2025 AIChE Annual Meeting

(15d) Quantifying the Evolution of Symmetry in Nucleation and Self-Assembly Using Novel Order Parameters

Authors

Domagoj Fijan - Presenter, University of Michigan
Brandon Butler, University of Michigan
Maria Ward Rashidi, University of Michigan
Sharon C. Glotzer, University of Michigan
Nucleation and crystallization processes are critical in diverse materials, such as colloidal, soft, molecular, metallic, and ionic crystals. Crystallization is a symmetry-breaking phase transition. Traditional order parameters (OP), such as Steinhardt's (SOP), have been widely used as proxies to study the evolution of order during crystallization, focusing on bond orientational order rather than directly quantifying symmetry. These parameters aggregate multiple symmetries into a single value, limiting their interpretability. To overcome these limitations, we introduce the Point Group Order Parameter (PGOP), which provides a continuous, bounded, per-particle measure of the point group symmetry of a particle's local environment. PGOP quantifies the congruence between a particle's environment and its symmetrized counterpart. We propose two PGOP variants: one capturing full point group symmetry and another characterizing the point group symmetry of the bond orientational order diagram. Naturally, such an OP is particularly useful for studying the development of order in crystals and quasicrystals. PGOP enables differentiation of simple crystals by identifying unique symmetries in their local environments and is highly effective in analyzing and distinguishing distinct local environments associated with different Wyckoff sites in complex crystals.

Nucleation is a rare and stochastic process, making it challenging to predict or identify. To address this, we developed dupin, a framework for event detection in molecular simulations. dupin enables systematic identification of crystallization events in large datasets. It can also operate in 'online' mode for real-time detection of rare events during simulations. We demonstrate its effectiveness by developing a specialized trajectory writer to capture rare events, such as nucleation, with high temporal resolution. This approach minimizes storage while maintaining negligible computational overhead.

Using these two tools in tandem allows us to study the evolution of nucleation and subsequent growth with unprecedented detail and interpretability, enabling us to better understand the nature and richness of the crystallization process. We demonstrate this through a study of nucleation in a Lennard-Jones liquid using HOOMD-blue.