# Emergence of Frank–Kasper Phases from Chemically Simple Block Copolymer: Poly(ethylene oxide)-block-polyisoprene and Its Dry-Brush Blends

## TL;DR

The study shows that a specific block copolymer can form complex Frank–Kasper phases, which are rarely seen in simple polymer systems.

## Contribution

A new linear diblock system, PEO-b-PI, is identified as capable of forming the FK σ phase, with expanded phase stability through blending.

## Key findings

- PEO-b-PI forms the FK σ phase with a conformational asymmetry parameter ε ≈ 1.26.
- Dry-brush blending with h-PEO enables a sequence of phase transitions from BCC to C15.
- The Laves C15 phase remains stable at nearly symmetric compositions, beyond typical stability limits.

## Abstract

The Frank–Kasper
(FK) phases, also known as tetrahedrally
close-packed structures, represent a unique class of ordered morphologies
characterized by large unit cells with multiple nonequivalent lattice
sites. To date, only a limited number of linear AB-type block copolymers
(BCPs) have been shown to form FK phases. Here, we systematically
investigate a sphere-forming poly­(ethylene oxide)-block-poly­(1,4-isoprene) (PEO-b-PI) with a conformational
asymmetry parameter ε ≈ 1.26 and identify it as a new
linear diblock system capable of forming the FK σ phase. In
the neat PEO-b-PI, an abrupt enlargement of micelle
size was observed across the BCC-to-σ lattice transition, despite
a reduction in diblock molecular weight, indicating the pronounced
influence of lattice symmetry on micelle dimensions at the onset of
FK phase formation. To further expand the accessible FK phase regime,
we employed a dry-brush blending strategy by incorporating homopolymer
PEO (h-PEO) into a BCC-forming PEO-b-PI. With increasing
h-PEO content, the blends exhibited a lyotropic BCC → σ
→ C14 → C15 phase transition sequence consistent with
the theoretical predictions. Detailed structural analysis revealed
systematic variations in micelle characteristics with h-PEO composition,
arising from the interplay among different free energy components.
Notably, the FK phases in this system were stabilized over an unusually
broad composition window, allowing the Laves C15 phase to persist
up to nearly symmetric compositions, significantly beyond the stability
limits reported for conventional BCP/homopolymer blends.