Systematic Coarse-Graining of Polymer Field Theories by Phase Field Mapping*

Phase field mapping is a novel coarse-graining technique for polymer field theories adapted from the force-matching method for particle theories. It uses a complex-valued d+1-dimensional field theory to produce a real-valued d-dimensional field theory that is more computationally efficient to simulate. The mapping can be done from an inexpensive calculation in the fine-grained theory, such as a self-consistent field theoretic (SCFT) simulation in one spatial dimension. The resulting optimized phase field (OPF) model is similar in form to polymer density functional theories and just as fast to simulate, but it approximates the fine-grained theory directly rather than asymptotically. We apply the method to two systems−a diblock copolymer melt, and a homopolymer/diblock blend−and compare the OPF models' performance to SCFT in terms of their predicted structures, length scales and energy scales.