Pattern evolution of an edge-dislocation array in a lyotropic lamellar phase confined in a wedge-shaped cell: Defect formation, relaxation, and recombination

When a system undergoes a first-order phase transition from a disordered to an ordered state, the local energy is first minimized. This local energy minimization often prevents a system from reaching the global energy minimum state and leads to trapping in an imperfectly ordered state with many defects. In soft matter, however, a system can further relax to the global energy minimum state via slow relaxation due to its softness and fluidity. We study this relaxation process, using a lyotropic lamellar phase in a wedge-shaped cell as a model system. A lyotropic smectic liquid crystal has a large repeat unit (here, an interlayer spacing d) up to ∼0.1 μm, and thus the motion of an individual edge dislocation in the lamellar phase can be directly observed with optical microscopy. Furthermore, a rather macroscopic spatial confinement (size h) can produce strong confinement effects, since d/h can still be large due to the largeness of d. These properties allow us to study the detailed kinetics of the relaxation process. We follow the time evolution of an edge dislocation array over 100 h from its initial stage. We reveal that the pattern evolution of an edge-dislocation array is the relaxation process of excess dislocation lines that formed initially toward the equilibrium configuration, and it is characterized by the motion of "nodes" of the topologically connected edge-dislocation network. We clarify the elementary process of this relaxation from a local to the global energy minimum state.