C60
C60, also known as Buckminsterfullerene is composed of carbon atoms.
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Models
Girifalco potential
The Girifalco intermolecular pair potential is given by [1] (Eq. 4):
![{\displaystyle \Phi (r)=-\alpha \left[{\frac {1}{s(s-1)^{3}}}+{\frac {1}{s(s+1)^{3}}}-{\frac {2}{s^{4}}}\right]+\beta \left[{\frac {1}{s(s-1)^{9}}}+{\frac {1}{s(s+1)^{9}}}-{\frac {2}{s^{10}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/283401221466ce68eda644a68cb8248aa26fbe70)
where
where is the number of atoms on each sphere, i.e. N=60.
Approximate non-conformal potential
The Approximate non-conformal potential (ANC) for the C60 fullerene is given by (Eq 6 in [2]):
![{\displaystyle \Phi _{12}(z)=\epsilon \left[{\frac {1-a}{(z^{3}/S+1-1/S)^{1/3}-a}}\right]^{12}-2\epsilon \left[{\frac {1-a}{(z^{3}/S+1-1/S)^{1/3}-a}}\right]^{6}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/57f57c6529abccc518c1d12e840eed2a3fe670a9)
where
- = 1.0281 nm
- = 0.09574 is the hard-core diameter in units of
- = 3297.28 K is the well depth
- = 0.4120 is a softness parameter
Phase diagram
Liquid phase
Gel phase
Simulations of the Girifalco potential indicate a possible gel composed solely of C60 molecules [8]
References
- ↑ L. A. Girifalco "Molecular properties of fullerene in the gas and solid phases", Journal of Physical Chemistry 96 pp. 858-861 (1992)
- ↑ Jesús Eloy Ramos "Effective intermolecular potential and critical point for C60 molecule", Chemical Physics 492 pp. 5-11 (2017)
- ↑ Ailan Cheng, Michael L. Klein and Carlo Caccamo "Prediction of the phase diagram of rigid C60 molecules", Physical Review Letters 71 pp. 1200-1203 (1993)
- ↑ L. Mederos and G. Navascués "High-temperature phase diagram of the fullerene C60" Physical Review B 50 pp. 1301-1304 (1994)
- ↑ M. Hasegawa and K. Ohno "Monte Carlo simulation study of the high-temperature phase diagram of model C60 molecules", Journal of Chemical Physics 111 pp. 5955- (1999)
- ↑ Pedro Orea "Phase diagrams of model C60 and C70 fullerenes from short-range attractive potentials", Journal of Chemical Physics 130, 104703 (2009)
- ↑ M. H. J. Hagen, E. J. Meijer, G. C. A. M. Mooij, D. Frenkel and H. N. W. Lekkerkerker "Does C60 have a liquid phase?", Nature 365 pp. 425-426 (1993)
- ↑ C. Patrick Royall, and Stephen R. Williams "C60: the first one-component gel?", arXiv:1102.2959v1 (cond-mat.soft) 15 Feb 2011)
Related reading
- C. Caccamo "Modified-hypernetted-chain determination of the phase diagram of rigid C60 molecules", Physical Review B 51 pp. 3387-3390 (1995)
- M. Hasegawa and K. Ohno "Density functional theory for the phase diagram of rigid C60 molecules", Physical Review E 54 pp. 3928-3932 (1996)
- C. Caccamo, D. Costa, and A. Fucile "A Gibbs ensemble Monte Carlo study of phase coexistence in model C60", Journal of Chemical Physics 106 pp. 255- (1997)
- M. Bahaa Khedr, S. M. Osman and M.S. Al Busaidi "Surface tension, shear viscosity and isothermal compressibility of liquid C60 along the liquid-vapour coexistence", Molecular Physics 107 pp. 1355-1366 (2009)
- Minkyu Kim, Jaeeon Chang and Stanley I. Sandler "Monte Carlo simulations for the free energies of C60 and C70 fullerene crystals by acceptance ratio method and expanded ensemble method", Journal of Chemical Physics 140 084110 (2014)
- D. M. Edmunds, P. Tangney, D. D. Vvedensky and W. M. C. Foulkes "Free-energy coarse-grained potential for C60", Journal of Chemical Physics 143 164509 (2015)