On the Stability of Fullerenes

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Shiraz University

Abstract

Fullerenes have wide application in various fields including electronic and optic, medical science, biotechnology and have received a lot of recent chemists and mathematicians’ attention. Due to many applications of fullerenes, the study of their stability is important. In this paper, we study the effective parameters that affect the fullerene's stability and then according to these parameters, we introduce a new function to examine the stability of every fullerene. By using this function, we determine the stable isometric of each fullerene in a unique way.

Keywords

Main Subjects


1. H. Abeledo and G. W. Atkinson, Unimodularity of the Clar number
problem, Linear Algebra Appl. 420 (2007) 441–448.
2. M. B. Ahmadi, E. Farhadi and V. Amiri Khorasani, On computing the Clar
number of a fullerene using optimization techniques, MATCH Commun.
Math. Comput. Chem. 75 (2016) 695–701.
3. J. Aihara, Weighted HOMO-LUMO energy separation as an index of
kinetic stability for fullerenes, Theor. Chem. Acc. 102 (1999) 134 – 138.
4. S. J. Austin, P. W. Fowler, P. Hansen, D. E. Manolopoulos and M. Zheng,
Fullerene isomers of c60. Kekul´e counts versus stability, Chem. Phys. Lett.
228 (1994) 478–484.
5. A. T. Balaban, X. Liu, D. J. Klein, D. Babics, T. G. Schmalz, W. A. Seitz
and M. Randić, Graph invariants for fullerenes, J. Chem. Inf. Comput. Sci.
35 (1995) 396–404.
6. S. Bosi, T. DaRos, G. Spalluto and M. Prato, Fullerene derivatives: an
attractive tool for biological applications, European J. Med. Chem. 38
(2003) 913–923.
7. E. E. B. Campbell, P. W. Fowler, D. Mitchell and F. Zerbetto, Increasing
cost of pentagon adjacency for larger fullerenes, Chem. Phys. Lett. 250
(1996) 544–548.
8. E. Clar, The Aromatic Sextet, Wiley, London, 1972.
9. S. M. Daugherty, Independent Sets and Closed Shell Independent Sets of
Fullerenes, PhD thesis, Univ. Victoria, 2009.
10. T. Došlić, Finding more matchings in leapfrog fullerenes, J. Math. Chem.
45 (2009) 1130–1136.
11. T. Došlić, Leapfrog fullerenes have many perfect matchings, J. Math.
Chem. 44 (2008) 1–4.
12. S. Fajtlowicz and C. E. Larson, Graph theoretic independence as a
predictor of fullerene stability, Chem. Phys. Lett. 377 (2003) 485−490.
13. A. H. Faraji and P. Wipf, Nanoparticles in cellular drug delivery, Bioorg.
Med. Chem. 17 (2009) 2950–2962.
14. P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Dover Pub.,
Mineola, 2006.
15. B. Grünbaum and T. Motzkin, The number of hexagons and the simplicity
of geodesics on certain polyhedra, Canad. J. Math. 15 (1963) 744–751.
16. G. K. Gueorguiev and J. M. Pacheco, Structural and electronic properties of
􀜥􀬷􀬺, J. Chem. Phys. 114 (2001) 6068–6071.
17. I. Gutman and S. J. Cyvin, Introduction to the Theory of Benzenoid
Hydrocarbons, Springer, Berlin, 1989.
18. F. Kardoš, D. Král', J. Miškuf and J.-S. Sereni, Fullerene graphs have
exponentially many perfect matchings, J. Math. Chem. 46 (2) (2009) 443–
447.
19. S. Klavžar, K. Salem and A. Taranenko, Maximum cardinality resonant
sets and maximal alternating sets of hexagonal systems, Comput. Math.
Appl. 59 (2010) 506–513.
20. D. J. Klein and A. T. Balaban, Clarology for conjugated carbon nanostructures:
Molecules, polymers, graphene, defected graphene, fractal
benzenoids, fullerenes, nano-tubes, nano-cones, nano-tori, etc, Open Org.
Chem. J. 5 (2011) 27–61.
21. H. W. J. Kroto, R. Heath, S. C. O’Brien, R. F. Curland and R. E. Smalley,
􀜥􀬺􀬴 Buckminster fullerene, Nature 318 (1985) 162–163.
22. K. Kutnar and D. Marušič, On cyclic edge-connectivity of fullerenes,
Discrete Appl. Math. 156 (2008) 1661–1669.
23. X. Liu, D. J. Klein and T. G. Schmalz, Favorable Structures for Higher
Fullerene, Chem. Phys. Lett. 188 (1992) 550 –554.
24. X. Liu, D.J. Klein, T.G. Schmalz, W.A. Seitz, Generation of Carbon–Cage
Polyhedra, J. Comput. Chem. 12 (1991) 1252–1259.
25. W. Myrvold, B. Bultena, S. Daugherty, B. Debroni, S. Girn, M.
Minchenko, J. Woodcock and P. W. Fowler, Fui Gui: A graphical user
interface for investigating conjectures about fullerenes, Match Commun.
Math. Comput. Chem. 58 (2007) 403–422.
26. T. Réti, On the combinatorial characterization of fullerene graphs, Acta
Polytech. Hung. 6 (2009) 85–93.
27. M. Salami and M. B. Ahmadi, A mathematical programming model for
computing the Fries number of a fullerene, Appl. Math. Model. 39 (2015)
5473–5479.
28. W. Q. Tian, J. K. Feng, Y. A. Wang and Y. Aoki, Search for suitable
approximation methods for fullerene structure and relative stability studies:
Case study with 􀜥􀬹􀬴, J. Chem. Phys. 125 (2006) 2–10.
29. J. Venturini, E. Koudoumas, S. Couris, J. M. Janot, P. Seta, C. Mathis and
S. Leach, Optical limiting and nonlinear optical absorption properties of
c60-polystyrene star polymer films: 􀜥􀬺􀬴 concentration dependence, J.
Mater. Chem. 12 (2002) 2071–2076.
30. H. Zhang, D. Ye and W. Shiu, Forcing matching numbers of fullerene
graphs, Discrete Appl. Math. 158 (2010) 573–582.
31. H. Zhang, D. Ye and Y. Liu, A combination of Clar number and Kekulé
count as an indicator of relative stability of fullerene isomers of c60, J.
Math. Chem. 48 (2010) 733–740.