Convolution of the physical point cloud for predicting the self-assembly of colloidal particles

Abstract

This paper presents a novel algorithm for predicting the kinetic and thermodynamic pathways of colloidal systems. The approach involves constructing a physical point cloud from inter-particle stress information extracted from randomly distributed colloidal particles and embedding it into a graph convolutional network (GCN). In the field of pattern recognition, GCNs are widely utilized to classify arbitrary 3D objects by learning multidimensional relationships within feature spaces defined by spatial coordinates. In contrast, our study constructs a feature space based on the micromechanical stresses imparted on colloidal particles during their self-assembly, rather than relying on spatial information. This enables predictive functionality within the classification task. Using this method, we discover for the first time that the convolution of canonical physical information can predict the self-assembly of colloids by observing only the initial configurations of colloidal particles, whereas conventional pattern recognition techniques using spatial information could only recognize phase transitions near completion. The phases predicted by our model are not limited to liquid-like dispersions and solid–liquid phase separations, where thermodynamic equilibrium differs, but also include sample-spanning gel structures, where only kinetics differ while thermodynamics remain the same. Furthermore, although we train the semantic stress relationships that constitute each phase of the network using same-sized particles with a pre-specified inter-particle interaction, our algorithm demonstrates generalized predictive performance even for suspensions with randomly distributed particle sizes. Our results make it possible to predict the phase behavior of colloidal systems where traditional theoretical approaches have been challenging or impossible due to the inherent complexity of the colloidal system. Given that colloids are characterized by extremely small length scales, long times are required for observable macroscopic changes resulting from self-assembly. Therefore, this study is expected to serve as a highly useful decision-support method for engineering soft matter with desired morphologies.