Double square well model: Difference between revisions
Carl McBride (talk | contribs) m (Added a comment.) |
Carl McBride (talk | contribs) m (Added an expression for the potential.) |
||
| Line 1: | Line 1: | ||
{{stub-general}} | {{stub-general}} | ||
The '''double square well model''' can be seen as a variant (or ''vice versa'') of the [[square shoulder + square well model]]. | The '''double square well model''' can be seen as a variant (or ''vice versa'') of the [[square shoulder + square well model]]. In other words | ||
:<math> | |||
\Phi_{12}\left( r \right) = | |||
\left\{ \begin{array}{ccc} | |||
\infty & ; & r < \sigma \\ | |||
- \epsilon_1 & ; &\sigma \le r < \lambda_1 \sigma \\ | |||
- \epsilon_2 & ; &\lambda_1\sigma \le r < \lambda_2 \sigma \\ | |||
0 & ; & r \ge \lambda_2 \sigma \end{array} \right. | |||
</math> | |||
where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon_1</math> and <math>\epsilon_2</math> are the well ''depths'' (<math>\epsilon_1,\epsilon_2>0</math>), <math>r</math> is the distance between site 1 and site 2 where <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, σ is the hard core diameter | |||
and <math>\lambda_1,\lambda_2>1</math> | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1103/PhysRevLett.81.4895 M. Reza Sadr-Lahijany, Antonio Scala, Sergey V. Buldyrev, and H. Eugene Stanley "Liquid-State Anomalies and the Stell-Hemmer Core-Softened Potential", Physical Review Letters '''81''' pp. 4895-4898 (1998)] | |||
#[http://dx.doi.org/10.1063/1.3043571 J. R. Solana "Thermodynamic properties of double square-well fluids: Computer simulations and theory", Journal of Chemical Physics '''129''' 244502 (2008)] | #[http://dx.doi.org/10.1063/1.3043571 J. R. Solana "Thermodynamic properties of double square-well fluids: Computer simulations and theory", Journal of Chemical Physics '''129''' 244502 (2008)] | ||
[[category: models]] | [[category: models]] | ||
Revision as of 15:38, 2 January 2009
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
The double square well model can be seen as a variant (or vice versa) of the square shoulder + square well model. In other words
- 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}\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r < \sigma \\ - \epsilon_1 & ; &\sigma \le r < \lambda_1 \sigma \\ - \epsilon_2 & ; &\lambda_1\sigma \le r < \lambda_2 \sigma \\ 0 & ; & r \ge \lambda_2 \sigma \end{array} \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 \Phi_{12}(r)} is the intermolecular pair potential, 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_1} and 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_2} are the well depths (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_1,\epsilon_2>0} ), 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} is the distance between site 1 and site 2 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|} , σ is the hard core diameter and 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 \lambda_1,\lambda_2>1}
References
- M. Reza Sadr-Lahijany, Antonio Scala, Sergey V. Buldyrev, and H. Eugene Stanley "Liquid-State Anomalies and the Stell-Hemmer Core-Softened Potential", Physical Review Letters 81 pp. 4895-4898 (1998)
- J. R. Solana "Thermodynamic properties of double square-well fluids: Computer simulations and theory", Journal of Chemical Physics 129 244502 (2008)