Double square well model: Difference between revisions
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The '''double square well model''' <ref>[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)]</ref> 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> | |||
==Two-dimensional system== | |||
<ref>[http://dx.doi.org/10.1063/1.4735093 Ahmad M. Almudallal, Sergey V. Buldyrev, and Ivan Saika-Voivod "Phase diagram of a two-dimensional system with anomalous liquid properties", Journal of Chemical Physics '''137''' 034507 (2012)]</ref> | |||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[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]] | ||
Latest revision as of 15:51, 18 July 2012
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The double square well model [1] 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
Two-dimensional system[edit]
References[edit]
- ↑ 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)
- ↑ Ahmad M. Almudallal, Sergey V. Buldyrev, and Ivan Saika-Voivod "Phase diagram of a two-dimensional system with anomalous liquid properties", Journal of Chemical Physics 137 034507 (2012)
- Related reading