Phase behaviors and ordering dynamics of diblock copolymer self-assembly directed by lateral hexagonal confinement.

The thermodynamics and kinetics of the self-assembly of cylinder-forming diblock copolymers directed by the lateral confinement of hexagons have been studied by the combination of self-consistent field theory (SCFT) calculation and time-dependent Ginzburg-Landau (TDGL) theory simulation. The SCFT calculations are used to determine the stability of candidate 2D and 3D equilibrium phases formed in small-size hexagons. Our phase diagram predicts the existence of stable phase regions with respect to the hexagonal size, which is centered around the optimal size with an extent of about a period, for the phases of perfect hexagonal cylinders. Our TDGL simulations reveal that the ordering event, in which the structure evolves toward the perfect state, occurs stochastically according to the Poisson distribution, and the ordering time grows roughly with a power-law relation of the hexagonal size. This prediction is helpful to estimate the annealing time for larger systems with the knowledge of the annealing time of a small system in experiments.