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| Line 4: |
Line 4: |
| \Phi(r) = \left\{ | | \Phi(r) = \left\{ |
| \begin{array}{ll} | | \begin{array}{ll} |
| \infty & {\rm if} \; r < \sigma \\ | | \infty |
| 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.
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| </math>
| |
| | |
| where <math>\Phi(r)</math> is the [[intermolecular pair potential]], <math>W_r > 0</math> and <math>W_a < 0</math>.
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| | |
| Graphically, one has:
| |
| [[Image:Ramp_potential.png|center]]
| |
| where the red line represents an attractive implementation of the model, and the green line a repulsive implementation.
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| | |
| | |
| | |
| ==References==
| |
| #[http://dx.doi.org/10.1103/PhysRevLett.24.1284 P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters '''24''' pp. 1284 - 1287 (1970)]
| |
| #[http://dx.doi.org/10.1063/1.1677857 G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' '''56''', pp. 4274-4286 (1972)]
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| #[http://dx.doi.org/10.1063/1.480241 E. A. Jagla "Core-softened potentials and the anomalous properties of water", Journal of Chemical Physics' '''111''', pp. 8980-8986 (1999)]
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| #[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)]
| |
| [[Category:models]]
| |
| [[category:Polyamorphic systems]]
| |
Revision as of 07:54, 5 July 2007
The ramp model is described by:
- <math>
\Phi(r) = \left\{
\begin{array}{ll}
\infty