Continuous shouldered well model: Difference between revisions
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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): | |||
The '''continuous shouldered well model''' is given by ( | |||
:<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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where <math>\Phi_{12}</math> is the [[intermolecular pair potential]], <math>U_R</math> is the energy of the repulsive shoulder, <math>U_A</math> is the energy of the attractive well, <math>a</math> is the diameter of the particles, and <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>. | where <math>\Phi_{12}</math> is the [[intermolecular pair potential]], <math>U_R</math> is the energy of the repulsive shoulder, <math>U_A</math> is the energy of the attractive well, <math>a</math> is the diameter of the particles, and <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>. | ||
==References== | ==References== | ||
<references/> | |||
'''Related reading''' | |||
*[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 of Chemical 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/10.1063/1.4809744 Matej Huš , Matja Zalar and Tomaz Urbic "Correctness of certain integral equation theories for core-softened fluids", Journal of Chemical Physics '''138''' 224508 (2013)] | |||
*[http://dx.doi.org/10.1063/1.4909550 L. A. Cervantes, G. Jaime-Muñoz, A. L. Benavides, J. Torres-Arenas, and F. Sastre "Discrete perturbation theory for continuous soft-core potential fluids", Journal of Chemical Physics '''142''' 114501 (2015)] | |||
*[http://dx.doi.org/10.1016/j.molliq.2016.10.030 Miha Lukšič, Barbara Hribar-Lee, and Orest Pizio "Phase behaviour of a continuous shouldered well model fluid. A grand canonical Monte Carlo study", Journal of Molecular Liquids '''228''' pp. 4-10 (2017)] | |||
[[Category: Models]] | [[Category: Models]] | ||
Latest revision as of 13:48, 3 February 2017
The continuous shouldered well model (CSW) is given by ([1] Eq. 1):
![{\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc66fc37940b5e744613ca304f08b86ec9574a5)
where is the intermolecular pair potential, is the energy of the repulsive shoulder, is the energy of the attractive well, 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[edit]
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 of Chemical 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)
- L. A. Cervantes, G. Jaime-Muñoz, A. L. Benavides, J. Torres-Arenas, and F. Sastre "Discrete perturbation theory for continuous soft-core potential fluids", Journal of Chemical Physics 142 114501 (2015)
- Miha Lukšič, Barbara Hribar-Lee, and Orest Pizio "Phase behaviour of a continuous shouldered well model fluid. A grand canonical Monte Carlo study", Journal of Molecular Liquids 228 pp. 4-10 (2017)