Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system

TL;DR

This study combines Monte Carlo simulations and density functional theory to analyze pattern formation in a two-dimensional system of particles with a hard core and square shoulder, revealing how liquid structures evolve into various ordered phases.

Contribution

It introduces a combined simulation and theoretical approach to predict and analyze pattern formation in core-shell particle systems, highlighting the role of static structure factors.

Findings

Liquid structure develops long wavelength modulations upon cooling

Various patterned phases such as clusters and stripes form at lower temperatures

Liquid state structure factor $S(k)$ can predict the emergence of ordered phases

Abstract

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte-Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterised by long wavelength density modulations, and on further cooling forms a variety of other phases, including clustered, striped and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are bench-marked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor $S(k)$ for wavenumber $k$ is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.