Optimized Phase Field Model for Diblock Copolymer Melts

Self-consistent field theory (SCFT) is a versatile framework for investigating self-assembly and thermodynamic properties in broad classes of polymer systems. Nonetheless, it is expensive to implement in higher space dimensions d as propagator fields of d + 1 dimensions must be resolved in a numerical SCFT simulation. In principle, SCFT can be exactly reduced to a phase field (or density functional) theory involving only d-dimensional species density fields, but the density functional of the reduced theory is not known analytically. Although asymptotic approximations to the functional are available in the literature, e.g., the Ohta Kawasaki (OK) model for diblock copolymers, these functionals tend to produce inaccurate and unreliable predictions. Here, we present a phase field mapping technique adapted from force-matching concepts in the particle coarse-graining literature to best-fit coefficients in a trial density functional using data obtained from low-dimensional SCFT simulations. Such a mapping scheme results in an optimized phase field (OPF) model with improved accuracy over ad hoc choices of the fit parameters. We demonstrate the method by generating an OPF model for diblock copolymer melts, either symmetric or asymmetric, and we study its accuracy and transferability. We show that compared to the OK model, the OPF model makes significantly more accurate predictions of microphase domain periods. The OPF model also semi-quantitatively captures densities and energies, making it useful for computationally intensive applications, either on its own or in a multiscale approach alongside SCFT.