Square shoulder + square well model
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 \(\Phi_{12}(r)\) is the intermolecular pair potential, \(\epsilon_1\) and \(\epsilon_2\) 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 \(\lambda_1,\lambda_2>1\)
[edit] Liquid-liquid transition
For certain parameter sets the square shoulder + square well model has a liquid-liquid transition along with a corresponding liquid-liquid critical point
[edit] References
- ↑ Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley "Generic mechanism for generating a liquid-liquid phase transition", Nature 409 pp. 692-695 (2001)
- ↑ Giancarlo Franzese, Gianpietro Malescio, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Metstable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly", Physical Review E 66 051206 (2002)
- ↑ Anna Skibinsky, Sergey V. Buldyrev, Giancarlo Franzese, Gianpietro Malescio, and H. Eugene Stanley, "Liquid-liquid phase transitions for soft-core attractive potentials", Physical Review E 69 061206 (2004)
- ↑ Gianpietro Malescio, Giancarlo Franzese, Anna Skibinsky, Sergey V. Buldyrev, and H. Eugene Stanley, "Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range", Physical Review E 71 061504 (2005)
- Related reading
- 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)
- 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)
- 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)
