Thermodynamics and Kinetics of Defect Motion and Annihilation in the Self-Assembly of Lamellar Diblock Copolymers

The thermodynamics of dislocations in thin films of lamella-forming diblock copolymers and their climb and glide motions are investigated using single-chain-in-mean-field (SCMF) simulations and self-consistent field theory (SCFT) in conjunction with the string method. The glide motion of a defect perpendicular to the stripe pattern is characterized by large free energy barriers. The barriers not only stem from altering the domain topology; an additional barrier arises from a small-amplitude but long-range domain displacement. In contrast, the climb motion along the stripes does not involve a free energy barrier in accord with the continuous translational invariance along the stripe. Thus, the perpendicular distance (impact parameter) between a pair of defects is approximately conserved. Dislocation pairs with opposite Burgers vectors attract each other and move toward each other (collide) via climb motion. We find that the forces between apposing defects significantly depend on system size, and the Peach Koehler force in smectic structures only becomes accurate for extremely large system sizes. Moreover, we observe in SCMF simulations that the defect annihilation time qualitatively and nonmonotonously depends on the defects' perpendicular distance and rationalize this finding by the collective kinetics along the minimum free energy path (MFEP) and the single-chain dynamics in an inhomogeneous environment.