Flexoelectric instability in bent-core nematic liquid crystals

We develop a theoretical model for the flexoelectric instability in bent-core nematic liquid crystals, focusing on the coupling between elastic distortions and an external electric field through flexoelectric polarization. The analysis is carried out in the nematic phase close to the twist-bend transition, where both the flexoelectric coefficients and the effective bend elastic constant exhibit strong temperature dependence. Within a Landau–de Gennes framework, we derive analytical expressions for the threshold electric field and the corresponding wave vector of the emerging periodic modulation by minimizing the total free energy and assuming K1=K2. Numerical simulations illustrate the temperature dependence of the threshold parameters and the role of dielectric anisotropy and elastic constants. The results indicate that the flexoelectric instability may occur only within a finite temperature interval above the transition into the twist-bend phase and that both the threshold electric field and the periodic structure’s wave vector decrease as the temperature decreases.