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Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range
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We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy
U
R
(
U
A
)
and the repulsive (attractive) range
w
R
(
w
A
)
the relation
U
R
∕
U
A
∝
w
R
∕
w
A
holds for short soft-core ranges, while
U
R
∕
U
A
∝
3
w
R
∕
w
A
holds for large soft-core ranges.
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MALESCIO, Gianpietro, et al. Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range. Physical Review E. 2005. Vol. 71, num. 6, pags. 061504-1-061504-8. ISSN 1063-651X. [consulted: 4 of August of 2026]. Available at: https://hdl.handle.net/2445/18838