| Block copolymers microphase separate into ordered structures with domains on a nanometer length scale, which can then be used as a template for nanoparticles. This research provides insight into the fundamental physics that govern phase behavior and properties of these materials.; We perform discontinuous molecular dynamics simulations on systems containing neat diblock copolymers modeled as chains of tangent hard spheres with square shoulder repulsions between unlike species at different chain lengths, volume fractions and interaction strengths. The resulting phase diagrams for chains of length 10 and 20 contain disordered, lamellae, perforated lamellae, cylindrical and BCC spherical phases. Contrary to theoretical predictions, the perforated lamellar phase is stable near regions of predicted gyroid stability. Variation of the structural spacing, internal energy and entropy with interaction strength is consistent with theoretical results for the strong segregation limit.; We then study diblock copolymer/nanoparticle composites, with nanoparticles modeled as hard spheres with a square shoulder repulsion with one of the copolymer blocks. The phase diagrams calculated for nanoparticles of various sizes and interaction strengths display lamellae, perforated lamellae, cylinders, disordered phases and regions of two-phase coexistence. The nanoparticles concentrate within the favorable domain; the lamellar spacing increases with nanoparticle volume fraction, but decreases with nanoparticle size. The locations of the phase transitions agree qualitatively with theoretical predictions, but the concentration profiles are inconsistent with theoretical predictions. The variation of the spacing with nanoparticle volume fraction is consistent with experimental data.; An algorithm was developed to locate the appropriate box length to use in equilibrium simualtions of periodic structures. We tested the algorithm against a Monte Carlo algorithm that maintains constant volume while allowing the box lengths to vary. The box length search algorithm converges to the same box legnth as the Monte Carlo algorithm, but is at least two orders of magnitude faster.; We developed a method to construct concentration profiles from the inverse Fourier transform of the simulation structure factor. Concentration profiles from multiple snapshots can be translated to a common position for averaging. The method can be used to uncover the relationship between parts of the structure factor and structural features. |
