Theory of the splay nematic phase: Single vs. double splay

Recent experiments have reported a novel splay nematic phase, which has alternating domains of positive and negative splay. To model this phase, previous studies have considered a 1D splay modulation of the director field, accompanied by a 1D modulation of polar order. When the flexoelectric coupling between splay and polar order becomes sufficiently strong, the uniform nematic state becomes unstable to the formation of a modulated phase. Here, we re-examine this theory in terms of a new approach to liquid crystal elasticity, which shows that pure splay deformation is double splay rather than planar single splay. Following that reasoning, we propose a structure with a 2D splay modulation of the director field, accompanied by a 2D modulation of polar order, and show that the 2D structure generally has a lower free energy than the 1D structure.

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