Square shoulder model

The square shoulder model is given by

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, $\epsilon$ 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

References

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)
• 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)
• 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)