Ramp model: Difference between revisions

Revision as of 15:48, 27 February 2009

The ramp model, proposed by Jagla ^[1] and sometimes known as the Jagla model, 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 $\Phi _{12}(r)$ 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.

For the particular case $W_{r}^{*}=3.5;W_{a}^{*}=-1.0,d_{a}^{*}=1.72,d_{c}^{*}=3.0$ , the liquid-vapour critical point is located at ^[2]:

T_{c}^{*}=1.487\pm 0.003

\rho _{c}\sigma ^{3}=0.103\pm 0.001

p_{c}^{*}\simeq 0.042

and the liquid-liquid critical point:

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

Related literature

@@ Line 20: / Line 20: @@
 ==Critical points==
 For the particular case <math> W_r^*=3.5; W_a^*=-1.0, d_a^*=1.72, d_c^*=3.0 </math>,
-the liquid-vapour critical point   is located at:
+the liquid-vapour critical point   is located at
 <ref>
 [http://dx.doi.org/10.1063/1.2748043  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)]
-</ref>
+</ref>:
 :<math>T_c^* = 1.487 \pm 0.003</math>
@@ Line 29: / Line 29: @@
 :<math>p_c^* \simeq 0.042</math>
-and the liquid-liquid critical point:
+and the [[Polyamorphic systems |liquid-liquid]] critical point:
 :<math>T_c^* \simeq 0.378 \pm 0.003</math>