The recently discovered twist-bend nematic phase of achiral bent-shaped molecules, N_TB, has a doubly degenerate ground-state with a periodically modulated heliconical structure and unusual distortion elasticity, the theoretical description of which is still debated. We show that the N_TB phase has the same macroscopic symmetry as another periodic mesophase, the chiral smectic-A, SmA*. Based on this N_TB/SmA* analogy, we develop a coarse-grained elastic model for the N_TB phase. Adopting one of the existing microscopic N_TB elastic models, we calculate the coarse-grained elastic constants, coherence and penetration lengths in terms of a few Frank-like nematic elastic coefficients that can be measured in macroscopic experiments. The same coarse-grained approach, applied to different local elastic models, may provide an efficient experimental test of their validity. We show that the anisotropy of the N_TB coarse-grained elasticity is opposite to that of the SmA*, leading probably to different configurations of some of the defects of the “layered” N_TB structure. Moreover, we argue that the intrinsic chiral frustration of the N_TB phase may be resolved by penetration of the twist field into the bulk through a network of screw dislocations of the N_TB pseudo-layers, resulting in a twist-bend analogue of the twist grain boundary phase TGB_A.

We investigate two different textures of smectic A liquid crystals. These textures are particularly symmetric when they are observed at crossed polars optical microscopy. For both textures, a model has been made in order to examine the link between the defective macroscopic texture and the microscopic disposition of the layers. We present in particular in the case of some hexagonal tiling of circles (similar to the Apollonius tiling) some numeric simulation in order to visualize the smectic layers. We discuss of the nature of the smectic layers, which permit to assure their continuity from one focal conic domain to another adjacent one.

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

The recently discovered twist-bend nematic phase, N_TB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the N_TB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the N_TB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the N_TB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the N_TB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the N_TB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the N_TB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.

There are two categories of helical line defects in Sm-A phases: screw dislocations of small Burgers vectors and double helices (DHs), whose macroscopic configuration constitutes a mode of splitting of screw dislocations of giant Burgers vectors. Their counterparts in Sm-A$\ast${}'s (Sm-A's with chiral molecules) show a number of differences with the former and are investigated theoretically on the basis of recent observations [C. Meyer et al., Liq. Cryst. 37, 1047 (2010)]. The first part of the paper is a short review of the main features of helical defects in Sm-A's proper. In Sm-A$\ast${}'s, small Burgers vector screw dislocations with the same chirality as the high-temperature N$\ast${} phase are favored over the opposite ones, a result that is related to the defect core singularity. This is also true for the macroscopic DH$\ast${}s for a more subtle reason; we advance that the DH$\ast${} nucleation at the N$\ast${}$\rightarrow${}Sm-A$\ast${} transition stems from a peculiar texture of the cybotactic groups, akin in the ideal case to a set of two twisted $\chi${} disclinations in the N$\ast${} phase, linked by a stacking fault of continuous disclinations. This stacking fault vanishes in the Sm-A$\ast${} phase, and one recovers a DH$\ast${} much similar to a DH but with the appropriate chirality. Cases that differ from ideality are described: they involve small Burgers vector screw dislocations and can be evoked to explain the numerous observed distorted double helices (the Darboux condition is not obeyed) and twisted ribbons. The case when the N$\ast${}$\rightarrow${}Sm-A$\ast${} transition is type II (presence of a twist grain boundary phase in between) is briefly discussed.

We have analysed optical microscopy observations of focal conic domains (FCDs) with imperfect ellipses on the basis of the theoretical concepts developed by Kleman et al. (Philos. Mag. 2006, 86, 4439). Two types of imperfect ellipses are observed: with kinks (elementary imperfections resulting from a topological interaction of a disclination with a dislocation, at their point of junction) being either in the ellipse plane (‘mouse’) or perpendicular to it (‘turtle’). The experimental conditions for the observation of imperfect FCDs of both types are described. A model describing the shape of a mouse‐type ellipse is compared with observations. Two experimental observations in nematogenic smectics (i.e. which have a smectic → nematic transition) emphasise the predominant role of kinks in dynamical phenomena involving dislocations and FCDs: (i) a reversible and sudden temperature‐induced transformation between two FCD textures, i.e. FCDs with fewer kink‐carrying distortions (called isometric textures) and the higher temperature FCDs with a proliferation of kinks (called non‐isometric); (ii) a shrinking of the ellipses upon heating, up to their sudden and total disappearance at a temperature well below the phase transition. In contrast, in a non‐nematogenic smectic, the ellipse size does not vary upon heating until the appearance of the isotropic phase.