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 | 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 | ||
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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 | 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> | and <math>\lambda_1,\lambda_2>1</math> | ||
==Critical points== | ==Liquid-liquid transition== | ||
For certain parameter sets the square shoulder + square well model has a [[Polyamorphic systems | liquid-liquid transition]] along with a corresponding liquid-liquid [[Critical points | critical point]] | |||
<ref>[http://dx.doi.org/10.1038/35055514 Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley "Generic mechanism for generating a liquid-liquid phase transition", Nature '''409''' pp. 692-695 (2001)]</ref> | |||
<ref>[http://dx.doi.org/10.1103/PhysRevE.66.051206 Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Metstable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly", Physical Review E '''66''' 051206 (2002)]</ref> | |||
<ref>[http://dx.doi.org/10.1103/PhysRevE.69.061206 Anna Skibinsky, Sergey V. Buldyrev, Giancarlo Franzese, Gianpietro Malescio, and H. Eugene Stanley, "Liquid-liquid phase transitions for soft-core attractive potentials", Physical Review E '''69''' 061206 (2004)]</ref> | |||
<ref>[http://dx.doi.org/10.1103/PhysRevE.71.061504 Gianpietro Malescio, Giancarlo Franzese, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range", Physical Review E '''71''' 061504 (2005)]</ref>. | |||
==See also== | |||
*[[Double square well model]] | |||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[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)] | |||
*[http://dx.doi.org/10.1063/1.2982162 Shiqi Zhou, A. Lajovic, and A. Jamnik "Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation", Journal of Chemical Physics '''129''' 124503 (2008)] | |||
[[Category: Models]] | [[Category: Models]] | ||
[[category: Polyamorphic systems]] | [[category: Polyamorphic systems]] | ||
Latest revision as of 15:51, 18 July 2012
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
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
Liquid-liquid transition[edit]
For certain parameter sets the square shoulder + square well model has a liquid-liquid transition along with a corresponding liquid-liquid critical point [1] [2] [3] [4].
See also[edit]
References[edit]
- ↑ Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley "Generic mechanism for generating a liquid-liquid phase transition", Nature 409 pp. 692-695 (2001)
- ↑ Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Metstable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly", Physical Review E 66 051206 (2002)
- ↑ Anna Skibinsky, Sergey V. Buldyrev, Giancarlo Franzese, Gianpietro Malescio, and H. Eugene Stanley, "Liquid-liquid phase transitions for soft-core attractive potentials", Physical Review E 69 061206 (2004)
- ↑ Gianpietro Malescio, Giancarlo Franzese, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range", Physical Review E 71 061504 (2005)
- Related reading
- 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)
- Shiqi Zhou, A. Lajovic, and A. Jamnik "Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation", Journal of Chemical Physics 129 124503 (2008)