Mean-field models of structure and dispersion of polymer-nanoparticle mixtures

We review some recent research developments in coarse-grained modeling based on mean-field approaches of the equilibrium dispersion and structure of polymer nanoparticle composites. We focus on three issues: (i) dispersion and phase behavior of particles in homopolymer matrices; (ii) dispersion in mixtures of homopolymers with grafted nanoparticles; (iii) self-assembly and organization of nanoparticles in block copolymer matrices. In each of these topics, we highlight that the dispersability and the resulting structure of the nanoparticle suspension may exhibit far more complexities than one may deduce using simple miscibility criterion involving the energetic interactions between the polymer matrix and the particle. In each case, we review our own research contributions accompanied by a brief discussion of related theoretical studies and some possible future directions.