Mesophases of soft-sphere aggregates

TL;DR

This paper develops a theoretical framework to predict and analyze the stable mesophases formed by soft-sphere particles with complex interactions, covering various morphologies and temperature regimes.

Contribution

It introduces a systematic mean-field approach combined with level surface analysis to predict mesophase stability across different clustering potentials and temperature conditions.

Findings

Predicts a sequence of stable phases including lamella, hexagonal, and cubic structures.

Analyzes finite-temperature effects on the stability of bicontinuous structures like gyroid.

Identifies the stability of bicontinuous cluster morphology in weakly segregated regimes.

Abstract

Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a level surface analysis of the periodic structures of soft-sphere aggregates to study stable morphologies for all clustering potentials. We develop a systematic approach to the thermodynamics of mesophase assembly in the low-temperature, strong-segregation and predict a generic sequence of phases including lamella, hexagonal-columnar and body-center cubic phases, as well as the associated inverse structures. We discuss the finite-temperature corrections to strong segregation theory in terms of Sommerfeld-like expansion and how these corrections affect the thermodynamic stability of bicontinuous mesophase structures, such as gyroid. Finally, we explore the opposite limit of weakly-segregated particles, and predict the generic stability of a bicontinuous cluster morphology within the mean-field phase diagram.