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

## TL;DR

This study models a binary mixture of hard particles on a lattice, revealing three stable phases, a fluid-fluid critical point, and density anomalies, providing insights into simplified thermodynamic behaviors of complex fluids.

## Contribution

It introduces a simplified lattice model with hard-core interactions that exhibits phase separation, critical phenomena, and density anomalies, advancing understanding of fluid behavior with minimal assumptions.

## Key findings

- Discovery of fluid-fluid demixing with a critical point.
- Identification of a triple-point involving fluid and solid-like phases.
- Observation of density minima indicating thermodynamic anomalies.

## 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.