Multistable nematic wells: modelling perspectives, recent results and new directions

Abstract

This review article is a consolidated but not exhaustive account of recent modelling and numerical work on nematic-filled square or cuboid shaped wells with planar degenerate boundary conditions. This seemingly simple geometry can be modelled with a simplistic Oseen-Frank approach or a more sophisticated twodimensional and three-dimensional Landau-de Gennes approach. We discuss these approaches, reconcile the findings and in doing so, elucidate the complex interplay between material properties, temperature, geometry and boundary conditions in both equilibrium and non-equilibrium phenomena. We largely focus on static equilibria with some discussion on metastable or transient states of experimental relevance.

Tailored morphologies in two-dimensional ferronematic wells

“…This reduced 2D approach can be rigorously justified for severely confined systems where the height of the system is much smaller than the cross-sectional dimensions [12]. By analogy with the experimental work reported in [8], we assume tangent boundary conditions for the NLC (also see [13][14][15] for experimental methods) which requires that on the square edges, the NLC directors are tangent to the edges. Further, we assume that the MNPs can be treated so that their magnetic moments align with the nematic director on the square edges.…”

“…Further, we assume that the MNPs can be treated so that their magnetic moments align with the nematic director on the square edges. We build on the phenomenological approach in [15] and model the observed spatial patterns as minimizers of an appropriately defined free energy, that contains a magneto-nematic coupling energy. Mathematically, this is equivalent to solving a coupled system of nonlinear partial differential equations, and the coupling term introduces new mathematical difficulties.…”

Electrically Tuneable Optical Diffraction Gratings Based on a Polymer Scaffold Filled with a Nematic Liquid Crystal

“…Other interesting challenges are 2D and 3D LC-polymer-based diffractive structures. Based on preliminary experiments with 2D LC-polymer gratings [ 81 , 82 , 83 , 84 ], which allow multistable LC orientational profiles within a unit cell, it is necessary to construct an RCWA-based model to simulate the diffraction properties of such structures. This will enable precise identification and mapping of (meta)stable LC configurations within polymeric square wells.…”

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

“…The most prominent type of ordering, which is typically found in liquid crystals, is orientational (nematic) ordering, where the characteristically shaped subunits, i.e, molecules or colloidal particles in close proximity, show a tendency to align. If this preferred order gets frustrated, e.g., by confinement to a finite container [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], constraining on a surface [50][51][52][53][54][55][56][57] or insertion of obstacles [58][59][60][61][62][63][64][65][66][67], topological defects emerge, which are discontinuities in the ordered structures that can display particlelike properties themselves [6,16,[68][69][70]. * Rene.Wittmann@hhu.de FIG.…”