It is easy to understand the self-assembly of particles with anisotropic shapes or interactions (for example, cobalt nanoparticles or proteins) into highly extended structures. However, there is no experimentally established strategy for creating a range of anisotropic structures from common spherical nanoparticles. We demonstrate that spherical nanoparticles uniformly grafted with macromolecules ('nanoparticle amphiphiles') robustly self-assemble into a variety of anisotropic superstructures when they are dispersed in the corresponding homopolymer matrix. Theory and simulations suggest that this self-assembly reflects a balance between the energy gain when particle cores approach and the entropy of distorting the grafted polymers. The effectively directional nature of the particle interactions is thus a many-body emergent property. Our experiments demonstrate that this approach to nanoparticle self-assembly enables considerable control for the creation of polymer nanocomposites with enhanced mechanical properties. Grafted nanoparticles are thus versatile building blocks for creating tunable and functional particle superstructures with significant practical applications.

We review a class of new computer simulation methods for polymeric fluids and other soft condensed matter systems that are based on an underlying field-theoretic description. These methods, while still in an early stage of development, show considerable promise for studying the equilibrium properties of many-component systems capable of intricate self-assembly, such as solutions and blends containing block and graft copolymers. Field-theoretic simulation methods also provide a great deal of flexibility in model building and coarse graining, and appear to be particularly well suited to treat systems with soft, long-range interactions, such as polyelectrolytes. We attempt to connect various related theoretical approaches, such as self-consistent field theory and dynamic density functional theory, within a common framework.

We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.

We present a Monte Carlo approach to incorporating the effect of thermal fluctuations in field theories of polymeric fluids. This method is applied to a field-theoretic model of a ternary blend of AB diblock copolymers with A and B homopolymers. We find a shift in the line of order-disorder transitions from their mean-field values, as well as strong signatures of the existence of a bicontinuous microemulsion phase in the vicinity of the mean-field Lifshitz critical point. This is in qualitative agreement with a recent series of experiments conducted with various three-dimensional realizations of this model system. Further, we also compare our results and the performance of the presently proposed simulation method to that of an alternative method involving the integration of complex Langevin dynamical equations.