Ramp model

The ramp model, proposed by Jagla, is described by:

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{cc}\mathrm{\infty }& r<\sigma \\ W_r-(W_r-W_a)\frac{r-\sigma }{d_a-\sigma }& \sigma \le r\le d_a\\ W_a-W_a\frac{r-d_a}{d_c-d_a}& d_a<r\le d_c\\ 0& r>d_c\end{array}$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$, $W_r>0$ 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.

Critical points

The liquid-vapour critical point is located at (Ref. 4)

$T_c^{*}=1.487\pm 0.003$

${\rho }_c{\sigma }^3=0.103\pm 0.001$

$p_c^{*}\simeq 0.042$

The liquid-liquid critical point is located at (Ref. 4)

$T_c^{*}\simeq 0.378\pm 0.003$

${\rho }_c{\sigma }^3\simeq 0.380\pm 0.002$

$p_c^{*}/T_c^{*}\simeq 0.49\pm 0.01$

See also

• Polyamorphism: Ramp model

References

1. E. A. Jagla "Core-softened potentials and the anomalous properties of water", Journal of Chemical Physics' 111, pp. 8980-8986 (1999)
2. 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)