Abstract
Topological defects including point defects, disclinations and walls, emerging from symmetry breaking phase transitions, play a pivotal role in ordered systems ranging from cosmology to liquid crystals. This dissertation explores the elasticity, topological structures and transformations of defects during nematic to smectic or to ferroelectric phase transitions through experiments, simulations, and theoretical analyses.
First, we quantify the elastic properties of disclinations in nematic liquid crystals, including line tension, torsional rigidity, and twist–shear coupling. The twist–shear coupling coefficient is nonpositive, driving the helical shape of disclinations under combined twist and shear deformations. This model extends to nonsingular defects and accurately predicts defect configurations in both active and flow-driven nematic systems.
Next, we uncover the topological structure of π walls in ferroelectric nematic phases, which consist of two half-integer surface disclinations anchored on opposing substrates of a nematic cell, enclosing a chiral π-twist domain. This degenerate arrangement generates kinks and antikinks that partition chirality-inverted subdomains, analogous to spin configurations in an Ising chain. Field-driven polar switching occurs via a two-stage disclination annihilation process, governed by the hierarchical structure of π walls.
In addition, we investigate the evolution of point defects during isotropic-nematic-smectic phase transitions in hybrid cells. Upon thermal excitation from the smectic-A to the nematic phase, a toric focal conic domain transforms into a +1 converging boojum defect, eventually adopting a concentric configuration. This sequence arises from the reduction in bend and twist elastic moduli relative to the splay modulus, as validated by our Landau-de Gennes free energy modeling.
Finally, we examine the transformations of disclinations during the nematic to ferroelectric phase transitions. Half-integer disclinations become topologically unstable in polar phases, migrating to surfaces as spatial charge carriers (integer or topological neutral). Integer defects evolve into hybrid defects including boojums, merons, and monopoles through topological instability and energy minimization. This framework provides insights into defect evolution across discrete symmetry breaking transitions, with potential implications for cosmology.