Geometrical Model Based Refinements in Nanotube Chiral Indices

ABSTRACT

There is demonstrated how it is possible to refine graphitic nanotubes’ chiral indices based on the appropriate geometrical model for their structure.

There is demonstrated how it is possible to refine graphitic nanotubes’ chiral indices based on the appropriate geometrical model for their structure.

Cite this paper

nullL. Chkhartishvili and T. Berberashvili, "Geometrical Model Based Refinements in Nanotube Chiral Indices,"*World Journal of Nano Science and Engineering*, Vol. 1 No. 2, 2011, pp. 45-50. doi: 10.4236/wjnse.2011.12007.

nullL. Chkhartishvili and T. Berberashvili, "Geometrical Model Based Refinements in Nanotube Chiral Indices,"

References

[1] S. Iijima, “Helical Microtubules of Graphitic Carbon,” Nature, Vol. 354, No. 6348, 1991, pp. 56-58.

[2] A. Jorio, M. S. Dresselhaus, M. Saito and G. Dresselhaus, “Raman Spectroscopy in Graphene Related Systems,” Wiley–VCH, Berlin, 2011.

[3] N. G. Chopra, R. J. Luyken, K. Cherrey, V. H. Crespi, M. L. Cohen, S. G. Louie and A. Zettl, “Boron Nitride Nanotubes,” Science, Vol. 269, No. 5226, 1995, pp. 966-967.

[4] Y. Zhang and K. Suenaga, C. Colliex and S. Iijima, “Coaxial Nanocable: Silicon Carbide and Silicon Oxide Sheathed with Boron Nitride and Carbon,” Science, Vol. 281, No. 5379, 1998, pp. 973-975.

[5] X. Blasé, J.-C. Charlier, A. de Vita and R. Car, “Structural and Electronic Properties of Composite BxCyNz Nanotubes and Heterojunctions,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 293-300.

[6] V. V. Pokropivny, V. V. Skorokhod, G. S. Oleinik, A. V. Kurdyumov, T .S. Bartnitskaya, A. V. Pokropivny, A. G. Sisonyuk and D. M. Sheichenko, “Boron Nitride Analogs of Fullerenes (the Fulborenes), Nanotubes, and Fullerites (the Fulborenites),” Journal of Solid State Chemistry, Vol. 154, No. 1, 2000, pp. 214-222.

[7] S. M. Nakhmanson, A. Cazolari, V. Meunier, J. Bernholc and M. Boungiorno Nardeli, “Spontaneous Polarization and Piezoelectricity in Boron Nitride Nanotubes,” Physical Review B, Vol. 67, No. 235406, 2003, 5 pp.

[8] N. Sai and E. J. Mele, “Microscopic Theory for Nanotube Piezoelectricity,” Physical Review B, Vol. 68, No. 241405(R), 2003, 3 pp.

[9] W.-Q. Han, C. W. Chang and A. Zettl, “Encapsulation of One-Dimensional Potassium Halide Crystals within BN Nanotubes,” Nano Letters, Vol. 4, No. 7, 2004, pp. 1455- 1357.

[10] K. Yum and M.-F. Yu, “Measurement of Wetting Properties of Individual Boron Nitride Nanotubes with the Wilhelmy Method Using a Nanotube-Based Force Sensor,” Nano Letters, Vol. 6, No. 2, 2006, pp. 329-333.

[11] Ch. Zhi, Y. Bando, Ch. Tang and D. Golberg, “Engineering of Electronic Structure of Boron-Nitride Nanotubes by Covalent Functionalization,” Physical Review B, Vol. 74, No. 153413, 2006, 4 pp.

[12] S. A. Shevlin and Z. X. Guo, “Hydrogen Sorption in Defective Hexagonal BN Sheets and BN Nanotubes,” Physical Review B, Vol. 76, No. 024104, 2007, 11 pp.

[13] E. Durgun, Y.-R. Jang and S. Ciraci, “Hydrogen Storage Capacity of Ti-doped Boron-Nitride and B/Be-Substituted Carbon Nanotubes,” Physical Review B, Vol. 76, No. 073413, 2007, 4 pp.

[14] Q. Wu, Zh. Hu, X. Wang, Y. Lu, X. Chen, H. Xu and Y. Chen, “Synthesis and Characterization of Faceted Hexagonal Aluminum Nitride Nanotubes,” Journal of the American Chemical Society, Vol. 125, No. 34, 2003, pp. 10176-10177.

[15] J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan and H.-J. Choi, P. Yang, “Single-Crystal Gallium Nitride Nanotubes,” Nature, Vol. 422, No. 6932, 2003, pp. 599-602.

[16] J. Q. Hu, Q. Li, X. M. Meng, C. S. Lee and S. T. Lee, “Thermal Reduction Route to the Fabrication of Coaxial Zn / ZnO Nanocables and ZnO Nanotubes,” Chemistry of Materials, Vol. 15, No. 1, 2003, pp. 305-308.

[17] Y. J. Xing, Z. H. Xi, Z. Q. Xue, X. D. Zhang, J. H. Song, R. M. Wang, J. Xu, Y. Song, S. L. Zhang and D. P. Yu, “Optical Properties of the ZnO Nanotubes Synthesized via Vapor Phase Growth,” Applied Physics Letters, Vol. 83, No. 9, 2003, pp. 1689-1691.

[18] X. H. Zhang, S. Y. Xie, Zh. Y. Jiang, X. Zhang, Zh.-Q. Tian, Zh.-X. Xie, R.-B. Huang and L. S. Zheng, “Rational Design and Fabrication of ZnO Nanotubes from Nanowire Templates in a Microwave Plasma System,” Journal of Physical Chemistry B, Vol. 107, No. 37, 2003, pp. 10114-10118.

[19] S. Erkoc and H. K?kten, “Structural and Electronic Properties of Single-Wall ZnO Nanotubes,” Physica E, Vol. 28, No. 2, 2005, pp. 162-170.

[20] H. Zhang, Sh. Zhang, Sh. Pan, G. Li and J. Hou, “A Simple Solution Route to ZnS Nanotubes and Hollow Nanospheres and Their Pptical Properties,” Nanotechnology, Vol. 15, No. 8, 2004, pp. 945-948.

[21] Y. Ch. Zhu, Y. Bando and Y. Uemura, “ZnS?Zn Nanocables and ZnS Nanotubes,” Chemical Communications, No. 7, 2003, pp. 836-837.

[22] M. S. Dresselhaus, G. Dresselhaus and R. Saito, “Carbon Fibers Based on C60 and Their Symmetry,” Physical Review B, Vol. 45, No. 11, 1992, pp. 6234-6242.

[23] R. A. Jishi, M. S. Dresselhaus and G. Dresselhaus, “Symmetry Properties of Chiral Carbon Nanotubes,” Physical Review B, Vol. 47, No. 24, 1993, pp. 16671- 16674.

[24] M. S. Dresselhaus, G. Dresselhaus and R. Saito, “Physics of Carbon Nanotubes,” Carbon, Vol. 33, No. 7, 1995, pp. 883-891.

[25] A. Rubio, J. L. Corkill and M. L. Cohen, “Theory of Graphitic Boron Nitride Nanotubes,” Physical Review B, Vol. 49, No. 7, 1994-I, pp. 5081-5084.

[26] B. J. Cox and J. M. Hill, “Exact and Approximate Geometric Parameters for Carbon Nanotubes Incorporating Curvature,” Carbon, Vol. 45, No. 7, 2007, pp. 1453- 1462.

[27] B. J. Cox and J. M. Hill, “Geometric structure of Ultra-Small Carbon Nanotubes,” Carbon, Vol. 46, No. 4, 2008, pp. 711-713.

[28] R. K. F. Lee, B. J. Cox and J. M. Hill, “The Geometric Structure of Single-Walled Nanotubes,” Nanoscale, Vol. 2, No. 6, 2010, pp. 859-872.

[29] L. S. Chkhartishvili, “On Sizes of Boron Nitride Nanotubes,” In: I. M. Neklyudov and V. M. Shulayev, Eds., Thin Films in Optics and Nanoelectronics, NSC “KhIPT”–PPP “Contrast”, Kharkiv, 2006, pp. 367-373.

[30] L. S. Chkhartishvili, “Equilibrium Geometry of Ultra-Small-Radius Boron Nitride Nanotubes,” Material Science of Nanostructures, No. 1, 2009, pp. 33-44.

[31] L. Chkhartishvili, “Boron Nitride Nanosystems of Regular Geometry,” Journal of Physics: Conference Series, Vol. 176, No. 012014, 2009, 17 pp.

[32] L. S. Chkhartishvili and T. M. Berberashvili, “Sequences of Layers in Binary Compounds Multi-Walled Nanotubes and Multi-Shelled Fullerenes,” Material Science of Nanostructures, No. 3, 2010, pp. 20-28.

[33] L. Chkhartishvili, “Quasi-Classical Theory of Substance Ground State,” Technical University Press, Tbilisi, 2004.

[34] L. S. Chkhartishvili, “Volume of the Intersection of Three Spheres,” Mathematical Notes, Vol. 69, No. 3, 2001, pp. 421-428.

[35] L. S. Chkhartishvili, “Iterative Solution of the Secular Equation,” Mathematical Notes, Vol. 77, No. 1, 2005, pp. 273-279.

[36] L. Chkhartishvili and I. Murusidze, “Molar Binding Energy of Zigzag and Armchair Single-Walled Boron Nitride Nanotubes,” Materials Sciences and Applications, Vol. 1, No. 4, 2010, pp. 223-246.

[37] H. Chen and E. Ruckenstein, “The Driving Force of Channel Formation in Triheteropolymers Confined in Nanocylindrical Tubes,” Journal of Chemical Physics, Vol. 130, No. 024901, 2009, 5 pp.

[38] H. Chen and E. Ruckenstein, “Nanostructures Self-Assembled in Polymer Solutions Confined in Cylindrical Nanopores,” Langmuir, Vol. 25, No. 20, 2009, pp. 12315-12319.

[39] H. Chen and E. Ruckenstein, “The Structure of Nanochannels Formed by Block Copolymer Solutions Confined in Nanotubes,” Journal of Chemical Physics, Vol. 131, No. 114904, 2009, 6 pp.

[40] H. Chen and E. Ruckenstein, “Relation between Molecular Orientation and Morphology of a Multiblock Copolymer Melt Confined in Cylindrical Nanopores,” Polymer, Vol. 51, No. 4, 2010, pp. 968-974.

[41] D. Y. Joh, L. H. Herman, S.-Y. Ju, J. Kinder, M. A. Segal, J. N. Johnson, G. K. L. Chan and J. Park, “On-Chip Rayleigh Imaging and Spectroscopy of Carbon Nanotubes,” Nano Letters, Vol. 11, No. 1, 2011, pp. 1-7.

[42] J. Kunstman, A. Quandt and I. Boustani, “An Approach to Control the Radius and the Chirality of Nanotubes,” Nanotechnology, Vol. 18, No. 155703, 2007, 3 pp.

[43] A. Zobelli, C.P. Ewels, A. Gloter, G. Seifert, O. Stephan, S. Csillag and C. Colliex, “Defective Structure of BN Nanotubes: From Single Vacancies to Dislocation Lines,” Nano Letters, Vol. 6, No. 9, 2006, pp. 1955-1960.

[1] S. Iijima, “Helical Microtubules of Graphitic Carbon,” Nature, Vol. 354, No. 6348, 1991, pp. 56-58.

[2] A. Jorio, M. S. Dresselhaus, M. Saito and G. Dresselhaus, “Raman Spectroscopy in Graphene Related Systems,” Wiley–VCH, Berlin, 2011.

[3] N. G. Chopra, R. J. Luyken, K. Cherrey, V. H. Crespi, M. L. Cohen, S. G. Louie and A. Zettl, “Boron Nitride Nanotubes,” Science, Vol. 269, No. 5226, 1995, pp. 966-967.

[4] Y. Zhang and K. Suenaga, C. Colliex and S. Iijima, “Coaxial Nanocable: Silicon Carbide and Silicon Oxide Sheathed with Boron Nitride and Carbon,” Science, Vol. 281, No. 5379, 1998, pp. 973-975.

[5] X. Blasé, J.-C. Charlier, A. de Vita and R. Car, “Structural and Electronic Properties of Composite BxCyNz Nanotubes and Heterojunctions,” Applied Physics A, Vol. 68, No. 3, 1999, pp. 293-300.

[6] V. V. Pokropivny, V. V. Skorokhod, G. S. Oleinik, A. V. Kurdyumov, T .S. Bartnitskaya, A. V. Pokropivny, A. G. Sisonyuk and D. M. Sheichenko, “Boron Nitride Analogs of Fullerenes (the Fulborenes), Nanotubes, and Fullerites (the Fulborenites),” Journal of Solid State Chemistry, Vol. 154, No. 1, 2000, pp. 214-222.

[7] S. M. Nakhmanson, A. Cazolari, V. Meunier, J. Bernholc and M. Boungiorno Nardeli, “Spontaneous Polarization and Piezoelectricity in Boron Nitride Nanotubes,” Physical Review B, Vol. 67, No. 235406, 2003, 5 pp.

[8] N. Sai and E. J. Mele, “Microscopic Theory for Nanotube Piezoelectricity,” Physical Review B, Vol. 68, No. 241405(R), 2003, 3 pp.

[9] W.-Q. Han, C. W. Chang and A. Zettl, “Encapsulation of One-Dimensional Potassium Halide Crystals within BN Nanotubes,” Nano Letters, Vol. 4, No. 7, 2004, pp. 1455- 1357.

[10] K. Yum and M.-F. Yu, “Measurement of Wetting Properties of Individual Boron Nitride Nanotubes with the Wilhelmy Method Using a Nanotube-Based Force Sensor,” Nano Letters, Vol. 6, No. 2, 2006, pp. 329-333.

[11] Ch. Zhi, Y. Bando, Ch. Tang and D. Golberg, “Engineering of Electronic Structure of Boron-Nitride Nanotubes by Covalent Functionalization,” Physical Review B, Vol. 74, No. 153413, 2006, 4 pp.

[12] S. A. Shevlin and Z. X. Guo, “Hydrogen Sorption in Defective Hexagonal BN Sheets and BN Nanotubes,” Physical Review B, Vol. 76, No. 024104, 2007, 11 pp.

[13] E. Durgun, Y.-R. Jang and S. Ciraci, “Hydrogen Storage Capacity of Ti-doped Boron-Nitride and B/Be-Substituted Carbon Nanotubes,” Physical Review B, Vol. 76, No. 073413, 2007, 4 pp.

[14] Q. Wu, Zh. Hu, X. Wang, Y. Lu, X. Chen, H. Xu and Y. Chen, “Synthesis and Characterization of Faceted Hexagonal Aluminum Nitride Nanotubes,” Journal of the American Chemical Society, Vol. 125, No. 34, 2003, pp. 10176-10177.

[15] J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan and H.-J. Choi, P. Yang, “Single-Crystal Gallium Nitride Nanotubes,” Nature, Vol. 422, No. 6932, 2003, pp. 599-602.

[16] J. Q. Hu, Q. Li, X. M. Meng, C. S. Lee and S. T. Lee, “Thermal Reduction Route to the Fabrication of Coaxial Zn / ZnO Nanocables and ZnO Nanotubes,” Chemistry of Materials, Vol. 15, No. 1, 2003, pp. 305-308.

[17] Y. J. Xing, Z. H. Xi, Z. Q. Xue, X. D. Zhang, J. H. Song, R. M. Wang, J. Xu, Y. Song, S. L. Zhang and D. P. Yu, “Optical Properties of the ZnO Nanotubes Synthesized via Vapor Phase Growth,” Applied Physics Letters, Vol. 83, No. 9, 2003, pp. 1689-1691.

[18] X. H. Zhang, S. Y. Xie, Zh. Y. Jiang, X. Zhang, Zh.-Q. Tian, Zh.-X. Xie, R.-B. Huang and L. S. Zheng, “Rational Design and Fabrication of ZnO Nanotubes from Nanowire Templates in a Microwave Plasma System,” Journal of Physical Chemistry B, Vol. 107, No. 37, 2003, pp. 10114-10118.

[19] S. Erkoc and H. K?kten, “Structural and Electronic Properties of Single-Wall ZnO Nanotubes,” Physica E, Vol. 28, No. 2, 2005, pp. 162-170.

[20] H. Zhang, Sh. Zhang, Sh. Pan, G. Li and J. Hou, “A Simple Solution Route to ZnS Nanotubes and Hollow Nanospheres and Their Pptical Properties,” Nanotechnology, Vol. 15, No. 8, 2004, pp. 945-948.

[21] Y. Ch. Zhu, Y. Bando and Y. Uemura, “ZnS?Zn Nanocables and ZnS Nanotubes,” Chemical Communications, No. 7, 2003, pp. 836-837.

[22] M. S. Dresselhaus, G. Dresselhaus and R. Saito, “Carbon Fibers Based on C60 and Their Symmetry,” Physical Review B, Vol. 45, No. 11, 1992, pp. 6234-6242.

[23] R. A. Jishi, M. S. Dresselhaus and G. Dresselhaus, “Symmetry Properties of Chiral Carbon Nanotubes,” Physical Review B, Vol. 47, No. 24, 1993, pp. 16671- 16674.

[24] M. S. Dresselhaus, G. Dresselhaus and R. Saito, “Physics of Carbon Nanotubes,” Carbon, Vol. 33, No. 7, 1995, pp. 883-891.

[25] A. Rubio, J. L. Corkill and M. L. Cohen, “Theory of Graphitic Boron Nitride Nanotubes,” Physical Review B, Vol. 49, No. 7, 1994-I, pp. 5081-5084.

[26] B. J. Cox and J. M. Hill, “Exact and Approximate Geometric Parameters for Carbon Nanotubes Incorporating Curvature,” Carbon, Vol. 45, No. 7, 2007, pp. 1453- 1462.

[27] B. J. Cox and J. M. Hill, “Geometric structure of Ultra-Small Carbon Nanotubes,” Carbon, Vol. 46, No. 4, 2008, pp. 711-713.

[28] R. K. F. Lee, B. J. Cox and J. M. Hill, “The Geometric Structure of Single-Walled Nanotubes,” Nanoscale, Vol. 2, No. 6, 2010, pp. 859-872.

[29] L. S. Chkhartishvili, “On Sizes of Boron Nitride Nanotubes,” In: I. M. Neklyudov and V. M. Shulayev, Eds., Thin Films in Optics and Nanoelectronics, NSC “KhIPT”–PPP “Contrast”, Kharkiv, 2006, pp. 367-373.

[30] L. S. Chkhartishvili, “Equilibrium Geometry of Ultra-Small-Radius Boron Nitride Nanotubes,” Material Science of Nanostructures, No. 1, 2009, pp. 33-44.

[31] L. Chkhartishvili, “Boron Nitride Nanosystems of Regular Geometry,” Journal of Physics: Conference Series, Vol. 176, No. 012014, 2009, 17 pp.

[32] L. S. Chkhartishvili and T. M. Berberashvili, “Sequences of Layers in Binary Compounds Multi-Walled Nanotubes and Multi-Shelled Fullerenes,” Material Science of Nanostructures, No. 3, 2010, pp. 20-28.

[33] L. Chkhartishvili, “Quasi-Classical Theory of Substance Ground State,” Technical University Press, Tbilisi, 2004.

[34] L. S. Chkhartishvili, “Volume of the Intersection of Three Spheres,” Mathematical Notes, Vol. 69, No. 3, 2001, pp. 421-428.

[35] L. S. Chkhartishvili, “Iterative Solution of the Secular Equation,” Mathematical Notes, Vol. 77, No. 1, 2005, pp. 273-279.

[36] L. Chkhartishvili and I. Murusidze, “Molar Binding Energy of Zigzag and Armchair Single-Walled Boron Nitride Nanotubes,” Materials Sciences and Applications, Vol. 1, No. 4, 2010, pp. 223-246.

[37] H. Chen and E. Ruckenstein, “The Driving Force of Channel Formation in Triheteropolymers Confined in Nanocylindrical Tubes,” Journal of Chemical Physics, Vol. 130, No. 024901, 2009, 5 pp.

[38] H. Chen and E. Ruckenstein, “Nanostructures Self-Assembled in Polymer Solutions Confined in Cylindrical Nanopores,” Langmuir, Vol. 25, No. 20, 2009, pp. 12315-12319.

[39] H. Chen and E. Ruckenstein, “The Structure of Nanochannels Formed by Block Copolymer Solutions Confined in Nanotubes,” Journal of Chemical Physics, Vol. 131, No. 114904, 2009, 6 pp.

[40] H. Chen and E. Ruckenstein, “Relation between Molecular Orientation and Morphology of a Multiblock Copolymer Melt Confined in Cylindrical Nanopores,” Polymer, Vol. 51, No. 4, 2010, pp. 968-974.

[41] D. Y. Joh, L. H. Herman, S.-Y. Ju, J. Kinder, M. A. Segal, J. N. Johnson, G. K. L. Chan and J. Park, “On-Chip Rayleigh Imaging and Spectroscopy of Carbon Nanotubes,” Nano Letters, Vol. 11, No. 1, 2011, pp. 1-7.

[42] J. Kunstman, A. Quandt and I. Boustani, “An Approach to Control the Radius and the Chirality of Nanotubes,” Nanotechnology, Vol. 18, No. 155703, 2007, 3 pp.

[43] A. Zobelli, C.P. Ewels, A. Gloter, G. Seifert, O. Stephan, S. Csillag and C. Colliex, “Defective Structure of BN Nanotubes: From Single Vacancies to Dislocation Lines,” Nano Letters, Vol. 6, No. 9, 2006, pp. 1955-1960.