Simulating the morphology and mechanical properties of filled diblock copolymers.

We couple a morphological study of a mixture of diblock copolymers and spherical nanoparticles with a micromechanical simulation to determine how the spatial distribution of the particles affects the mechanical behavior of the composite. The morphological studies are conducted through a hybrid technique, which combines a Cahn-Hilliard (CH) theory for the diblocks and a Brownian dynamics (BD) for the particles. Through these "CH-BD" calculations, we obtain the late-stage morphology of the diblock-particle mixtures. The output of this CH-BD model serves as the input to the lattice spring model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM bonds. A stress is applied to the LSM lattice, and we calculate the local strain fields and overall elastic response of the material. We find that the confinement of nanoparticles within a given domain of a bicontinous diblock mesophase causes the particles to percolate and form essentially a rigid backbone throughout the material. This continuous distribution of fillers significantly increases the reinforcement efficiency of the nanoparticles and dramatically increases the Young's modulus of the material. By integrating the morphological and mechanical models, we can isolate how modifications in physical characteristics of the particles and diblocks affect both the structure of the mixture and the macroscopic behavior of the composite. Thus, we can establish how choices made in the components affect the ultimate performance of the material.