Two-dimensional colloidal fluids exhibiting pattern formation

TL;DR

This paper investigates pattern formation in two-dimensional colloidal fluids with competing interactions, using lattice-gas models, Monte Carlo simulations, and density functional theory to analyze phase behavior and morphological transitions.

Contribution

It introduces a lattice-gas model combined with DFT and simulations to study microphase separation and morphologies in colloidal fluids with competing interactions.

Findings

DFT predictions align with simulation results in unstable regions.

Heat capacity peaks at morphological transition points.

Continuum DFT mapping simplifies stability analysis.

Abstract

Fluids with competing short range attraction and long range repulsive interactions between the particles can exhibit a variety of microphase separated structures. We develop a lattice-gas (generalised Ising) model and analyse the phase diagram using Monte Carlo computer simulations and also with density functional theory (DFT). The DFT predictions for the structures formed are in good agreement with the results from the simulations, which occur in the portion of the phase diagram where the theory predicts the uniform fluid to be linearly unstable. However, the mean-field DFT does not correctly describe the transitions between the different morphologies, which the simulations show to be analogous to micelle formation. We determine how the heat capacity varies as the model parameters are changed. There are peaks in the heat capacity at state points where the morphology changes occur. We also map the lattice model onto a continuum DFT that facilitates a simplification of the stability analysis of the uniform fluid.