Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals

Abstract

We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second-order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase composed of twist-bend or splay-bend deformations. To test the predictions of Landau theory, we perform Monte Carlo simulations to find the director and polarization configurations as functions of temperature, applied electric field, and interaction parameters.

Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB–N phase transition

“…One of the most important concerns arises from the fact that the theory needs a drastic simplification of the number of terms and the simplified version predicts a secondorder N TB -N phase transition, which is not supported by experimental determinations. 3,6,26 In the case of flexoelectric coupling, Shamid et al 11 have considered the polar order as an additional order parameter, but again such a Landau theory needs to be simplified and the approximate solution also predicts a secondorder N TB -N phase transition. The same authors 11 proposed the definition of an effective bend elastic constant (K eff 3 ) which could be negative in the N TB phase and positive in the uniform nematic phase.…”

“…3,6,26 In the case of flexoelectric coupling, Shamid et al 11 have considered the polar order as an additional order parameter, but again such a Landau theory needs to be simplified and the approximate solution also predicts a secondorder N TB -N phase transition. The same authors 11 proposed the definition of an effective bend elastic constant (K eff 3 ) which could be negative in the N TB phase and positive in the uniform nematic phase. The problem here is that at the phase transition, K eff 3 as defined by Shamid et al, 11 tends to minus infinity and there have been no experimental indications of this possibility.…”

Twist-bend heliconical chiral nematic liquid crystal phase of an achiral rigid bent-core mesogen

“…In the N* and SmC* phases, the molecules are rod-like and chiral, while the N TB and SmCP phases can be formed by bent, achiral molecules. Due to their rigid, bent molecular shape, the flexoelectric response resulting from linear coupling between the polar order normal to the director and bend director deformations is much larger for bent-core liquid crystals than for rod-like liquid crystals [20] and this flexoelectricity 7 enhances the heliconical structure with twist and bend molecular deformation in the N TB phase [21,22]. However, in order to form the N TB phase instead of the SmCP, the tendency for layering must be weak or absent.…”

Polar interactions between bent–core molecules as a stabilising factor for inhomogeneous nematic phases with spontaneous bend deformations

“…For example, the periodic structures may contain various polarization waves [23], and one nonconventional has indeed been confirmed by simple molecular modeling [24]. Further extension of the phenomenological model [17] takes into account also the biaxial ordering in bent-core systems [25]. More general phenomenological approach is built upon an extension of the Landau-de Gennes theory [26] with a possibility of the direct transition from the isotropic to the N TB phase [27] which has recently been observed experimentally [28,29].…”

“…This, in turn, can be explained by assuming that the system is close to the virtual ferroelectric phase. Then the reduction may be determined by the negative flexoelectric [15,16] correction which is anomalously large due to pretransitional effects [17,18]. In our recent paper [18] we have calculated the flexoelectric coefficients and the effective elastic constants of bent-core nematics with transverse electric dipoles using the same molecular model and have shown how the bend elastic constant can vanish at a certain temperature.…”