Predicting the self-assembled morphology and mechanical properties of mixtures of diblocks and rod-like nanoparticles

We couple a morphological study of a mixture of diblock copolymers and rod-like, solid nanoparticles with a micromechanical simulation to determine how the spatial distribution and aspect ratio of the particles affects the mechanical behavior of the composite. The morphological studies are conducted through the SCF/DFT technique, which couples the self-consist field theory (SCFT) for the diblocks and a density functional theory (DFT) for parallelepiped particles. Through the SCF/DFT calculations, we obtain the equilibrium morphology of the diblock/particle mixtures. We find that the distribution of particles within the polymers is dependent not only on the relative interaction energies between the particles and the different blocks, but also on the aspect ratio of the rod-like solids. The output of the SCF/DFT 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 stress and strain fields and overall elastic response of the material. We find that high aspect ratio rods can dramatically increase 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.