Stability of monolayers and bilayers in a copolymer-homopolymer blend model

TL;DR

This paper analyzes the stability of layered monolayer and bilayer structures in a diblock copolymer-homopolymer blend model using variational calculus and Fourier analysis, providing explicit stability criteria and mathematical tools.

Contribution

It introduces a detailed stability analysis of layered structures in a copolymer-homopolymer blend model, including explicit calculations of derivatives and the Green's function for the Laplacian.

Findings

Characterized stability conditions for monolayers and bilayers

Derived the Green's function for the Laplacian on a periodic strip

Developed a Fourier series approach for interface perturbations

Abstract

We study the stability of layered structures in a variational model for diblock copolymer-homopolymer blends. The main step consists of calculating the first and second derivative of a sharp-interface Ohta-Kawasaki energy for straight mono- and bilayers. By developing the interface perturbations in a Fourier series we fully characterise the stability of the structures in terms of the energy parameters. In the course of our computations we also give the Green's function for the Laplacian on a periodic strip and explain the heuristic method by which we found it.