Continuous shouldered well model

The continuous shouldered well model (CSW) is given by ( 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, 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_R} 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 $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$.

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 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)