Elastic continuum theory: Towards understanding of the twist-bend nematic phases

Abstract

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

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

“…At first glance, q 0 should take a finite value even if j at the phase transition is null. This result agrees with the consideration of Kats and Lebedev 51 and also with one of the conclusions of Barbero et al 53 Eqn (15) takes the following form by substituting eqn (16) and reordering in powers of j:…”

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

“…One notes that there exists also an alternative description based on the analogy between one period of the N TB phase and one smectic layer [30][31][32]. In addition, phenomenological models of the N TB phase have been proposed [33,34] where the vanishing bend elastic constant is not necessary for stabilization of the corresponding modulated structure.…”

Fluctuation Modes of a Twist-Bend Nematic Liquid Crystal

“…Kats and Lebedev [19] 10 nm scale along the direction of the nematic directorn, as the twist-bend phase order parameter. Alternatively, Virga [20] and Barbero et al [21] introduce a helix axist, witĥ n ·t ¼ cos β, and analyze the elastic properties oft. Reference [21] further analyzes the uniform nematic to a twist-bend nematic transition.…”