The 2D phase diagram associated with a PDE model for self-assembly of diblock copolymers

Diblock copolymers are macromolecules formed by grafting together two polymer chains of types A and B respectively. Melts of these macromolecules exhibit an amazing ability for self-assembly into A- and B-rich domains, which resemble highly regular periodic structures, such as lamellae, spheres, cylindrical tubes, and gyroids. Understanding the process by which these structures are created may ultimately enable the synthesis of materials with tailored properties. The goal of this thesis is the computation of a two-dimensional phase diagram for self- assembly of diblock copolymers. The self-assembly process is modeled by a modified Cahn- Hilliard equation, which is derived as a gradient flow of the nonlocal Cahn-Hilliard energy. We choose a pseudospectral exponential time differencing scheme to numerically simulate solutions of the PDE. Furthermore, we apply center manifold theory to obtain specific characterizations of the phase boundaries. These results are used as guidance for numerical extension of the phase diagram.