, M.S.; Dresselhausc, G.; Jorio, A.; Filho, A.G.S.; Saito, R. Raman spectroscopy on isolated single wall carbon nanotubes. Carbon 2002, 40, 2043–2061. [Google Scholar] [CrossRef]
- Fantini, C.; Jorio, A.; Souza, M.; Strano, M.S.; Dresselhaus, M.S.; Pimenta, M.A. Optical transition energies for carbon nanotubes from resonant Raman spectroscopy: Environment and temperature effects. Phys. Rev. Lett. 2004, 93, 147406. [Google Scholar]
- Telg, H.; Maultzsch, J.; Reich, S.; Thomsen, C. Resonant-Raman intensities and transition energies of the E11 transition in carbon nanotubes. Phys. Rev. B 2006, 74, 115415. [Google Scholar]
- Hagen, A.; Hertel, T. Quantitative analysis of optical spectra from individual single-wall carbon nanotubes. Nano Lett. 2003, 3, 383–388. [Google Scholar] [CrossRef]
- Lian, Y.; Maeda, Y.; Wakahara, T.; Akasaka, T.; Kazaoui, S.; Minami, N.; Choi, N.; Tokumoto, H. Assignment of the fine structure in the optical absorption spectra of soluble single-walled carbon nanotubes. J. Phys. Chem. B 2003, 107, 12082–12087. [Google Scholar] [CrossRef]
- Namkung, M.; Williams, P.A.; Mayweather, C.D.; Wincheski, B.; Park, C.; Namkung, J.S. Chirality Characterization of Dispersed Single Wall Carbon Nanotubes. In Proceedings of the NASA MRS Spring Meeting, San Francisco, CA, USA, 28 March–1 April 2005.
- Berciaud, S.; Cognet, L.; Poulin, P.; Weisman, R.B.; Lounisa, B. Absorption spectroscopy of individual single-walled carbon nanotubes. Nano Lett. 2007, 7, 1203–1207. [Google Scholar] [CrossRef]
- Araujo, P.T.; Doorn, S.K.; Kilina, S.; Tretiak, S.; Einarsson, E.; Maruyama, S.; Chacham, H.; Pimenta, M.A.; Jorio, A. Third and fourth optical transitions in semiconducting carbon nanotubes. Phys. Rev. Lett. 2007, 98, 067401. [Google Scholar]
- Weisman, R.B. Fluorimetric characterization of single-walled carbon nanotubes. Anal. Bioanal. Chem. 2010, 396, 1015–1023. [Google Scholar] [CrossRef]
- 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 2002, 298, 2361. [Google Scholar]
- O’Connell, M.J.; Bachilo, S.M.; Huffman, C.B.; Moore, V.C.; Strano, M.S.; Haroz, E.H.; Rialon, K.L.; Boul, P.J.; Noon, W.H.; Kittrell, C. Bandgap fluorescence from individual single-walled carbon nanotubes. Science 2002, 297, 5581–5593. [Google Scholar]
- Tsyboulski, D.A.; Rocha, J.D.R.; Bachilo, S.M.; Cognet, L.; Weisman, R.B. Structure-dependent fluorescence efficiencies of individual single-walled carbon nanotubes. Nano Lett. 2007, 7, 3080–3085. [Google Scholar]
- Jones, M.; Engtrakul, C.; Metzger, W.K.; Ellingson, R.J.; Nozik, A.J.; Heben, M.J.; Rumbles, G. Analysis of photoluminescence from solubilized single-walled carbon nanotubes. Phys. Rev. B 2005, 71, 115426. [Google Scholar]
- Sauvajol, J.L.; Anglaret, E.; Rols, S.; Alvarez, L. Phonons in single wall carbon nanotube bundles. Carbon 2002, 40, 1697–1714. [Google Scholar] [CrossRef]
- Venkateswaran, U.D.; Rao, A.M.; Richter, E.; Menon, M.; Rinzler, A.; Smalley, R.E.; Eklund, P.C. Probing the single-wall carbon nanotube bundle: Raman scattering under high pressure. Phys. Rev. B 1999, 59, 10928. [Google Scholar]
- Kane, C.L.; Mele, E.J. The ratio problem in single carbon nanotube fluorescence spectroscopy. Phys. Rev. Lett. 2003, 90, 207401. [Google Scholar] [CrossRef]
- Correa, J.D.; da Silva, A.J.R.; Pacheco, M. Tight-binding model for carbon nanotubes from ab-initio calculations. J. Phys. Condens. Matter 2010, 22, 275503. [Google Scholar] [CrossRef]
- Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejon, P. Tight-binding description of graphene. Phys. Rev. B 2002, 66, 035412. [Google Scholar]
- Zόlyomi, V.; Kürti, J. First-principles calculations for the electronic band structures of small diameter single-wall carbon nanotubes. Phys. Rev. B 2004, 70, 085403. [Google Scholar] [CrossRef]
- Popov, V.N. Curvature effects on the structural, electronic and optical properties of isolated single-walled carbon nanotubes within a symmetry-adapted non-orthogonal tight-binding model. New J. Phys. 2004, 6, 17. [Google Scholar] [CrossRef]
- Ding, J.W.; Yan, X.H.; Cao, J.X. Analytical relation of band gaps to both chirality and diameter of single-wall carbon nanotubes. Phys. Rev. B 2002, 66, 073401. [Google Scholar] [CrossRef]
- Jorio, A.; Araujo, P.; Doorn, S.K.; Maruyama, S.; Chacham, H.; Pimenta, M.A. The Kataura plot over broad energy and diameter ranges. Phys. Stat. Sol. B 2006, 243, 3117–3121. [Google Scholar] [CrossRef]
- Reich, S.; Thomsen, C. Chirality dependence of the density-of-states singularities in carbon nanotubes. Phys. Rev. B 2000, 62, 4273. [Google Scholar]
- Saito, R.; Dresselhaus, G.; Dresselhaus, M.S. Trigonal warping effect of carbon nanotubes. Phys. Rev. B 2000, 61, 2981–2990. [Google Scholar] [CrossRef]
- Sfeir, M.Y.; Beetz, T.; Wang, F.; Huang, L.; Huang, X.M.H.; Huang, M.; Hone, J.; O’Brien, S.; Misewich, J.A.; Heinz, T.F.; et al. Optical spectroscopy of individual single-walled carbon nanotubes of defined chiral structure. Science 2006, 312, 554–556. [Google Scholar]
- Liu, K.; Deslippe, J.; Xiao, F.; Capaz, R.B.; Hong, X.; Aloni, S.; Zettl, A.; Wang, W.; Bai, X.; Louie, S.G.; et al. An atlas of carbon nanotube optical transitions. Nat. Nanotechnol. 2012, 7, 325–329. [Google Scholar]
- Nugraha, A.R.T.; Saito, R.; Sato, K.; Araujo, P.T.; Jorio, A.; Dresselhaus, M.S. Dielectric constant model for environmental effects on the exciton energies of single wall carbon nanotubes. Appl. Phys. Lett. 2010, 97, 091905. [Google Scholar]
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Arefin, M.S. Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data. Nanomaterials 2013, 3, 1-21. https://doi.org/10.3390/nano3010001
Arefin MS. Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data. Nanomaterials. 2013; 3(1):1-21. https://doi.org/10.3390/nano3010001
Chicago/Turabian StyleArefin, Md Shamsul. 2013. "Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data" Nanomaterials 3, no. 1: 1-21. https://doi.org/10.3390/nano3010001