# Uniform phases in fluids of hard isosceles triangles: one component and binary mixtures

## TL;DR

This paper develops a scaled particle theory for mixtures of hard isosceles triangles, revealing complex phase behaviors including triatic, nematic, and critical points, with implications for understanding similar 3D mixtures.

## Contribution

It introduces a theoretical framework for hard isosceles triangle mixtures, uncovering new phase stability regions and phase transition phenomena not previously characterized.

## Key findings

- Discovery of stable triatic phase in certain mixtures
- Identification of first-order isotropic-nematic and nematic-nematic transitions
- Existence of a Landau point with coalescing phase transitions

## Abstract

We formulate the scaled particle theory for a general mixture of hard isosceles triangles and calculate different phase diagrams for the one-component fluid and for certain binary mixtures. The fluid of hard triangles exhibits a complex phase behavior: (i) the presence of a triatic phase with sixfold symmetry, (ii) the isotropic-uniaxial nematic transition is of first order for certain ranges of aspect ratios, and (iii) the one-component system exhibits nematic-nematic transitions ending in critical points. We found the triatic phase to be stable not only for equilateral triangles but also for triangles of similar aspect ratios. We focus the study of binary mixtures on the case of symmetric mixtures: equal particle areas with aspect ratios ($\kappa_i$) symmetric with respect to the equilateral one: $\kappa_1\kappa_2=3$. For these mixtures we found, aside from first-order isotropic-nematic and nematic-nematic transitions (the latter ending in a critical point): (i) A region of triatic phase stability even for mixtures made of particles that do not form this phase at the one-component limit, and (ii) the presence of a Landau point at which two isotropic-nematic first-order transitions and a nematic-nematic demixing transition coalesce. This phase behavior is analog to that of a symmetric three-dimensional mixture of rods and plates.