Chain trajectories, domain shapes and terminal boundaries in block copolymers

TL;DR

This paper introduces a method to analyze molecular packing in block copolymer melts using chain trajectories derived from self-consistent field theory, linking chain conformations to mesophase geometry.

Contribution

It presents a novel approach to extract and analyze chain conformations in complex morphologies, connecting molecular-level details to domain boundaries and packing frustration.

Findings

Chain trajectories reveal local packing features like bending and tilt.

Explicit link established between chain conformations and medial geometry.

Analysis applies to 2D and 3D morphologies, including spherical and bicontinuous structures.

Abstract

The packing geometry of macromolecules in complex mesophases is of key importance to self-organization in synthetic and biological soft materials. While approximate or heuristic models rely on often-untested assumptions about how flexible molecules "fit in" to distinct locations of complex assemblies, physical assemblies derive from ensembles of fluctuating conformations, obscuring the connection between mesophase geometry and the underlying arrangements. Here, we present an approach to extract and analyze features of molecular packing in diblock block copolymer (BCP) melts, a prototypical soft matter system, based on the statistical description of chain conformations in self-consistent field (SCF) theory. We show how average BCP chain trajectories in ordered morphologies can be analyzed from the SCF-derived orientational order parameter of chain segments. We use these extracted trajectories to analyze the features of local packing geometry, including chain bending and tilt, as well as the terminal boundaries that delineate distinct domains in ordered BCP morphologies. We illustrate this analysis by focusing on measurable features of packing frustration in 2D (columnar) and 3D (spherical and bicontinuous) morphologies, notably establishing an explicit link between chain conformations in complex morphologies and their medial geometry.