Ramp model: Difference between revisions

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This solid phase presents re-entrant melting, i.e. this solid melts into the fluid phase as the pressure is increased.
This solid phase presents re-entrant melting, i.e. this solid melts into the fluid phase as the pressure is increased.


=== Lattice Gas Repulsive Ramp ===
=== Repulsive Ramp Lattice Gas Model ===
Recently, similar  behaviour has been found in a three-dimensional [[lattice gas|lattice gas]] ramp model  
Recently, similar  behaviour has been found in a three-dimensional Repulsive
Ramp [[lattice gas|Lattice Gas]] model  
<ref>
<ref>
[http://dx.doi.org/10.1080/00268970902729269  Johan Skule Hoye,  Enrique Lomba, and  Noe Garcia Almarza, "One- and three-dimensional lattice models with two repulsive ranges: simple systems with complex phase behaviour",  Molecular Physics ''iFirst'' (2009)]
[http://dx.doi.org/10.1080/00268970902729269  Johan Skule Hoye,  Enrique Lomba, and  Noe Garcia Almarza, "One- and three-dimensional lattice models with two repulsive ranges: simple systems with complex phase behaviour",  Molecular Physics ''iFirst'' (2009)]

Revision as of 16:30, 6 March 2009

The ramp model, proposed by Jagla [1] and sometimes known as the Jagla 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.

Critical points

For the particular case , the liquid-vapour critical point is located at [2]:

and the liquid-liquid critical point:

Repulsive Ramp Model

In the repulsive ramp case, where , neither liquid-vapor nor liquid-liquid stable equilibria occur [2]. However, for this model a low density crystalline phase has been found. This solid phase presents re-entrant melting, i.e. this solid melts into the fluid phase as the pressure is increased.

Repulsive Ramp Lattice Gas Model

Recently, similar behaviour has been found in a three-dimensional Repulsive Ramp Lattice Gas model [3]

The system is defined on a simple cubic lattice. The interaction is that of a Lattice hard sphere model with exclusion of nearest neighbors of occupied positions plus a repulsive interaction with next-to-nearest neighbors.

The potential energy of the system is then given by:

where  ; refers to all the pairs of sites that are second neighbors, and indicates the occupation of site (0 indicates empty site, 1 indicates occupied site).

See also

References

Related literature