Difference between revisions of "C60"

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where <math>N</math> is the number of atoms on each sphere, i.e. N=60.
 
where <math>N</math> is the number of atoms on each sphere, i.e. N=60.
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====Approximate non-conformal potential====
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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>):
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:<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>
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where
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* <math>z := r/r_m</math>
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* <math>r_m</math> = 1.0281 nm
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* <math> a </math> = 0.09574 is the hard-core diameter in units of <math>r_m</math>
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* <math> \epsilon </math> = 3297.28 K is the well depth
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* <math>S</math> = 0.4120 is a softness parameter
 +
 
==Phase diagram==
 
==Phase diagram==
 
<ref>[http://dx.doi.org/10.1103/PhysRevLett.71.1200      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)]</ref>
 
<ref>[http://dx.doi.org/10.1103/PhysRevLett.71.1200      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)]</ref>

Latest revision as of 19:01, 3 January 2018

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


<jmol>

 <jmolApplet>
 <script>set spin X 10; spin on</script>
 <size>200</size>
 <color>lightgrey</color>
   <wikiPageContents>C60.pdb</wikiPageContents>
</jmolApplet>
</jmol>
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^2A}{12(2a)^6}
\beta = \frac{N^2B}{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