Elastic properties in the nematic phase of a ferroelectric nematic liquid crystal with flexoelectric contributions

The liquid crystalline ferroelectric nematic (N_F) phase is well known for its distinctive physical and electrical properties, namely the bulk polarity. It is therefore important to consider whether the nematic bulk properties are affected by very highly polar molecules and underlying polar phases. In this paper, we present a detailed temperature-dependence of the splay (K₁₁) and bend (K₃₃) elastic constants, and the Fréedericksz threshold voltage for a positive dielectric anisotropy LC mixture exhibiting both non-polar (N) and polar (N_F) nematic phases, and include theoretical discussions. Such properties are compared to those of two conventional nematic liquid crystals (NLCs). In the N_F LC mixture, we show a marked reduction in the splay elastic constant (1.8-0.5 pN) and the threshold voltage (150-35 mV), across the nematic phase, at temperatures much lower than the nematic to isotropic transition. The values for K₁₁ and V_th linearly extrapolate to 0 pN and 0 V respectively, at the nematic to the intermediate nematic (N_X) phase transition. Such reduction in the splay elastic constant, which is a deviation from conventional nematic behaviour, is attributed to flexoelectric coupling becoming significant at these temperatures. Corrections with temperature dependent flexoelectric coupling for the elastic constants, dielectric permittivity, and Fréedericksz threshold voltage, are discussed in detail.