Widom-Rowlinson model: Difference between revisions

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The Widom-Rowlinson model (Ref. 1) for mixtures takes the form:
[[Image:2D_Widom_Rowlinson.png|thumb|Simulation snapshot of  phase separation in two-dimensions.]]
The '''Widom-Rowlinson model''' <ref>[http://dx.doi.org/10.1063/1.1673203 B. Widom and J. S. Rowlinson, "New Model for the Study of Liquid–Vapor Phase Transitions", Journal of Chemical Physics  '''52''', pp. 1670-1684  (1970)]</ref>  for mixtures takes the form:


<math> V \left( r_{ij} \right) =  0 </math>;  if <math> i </math> and <math> j</math> are particles of the same species
:<math> \Phi \left( r_{ij} \right) =  0 </math>;  if <math> i </math> and <math> j</math> are particles of the same species


<math> V \left( r_{ij} \right) =  V_{HS}(r_{ij});  </math> if <math> i </math> and <math> j</math> belong to different species,
:<math> \Phi \left( r_{ij} \right) =  \Phi_{HS}(r_{ij});  </math> if <math> i </math> and <math> j</math> belong to different species,
 
with <math> V_{HS}(R) </math> is the [[hard sphere]] pair potential


where <math> \Phi_{HS}(r) </math> is the [[hard sphere model | hard sphere]] [[intermolecular pair potential]].
==Surface tension==
The [[surface tension]] of the Widom-Rowlinson model has also been studied
<ref>[http://dx.doi.org/10.1063/1.2751153 E. de Miguel, N. G. Almarza and G. Jackson "Surface tension of the Widom-Rowlinson model", Journal of Chemical Physics '''127''' 034707 (2007)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2806279 Yuri Djikaev "The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations", Journal of Chemical Physics '''128''' 014712 (2008)]</ref>
== References ==
== References ==
# B. Widom and J. S. Rowlinson, New Model for the Study of Liquid–Vapor Phase Transitions, J. Chem. Phys. 52, 1670 (1970)
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1080/00268977200101921 T. W. Melnyk,  J. S. Rowlinson and B. L. Sawford "The penetrable sphere and related models of liquid—vapour equilibrium" Molecular Physics '''24''' pp. 809-831 (1972)]
[[Category: Models]]

Latest revision as of 14:17, 1 October 2009

Simulation snapshot of phase separation in two-dimensions.

The Widom-Rowlinson model [1] for mixtures takes the form:

; if and are particles of the same species
if and belong to different species,

where is the hard sphere intermolecular pair potential.

Surface tension[edit]

The surface tension of the Widom-Rowlinson model has also been studied [2] [3]

References[edit]

Related reading