Exploring Nanoparticle Structure and Thermodynamics Using Field-Theoretic Simulations

While polymer nanocomposites have been an active area of research for multiple decades due to their utility in designing systems with controlled optical, mechanical, and barrier properties, numerous unresolved questions surround the field. Most tellingly, phase diagrams are only accepted for the simplest of systems, and direct mappings between theoretical and experimental phase diagrams are rare in the field. In recent years, our group has developed a suite of field-theoretic simulations techniques to study inhomogeneous polymer/nanoparticle composites, which we call the polymer nanocomposite field theory, PNC-FT. By incorporating the nanoparticles at essentially the same level as the polymers, the framework is amenable to analytical treatment, field-theoretic simulations that sample the fully-fluctuating model without approximation, and with our recent dynamic mean-field theory techniques. In this talk, I will describe the key features of our models and some of our recent applications to study both equilibrium and non-equilibrium processes in polymer/nanoparticle systems. In one example, I will show how our non-equilibrium methods capture the structure of polymer-grafted nanoparticles that are cast from solvent with a polymer matrix and not amenable to thermal annealing. We find that the experiments do not observe macrophase separation even in conditions where it is expected due to the kinetic arrest of the system. In another example, I will describe a detailed picture of the thermodynamics of block copolymer nanocomposites, where we find that the interactions between nanoparticles is mediated by the chain entropy and the interfacial tension between the domains of a microphase separated block copolymer.