Stability of frozen waves in the Modified Cahn--Hilliard model

TL;DR

This paper investigates the existence and stability of frozen wave patterns in diblock copolymers modeled by the modified Cahn--Hilliard equation, revealing multiple stable states that can form from various initial conditions.

Contribution

It demonstrates the range of stable frozen waves in the modified Cahn--Hilliard model and their potential to emerge from general initial conditions, expanding understanding of pattern formation in copolymers.

Findings

Multiple stable frozen waves exist in the model.

Stable waves can emerge from diverse initial conditions.

Implications for nanostructure templating in materials science.

Abstract

We examine the existence and stability of frozen waves in diblock copolymers with local conservation of the order parameter, which are described by the modified Cahn--Hilliard model. It is shown that a range of stable waves exists and each can emerge from a `general' initial condition (not only the one with the lowest density of free energy). We discuss the implications of these results for the use of block copolymers in templating nanostructures.