Abstract
Significant progress towards the development of microscopic predictive theories of the equilibrium structure, polymer-mediated interactions, and phase behavior of polymer nanocomposites has been made recently based on liquid state integral equation, density functional, and self-consistent mean field approaches. The basics of these three theoretical frameworks are summarized, and selected highlights of their recent applications discussed for spherical, nonspherical, and polymer-grafted nanoparticles dissolved in athermal and adsorbing concentrated solutions and homopolymer melts. The role of nanoparticle size, volume fraction, and interfacial cohesive interactions is emphasized, especially with regards to their influence on filler dispersion and spatial ordering via entropic depletion attraction, polymer adsorption-mediated steric stabilization, and local bridging of nanoparticles. Some of the many remaining theoretical challenges and open fundamental questions are summarized.