A Geometric Theory of Diblock Copolymer Phases

TL;DR

This paper uses geometric and theoretical analysis to study the phase behavior of diblock copolymers, identifying conditions under which the A15 lattice phase is favored or stable.

Contribution

It introduces a geometric framework for analyzing diblock copolymer phases and demonstrates the stability of the A15 phase in branched diblocks.

Findings

A15 lattice is favored as blocks become more symmetric.

The A15 phase is metastable but not equilibrium for symmetric diblocks.

The A15 phase is stable in branched diblocks.

Abstract

We analyze the energetics of sphere-like micellar phases in diblock copolymers in terms of well-studied, geometric quantities for their lattices. We argue that the A15 lattice with Pm3n symmetry should be favored as the blocks become more symmetric and corroborate this through a self-consistent field theory. Because phases with columnar or bicontinuous topologies intervene, the A15 phase, though metastable, is not an equilibrium phase of symmetric diblocks. We investigate the phase diagram of branched diblocks and find thatthe A15 phase is stable.