Title: Step evolution in two-dimensional diblock copolymer films,
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.