Statistical mechanics of the flexoelectric effect in nematic liquid crystals

Flexoelectricity is the phenomenon in which polarization is induced by imposed deformations of the director field in nematic liquid crystals. Recent experiments [1,2] have found that the flexoelectric effect is three orders of magnitude greater for bent-core liquid crystals than for conventional rod-like liquid crystals. To understand this experimental result, we develop a lattice model for the statistical mechanics of the flexoelectric effect. We perform Monte Carlo simulations and mean-field calculations to find the behavior as a function of interaction parameters, temperature, and applied electric field. The resulting phase diagram has four phases: isotropic, uniaxial nematic, biaxial nematic, and polar. In the uniaxial and biaxial nematic phases, there is a large splay or bend flexoelectric effect, which diverges as the system approaches the nematic-polar transition. This model may explain the large bend flexoelectric coefficient observed in bent-core liquid crystals, which have a tendency toward polar order. [1] J. Harden, B. Mbanga, N. Eber, K. Fodor-Csorba, S. Sprunt, J. T. Gleeson, and A. Jakli, Phys. Rev. Lett. 97,157802 (2006). [2] J. Harden, R. Teeling, J. T. Gleeson, S. Sprunt, and A.Jakli, Phys. Rev. E 78, 031702 (2008).