Using Generative Cellular Automata to Study the Chiral Morphogenesis of Gold

Background and Objectives

Chirality is ubiquitous in nature and can be transferred and amplified between systems through specific molecular interactions and multi-scale couplings. However, the mechanisms of chiral formation and the critical steps during the growth process are not yet fully understood. In this study, we trained a generative cellular automaton (CA) neural network based on experimental results to identify two distinguishable pathways of chiral morphogenesis in gold nanoparticles from non-chiral to chiral forms. Chirality is initially determined by the properties of asymmetrical growth along the boundaries of enantiomerically high-index facets. The deep learning-based interpretation of chiral morphology generation not only provides theoretical understanding but also allows us to predict unprecedented crossover pathways and their resulting morphologies.

Authors and Institutions

This paper was authored by Sang Won Im, Dongsu Zhang, Jeong Hyun Han, Ryeong Myeong Kim, Changwoon Choi, Young Min Kim, and Ki Tae Nam. It involves the Department of Materials Science and Engineering, Institute of New Media and Communications, and the Department of Electrical and Computer Engineering at Seoul National University. The article has been accepted and published online by Nature Materials.

Research Process

This study uncovered the growth process of gold nanoparticles from non-chiral to chiral forms through a series of experiments and deep learning model training. The research process is as follows:

a) Research Methods and Algorithms

1. Experimental Observation:

   • The initial seed is a 50 nm rhombic dodecahedron (RD) surrounded by {110} surfaces.
   • An intermediate chiral form (H3 intermediate) is formed when the seed grows to 100 nm, showing prominent vertices and curved edges.
   • The final chiral morphology (H3) is formed at 150 nm, characterized by a chiral indentation at the center and a cubic appearance.

2. Development of Cellular Automaton Model:

   • Using the Generative Cellular Automaton (GCA) method, the model constructs transition sequences based on neural networks to evolve to the final morphology without predefined rule constraints.
   • Sparse convolutional neural networks (Sparse CNN) predict local transformation probabilities for each cell, resulting in crystal surface growth patterns.

3. Training and Inference Process:

   • The model is trained with images of shape growth observed experimentally, with the intermediate form (H3 intermediate) playing a critical role in the training process.
   • Infusion training is used to make the intermediate state of the model during training closer to experimental results.

b) Experimental Results

1. H3 Chiral Morphology Generation Model (RDH3):

   • In the early stages, atoms primarily add at the trihedral vertices, leading to the formation of chiral edges.
   • In the intermediate stage, high-index microstructures form, and edges gradually curve towards <111> direction, forming the final H3 shape.
   • Verification of the model’s accuracy was done through comparisons of scanning electron microscopy (SEM) images and circular dichroism spectra.

2. H1 Chiral Morphology Generation Model (CBH1):

   • Starting from a 50 nm cube seed, an intermediate chiral form (H1 intermediate) is formed at 100 nm, exhibited as a triangular structure at the vertices and an elevated center.
   • The model describes the transition process from the initial seed to the final H1 shape and successfully predicts the complex growth pathway.

3. Crossover Pathways:

   • The RDH3 model can transition from the H3 intermediate state to the CBH1 mode, achieving shape generation from H3 intermediate to H1.
   • However, the reverse transition from the CBH1 intermediate state to RDH3 is not feasible.

c) Research Conclusions

By combining deep learning with generative cellular automata, this study uncovers the key mechanisms of chiral morphogenesis in gold nanoparticles, theoretically validating the possibilities of different growth pathways and their intersections. This not only provides new perspectives for understanding the chiral growth of nanomaterials but also opens new avenues for predicting and designing novel chiral structures.

d) Research Highlights

• The combination of deep learning and generative cellular automata reveals the growth mechanism of complex three-dimensional morphologies.
• For the first time, the detailed growth pathway of gold nanoparticles from non-chiral to chiral forms is systematically described.
• The critical roles of different intermediate forms in the generation of final shapes are established.

e) Other Valuable Information

The deep learning algorithms and experimental data used in this study are publicly available on GitHub (https://github.com/sangwonim/gca-chiral-morphogenesis) for reproduction and further research. Moreover, the sparse convolutional neural network method used in the model offers important references for studying other complex crystal structures.

Summary

Through the methods of deep learning and generative cellular automata, this research systematically unveils the mechanisms of chiral morphogenesis in gold nanoparticles, providing theoretical foundations and application prospects for understanding and designing chiral nanostructures. These findings are not only scientifically valuable in the field of nanomaterials but also potentially applicable to the study of chiral transfer mechanisms in biological systems.