Square shoulder model: Difference between revisions
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'''Related reading''' | '''Related reading''' | ||
*[http://dx.doi.org/10.1088/0953-8984/9/1/001 A R Denton and H Löwen "Isostructural solid - solid transitions in square-shoulder systems", Journal of Physics: Condensed Matter '''9''' pp. L1-L5 (1997)] | *[http://dx.doi.org/10.1088/0953-8984/9/1/001 A. R. Denton and H Löwen "Isostructural solid - solid transitions in square-shoulder systems", Journal of Physics: Condensed Matter '''9''' pp. L1-L5 (1997)] | ||
*[http://dx.doi.org/10.1088/0953-8984/9/2/006 Peter Bolhuis and Daan Frenkel "Isostructural solid - solid transitions in systems with a repulsive `shoulder' potential", Journal of Physics: Condensed Matter '''9''' pp. 381-387 (1997)] | *[http://dx.doi.org/10.1088/0953-8984/9/2/006 Peter Bolhuis and Daan Frenkel "Isostructural solid - solid transitions in systems with a repulsive `shoulder' potential", Journal of Physics: Condensed Matter '''9''' pp. 381-387 (1997)] | ||
*[http://dx.doi.org/10.1063/1.3006065 Gernot J. Pauschenwein and Gerhard Kahl "Zero temperature phase diagram of the square-shoulder system", Journal of Chemical Physics '''129''' 174107 (2008)] | *[http://dx.doi.org/10.1063/1.3006065 Gernot J. Pauschenwein and Gerhard Kahl "Zero temperature phase diagram of the square-shoulder system", Journal of Chemical Physics '''129''' 174107 (2008)] | ||
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*[http://dx.doi.org/10.1080/00268976.2011.562472 S. B. Yuste, A. Santos and M. López de Haro "Structure of the square-shoulder fluid", Molecular Physics '''109''' pp. 987-995 (2011)] | *[http://dx.doi.org/10.1080/00268976.2011.562472 S. B. Yuste, A. Santos and M. López de Haro "Structure of the square-shoulder fluid", Molecular Physics '''109''' pp. 987-995 (2011)] | ||
*[http://dx.doi.org/10.1063/1.4801659 S. P. Hlushak, P. A. Hlushak, and A. Trokhymchuk "An improved first-order mean spherical approximation theory for the square-shoulder fluid", Journal of Chemical Physics '''138''' 164107 (2013)] | *[http://dx.doi.org/10.1063/1.4801659 S. P. Hlushak, P. A. Hlushak, and A. Trokhymchuk "An improved first-order mean spherical approximation theory for the square-shoulder fluid", Journal of Chemical Physics '''138''' 164107 (2013)] | ||
*[http://dx.doi.org/10.1080/00268976.2016.1154199 M. López de Haro, S. B. Yuste and A. Santos "Theoretical approaches to the structural properties of the square-shoulder fluid", Molecular Physics '''114''' pp. 2382-2390 (2016)] | |||
[[Category: Models]] | [[Category: Models]] | ||
Revision as of 14:55, 14 September 2016
The square shoulder model is given by [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}\left( r \right) = \left\{ \begin{array}{ccc} \infty & ; & r < \sigma \\ \epsilon & ; &\sigma \le r < \lambda \sigma \\ 0 & ; & r \ge \lambda \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} is the height of the shoulder, 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 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 diameter and λ > 1.
Direct correlation function
The direct correlation function [2]
Equation of State
[3].
Binary mixture
References
- ↑ J. M. Kincaid, G. Stell and E. Goldmark "Isostructural phase transitions due to core collapse. II. A three-dimensional model with a solid–solid critical point", Journal of Chemical Physics 65 pp. 2172-2179 (1976)
- ↑ I. Guillén-Escamilla, E. Schöll-Paschinger and R. Castañeda-Priego "A parametrisation of the direct correlation function for the square-shoulder fluid", Molecular Physics 108 pp. 141-150 (2010)
- ↑ 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)
- ↑ Gayatri Das, Nicoletta Gnan, Francesco Sciortino, and Emanuela Zaccarelli "Unveiling the complex glassy dynamics of square shoulder systems: Simulations and theory", Journal of Chemical Physics 138 134501 (2013)
Related reading
- A. R. Denton and H Löwen "Isostructural solid - solid transitions in square-shoulder systems", Journal of Physics: Condensed Matter 9 pp. L1-L5 (1997)
- Peter Bolhuis and Daan Frenkel "Isostructural solid - solid transitions in systems with a repulsive `shoulder' potential", Journal of Physics: Condensed Matter 9 pp. 381-387 (1997)
- Gernot J. Pauschenwein and Gerhard Kahl "Zero temperature phase diagram of the square-shoulder system", Journal of Chemical Physics 129 174107 (2008)
- Shiqi Zhou and J. R. Solana "Inquiry into thermodynamic behavior of hard sphere plus repulsive barrier of finite height", Journal of Chemical Physics 131 204503 (2009)
- S. B. Yuste, A. Santos and M. López de Haro "Structure of the square-shoulder fluid", Molecular Physics 109 pp. 987-995 (2011)
- S. P. Hlushak, P. A. Hlushak, and A. Trokhymchuk "An improved first-order mean spherical approximation theory for the square-shoulder fluid", Journal of Chemical Physics 138 164107 (2013)
- M. López de Haro, S. B. Yuste and A. Santos "Theoretical approaches to the structural properties of the square-shoulder fluid", Molecular Physics 114 pp. 2382-2390 (2016)