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):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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]}

where

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle s={\frac {r}{2a}}}

\alpha ={\frac {N^{2}A}{12(2a)^{6}}}

\beta ={\frac {N^{2}B}{90(2a)^{12}}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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]):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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} }

where

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z := r/r_m}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_m} = 1.0281 nm
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a } = 0.09574 is the hard-core diameter in units of $r_{m}$
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon } = 3297.28 K is the well depth
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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