# From Compact to Open Clusters in Systems with Competing Interactions

## TL;DR

This study investigates how varying attraction strength in a simple isotropic model affects the formation and stability of clusters, revealing distinct behaviors and thermodynamic signatures for compact versus open clusters.

## Contribution

It demonstrates the impact of attraction strength on cluster morphology and stability, providing new insights into the design and detection of self-assembled clusters in various systems.

## Key findings

- Attraction-dominated particles form stable, compact clusters similar to micelles.
- Repulsion-dominated particles form open, short-lived clusters.
- Osmotic pressure behavior distinguishes between compact and open cluster formation.

## Abstract

Colloidal particles, amphiphiles, and functionalized nanoparticles are examples of systems that frequently exhibit short-range attractions coupled with long-range repulsions. In this work, we observe striking differences in the dynamics of self-assembled clusters that form in a simple isotropic model of such systems when the strength of attraction is varied. We find that while attraction-dominated particles self-assemble into compact clusters with properties similar to micelles formed by amphiphilic molecules, repulsion-dominated particles self-assemble into open clusters which have much shorter life-times. There is also a significantly different dependence of the solution osmotic pressure versus composition: formation of compact clusters causes a decrease in the pressure vs. density slope, while formation of open clusters does not effect the pressure. This thermodynamic quantity turns out to be much more sensitive in picking out different clustering characteristics than the overall aggregation curves or cluster shapes. Our results have significant implications in developing design principles for stable cluster self-assembly and detection in both laboratory settings and in computer simulations.