Phase Diagram of Diblock Copolymer Melt in Dimension d=5

TL;DR

This paper extends the phase diagram analysis of diblock copolymer melts to five-dimensional space using self-consistent field theory, predicting new stable nanophases and comparing theoretical predictions with strong segregation theory.

Contribution

It provides the first detailed phase diagram of diblock copolymers in 5D, revealing new stable phases and differences from existing theories in higher dimensions.

Findings

Predicted five stable nanophases in 5D space.

Found S5 nanophase stability between S4 and disordered phases.

Order-disorder transition lines vary weakly with dimension d.

Abstract

Using the self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d = 5. This is an extension of a previous work for d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B , quantified by the product \c{hi} N. We predict 5 stable nanophases: layers, cylinders, 3 D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large \c{hi}N, the order-order transition compositions are determined by the strong segregation theory (SST) in its simplest form. While the predictions of the SST theory are close to the corresponding SCFT extrapolations for d=4, the extrapolations for d=5 significantly differ from them. We find that the S5 nanophase is stable in a narrow strip between the ordered S4 nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected.