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.

References in corpus (30)

• Coulomb and Liquid Dimer Models in Three Dimensions
• On the orientational ordering of long rods on a lattice
• Monte Carlo simulations of 2d hard core lattice gases
• The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
• Crystallization and phase-separation in non-additive binary hard-sphere mixtures
• Phase transitions in a system of hard rectangles on the square lattice
• Triangular Trimers on the Triangular Lattice: an Exact Solution
• Multiple Phase Transitions in Extended Hard Core Lattice Gas Models in Two Dimensions
• Phase behavior of hard-core lattice gases: A Fundamental Measure approach
• Liquid-Liquid Phase Transition in Supercooled Silicon
• Rosenfeld functional for non-additive hard spheres
• Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice
• The isotropic-nematic transition for hard rods on a three--dimensional (3D) cubic lattice
• Demixing behavior in two-dimensional mixtures of anisotropic hard bodies
• Cluster-variation approximation for a network-forming lattice-fluid model
• Colloids, polymers, and needles: Demixing phase behavior
• Critical Behavior of the Widom-Rowlinson Lattice Model
• Virial coefficients, thermodynamic properties, and fluid-fluid transition of nonadditive hard-sphere mixtures
• Demixing and orientational ordering in mixtures of rectangular particles
• Different phases of a system of hard rods on three dimensional cubic lattice
• High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas
• Solution of an associating lattice gas model with density anomaly on a Husimi lattice
• Discontinuous phase transition in a dimer lattice gas
• Ordering of hard rectangles in strong confinement
• Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice
• Phase diagram of a system of hard cubes on the cubic lattice
• Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles
• Structure and phase equilibria of the Widom-Rowlinson model
• Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly
• Three-phase point in a binary hard-core lattice model?

Cited by in corpus (7)

• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• The freezing phase transition in hard core lattice gases on triangular lattice with exclusion up to seventh next-nearest neighbor
• Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes
• Fluid-fluid demixing and density anomaly in a ternary mixture of hard spheres
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases
• Entropy of fully-packed rigid rods on generalized Husimi trees: a route to the square lattice limit