Parameterized Density Functional Models for Block Copolymer Melts

TL;DR

This paper develops a generalized density functional model for block copolymer melts, incorporating a nonlocal transformation that captures microemulsion structures and aligns well with experimental data.

Contribution

It introduces a systematic parameterization of the free energy for copolymer blends, improving upon previous models by preserving key structural features without adjustable parameters.

Findings

The model reproduces microemulsion structure factors.

Phase diagrams match experimental and mean field results.

Simulated small angle x-ray data aids in morphology classification.

Abstract

The derivation of density functional energies from the random phase approximation of self-consistent mean field theory is generalized and applied to a binary blend of diblock copolymers and homopolymers. A nonlocal transformation is incorporated into the density functional model prior to the strong segregation extrapolation step employed by Uneyama and Doi. The transformation affords a systematic parameterization of the free energy that preserves key structural features such as scattering structure factor. A simple choice of transformation is shown to incorporate the Tuebner and Strey microemulsion structure factor and provide a reduction to the microemulsion free energy. Without adjustable parameters, the associated phase diagrams are compared to experimental and self consistent mean field based results. A gradient descent of the free energy recovers dependence of end-state morphology on initial configurations, and identifies coexisting microstructures and transitions to two-phase behavior. Small angle x-ray data is simulated and used in classification of microphase morphology.