Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional hard disk mixtures

TL;DR

This study uses density functional theory to analyze phase diagrams and surface tensions in two-dimensional additive and nonadditive hard disk mixtures, revealing how size ratio influences phase behavior and interfacial properties.

Contribution

It provides the first detailed phase diagrams and surface tension calculations for 2D hard disk mixtures across all size ratios, including nonadditive models, using advanced density functional methods.

Findings

Phase diagrams are qualitatively similar to 3D mixtures.

Surface tensions decrease with the addition of a second species.

A broadening of coexistence regions occurs for small size ratios.

Abstract

Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional hard disk mixtures are determined for the whole range of size ratios $q$ between disks, assuming random disorder in the crystal phase. The fluid-crystal transitions are first-order due to the assumption of a periodic unit cell in the density functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard sphere mixtures. For the nonadditive case, a broadening of the fluid-crystal coexistence region is found for small $q$ whereas for higher $q$ a vapor--fluid transition intervenes. In the additive case, we find a sequence of spindle type, azeotropic and eutectic phase diagrams upon lowering $q$ from 1 to 0.6. The transition from azeotropic to eutectic is different from the three-dimensional case. Surface tensions in general become smaller (up to a factor 2) upon addition of a second species and they are rather small. The minimization of the functionals proceeds without restrictions and optimized graphics card routines are used.