We report precise birefringence measurements in the nematic, N, and in the twist-bend nematic, N_TB, phases of the odd liquid crystal dimer CB7CB. The birefringence results obtained in large monodomains of the N_TB phase strongly support its heliconical structure with doubly degenerate handedness and provide the temperature dependence of the conical tilt angle, θ. The birefringence measured in planar wall defects separating the monodomains with opposite sign of the chirality suggests a splay-bend structure of the nematic in this region, enabling a smooth transition between the adjacent right- and left-handed heliconical domains.

An electric field–induced, symmetry-breaking, transition from N _TB to N _SB nematics reveals the importance of local biaxiality.

We measure the azimuthal anchoring strength and easy axis gliding of the nematic 5CB on weakly anisotropic substrate. We study the anchoring evolution at a time scale ranging from a few minutes up to a few months. We separate approximately the elastic and the viscous response and we obtain the gliding velocity as a function of the applied torque. We discuss the observed gliding times and nonlinear gliding viscosity.

The twist-bend nematic, N_TB, has unusual elastic properties. Contrary to the usual nematic, the N_TB director n is spontaneously distorted, resulting in a heliconical structure with small period and doubly degenerate handedness. Different models have been proposed so far, and are still actively debated, to describe the N_TB properties on the microscopic scale. On the macroscopic scale, we propose a symmetry-based analogy between the N_TB and the SmA* phases. Introducing a complex order parameter, we write the macroscopic N_TB energy by analogy with the de Gennes’ SmA* description. By coarse graining, based on the elastic-instability local model, we calculate the macroscopic elastic constants and characteristic lengths in terms of a few Frank-like elastic coefficients. We discuss the inverse elastic anisotropy of the N_TB phase, compared with the SmA*, and its impact on the structure of the N_TB defects. We extend the coarse-grained (CG) model to investigate the macroscopic response to electric fields, and the surface anchoring alignment and the microscopic distortions of the N_TB phase. Finally, we suggest the existence of a N_TB analogue of the twist grain boundary phase TGB_A, with a penetration of the twist field in the bulk through a network of screw dislocations of the N_TB pseudo-layers. GRAPHICAL ABSTRACT

Stimulated by the paper that precedes this, our aim is to correct an error made concerning the twist-bend nematic phase and to place its development, both theoretical and experimental, in their proper context. The prediction starts with R.B.Meyer in 1973 but then jumps to 2001 and a different direction with I. Dozov and to 2002 with R. Memmer. There was then a gap until 2011 when a team of thirteen European scientists, while studying a liquid crystal dimer formed from achiral bent molecules, identified a nematic phase as the missing twist-bend nematic. This was based on a detailed study of its defining characteristics such as the chirality of the phase and its helicoidal structure with its degenerate handedness. This discovery proved to be of considerable interest and has prompted numerous investigations resulting in the discovery of many other mesogens forming the twist-bend nematic phase. However, as we shall see this view has not been universally shared; indeed, amongst others, Samulski, Vanakaras and Photinos claim that cyanobiphenyl mesogens instead of producing the N_TB nematic, form the polar twisted phase, N_PT so that the twist-bend nematic has yet to be discovered. It is this error that we shall correct.The Doubly Degenerate Heliconical Structure The Doubly Degenerate Heliconical Structure

Nematic twist-bend phases (N_TB) are new types of nematic liquid crystalline phases with attractive properties for future electro-optic applications. However, most of these states are monotropic or are stable only in a narrow high temperature range. They are often destabilized under moderate cooling, and only a few single compounds have shown to give room temperature N_TB phases. Mixtures of twist-bend nematic liquid crystals with simple nematogens have shown to strongly lower the nematic to N_TB phase transition temperature. Here, we examined the behaviour of new types of mixtures with the dimeric liquid crystal [4′,4′-(heptane-1,7-diyl)bis(([1′,1″-biphenyl]4″-carbo-nitrile))] (CB7CB). This now well-known twist-bend nematic liquid crystal presents a nematic twist-bend phase below T ≈ 104 °C. Mixtures with other monomeric alkyl or alkoxy -biphenylcarbonitriles liquid crystals that display a smectic A (SmA) phase also strongly reduce this temperature. The most interesting smectogen is 4′-Octyl-4-biphenylcarbonitrile (8CB), for which a long-term metastable N_TB phase is found at room and lower temperatures. This paper presents the complete phase diagram of the corresponding binary system and a detailed investigation of its thermal, optical, dielectric, and elastic properties.