Defect Textures in Polygonal Arrangements of Cylindrical Inclusions in Cholesteric Liquid Crystal Matrices
A systematic computational and scaling analysis of defect textures in polygonal arrangement of cylindrical particles embedded in a cholesteric (Ch) liquid crystal matrix is performed using the Landau de Gennes model for chiral self assembly, with strong anchoring at the particles' surface. The defect textures and LC phases observed are investigated as a function of chirality, elastic anisotropy, particle polygonal arrangement and particle size. The presence of a polygonal network made of N circular inclusions results in defect textures of a net charge of -(N-2)/2 per unit polygonal cell. As the chirality increases, the LC matrix shows the following transition sequence: weakly twisted cholesterics, 2D blue phases with non-singular/ singular defect lattices, cholesteric phases with only disclinations, and fingerprint cholesteric textures with disclinations and dislocations. For monomeric mesogens at concentrations far from the I/Ch phase transition and low chirality, for a given symmetry of the LC phase, the particle with weaker (stronger) confinement results in a phase with lower (higher) elastic energy, while at high chirality the elastic energy of a LC phase is proportional to the number of particles that form the polygonal network. Thus, hexagonal (triangular) particle arrangement results in low elastic energy at low (high) chirality. For semiflexible polymeric mesogens (high elastic anisotropy), defect textures with fewer disclinations/ dislocations arise but due to layer distortions we find a higher elastic energy than monomeric mesogens. The defects arising in the simulations and the texture rules established are in agreement with experimental observations in cellulosic liquid crystal analogues such as plant cell wall and helical biological polymeric mesophases made of DNA, PBLG and xanthan.