Malescio, GianpietroFranzese, GiancarloSkibinsky, AnnaBuldyrev, V. S. (Vladimir Sergeevich)Stanley, H. Eugene (Harry Eugene), 1941-2011-07-072011-07-0720051063-651Xhttps://hdl.handle.net/2445/18838We 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.8 p.application/pdfeng(c) American Physical Society, 2005Cristal·lografiaEquacions d'estatCrystallographyEquations of stateinfo:eu-repo/semantics/article527068info:eu-repo/semantics/openAccess