# Self-Assembly of Spiral Patterns in Confined System with Competing Interactions

## TL;DR

This paper reports the discovery of chiral spiral patterns in confined colloidal systems with competing interactions, showing how symmetry breaking and thermal effects induce topological transitions from rings to spirals.

## Contribution

It demonstrates the formation of chiral spirals in SALR particle systems confined in hexagons, a phenomenon not previously observed, and explains the underlying mechanisms and conditions for their emergence.

## Key findings

- Spiral patterns can be induced by symmetry breaking with a wedge.
- Thermally induced defects can lead to spiral formation.
- Equilibrium spirals can spontaneously appear under certain conditions.

## Abstract

Colloidal particles in polymer solutions and functionalized nanoparticles often exhibit short-range attraction coupled with long-range repulsion (SALR) leading to the spontaneous formation of symmetric patterns. Chiral nanostructures formed by thin film of SALR particles have not been reported yet. In this study, we observe striking topological transitions from a symmetric pattern of concentric rings to a chiral structure of a spiral shape, when the system is in hexagonal confinement. We find that the spiral formation can be induced either by breaking the system symmetry with a wedge, or by melting of the rings. In the former case, the chirality of the spiral is determined by orientation of the wedge and thus can be controlled. In the latter, the spiral rises due to thermally induced defects and is absent in the average particle distribution that form highly regular hexagonal patterns in the central part of the system. These hexagonal patterns can be explained by interference of planar density waves. Thermodynamic considerations indicate that equilibrium spirals can appear spontaneously in any stripe-forming system confined in a hexagon with a small wedge, provided that certain conditions are satisfied by a set of phenomenological parameters.