Unconventional Mesophases Formed by Condensed Vector Waves in a Medium of Achiral Molecules

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

“…Later the same idea was pursued by Lorman and Mettout, 9 who proposed a theoretical Landau model based on local ferroelectric polarisation for the nematic-nematic transition, 10 which was further developed by others. 11,12 In 2001, Dozov 13 developed a purely elastic Landau theoretical model for achiral bent-core molecules in which elastic distortions induce local spontaneous bend in the nematic director, resulting in structural deviation from the uniformlyaligned nematic phase.…”

Dual Symmetry in Bent-Core Liquid Crystals and Unconventional Superconductors

“…The bent-core theory exhibits a quite remarkable analogy [7] with the theory of d-wave superconductors in 2D systems [15], such as high-T c lamellar superconductors or unconventional superfluid films. This analogy relies upon the fact that the two theories have the same "image group" [16], that is, the same set of matrices associated with the symmetries of the parent, isotropic or normal, phases.…”

“…Despite many attempts to describe these phases with acrobatic combinations of classical order parameters [3][4][5][6], smectic density waves, polarization, and tilt vectors, a simpler and more elegant description involving a single vector-wave order parameter [7,8] seems to us necessary to account of the available experimental data [7][8][9]. In particular, from the thermodynamical point of view OPEN ACCESS the fact that a direct transition occurs commonly between the isotropic liquid and the ordered phases is much more likely when a single order parameter is involved.…”

“…In particular, from the thermodynamical point of view OPEN ACCESS the fact that a direct transition occurs commonly between the isotropic liquid and the ordered phases is much more likely when a single order parameter is involved. This permits us to predict the structure of the stable phases together with their thermodynamical behaviour [7,8], and more specifically the behaviour of several important physical tensors describing, for instance, the biaxiality, electro-optic response and chirality of the predicted structures. In addition, we have successfully extended our model to almost all observed bi-dimensionally and tri-dimensionally ordered bent-core phases [9].…”

“…We have shown in Refs. [7,8] that this model permits to foresee the stabilization of four ordered phases, denoted by C, R, and EL corresponding, respectively, to linear, circular and elliptic polarizations of the order-parameter wave. R describes the smectic C P phase predicted in 1992 [10] and then observed in bent-core systems [10,11], EL describes the commonly observed B2 phase [12,13], and we have proposed that C is an unmodulated approximation of the intriguing B7 phase found in 1999 [2].…”