Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory

TL;DR

This paper develops a density functional theory for two-dimensional hard rods, accurately predicting their phase diagram and phases, validated against Monte Carlo simulations, and applicable to complex mixtures and inhomogeneous systems.

Contribution

The authors introduce an explicit density functional derived from fundamental mixed measure theory for 2D hard rods, enabling detailed phase diagram predictions.

Findings

Good agreement with Monte Carlo simulation data.

Phase diagram includes isotropic, nematic, smectic, and crystalline phases.

Functional applicable to multicomponent mixtures and inhomogeneous systems.

Abstract

A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed measure theory and freely minimized numerically for hard discorectangles. The phase diagram, which involves stable isotropic, nematic, smectic and crystalline phases, is obtained and shows good agreement with the simulation data. Our functional is valid for a multicomponent mixture of hard particles with arbitrary convex shapes and provides a reliable starting point to explore various inhomogeneous situations of two-dimensional hard rods and their Brownian dynamics.