Stable periodic patterns in 3D for the Ohta-Kawasaki problem

Jan Bouwe van den Berg
VU Amsterdam

The Ohta-Kawasaki model describes the evolution of diblock copolymer melts. When studying the dynamics on large domains it is observed that, depending on the parameter values, certain periodic patterns are selected. Working within an arbitrary space group symmetry, we explore the phase space, computing candidates of stable patterns, both with and without experimentally observed symmetries. We validate the phase diagram, identifying regions of parameter space where different spatially periodic structures are preferred. These patterns may be lamellar layers, hexagonally packed cylinders, body-centered or close-packed spheres, as well as double gyroids and `O70’ arrangements. Each computation is validated by a mathematical theorem, where we bound the truncation errors and apply a fixed point argument to establish a computer-assisted proof.