Machine learning assisted exploration of patchy triangle systems

Abstract

The field of two-dimensional patchy particles opens up research for a wide range of technical applications such as, but not limited to, membranes and surface layer applications. These patchy particles can be engineered at different scales using DNA folding, manufacturing of nano-particles or serve as a model system for molecules with similar geometrical shapes or bonding behavior. The aim of this work was to gain more understanding of the self-assembly behavior of triangular patchy particles for different particle and system parameters. To achieve this, a Monte Carlo simulation was performed to study the self-assembly of different types patchy tri- angles in the canonical ensemble. Visual examination of snapshots allows for a generation of state diagrams that serve as a reference for the automated classification on the basis of order parameters. Among the observed structures are chains, gels, porous, and close packed crystals which require the use of a set of different order parameters for a proper classification. The results of the self-assembly depend on both system and particle parameters, such as patch arrangements on the particle edge, referred to as patch topologies. A phenomena occurring when trying to identify clusters in high dimensional spaces is the so called Curse of Dimensionality, which can create different issues when the number of data points is too small for the data’s dimensions. To deal with this issue, the space spanned by multiple order parameters was reduced to two dimensions using the conventional Principal Component Analysis (PCA). Further utilization of state-of-the-art machine learning methods suggested the use of Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) to classify the now two-dimensional dataset into different groups of similar systems. This clustering method successfully categorized the systems into different observable phases, without a visual analysis of all singular snapshots. These results contribute to a refined understanding of self-organization processes for patchy triangles.