Symmetry-specific orientational order parameters for complex structures

TL;DR

This paper introduces a comprehensive set of symmetry-aware orientational order parameters, including novel Symmetrized Bond Order Parameters, to analyze complex self-assembled structures with anisotropic particles, enabling detailed domain and phase identification.

Contribution

It presents a new framework with symmetry-specific order parameters and a method to identify coherent domains in complex self-assembled structures, including amorphous phases.

Findings

Successfully identified crystalline domains in simulated systems.

Detected coherent clusters in non-space-filling amorphous structures.

Enhanced understanding of symmetry effects in self-assembly processes.

Abstract

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic, and bond orientational order, respectively. For the latter, a variation of classical bond order parameters is introduced that takes advantage of the symmetry of constituent particles, and/or expected crystalline phases. These Symmetrized Bond Order Parameters (SymBOPs) can be averaged over an entire system, or assigned locally to an individual bond. By combining that with bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. Not only does the methodology allow one to identify individual crystalline domains, but it also detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order.