Square shoulder + square well model: Difference between revisions
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The '''Square shoulder + square well''' model consists, as its name suggests, of a combination of the [[square shoulder model]] and the [[square well model]]. The model is given by | |||
:<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>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> | |||
==Critical points== | |||
See Ref. 2. | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1088/0953-8984/11/50/308 Andreas Lang, Gerhard Kahl, Christos N Likos, Hartmut Löwen and Martin Watzlawek "Structure and thermodynamics of square-well and square-shoulder fluids", Journal of Physics: Condensed Matter '''11''' pp. 10143-10161 (1999)] | #[http://dx.doi.org/10.1088/0953-8984/11/50/308 Andreas Lang, Gerhard Kahl, Christos N Likos, Hartmut Löwen and Martin Watzlawek "Structure and thermodynamics of square-well and square-shoulder fluids", Journal of Physics: Condensed Matter '''11''' pp. 10143-10161 (1999)] | ||
#[http://dx.doi.org/10.1063/1.2970884 W. Rzysko, O. Pizio, A. Patrykiejew, and S. Sokolowski "Phase diagram of a square-shoulder, square-well fluid revisited", Journal of Chemical Physics '''129''' 124502 (2008)] | |||
[[Category: Models]] | [[Category: Models]] | ||
[[category: Polyamorphic systems]] | [[category: Polyamorphic systems]] | ||
Revision as of 10:29, 25 September 2008
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The Square shoulder + square well model consists, as its name suggests, of a combination of the square shoulder model and the square well model. The model is given by
- 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 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}
Critical points
See Ref. 2.
References
- Andreas Lang, Gerhard Kahl, Christos N Likos, Hartmut Löwen and Martin Watzlawek "Structure and thermodynamics of square-well and square-shoulder fluids", Journal of Physics: Condensed Matter 11 pp. 10143-10161 (1999)
- W. Rzysko, O. Pizio, A. Patrykiejew, and S. Sokolowski "Phase diagram of a square-shoulder, square-well fluid revisited", Journal of Chemical Physics 129 124502 (2008)