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.Another type of asymmetry is a bent molecular shape, as occurs in dimers, trimers, and bent-core liquid crystals. 1 In the nematic phase of bent molecules, the bend flexoelectric effect is enhanced 2-4 and the bend elastic constant is reduced, because bend deformation is compatible with the molecular shape. As the temperature decreases, the bend elastic constant decreases further, and then the system has a transition from the uniform nematic phase into a modulated phase with spontaneous bend. Because it is impossible to fill space with pure uniform bend, the phase must have a more complex structure that includes another deformation mode. Normally, the system forms a twist-bend nematic (N T B ) phase, which has a heliconical structure with twist as well as bend. This phase has been investigated through many theoretical 5-13 and experimental [14][15][16][17][18][19][20] studies. An alternative theoretical possibility is a splay-bend nematic (N SB ) phase, which has a planar structure with splay as well as bend. 5,6,8 Considering that a bent molecular shape leads to spontaneous bend, one might ask whether a splayed or pear-like shape leads to spontaneous splay. This issue was considered in a theoretical