C60: Difference between revisions

Latest revision as of 18:01, 3 January 2018

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):

\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

s={\frac {r}{2a}}

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

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

\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

$z:=r/r_{m}$
$r_{m}$ = 1.0281 nm
$a$ = 0.09574 is the hard-core diameter in units of $r_{m}$
$\epsilon$ = 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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@@ Line 17: / Line 17: @@
 where <math>N</math> 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 <ref>[http://dx.doi.org/10.1016/j.chemphys.2017.05.014 Jesús Eloy Ramos "Effective intermolecular potential and critical point for C60 molecule", Journal of Chemical Physics '''492''' pp. 5-11 (2017)]</ref>):
+The [[Approximate non-conformal potential]] ('''ANC''') for the C60 fullerene is given by (Eq 6 in <ref>[http://dx.doi.org/10.1016/j.chemphys.2017.05.014 Jesús Eloy Ramos "Effective intermolecular potential and critical point for C60 molecule", Chemical Physics '''492''' pp. 5-11 (2017)]</ref>):
 :<math>\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} </math>