Twist-bend nematic phase from Landau-de Gennes perspective

The understanding of self-organization in the twist-bend nematic $(N_\text{TB})$ phase, identified in 2011 in liquid crystal dimers, is at the forefront of soft matter research worldwide. This new nematic phase develops structural chirality in the isotropic $(I)$ and the uniaxial nematic $(N_\text{U})$ phases, despite the fact that the molecules forming the structure are chemically achiral. Molecular, shape-induced flexopolarization provides a viable mechanism for a qualitative understanding of $N_\text{TB}$ and the related phase transitions. The key question that remains is whether with this mechanism one can also explain quantitatively the presently existing experimental data. To address this issue we propose a generalization of the mesoscopic Landau-de Gennes theory of nematics, where higher-order elastic terms of the alignment tensor are taken into account, in addition to the lowest-order flexopolarization coupling. The theory is not only capable of explaining the appearance of $N_\text{TB}$ but also stays in quantitative agreement with experimental data. In exemplary calculations, we take the data known for CB7CB flexible dimer - the "drosophila fly" in the studies of $N_\text{TB}$ [A. J\'{a}kli et al., Rev. Mod. Phys. 90, 045004 (2018)] - and estimate the constitutive parameters of the model from temperature variation of the nematic order parameter and the Frank elastic constants in the nematic phase. Then we seek for relative stability and properties of the isotropic, uniaxial nematic and twist-bend nematic phases. In particular, we evaluate various properties of $N_\text{TB}$, like temperature variation of the structure's wave vector, conical angle, flexopolarization, and remaining order parameters. We also look into the fine structure of $N_\text{TB}$, like its biaxiality - the property, which is difficult to access experimentally at the nanoscale.