Phase diagrams for sticky rods in bulk and in a monolayer from a lattice free-energy functional for anisotropic particles with depletion attractions

TL;DR

This paper develops a lattice-based density functional theory for anisotropic particles with depletion attractions, revealing complex phase diagrams including tricritical points and multiple liquid transitions in various dimensions.

Contribution

It introduces a fundamental measure functional for lattice models with anisotropic particles and effective attractions, enabling detailed analysis of phase behavior in bulk and monolayer systems.

Findings

Identification of tricritical points in 2D systems.

Observation of crossover from isotropic to nematic transitions in 3D.

Discovery of multiple stable critical points in monolayer systems.

Abstract

A density functional of fundamental measure type for a lattice model of anisotropic particles with hard-core repulsions and effective attractions is derived in the spirit of the Asakura-Oosawa model. Through polymeric lattice particles of various size and shape, effective attractions of different strength and range between the colloids can be generated. The functional is applied to the determination of phase diagrams for sticky rods of length $L$ in two dimensions, in three dimensions and in a monolayer system on a neutral substrate. In all cases, there is a competition between ordering and gas-liquid transitions. In two dimensions, this gives rise to a tricritical point, whereas in three dimensions, the isotropic-nematic transition crosses over smoothly to a gas-nematic liquid transition. The richest phase behavior is found for the monolayer system. For $L = 2$, two stable critical points are found corresponding to a standard gas-liquid transition and a nematic liquid-liquid transition. For $L = 3$, the gas-liquid transition becomes metastable.