Three stable phases and thermodynamic anomaly in a binary mixture of hard particles

Abstract

While the realistically modeling of the thermodynamic behavior of fluids usually demands elaborated atomistic models, much have been learned from simplified ones. Here, we investigate a model where point-like particles (with activity $z_0$) are mixed with molecules that exclude their first and second neighbors (i.e., cubes of lateral size $\lambda =\sqrt{3}a$, with activity $z_2$), both placed on the sites of a simple cubic lattice with parameter $a$. Only hard-core interactions exist among the particles, so that the model is athermal. Despite its simplicity, the grand-canonical solution of this model on a Husimi lattice built with cubes revels a fluid-fluid demixing, yielding a phase diagram with two fluid phases (one of them dominated by small particles - $F0$) and a solid-like phase coexisting at a triple-point. Moreover, the fluid-fluid coexistence line ends at a critical point. An anomaly in the total density (${\rho }_T$) of particles is also found, which is hallmarked by minima in the isobaric curves of ${\rho }_T$ versus $z_0$ (or $z_2$). Interestingly, the line of minimum density cross the phase diagram starting inside the region where both fluid phases are stable, passing through the $F0$ one and ending deep inside its metastable region, in a point where the spinodals of both fluid phases cross each other.

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Cited by in corpus (3)

• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Fluid-fluid demixing and density anomaly in a ternary mixture of hard spheres
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases