Abstract
A discrete summation method has been developed to calculate the dispersion interaction potential between two C60 fullerene molecules and applied to the fullerene–argon and fullerene–helium systems. The pair-wise atom-atom potentials for carbon–carbon, carbon–argon and carbon–helium interactions were described by the Lennard-Jones (6-12) expression and considered to be additive. Increased accuracy of these calculations was achieved by accounting for the radius and positions of each carbon atom in fullerene by taking into consideration the irregularity of hexagons in the fullerene structure.
As we understand, a discrete summation method has not been employed for the calculation of the C60–C60 interaction. Additionally, the method provides a mechanism to calculate the interaction potential for different directions of approach and orientations of fullerene molecules. These differences reach up to 6% at the minimum energy position when comparing approaching hexagons compared to pentagons.
The description of the calculated interaction potential energy of molecular C60–C60 fullerene that we propose is a physically grounded equation, which has provided excellent fit with the dispersion interaction data. We show that this equation is less complex in structure, while providing a higher accuracy (1% or less inaccuracy) than, for instance Girifalco’s (1992) equation, which gives inaccuracy in the range 4–5% when employed on our data. The proposed equation was further modified to provide a successful analytical description of the argon-fullerene interaction energy and an estimate of the resultant Henry constant and isosteric heat of adsorption.
Finally these equations were used to calculate the variation of these Henry constants with temperature for the helium–fullerene system indicating that at room temperature the excess adsorption is negative and that the resulting error when used as a volumetric calibrant, although not unduly significant, is not negligible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bosi, S., Da Ros, T., Spalluto, G., Prato, M.: Fullerene derivatives: an attractive tool for biological applications. Eur. J. Med. Chem. 38, 913–923 (2003)
Constrabaris, G., Halsey, G.D. Jr.: Interaction of single argon atoms with graphitized carbon black P-33 (2700). J. Chem. Phys. 27, 1433–1434 (1957)
Gharbi, N., Pressac, M., Hadchouel, M., Szwarc, H., Wilson, S.R., Moussa, F.: [60] fullerene is a powerful antioxidant in vivo with no acute or subacute toxicity. Nano Lett. 5, 2578–2585 (2005)
Giakos, G.C., Meehan, K., Tuma, M.: Exploitation of enhanced fluorescence via cross-coupling principles toward the design of an optical integrated thin-film sensor for nanotechnology and biomedical applications. IEEE Trans. Instrum. Meas. 51, 970–975 (2002)
Girard, C., Lambin, P., Dereux, A., Lucas, A.A.: van der Waals attraction between two C60 fullerene molecules and physical adsorption of C60 on graphite and other substrates. Phys. Rev. B 49, 11425–11432 (1994)
Girifalco, L.A.: Molecular properties of C60 in the gas and solid phases. J. Phys. Chem. 96, 858–861 (1992)
Gray, C.G., Gubbins, K.E.: Theory of Molecular Fluids. Fundamentals, vol. 1. Clarendon, Oxford (1984), p. 112
Hebard, A.F., Rosseinsky, M.J., Haddon, R.C., Murphy, D.W., Glarum, S.H., Palstra, T.T.M., Ramirez, A.P., Kortan, A.R.: Superconductivity at 18 K in potassium-doped C60. Nature (London) 350, 600–601 (1991)
Kihara, T.: Virial coefficients and models of molecules in gases. Rev. Mod. Phys. 25, 831–843 (1953)
Mainwaring, D., Jakubov, T., Calvitto, L.: Potential energy distributions within and on single-walled and double-walled nanotubes. J. Nanopart. Res. 7, 59–73 (2005)
Moore, J.H., Spencer, N.D. (eds.): Encyclopedia of Chemical Physics and Physical Chemistry. Fundamentals, vol. 1. Institute of Physics, Bristol (2001)
Pacheco, J.M., Prates Ramalho, J.P.: First-principles determination of the dispersion interaction between fullerenes and their intermolecular potential. Phys. Rev. Lett. 79, 3873–3876 (1997)
Pichet, W.E.: Cagey carbon conundrums. Nature (London) 351, 602–603 (1991)
Saunders, M., Cross, R.J., Jimenez-Vasquez, H.A., Shimsi, R., Khong, A.: Noble gas atoms inside fullerenes. Science 271, 1693–1697 (1996)
Sprik, M., Cheng, A., Klein, M.L.: Modeling the orientational ordering transition in solid C60. J. Phys. Chem. 96, 2027–2029 (1992)
Wang, S., Yang, J.L., Li, Y.L., Lin, H.Z., Guo, Z.X., Xiao, S.X., Shi, Z.Q., Zhu, D.B., Woo, H.S., Carroll, D.L., Kee, I.S., Lee, J.H.: Composites of C60 based poly(phenylene vinylene) dyad and conjugated polymer for polymer light-emitting devices. Appl. Phys. Lett. 80, 3847–3849 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jakubov, T.S., Mainwaring, D.E. Direct calculations of the dispersion interaction between fullerenes and their equation for the potential energy. Adsorption 14, 727–732 (2008). https://doi.org/10.1007/s10450-008-9110-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10450-008-9110-4