Ramp model: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
mNo edit summary
Line 1: Line 1:
The '''Ramp''' model is described by:
The '''ramp model''' is described by:


:<math>
:<math>
u(r) = \left\{  
\Phi(r) = \left\{  
\begin{array}{ll}
\begin{array}{ll}
\infty & {\rm if} \; r < \sigma \\
\infty & {\rm if} \; r < \sigma \\
Line 11: Line 11:
</math>
</math>


where <math>W_r > 0</math> and <math>W_a < 0</math>.
where <math>\Phi(r)</math> is the [[intermolecular pair potential]], <math>W_r > 0</math> and <math>W_a < 0</math>.


Graphically, one has:
Graphically, one has:

Revision as of 13:57, 21 June 2007

The ramp model is described by:

where is the intermolecular pair potential, and .

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" arxiv.org/abs/cond-mat/0703509