Abstract.
Carbon nanostructures are of considerable interest owing to their unique mechanical and electronic properties. Experimentally, a wide variety of different shapes are obtained, including both spherical and spheroidal carbon onions. A spheroid is an ellipsoid with two major axes equal and the term onion refers to a multi-layered composite structure. Assuming structures of either concentric spherical or ellipsoidal fullerenes comprising n layers, this paper examines the interaction energy between adjacent shells for both spherical and spheroidal carbon onions. The Lennard-Jones potential together with the continuum approximation is employed to determine the equilibrium spacing between two adjacent shells. We also determine analytical formulae for the potential energy which may be expressed either in terms of hypergeometric or Legendre functions. We find that the equilibrium spacing between shells decreases for shells further out from the inner core owing to the decreasing curvature of the outer shells of a concentric structure.
Similar content being viewed by others
References
M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic Press, California, 1995)
H. Terrones, M. Terrones, New J. Phys. 5, 126.1 (2003)
S. Weber, Crystallography Picture Book (http://www.jcrystal.com/steffenweber/pb/)
Q. Zheng, Q. Jiang, Phys. Rev. Lett. 88, 045503 (2002)
Q. Zheng, J.Z. Liu, Q. Jiang, Phys. Rev. B 65, 245409 (2002)
H.B. Peng, C.W. Chang, S. Aloni, T.D. Yuzvinsky, A. Zettl, Phys. Rev. Lett. 97, 087203 (2006)
Z. Slanina, P. Pulay, S. Nagase, J. Chem. Theory Comput. 2, 782 (2006)
O.E. Glukhova, A.I. Zhbanov, A.G. Rezkov, Phys. Solid State 47, 390 (2005)
J.P. Lu, W. Yang, Phys. Rev. B 49, 11421 (1994)
H. Guérin, J. Phys. B: At. Mol. Opt. Phys. 30, L481 (1997)
M. Yoshida, E. Osawa, Full. Sci. Technol. 1, 55 (1993)
H. Kitahara, T. Oku, K. Suganuma, Eur. Phys. J. D 16, 361 (2001)
I. Narita, T. Oku, K. Suganumn, K. Hiraga, E. Aoyagi, J. Mater. Chem. 11, 1761 (2001)
S. Iglesias-Groth, J. Breton, C. Girardet, Chem. Phys. Lett. 265, 351 (1997)
L.A. Girifalco, M. Hodak, R.S. Lee, Phys. Rev. B 62, 13104 (2000)
M. Rieth, Nano-Engineering in Science and Technology: An Introduction to the World of Nano-Design (World Scientific Publishing Co. Pte. Ltd., Singapore, 2003)
P.J.F. Harris, Carbon Nanotubes and Related Structures (Cambridge University Press, England, 1999)
H.W. Kroto, K. McKay, Nature 331, 328 (1988)
S. Itoh, P. Ordejón, D.A. Drabold, R.M. Martin, Phys. Rev. B 53, 2132 (1996)
B.I. Dunlap, R. Zope, Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes (http://arxiv.org/abs/cond-mat/0603225)
M. Terrones, G. Terrones, H. Terrones, Struct. Chem. 13, 373 (2002)
F. Banhart, P.M. Agayan, Nature 382, 433 (1996)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, San Diego, 2000)
F.D. Colavecchia, G. Gasaneo, J.E. Miraglia, Comput. Phys. Comm. 138, 29 (2001)
A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions (McGraw-Hill, New York, 1953)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baowan, D., Thamwattana, N. & Hill, J. Continuum modelling of spherical and spheroidal carbon onions. Eur. Phys. J. D 44, 117–123 (2007). https://doi.org/10.1140/epjd/e2007-00159-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2007-00159-8