Defect textures in polygonal arrangements of cylindrical inclusions in cholesteric liquid crystal matrices

Abstract

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 (monomeric and polymeric mesogens), 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, in accordance with Zimmer's rule. 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 finally 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. A semi-quantitative phase diagram that shows different LC phase and defect textures as a function of chirality and elastic anisotropy is obtained. The inclusion of particles has a stabilizing effect on the LC phases, as they occupy λ +1 disclination cores, thereby reducing the free energy cost associated with these disclinations. The findings provide a comprehensive set of trends and mechanisms that contribute to the evolving understanding of biological plywoods and serve as a platform for future biomimetic applications.

Self-assembly Mechanisms in Plant Cell Wall Components

“…This measured value of elastic anisotropy agrees well with experimental measurements of elastic constants in biopolymeric mesophase of PBLG (in vitro) [65] and is further supported by bending and twisting costs estimated based on a continuum model for hexogonally packed chiral fi lament assemblies based on the Frank-Oseen formalism of LCs [66]. The defect textures predicted by the model obeys Zummer's rule that relates the net topological charge in a LC system with N secondary inclusions: -(N-2)/2 = -1 as observed in natural [54,55] and synthetic fi lled LCs [67]. The present model can be extended to explore other biologically relevant features of plywoods such as surface melting [21].…”

“…Periodic relief arising at the free surface of a helicoidal plywood in some fl owers' petals, and beetle exocuticle surfaces that play a key role in the iridescence of these structures, have been simulated using a mathematical model based on chiral self-assembly with air-surface interface driven by chiral capillarity [53]. This review article emphasizes the capability of theory and simulations based on anisotropic soft matter models [54][55][56][57][58] to yield testable and verifi able predictions of textural and rheological phenomena observed in real plant cell walls, in an attempt to verify the LC self-assembly model for plant cell wall synthesis and highlight the versatility of these models to simulate other biological/biomimetic systems. For an extensive review on mesoscopic models employed to quantitatively describe the structures and processes in biological systems, refer to [31,59].…”

“…The x mark indicates λ -1 disclination seen in Figure 6(b); (b) Cholesteric fi ngerprint texture at high elastic anisotropy υ=21, ξ/p 0 =0.05, N=4 (at steady state). The circled region encompasses Lehmann cluster, a quadrupolar defect interaction observed in in vitro DNA self-assembly [55]. (Adapted from ref.…”

“…(Adapted from ref. [55]) embedded fi bers, a theoretical model based on continuum elasticity theory for anisotropic membrane inclusions in lipid membranes was developed [74].…”

Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation

“…Topological defects appear in several systems that present some kind of ordering [12][13][14][15][16][17]. Alloys [18], semiconductors [19], polymers [20] and liquid crystals [21,22] are just a few examples. In particular, optical textures of liquid crystals [23][24][25] are known to be an excellent system for studying the dynamical behavior of defects.…”