  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.
