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 14:48, 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 .
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)