Exp-6 potential: Difference between revisions

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The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):
{{lowercase title}}
The '''exp-6 potential''' (or '''Exp-Six''' potential) is a modified form of the [[Buckingham potential]] and is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):


:<math> \Phi_{12}(r) =  \frac{\epsilon}{1-6/\alpha} \left[  \left( \frac{6}{\alpha} \right)  
:<math> \Phi_{12}(r) =  \frac{\epsilon}{1-6/\alpha} \left[  \left( \frac{6}{\alpha} \right)  
\exp \left[ \alpha \frac{1-r}{\sigma} \right]  - \left( \frac{\sigma}{r}\right)^6 \right] </math>
\exp \left[ \alpha \left( 1-\frac{r}{r_{min}} \right) \right]  - \left( \frac{r_{min}}{r}\right)^6 \right] </math>


where
where
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
* <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>
* <math> r_{min} </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)</math> is a minimum.
* <math> \epsilon </math> is the well depth (energy)
* <math> \epsilon </math> is the well depth (energy)
* <math>\alpha</math> is the "steepness" of the repulsive energy  
* <math>\alpha</math> is the "steepness" of the repulsive energy
==Melting point==
An approximate method to locate the melting point is given in <ref>[http://dx.doi.org/10.1063/1.3552948  Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics '''134''' 054120 (2011)]</ref>. See also <ref>[http://dx.doi.org/10.1080/00268976.2011.616544 Sergey A. Khrapak and Franz Saija "Application of phenomenological freezing and melting indicators to the exp-6 and Gaussian core potentials", Molecular Physics '''109''' pp. 2417-2421 (2011)]</ref>.
 
==See also==
==See also==
*[[Buckingham potential]]
*[[Buckingham potential]]
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*[http://dx.doi.org/10.1063/1.1840523  Marvin Ross  and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]
*[http://dx.doi.org/10.1063/1.1840523  Marvin Ross  and Berni Alder "Shock Compression of Argon. II. Nonadditive Repulsive Potential", Journal of Chemical Physics '''46''' pp. 4203-4210 (1967)]
*[http://dx.doi.org/10.1063/1.440106  Marvin Ross  and F. H. Ree  "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
*[http://dx.doi.org/10.1063/1.440106  Marvin Ross  and F. H. Ree  "Repulsive forces of simple molecules and mixtures at high density and temperature", Journal of Chemical Physics '''73''' pp. 6146-6152 (1980)]
*[http://dx.doi.org/10.1023/A:1024798909685 Teik-Cheng Lim "Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions", Journal of Mathematical Chemistry '''33''' pp. 279-285 (2003)]
[[category: models]]
[[category: models]]

Latest revision as of 10:04, 14 May 2015

The exp-6 potential (or Exp-Six potential) is a modified form of the Buckingham potential and is given by (Eq. 1 in [1]):

where

  • is the intermolecular pair potential between two particles or sites
  • is the value of at which is a minimum.
  • is the well depth (energy)
  • is the "steepness" of the repulsive energy

Melting point[edit]

An approximate method to locate the melting point is given in [2]. See also [3].

See also[edit]

References[edit]

Related reading