Advertisement

Journal of Mathematical Chemistry

, Volume 38, Issue 2, pp 233–246 | Cite as

On the number of Kekulé structures in capped zigzag nanotubes

  • Jianguo Qian
  • Fuji Zhang
Article

Abstract

Two theoretical formulae for the number of Kekulé structures in general capped zigzag nanotubes are established: one of which is by using the techniques of the transfer matrices, the other involves the eigenvalues of the transfer matrix which reveals the asymptotic behaviour of this index. In effective, according to the symmetric aspect of the tubule, the order of the transfer matrix could be notably decreased. As an application, the closed expressions for four types are given out and the relevant numerical results for those of length up to 50 are listed.

Keywords

Kekulé structure capped zigzag nanotube 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cyvin, S.J., Gutman, I. 1988Kekulé Structures in Benzenoid Hydrocarbons, Lecture Notes in Chemistry, 46Springer-VerlagBerlinGoogle Scholar
  2. 2.
    Pauling, L. 1932The Natural of Chemical BondCornell University pressIthacaGoogle Scholar
  3. 3.
    Kasteleyn, P.W. 1961Physica2712092255Google Scholar
  4. 4.
    Iijima, S. 1991Nature3455658Google Scholar
  5. 5.
    Iijima, S., Ichihashi, T. 1993Nature (London)363603Google Scholar
  6. 6.
    Bethune, D.S., Kiang, C.H., Vries, M.S., Gorman, G., Savoy, R., Vazquez, J., Reyers, R. 1993Nature (London)363605Google Scholar
  7. 7.
    Sachs, H., Hansen, P., Zheng, M. 1996Communications in Math. and Comput. Chem.33169241Google Scholar
  8. 8.
    Lin, C.D. 2004Chem., Inf. Comput. Sci.441320P. J.Google Scholar
  9. 9.
    J.G. Qian and F.J. Zhang, Kekulé count in capped armchair nanotubes, to appear on J. Molecular Struct.: THEOCHEMGoogle Scholar
  10. 10.
    Dresselhaus, M.S., Avouris, P.,  et al. 2001Introduction to carbon materials researchDresselhaus, M.S. eds. Carbon nanotubesSpringer-VerlagBerlin, Heidelberge, New YorkGoogle Scholar
  11. 11.
    Brinkmann, G., Fowler, P.W., Manolopoulos, D.E., Palser, A.H.R. 1999Chem. Phy. Lett.315335347Google Scholar
  12. 12.
    Klein, D.J., Zhu, H. 1996Disc. Appl. Math.67157173Google Scholar
  13. 13.
    Zhang, F.J., Zhou, M.K. 1988Disc. Appl. Math.20253260Google Scholar
  14. 14.
    Hall, M. 1986Combinatorial TheoryJohn Wiley and SonsNew YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematics and Science College of Xiamen UniversityFujianPR China

Personalised recommendations