Continuous shouldered well model: Difference between revisions
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The '''continuous shouldered well model''' is given by (<ref>[http://dx.doi.org/10.1016/j.molliq.2007.08.021 Giancarlo Franzese "Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly", Journal of Molecular Liquids '''136''' pp. 267-273 (2007)]</ref> Eq. 1): | The '''continuous shouldered well model''' ('''CSW''') is given by (<ref>[http://dx.doi.org/10.1016/j.molliq.2007.08.021 Giancarlo Franzese "Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly", Journal of Molecular Liquids '''136''' pp. 267-273 (2007)]</ref> Eq. 1): | ||
:<math>\Phi_{12}(r) = \frac{U_R}{1 + \exp [\Delta(r-R_R)/a]} -U_A \exp \left[ -\frac{(r-R_A)^2}{2\delta_A^2} \right] + \left(\frac{a}{r}\right)^{24}</math> | :<math>\Phi_{12}(r) = \frac{U_R}{1 + \exp [\Delta(r-R_R)/a]} -U_A \exp \left[ -\frac{(r-R_A)^2}{2\delta_A^2} \right] + \left(\frac{a}{r}\right)^{24}</math> | ||
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*[http://dx.doi.org/10.1063/1.2830706 Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics '''128''' 064901 (2008)] | *[http://dx.doi.org/10.1063/1.2830706 Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics '''128''' 064901 (2008)] | ||
*[http://dx.doi.org/10.1063/1.3463424 Pol Vilaseca and Giancarlo Franzese "Softness dependence of the anomalies for the continuous shouldered well potential", Journal of Chemical Physics '''133''' 084507 (2010)] | *[http://dx.doi.org/10.1063/1.3463424 Pol Vilaseca and Giancarlo Franzese "Softness dependence of the anomalies for the continuous shouldered well potential", Journal of Chemical Physics '''133''' 084507 (2010)] | ||
*[http://dx.doi.org/10.1063/1.4809744 Matej Huš , Matja Zalar and Tomaz Urbic "Correctness of certain integral equation theories for core-softened fluids", Journal of Chemical Physics '''138''' 224508 (2013)] | |||
[[Category: Models]] | [[Category: Models]] | ||
Revision as of 17:03, 5 November 2013
The continuous shouldered well model (CSW) is given by ([1] Eq. 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}(r) = \frac{U_R}{1 + \exp [\Delta(r-R_R)/a]} -U_A \exp \left[ -\frac{(r-R_A)^2}{2\delta_A^2} \right] + \left(\frac{a}{r}\right)^{24}}
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}} is the intermolecular pair potential, is the energy of the repulsive 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 U_A} is the energy of the attractive well, 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 a} is the diameter of the particles, 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 r := |\mathbf{r}_1 - \mathbf{r}_2|} .
References
Related reading
- Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics 128 064901 (2008)
- Pol Vilaseca and Giancarlo Franzese "Softness dependence of the anomalies for the continuous shouldered well potential", Journal of Chemical Physics 133 084507 (2010)
- Matej Huš , Matja Zalar and Tomaz Urbic "Correctness of certain integral equation theories for core-softened fluids", Journal of Chemical Physics 138 224508 (2013)