# Quantitative 3D Real‐Space Analysis of Photonic Supraparticles

## TL;DR

This paper introduces a new method to study photonic supraparticles using 3D real-space analysis, enabling detailed structural insights and classification.

## Contribution

The novel contribution is a quantitative 3D real-space analysis method for photonic supraparticles using confocal and STED microscopy combined with machine learning.

## Key findings

- The method enables accurate classification of supraparticle structures, including icosahedral and decahedral forms.
- It provides experimental insights into self-assembly pathways and defect formation mechanisms.
- The approach allows for photonic calculations based on real experimental data.

## Abstract

Supraparticles (SPs) are assemblies of smaller particles, and they form an interesting material class. One way through which these structures can be formed is self‐assembly (SA) in spherical confinement, and what makes them unique is that they combine the properties of the smaller particles with collective properties arising from the length scale on which these smaller particles are ordered. Additionally, the limited number of particles in an SP enables them to form structures that are not found in bulk systems. An example of this is icosahedral symmetry, which is the equilibrium structure for SPs up to several hundreds of thousands of particles. Although these icosahedral structures have been investigated through computer simulations and several experimental techniques have been used to analyze them in 3D, the number of experimental datasets published is so limited that no statistically relevant conclusions have been drawn so far. The experimental technique most commonly applied to study them is scanning electron microscopy (SEM), but with this, only quantitative information about the surface of the SPs can be obtained. By using a combination of 3D confocal and stimulated emission depletion (STED) microscopy on extremely well‐index‐matched (within 0.002) fluorescent core‐shell, colloidal silica spheres (of 442–478 nm in diameter with polydispersities below 1%), we obtained full 3D real‐space datasets of tens of SPs within several hours. The structures were classified based on bond order parameters and deviations from local centrosymmetry, using an unsupervised machine learning model. From this, we are able to correctly classify structures that are commonly misidentified using SEM. Additionally, the quantitative real‐space analysis gave experimental insights into the SA pathway and defect formation mechanisms of mostly icosahedral SPs.

This work shows that through quantitative 3D real‐space analysis, photonic supraparticles can be investigated in detail. By clustering and classifying all particles, structure features can easily be detected, and the internal structure can be quickly investigated. This methodology allows for quick identification of different crystal structures, such as icosahedral and decahedral, allowing for experimental insights into the crystallization pathway and the opportunity to perform photonic calculations on experimental data.