Statistical theory of flexoelectric effect in ferroelectric liquid crystals

•Ions create flexoelectric contribution into ferroelectric liquid crystals.•Molecular statistical approach reveals the induced dipole moment.•Landau approach explores the flexoelectric contribution created by the ions.•Helical stability of the phase is also confirmed by the ions.

The presence of impurity ions in a ferroelectric liquid crystal produces significant modulation in its polarization profile. We investigate this modulation both by a molecular statistical approach and by a suitable Landau–Ginzburg type free energy model. The molecular statistical approach predicts a value of the induced dipole moment into a host chiral mesogen by the electric field of the ions. The Landau–Ginzburg (LG) approach is based mainly on the flexoelectric effect that is generated by the ions through their electric field. The LG model captures the flexoelectric part of the polarization created by the distortion of the nematic director through the electric field of the ions. Then, the conditions of the helical stability of the chiral state are also investigated in the presence of ionic distortion of the nematic field in a ferroelectric medium.