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 \left( 1-\frac{r}{\sigma} \right) \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

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]):

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}(r) = \frac{\epsilon}{1-6/\alpha} \left[ \left( \frac{6}{\alpha} \right) \exp \left[ \alpha \left( 1-\frac{r}{r_{min}} \right) \right] - \left( \frac{r_{min}}{r}\right)^6 \right] }

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 r := |\mathbf{r}_1 - \mathbf{r}_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}(r) } is the intermolecular pair potential between two particles or sites
  • 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_{min} } is the value of 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} at which 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}(r)} is a minimum.
  • 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 } is the well depth (energy)
  • 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 \alpha} 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]

  1. ↑ Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics 22 pp. 169-186 (1954)
  2. ↑ Sergey A. Khrapak, Manis Chaudhuri, and Gregor E. Morfill "Freezing of Lennard-Jones-type fluids", Journal of Chemical Physics 134 054120 (2011)
  3. ↑ 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)

Related reading

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