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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: 27 of May of 2026]. Available at: https://hdl.handle.net/2445/18838

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