Abstract
We study planar nematic equilibria on a two‐dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect‐free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral‐like equilibrium which emerges as the defect‐free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect‐free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Highlights
Nematic liquid crystals (LCs) are classic examples of partially ordered materials that combine the fluidity of liquids with the orientational order of crystalline solids [1, 2]
Nematics have generated substantial scientific interest in recent years because of their unique optical, mechanical, and rheological properties [3] and, notably, nematics form the backbone of the multibillion dollar liquid crystal display (LCD) industry
We study nematic equilibria on a 2D annulus, with strong or weak tangential anchoring, modeled in the continuum OF theoretical framework
Summary
Nematic liquid crystals (LCs) are classic examples of partially ordered materials that combine the fluidity of liquids with the orientational order of crystalline solids [1, 2]. By computing the second variation of the anisotropic OF energy and studying the resulting eigenvalue problem directly, we obtain new stability diagrams for the defect-free state in terms of δ, ρ, α, and k. Such stability diagrams can provide useful insight into the response of the defect-free state to different types of azimuthal perturbations. Our idealized model suggests that it may be energetically preferable to have boundary defects either for large δ or for moderate values of α, but never with δ = 0 (elastic isotropy) and strong anchoring
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