Deformations induced by the electric field parallel to the heliconical axis of twist-bend nematics: theoretical analysis within various elasticity models

This paper is devoted to the director deformations which occur in twist-bend nematics (NTB) affected by the electric field parallel to the heliconical axis. The analysis is chiefly based on the results of numerical calculations which are performed within three elasticity theories, namely those developed by Dozov, Barbero and Shamid. It has been revealed how the pitch and the heliconical angle of the NTB structure depend on the electric field intensity and the values of material parameters. All the models considered indicate that the transition from a twist-bend nematic to an ordinary nematic is theoretically possible when the electric field is strong enough and reaches a threshold value Eth. The dependence of Eth on the material parameters has been investigated. The formulae for Eth have been derived wherever possible. The effects predicted by Dozov’s and Barbero’s theories result from the dielectric anisotropy of a liquid crystal. The mechanism of the distortions in Shamid’s model is different and therefore it has become a subject of discussion presented in this article. Finally, the additional contribution has been introduced to Shamid’s formula for the free energy density in order to include the phenomena related to the dielectric anisotropy of a twist-bend nematic.