Title: Complex-to-Real Mapping for Polymer Field Theories
Advisor: Glenn Fredrickson
Polymer field theory is a valuable tool for studying the behavior of dense polymer systems at near-atomistic length scales. In its most successful form, it is a complex-valued, d+1–dimensional theory that can be studied using fully-fluctuating simulations or at the level of self-consistent field theory (SCFT). This theory requires calculations using fields that depend on d spatial variables as well as a contour variable indicating the position along the polymer chain. In principle, it can be reduced to a simpler, real-valued, d-dimensional theory that is more efficient to simulate numerically—a phase field model—but these are typically less accurate due to approximations invoked in their derivations. We introduce and refine a new method for constructing phase field models, phase field mapping, that systematically parametrizes an optimized phase field (OPF) model using the output of inexpensive SCFT simulations. We develop an OPF model for the diblock copolymer melt and characterize its performance in terms of speed, accuracy, and transferability. Then we modify and generalize the model to produce a weakly compressible model suitable for running simulations in confined templates. In bulk and in confinement, the OPF model is faster to simulate than SCFT and more accurate than other phase field models. With these advantages, the OPF model is a useful alternative to complex-valued field theories.