Square shoulder + square well model

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The Square shoulder + square well model consists, as its name suggests, of a combination of the square shoulder model and the square well model. The model is given by


\Phi_{12}\left( r \right) = 
\left\{ \begin{array}{ccc}
\infty & ; & r < \sigma \\
 \epsilon_1 & ; &\sigma \le r < \lambda_1 \sigma \\
- \epsilon_2 & ; &\lambda_1\sigma \le r < \lambda_2 \sigma \\
0         & ; & r \ge \lambda_2 \sigma \end{array} \right.

where Φ12(r) is the intermolecular pair potential, ε1 and ε2 are the well depths, r is the distance between site 1 and site 2 where r := |\mathbf{r}_1 - \mathbf{r}_2|, σ is the hard core diameter and λ12 > 1

[edit] Critical points

See Ref. 2.

[edit] Liquid-liquid transition

For certain parameter sets the square shoulder + square well model has a liquid-liquid transition.

[edit] References

  1. 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)
  2. W. Rzysko, O. Pizio, A. Patrykiejew, and S. Sokolowski "Phase diagram of a square-shoulder, square-well fluid revisited", Journal of Chemical Physics 129 124502 (2008)
  3. Shiqi Zhou, A. Lajovic, and A. Jamnik "Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation", Journal of Chemical Physics 129 124503 (2008)
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