StrAPS: Structural Angular Power Spectrum for Discovering Novel Morphologies in Block Copolymers

TL;DR

This paper introduces a novel method using the angular power spectrum of the 3D structure factor to automatically identify and distinguish morphologies in block copolymers, reducing reliance on manual expertise.

Contribution

It presents a new analytical approach leveraging spherical harmonic decomposition of the structure factor for morphology classification in block copolymers.

Findings

Low-degree spherical harmonic coefficients effectively discriminate morphologies.

The method automates morphology detection without prior enumeration.

It provides a robust, signature-based classification tool.

Abstract

The morphologies of phase separating systems have formal distinctions such as symmetry groups, but the analysis protocol for labeling a particular phase field with a morphology requires manual expertise, arbitrary thresholds, or established signatures. In this work, it is investigated if the angular power spectrum of the 3D structure factor can discriminate between morphologies. The 3D structure factor is computed on configurations of phase separating block copolymers generated by coarse-grained molecular dynamics simulations. The shell of structure factor values containing the primary peaks is isolated. This 2D field on a sphere is decomposed into spherical harmonic modes of even polynomial degree $\ell\le 12$, then further reduced to the rotationally invariant angular power spectrum. It is found that these few coefficients for low $\ell$ discriminate robustly between different morphologies. This analysis serves as an automatic tool for flagging novel structures, without a need to enumerate the plausible morphologies in advance.