Square shoulder model

The square shoulder model is given by

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{ccc}\infty &;&r<\sigma \\\epsilon &;&\sigma \leq r<\lambda \sigma \\0&;&r\geq \lambda \sigma \end{array}}\right.$

where $\Phi _{12}(r)$ 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

Equation of State

Main article: Equations of state for the square shoulder model

References

Related reading

• J. M. Kincaid, G. Stell and E. Goldmark "Isostructural phase transitions due to core collapse. II. A three-dimensional model with a solid–solid critical point", Journal of Chemical Physics 65 pp. 2172-2179 (1976)
• 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)
• Gernot J. Pauschenwein and Gerhard Kahl "Zero temperature phase diagram of the square-shoulder system", Journal of Chemical Physics 129 174107 (2008)