Using Particle Swarm Optimization and Self-Consistent Field Theory to Discover Globally Stable Morphologies of Block Copolymers
Carol Tsai, Glenn H. Fredrickson
Abstract
We present a method for agnostically determining the globally stable and low-lying metastable mesophases of block copolymers by combining particle swarm optimization (PSO) and self-consistent field theory (SCFT). In the PSO-SCFT method, we exploit SCFT as a local optimizer by seeding SCFT simulations with reciprocal-space fields populated in a single shell by the PSO near a critical wavenumber. The PSO facilitates the search through a space of reciprocal-space SCFT seeds that relax to a variety of morphologies. We present benchmarking results for PSO-SCFT on two systems for which theoretical phase diagrams are well-established: the canonical AB diblock and the miktoarm star polymer AB4, the latter of which supports a rich variety of competing sphere structures. A specific implementation of PSO-SCFT is shown to identify the double gyroid morphology in AB diblock copolymer melts. Furthermore, PSO-SCFT successfully recovers both the A15 morphology at a composition where it is expected to be stable in miktoarm melts and several competitive metastable candidates. One of the latter is a sphere morphology with a crystal structure of Zr4Al3 that was identified as the hP7 Frank–Kasper phase, a morphology not seen before in block polymer systems. The PSO-SCFT method thus provides a promising framework for the automatic identification of low-free-energy structures in new block copolymer systems.