Ramp model

The ramp model is described by:

$\mathrm{\Phi }(r)=\{\begin{array}{cc}\mathrm{\infty }& r<\sigma \\ W_r-(W_r-W_a)\frac{r-\sigma }{d_a-\sigma }& \sigma \le r\le d_a\\ W_a-W_a\frac{r-d_a}{d_c-d_a}& d_a<r\le d_c\\ 0& r>d_c\end{array}$

where $\mathrm{\Phi }(r)$ is the intermolecular pair potential, $W_r>0$ and $W_a<0$.

Graphically, one has:

where the red line represents an attractive implementation of the model, and the green line a repulsive implementation.

References

1. P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters 24 pp. 1284 - 1287 (1970)
2. G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' 56, pp. 4274-4286 (1972)
3. E. A. Jagla "Core-softened potentials and the anomalous properties of water", Journal of Chemical Physics' 111, pp. 8980-8986 (1999)
4. E. Lomba, N. G. Almarza, C. Martin, C. McBride "Phase behaviour of attractive and repulsive ramp fluids: integral equation and computer simulation studies", Journal of Chemical Physics 126 244510 (2007)