C60

C₆₀, also known as Buckminsterfullerene is composed of carbon atoms.

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C₆₀

Models[edit]

Girifalco potential[edit]

The Girifalco intermolecular pair potential is given by ^[1] (Eq. 4):

Φ (r) = - α [\frac{1}{s (s - 1)^{3}} + \frac{1}{s (s + 1)^{3}} - \frac{2}{s^{4}}] + β [\frac{1}{s (s - 1)^{9}} + \frac{1}{s (s + 1)^{9}} - \frac{2}{s^{10}}]

where

s = \frac{r}{2 a}

α = \frac{N^{2} A}{12 (2 a)^{6}}

β = \frac{N^{2} B}{90 (2 a)^{12}}

where $N$ is the number of atoms on each sphere, i.e. N=60.

Approximate non-conformal potential[edit]

The Approximate non-conformal potential (ANC) for the C60 fullerene is given by (Eq 6 in ^[2]):

Φ_{12} (z) = ϵ {[\frac{1 - a}{(z^{3} / S + 1 - 1 / S)^{1 / 3} - a}]}^{12} - 2 ϵ {[\frac{1 - a}{(z^{3} / S + 1 - 1 / S)^{1 / 3} - a}]}^{6}

where

$z : = r / r_{m}$
$r_{m}$ = 1.0281 nm
$a$ = 0.09574 is the hard-core diameter in units of $r_{m}$
$ϵ$ = 3297.28 K is the well depth
$S$ = 0.4120 is a softness parameter

Phase diagram[edit]

^[3] ^[4] ^[5] ^[6]

Liquid phase[edit]

^[7]

Gel phase[edit]

Simulations of the Girifalco potential indicate a possible gel composed solely of C₆₀ molecules ^[8]

References[edit]

Related reading

[1] L. A. Girifalco "Molecular properties of fullerene in the gas and solid phases", Journal of Physical Chemistry 96 pp. 858-861 (1992)

[2] Jesús Eloy Ramos "Effective intermolecular potential and critical point for C60 molecule", Chemical Physics 492 pp. 5-11 (2017)

[3] 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)

[4] L. Mederos and G. Navascués "High-temperature phase diagram of the fullerene C60" Physical Review B 50 pp. 1301-1304 (1994)

[5] 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)

[6] Pedro Orea "Phase diagrams of model C60 and C70 fullerenes from short-range attractive potentials", Journal of Chemical Physics 130, 104703 (2009)

[7] 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)

[8] C. Patrick Royall, and Stephen R. Williams "C60: the first one-component gel?", arXiv:1102.2959v1 (cond-mat.soft) 15 Feb 2011)

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C60