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 λ = √ 3a, 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 -F 0) and a solidlike phase coexisting at a triple-point. Moreover, the fluid-fluid coexistence line ends at a critical point. An anomaly in the total density (ρ T ) of particles is also found, which is hallmarked by minima in the isobaric curves of ρ 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 F 0 one and ending deep inside its metastable region, in a point where the spinodals of both fluid phases cross each other. arXiv:1907.01028v1 [cond-mat.soft] 1 Jul 2019

Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes

“…From semi-analytical grand-canonical solutions of these models on Husimi lattices built with cubes (see Fig. 1a), we demonstrate that no fluid-fluid demixing occurs in such mixtures, in contrast with the 0NN-2NN one [24]. In fact, the thermodynamic behavior of the 0NN-1NN model is qualitatively the same described above for its counterpart on the square lattice.…”

“…We remark that such behavior is somewhat different from that found on the square lattice, where the LMD seems to end at the tricritical point [48,49]. On the other hand, it is similar to the LMD found for the 0NN-2NN mixture on the Husimi lattice built with cubes, which also ends inside the region where the fluid is metastable [24], indicating that this can be a general feature of the LMDs of such mixtures in the cubic lattice. Regardless the location of their end points, in all these systems the LMDs divide the fluid phase in two regions: a regular one, for small z 0 , ρ 0 and x 0 , where ∂ρ T /∂z 0 < 0, as expected; and the anomalous region, for large z 0 , ρ 0 and x 0 , where ∂ρ T /∂z 0 > 0.…”

“…An activity z k is associated with each kNN particle. The mixture 0NN-2NN (z 1 = 0 case) was already investigated by us in [24], so here we will focus on the cases z 2 = 0 and z 0 = 0, corresponding respectively to the mixtures 0NN-1NN and 1NN-2NN.…”

“…Following our previous study of the 0NN-2NN mixture [24], instead of investigating the models on the simple cubic lattice, we will solve them on a Husimi lattice built with cubes (see Fig. 1a).…”

“…The bulk free energy (per site) of each phase of the models can be calculated following the ansatz proposed by Gujrati [57], and discussed in detail for Husimi lattices built with cubes in Ref. [24]. For the 0NN-1NN model it reads…”