Density functional theory for a primitive model of nanoparticle-block copolymer mixtures

Amphiphilic block copolymers provide useful templates for fabrication of nanostructured materials that are appealing for a wide variety of applications. The preparation of polymer-particle hybrid materials requires a good understanding of the chemical nature and topology of the amphiphilic molecules as well as their interactions with the embedded nanoparticles. This article reports a density functional theory (DFT) for a coarse-grained model of block copolymer-nanoparticle mixtures that is able to account for the properties of particles and copolymers within a self-consistent framework. It predicts various well-organized structures that can be effectively controlled by adjusting the polymer chain length and polymer-particle interactions. Illustrative examples based on relatively short chains suggest that, in qualitative agreement with experiments, large particles tend to be excluded from a polymer brush near a solid substrate, whereas smaller particles may be dissolved. The DFT is able to capture the dispersion of large particles in the microdomain of block copolymer that is energetically favorable, but localization of smaller particles at the microdomain interfaces.