Ordering mechanisms in two-dimensional sphere-forming block copolymers

We study the coarsening dynamics of two-dimensional hexagonal patterns formed by single microdomain layers of block copolymers, using numerical simulations. Our study is focused on the temporal evolution of the orientational correlation length, the interactions between topological defects, and the mechanisms of coarsening. We find no free disclinations in the system; rather, they are located on large-angle grain boundaries, commonly where such boundaries bifurcate. The correlation lengths determined from the scattering function, from the density of dislocations, and from the density of disclinations exhibit similar behavior and grow with time according to a power law. The orientational correlation length also grows following a power law, but with a higher exponent than the other correlation lengths. The orientational correlation length grows via annihilation of dislocations, through preferential annihilation of small-angle grain boundaries due to poor screening of the strain field around dislocations located on small-angle grain boundaries. Consequently, the patterns are characterized by large-angle grain boundaries. The most commonly observed mechanism of coarsening is the collapse of smaller grains residing on the boundary of two larger grains delimited by large-angle grain boundaries. Simulations agree remarkably well with experimental results recently obtained.