Step evolution in two-dimensional diblock copolymer films

TL;DR

This paper introduces a phase-field model with an obstacle potential for simulating the formation and dynamics of free-surface structures, like steps, in two-dimensional diblock copolymer films, capturing their energetics and complex long-term behavior.

Contribution

It develops a novel phase-field model derived from self-consistent field theory that accurately captures step formation and surface dynamics in diblock copolymer films.

Findings

Model captures energetics of films with steps in 2D

Numerical approach resolves long-time free-surface structures

Model aligns with sharp interface limit

Abstract

The formation and dynamics of free-surface structures, such as steps or terraces and their interplay with the phase separation in the bulk are key features of diblock copolymer films. We present a phase-field model with an obstacle potential which follows naturally from derivations of the Ohta-Kawasaki energy functional via self-consistent field theory. The free surface of the film is incorporated into the phase-field model by including a third phase for the void. The resulting model and its sharp interface limit are shown to capture the energetics of films with steps in two dimensions. For this model, we then develop a numerical approach that is capable of resolving the long-time complex free-surface structures that arise in diblock copolymer films.