Abstract
ABSTRACTWe study nematic equilibria on a square with tangent Dirichlet conditions on the edges, in three different modelling frameworks: (i) the off-lattice Hard Gaussian Overlap and Gay–Berne models; (ii) the lattice-based Lebwohl–Lasher model; and the (iii) two-dimensional Landau-de Gennes model. We compare the modelling predictions, identify regimes of agreement and in the Landau-de Gennes case, find up to 21 different equilibria. Of these, two are physically stable.
Highlights
Nematic liquid crystals (LCs) are complex anisotropic liquids that combine the fluidity of liquids with a degree of long-range orientational order characteristic of solids, that is, the constituent nematic molecules typically align along some preferred directions, referred to as directors in the literature [1,2]
We numerically demonstrate the existence of hitherto unreported Landau-de Gennes (LdG) equilibria, which have multiple interior defects and though unstable, can be of importance in transient dynamics
The ‘bend’ vertices have a larger neighbourhood of reduced order and these regions can stretch along almost a third of the domain width, or retreat to become point defects at the corners. This is in line with the diagonal solutions reported in experimental work and macroscopic LdG models for this problem [9], and we expect to see reduced order near the vertices, originating from the mismatch in molecular alignments at the vertices
Summary
Nematic liquid crystals (LCs) are complex anisotropic liquids that combine the fluidity of liquids with a degree of long-range orientational order characteristic of solids, that is, the constituent nematic molecules typically align along some preferred directions, referred to as directors in the literature [1,2]. Like most complex materials, can be modelled using both microscopic molecular-level models and continuum phenomenological models. Continuum theories, such as the Oseen– Frank theory or the Landau-de Gennes (LdG) theory, have been hugely successful for nematic LCs, especially in the context of spatially inhomogeneous confined systems. Molecular-level theories that incorporate details about the molecular shape and molecular interactions have been used to simulate spatially homogeneous systems to estimate bulk properties or transition temperatures [3,4]. As experimentalists are able to design severely confined systems, it is desirable to simulate spatially inhomogeneous systems with more detailed molecular-level models which are computationally intensive, since the validity of continuum descriptions is not clear for small systems. We model a toy confined nematic system with boundaries using three different
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