Texture Rules for Concentrated Filled Nematics

Abstract

Defect textures in concentrated fiber-filled polygonal networks in nematic liquid crystals are analyzed using differential geometry and computational modeling based on Landau--de Gennes theory. Micron fibers exhibit singular cores of strength -1/2 for odd polygons and escaped cores of strength -(N-2)/2 for even polygons (N: number of sides), in agreement with experiments while simulations predict singular cores of strength -1/2 in submicron fibers. The computed textures satisfy physical and topological stability rules, and the total charge inside each polygon obeys the Poincaré-Brouwer theorem.

Modeling Textural Processes during Self-Assembly of Plant-Based Chiral-Nematic Liquid Crystals

“…From Table 2, it is evident that the presence of four circular inclusions result in defect textures of a net charge of −1 as predicted by Zimmer's rule [42,43]. The number of defects nucleated decreases with increasing elastic anisotropy.…”

“…The following defects were identified: τ +1/2 , τ −1/2 , λ ( Figures 5-7). At equilibrium, the number and type of defects arising in all the simulations obeys the rule [42,43] that states that the net charge of defects nucleated in a domain confined by four circular inclusions is always −1. This observation is in accord with defect texture studies on nematic LCs with inclusions [42].…”

“…At equilibrium, the number and type of defects arising in all the simulations obeys the rule [42,43] that states that the net charge of defects nucleated in a domain confined by four circular inclusions is always −1. This observation is in accord with defect texture studies on nematic LCs with inclusions [42]. The presented textural results comply with observations on the type of dislocation cores under the effect of confinement from Grandjean-Cano cholesteric wedge experiments [41]. )…”

“…Understanding the disclination line, defect nucleation and stabilization mechanism in helicoidal plywoods can be used as a model for gaining insight into similar phenomenon in other lamellar systems, such as diblock co-polymers and SmA LCs [41]. A computational modeling study of texture formation in a nematic carbonaceous mesophase matrix with embedded circular carbon fibers, has concluded that the number and type of disclinations that arise invariably obey the experimentally observed Zimmer's rule; the disclination line strength is equal to -(N-2)/2, where N is the number of inclusions [42,43]. A Landau-de Gennes type model for defect coarsening process of the isotropic/smectic-A phase transition, has been used to simulate elementary a b dislocations, total dislocation content and defect annihilation laws for smectic disclinations has been established [44].…”

Entropic Behavior of Binary Carbonaceous Mesophases

“…Carbonaceous mesophases (CMs), first reported by Brooks and Taylor [5], are DNLC mixtures obtained from petroleum pitches and synthetic naphthalene precursors [6]. The composition, polydispersity, and molecular orientation of CMs play a significant role on the final properties of cokes [7], carbon foams, carbon/carbon composites [8], and carbon fibers [9][10][11][12]. Figure 2.…”