# Self-Assembly Formed by Spherical Patchy Particles with Long-Range Attraction

## TL;DR

This study investigates how spherical patchy particles with long-range attraction self-assemble into various structures in two dimensions, revealing the influence of patch coverage and pressure on the resulting arrangements.

## Contribution

It demonstrates the formation of diverse stable structures from patchy particles with long-range attraction, highlighting the effects of patch coverage and pressure, which was not extensively studied before.

## Key findings

- High pressure favors triangular lattices at small patch coverage.
- Low pressure leads to chain-like and square cluster formations.
- Large patch coverage results in the formation of square clusters.

## Abstract

We report on self-assemblies formed from spherical patchy particles interacting by a long-range attraction through a patch region in a two-dimensional system. We performed Monte Carlo simulations to find stable structures in a system with constant number of particles under constant temperature and constant pressure (NPT system), in which particles interact via the Kern--Frenkel potential. We also performed Brownian dynamics simulations employing an interaction potential similar to the Kern--Frenkel potential to study the formation of those structures. For long-range attractive potentials, we describe how these stable structures and their formation depend on the coverage of the patch. Under high pressure, when the coverage is small, triangular lattices are formed as reported in previous papers. From our simulations, we find when the pressure is low short chain-like structures, in which the distance between particles is long, and square clusters, which are not formed with a short-range attractive potential, are formed. When the coverage of the patch region is large, square clusters are formed since the interaction between particles is stronger than that for with small coverage When the coverage ratio is larger than 0.5, the direction of the patch is perpendicular to the plane in which the particles are placed.