Clusters, columns, and lamellae - minimum energy configurations in core softened potentials

TL;DR

This paper demonstrates that particles with a square-shoulder potential can self-organize into complex, low-symmetry structures like clusters, columns, or lamellae at low pressure, with high-pressure conditions favoring high-symmetry arrangements, using genetic algorithms and mean-field analysis.

Contribution

It introduces a novel application of genetic algorithms to identify complex low-symmetry structures in core-softened potentials, expanding understanding of self-assembly behaviors.

Findings

Particles form complex structures at low pressure

High pressure favors high-symmetry structures

Genetic algorithms effectively find equilibrium configurations

Abstract

We give evidence that particles interacting via the simple, radially symmetric square-shoulder potential can self-organize in highly complex, low-symmetry lattices, forming thereby clusters, columns, or lamellae; only at high pressure compact, high-symmetry structures are observed. Our search for these ordered equilibrium structures is based on ideas of genetic algorithms, a strategy that is characterized by a high success rate. A simple mean-field type consideration complements these findings and locates in a semi-quantitative way the cross-over between the competing structures.