Ordered Phases of Diblock Copolymer Micelles in Selective Solvent

TL;DR

This paper develops a mean-field model to study phase transitions in diblock copolymer micelles, revealing thermotropic and lyotropic shifts between cubic phases driven by entropy and inter-micelle interactions.

Contribution

It introduces a novel mean-field approach to explain the equilibrium coupling between micelle aggregation and lattice structure in selective solvents.

Findings

Identifies thermotropic and lyotropic phase transitions consistent with experiments.

Highlights entropy and inter-micelle repulsions as key stability mechanisms.

Shows how solvent selectivity influences micelle lattice density and structure.

Abstract

We propose a mean-field model to explore the equilibrium coupling between micelle aggregation and lattice choice in neutral copolymer and selective solvent mixtures. We find both thermotropic and lyotropic transitions from face-centered cubic to body-centered cubic ordered phases of spherical micelles, in agreement with experimental observations of these systems over a broad range of conditions. Stability of the non-closed packed phase can be attributed to two physical mechanisms: the large entropy of lattice phonons near crystal melting and the preference of the inter-micelle repulsions for the body-centered cubic structure when the lattice becomes sufficiently dense at higher solution concentrations. Both mechanisms are controlled by the decrease of micelle aggregation and subsequent increase of lattice density as solvent selectivity is reduced. These results shed new light on the relationship between micelle structure -- "crewcut" or "hairy" -- and long-range order in micelle solutions.