(70f) Level Set Strategy for Self Consistent Field Theory

We introduce level set methods to design new algorithms for self-consistent field theory (SCFT) in polymer physics. SCFT computes the structure and energy of inhomogeneous self-assembling polymers at thermodynamic equilibrium. Level set methods enable to represent the surface of an enclosing domain with an implicit function which in turn provides a powerful way to evolve a free surface. We introduce the concept of shape derivative into SCFT and rigorously derive expressions for the change of energy of a diblock copolymer melt with respect to its enclosing shape. The shape derivative is then used to embed SCFT into a variable shape simulation where the internal structure and the enclosing shape are coupled and evolve in tandem in order to reduce the energy. Finally an algorithm for the inverse geometric problem is presented. The algorithm finds a shape in order to obtain a desired internal structure of the confined polymeric material.