Abstract
Two simple least squares approaches for connecting two carbon nanos-tructures are determined here. We speculate that the basis of joining carbon nanos-tructures is an underlying requirement that each inter-atomic distance be as close as possible to the ideal carbon-carbon bond length, or that the bond angle be as close as possible to the ideal bond angle. Both least squares approaches to bond lengths and to bond angles are applied for three systems, including nanotori formed from two and three distinct carbon nanotube sections, the joining between a carbon nanotube and a flat graphene sheet and nanobuds, which comprise a carbon nanotube joined to a fullerene. Moreover, Euler's theorem is utilised to verify that the correct polygons occur at the connection sites. We comment that these purely geometrical approaches can be formally related to certain numerical energy minimisation methods used by a number of authors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baowan, D., Cox, B.J., Hill, J.M.: Two least squares analyses of bond lengths and bond angles for the joining of carbon nanotubes to graphemes. Carbon 45, 2972–2980 (2007).
Baowan, D., Cox, B.J., Hill, J.M.: Toroidal molecules formed from three distinct carbon nan-otubes. J. Math. Chem. 44, 515–527 (2008).
Baowan, D., Cox, B.J., Hill, J.M.: Junctions between a boron nitride nanotube and a boron nitride sheet. Nanotech. 19, 075704 (2008).
Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M. Jr., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995).
Cox, B.J., Hill, J.M.: New carbon molecules in the form of elbow-connected nanotori. J. Phys. Chem. 111, 10855–10860 (2007).
Cox, B.J., Hill, J.M.: Exact and approximate geometric parameters for carbon nanotubes incorporating curvature. Carbon 45, 1453–1462 (2007).
Dunlap, B.I.: Connecting carbon tubules. Phys. Rev. B 46, 1933–1936 (1992).
Dunlap, B.I.: Relating carbon tubules. Phys. Rev. B 49, 5643–5650 (1994).
Dunlap, B.I.: Constraints on small graphitic helices. Phys. Rev. B 50, 8134–8137 (1994).
Ihara, S., Itoh, S.: Helically coiled and toroidal cage forms of graphitic carbon. Carbon 33, 931–939 (1995).
Ihara, S., Itoh, S., Kitakami, J.: Toroidal forms of graphitic carbon. Phys. Rev. B 47, 12908– 12911 (1993).
Itoh, S., Ihara, S.: Toroidal forms of graphitic carbon. II. Elongated tori. Phys. Rev. B 48, 8323–8328 (1993).
Itoh, S., Ihara, S., Kitakami, J.: Toroidal form of carbon C60. Phys. Rev. B 47, 1703–1704 (1993).
Jin, Y., Yuan, F.G.: Simulation of elastic properties of single-walled carbon nanotubes. Comp. Sci. Technol. 63, 1507–1515 (2003).
Li, C., Chou, T.W.: A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003).
Nasibulin, A.G., Anisimov, A.S., Pikhitsa, P.V., Jiang, H., Brown, D.P., Choi, M., Kauppinen, E.I.: Investigations of nanobud formation. Chem. Phys. Lett. 446, 109–114 (2007).
Nasibulin, A.G., Pikhitas, P.V., Jiang, H., Brown, D.P., Krasheninnikov, A.V., Anisimov, A.S., Queipo, P., Moisala, A., Gonzalez, D., Lientschnig, G., Hassanien, A., Shandakov, S.D., Lolli, G., Resasco, D.E., Choi, M., Tomanek, D., Kauppinen, E.I.: A novel hybrid carbon material. Nature Nanotech. 2, 156–161 (2007).
Natsuki, T., Tantrakarn, K., Endo, M.: Efects of carbon nanotube structures on mechanical properties. Appl. Phys. A 79, 117–124 (2004).
Zhang, X.F., Zhang, Z.: Polygonal spiral of coil-shaped carbon nanotubules. Phys. Rev. B 52, 5313–5317 (1995).
Zhao, Y., Lin, Y., Yakobson, B.I.: Fullerene shape transformations via Stone—Wales bond rotations. Phys. Rev. B 68, 233403 (2003).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, B.V.
About this paper
Cite this paper
Baowan, D., Cox, B.J., Thamwattana, N., Hill, J.M. (2009). Two Minimisation Approximations for Joining Carbon Nanostructures. In: Pyrz, R., Rauhe, J.C. (eds) IUTAM Symposium on Modelling Nanomaterials and Nanosystems. IUTAM Bookseries, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9557-3_12
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9557-3_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9556-6
Online ISBN: 978-1-4020-9557-3
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)