Ramp model

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

$\Phi_{12}(r) = \left\{ \begin{array}{ll} \infty & {\rm if} \; r < \sigma \\ W_r - (W_r-W_a) \frac{r-\sigma}{d_a-\sigma} & {\rm if} \; \sigma \leq r \leq d_a \\ W_a - W_a \frac{r-d_a}{d_c-d_a} & {\rm if} \; d_a < r \leq d_c \\ 0 & {\rm if} \; r > d_c \end{array} \right.$

where $Φ 12 (r)$ 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.

[edit] 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)

$T_c^* \simeq 0.378 \pm 0.003$

$\rho_c \sigma^3 \simeq 0.380 \pm 0.002$

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

[edit] See also

Polyamorphism: Ramp model

[edit] References

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Categories: Models | Polyamorphic systems

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