Fundamental measure theory for mixtures of parallel hard cubes. II. Phase behavior of the one-component fluid and of the binary mixture

TL;DR

This paper uses fundamental measure theory to analyze phase transitions in mixtures of parallel hard cubes, revealing continuous freezing, demixing, and complex phase diagrams including metastability and polydispersity effects.

Contribution

It develops a method to study highly asymmetric binary mixtures by mapping them onto one-component systems, and explores their phase behavior including fluid-solid and solid-solid transitions.

Findings

Single-component fluid undergoes continuous transition to a solid with high vacancy density.

Binary mixture exhibits demixing for small edge-length ratios.

Polydispersity introduces fluid and solid metastability and isostructural transitions.

Abstract

A previously developed fundamental measure fucntional [J. Chem. Phys. vol.107, 6379 (1997)] is used to study the phase behavior of a system of parallel hard cubes. The single-component fluid exhibits a continuous transition to a solid with an anomalously large density of vacancies. The binary mixture has a demixing transition for edge-length ratios below 0.1. Freezing in this mixture reveals that at least the phase rich in large cubes lies in the region where the uniform fluid is unstable, hence suggesting a fluid-solid phase separation. A method is develop to study very asymmetric binary mixtures by taking the limit of zero size ratio (scaling the density and fugacity of the solvent as appropriate) in the semi-grand ensemble where the chemical potential of the solvent is fixed. With this procedure the mixture is exactly mapped onto a one-component fluid of parallel adhesive hard cubes. At any density and solvent fugacity the large cubes are shown to collapse into a close-packed solid. Nevertheless the phase diagram contains a large metastability region with fluid and solid phases. Upon introduction of a slight polydispersity in the large cubes the system shows the typical phase diagram of a fluid with an isostructural solid-solid transition (with the exception of a continuous freezing). Consequences about the phase behavior of binary mixtures of hard core particles are then drawn.