The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulated structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase N_TB is characterized by a heliconical structure with a pitch in the nanometric range, in agreement with experimental results. For a sample of finite thickness, we show that the wavevector of the stable periodic structure depends not only on the elastic parameters, but also on the anchoring energy, easy axis direction, and the thickness of the sample.

中文翻译：

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扭曲弯曲向列液晶的调制结构中的纳米节距

扩展的弗兰克弹性能量密度用于研究稳定的周期性调制结构的存在，该结构表现为表现出扭曲弯曲分子排列的基态。对于无界样品，我们表明扭曲弯曲向列相N _TB的特征是螺距为纳米范围的螺旋结构，与实验结果一致。对于有限厚度的样本，我们表明稳定周期结构的波矢不仅取决于弹性参数，而且还取决于锚固能量，易轴方向和样本的厚度。