Strong Orientational Coordinates and Orientational Order Parameters For Symmetric Objects

TL;DR

This paper introduces strong orientational coordinates (SOCs) for symmetric objects, enabling precise quantification of orientational order and correlations in systems of anisotropic particles, aiding simulations and analysis.

Contribution

It proposes a systematic method to construct SOCs that fully specify orientations of symmetric objects, advancing the analysis of orientational order in complex systems.

Findings

SOCs fully specify the orientation of symmetric objects.

SOCs facilitate quantification of local and global orientational order.

The method improves analysis and storage of rotational data in simulations.

Abstract

Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in self-assembly and in inducing complex order. The problem of identifying different types of order that can emerge in such systems can, however, be challenging. Here, we revisit the problem of quantifying orientational order in systems of building blocks with non-trivial rotational symmetries. We first propose a systematic way of constructing orientational coordinates for such symmetric building blocks. We call the arising tensorial coordinates strong orientational coordinates (SOCs) as they fully and exclusively specify the orientation of a symmetric object. We then use SOCs to describe and quantify local and global orientational order, and spatiotemporal orientational correlations in systems of symmetric building blocks. The SOCs and the orientational order parameters developed in this work are not only useful in performing and analyzing computer simulations of symmetric molecules or particles, but can also be utilized for the efficient storage of rotational information in long trajectories of evolving many-body systems.