Geometric strong segregation theory for compositionally asymmetric diblock copolymer melts

TL;DR

This paper investigates how the shape of the Wigner-Seitz cell influences the strong segregation behavior of asymmetric diblock copolymer melts, revealing that hexagonal arrangements minimize energy.

Contribution

It introduces a variational approach to quantify geometric effects on chain distortions and compares energies across different lattice geometries in the strong segregation limit.

Findings

Hexagonal lattice has the lowest energy among studied geometries.

Geometric constraints significantly affect chain configurations.

Explicit energy calculations for different lattice arrangements.

Abstract

We have identified the effect of the Wigner-Seitz cell geometry in the strong segregation limit of diblock copolymer melts with strong composition asymmetry. A variational problem is proposed describing the distortions of the chain paths due to the geometric constraints imposed by the cell shape. We computed the geometric excess energies for cylindrical phases arranged into hexagonal, square, and triangular lattices and explicitly demonstrated that the hexagonal lattice has the lowest energy for a fixed cell area.