Polymers are versatile molecules that can self-assemble into a variety of phases in solution. The phases that form can be controlled by varying the concentration, temperature, or pH of the solution. Inorganic particles added to a solution of functionalized polymers also self-assemble into novel polymer nanocomposite materials. The determination of phase diagrams of these systems, as well as detailed calculations of their properties, is accomplished using Molecular Dynamics (MD) simulations. Additionally, algorithms are developed that implement MD on recent Graphics Processing Unit (GPU) hardware capable of astounding levels of performance. A single inexpensive GPU runs a MD simulation at the same performance as 63 CPU cores in a distributed memory cluster.