The liquid-crystal dimer 1′′,7′′-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) exhibits two liquid-crystalline mesophases on cooling from the isotropic phase. The high-temperature phase is nematic; the identification and characterization of the other liquid-crystal phase is reported in this paper. It is concluded that the low-temperature mesophase of CB7CB is a new type of uniaxial nematic phase having a nonuniform director distribution composed of twist-bend deformations. The techniques of small-angle x-ray scattering, modulated differential scanning calorimetry, and dielectric spectroscopy have been applied to establish the nature of the nematic-nematic phase transition and the structural features of the twist-bend nematic phase. In addition, magnetic resonance studies (electron-spin resonance and ${}^2$H nuclear magnetic resonance) have been used to investigate the orientational order and director distribution in the liquid-crystalline phases of CB7CB. The synthesis of a specifically deuterated sample of CB7CB is reported, and measurements showed a bifurcation of the quadrupolar splitting on entering the low-temperature mesophase from the high-temperature nematic phase. This splitting could be interpreted in terms of the chirality of the twist-bend structure of the director. Calculations using an atomistic model and the surface interaction potential with Monte Carlo sampling have been carried out to determine the conformational distribution and predict dielectric and elastic properties in the nematic phase. The former are in agreement with experimental measurements, while the latter are consistent with the formation of a twist-bend nematic phase.

When a chiral dopant is dissolved in an achiral liquid crystal medium, the whole sample organizes into a helical structure with a characteristic length-scale of the order of microns. The relation between chirality at these quite different length-scales can be rationalized by a relatively simple model, which retains the relevant factors coming into play: the molecular shape of the chiral dopant, which controls the chirality of short range intermolecular interactions, and the elastic properties of the nematic environment, which control the restoring torques opposing distortion of the director. In this tutorial review the relation between molecular and phase chirality will be reviewed and several applications of the chiral doping of nematic LCs will be discussed. These range from the exploitation of the amplified molecular chirality for stereochemical purposes (e.g., the determination of the absolute configuration or the enantiomeric excess), to newer applications in physico–chemical fields. The latter take advantage of the periodicity of the chiral field, with length-scales ranging from hundreds to thousands of nanometres, which characterise the cholesteric phase.

The synthesis and characterisation of the nonsymmetric liquid crystal dimer, 1-(4-cyanobiphenyl-4′-yloxy)-6-(4-cyanobiphenyl-4′-yl)hexane (CB6OCB) is reported. An enantiotropic nematic (N)–twist-bend nematic (N_TB) phase transition is observed at 109 °C and a nematic–isotropic phase transition at 153 °C. The N_TB phase assignment has been confirmed using polarised light microscopy, freeze fracture transmission electron microscopy (FFTEM), ²H-NMR spectroscopy, and X-ray diffraction. The effective molecular length in both the N_TB and N phases indicates a locally intercalated arrangement of the molecules, and the helicoidal pitch length in the N_TB phase is estimated to be 8.9 nm. The surface anchoring properties of CB6OCB on a number of aligning layers is reported. A Landau model is applied to describe high-resolution heat capacity measurements in the vicinity of the N_TB–N phase transition. Both the theory and heat capacity measurements agree with a very weak first-order phase transition. A complementary extended molecular field theory was found to be in suggestive accord with the ²H-NMR studies of CB6OCB-d₂, and those already known for CB7CB-d₄. These include the reduced transition temperature, T N_TBN /T_NI, the order parameter of the mesogenic arms in the N phase close to the N_TB–N transition, and the order parameter with respect to the helix axis which is related to the conical angle for the N_TB phase.

The helical organization of cholesteric liquid crystals is omnipresent in living matter. Achieving control over the structure of the cholesteric helix consequently holds great potential for developing stimuli-responsive materials matching the level of sophistication of biological systems. In particular, inversion of a cholesteric helix is associated with inversion of the circular polarization of the light it reflects. While control over the cholesteric period has been thoroughly investigated, reports on helix inversion are scarcer. Predicting which systems display helix inversion also remains a challenge because of the subtle balance of contributions underlying this phenomenon. Here we provide an overview on recent advances in controlling and understanding helix inversion in cholesteric liquid crystals.

It has been found that bent-shaped achiral molecules can form a liquid crystal phase, called the Twist-Bend Nematic (N_TB), which is locally polar and spontaneously twisted having a tilted director, with a conglomerate of degenerate chiral domains with opposite handedness and pitch of a few molecular lengths. Here, using a major extension of the Maier–Saupe molecular field theory, we can describe the transition from the nematic (N) to the N_TB phase. We provide a consistent picture of the structural and elastic properties in the two phases, as a function of the molecular bend angle, and show that on approaching the transition there is a gradual softening of the bend mode in the N phase. This points to the crucial role of the molecular shape for the formation of modulated nematic phases and their behaviour.

An explicit form for the orientating potential acting in uniaxial liquid crystal phases is derived, by analogy with the surface anchoring potential which determines the orientation of macroscopic anisometric particles. The surface of a molecule is determined by describing the molecule as an assembly of van der Waals spheres. The model is successfully applied to predict the ordering tensors for a variety of systems, namely, solutions in nematic solvents of small and rigid probes, or relatively long n-alkanes with many degrees of internal freedom, and pure nematogens formed by aromatic cores attached to flexible chains.