Structure and grating efficiency of thin cells filled by a twist-bend nematic liquid crystal.

A twist-bend nematic (N_{TB}) liquid crystalline phase spontaneously forms modulated structures on a microscale level when confined in thin planar cells. Preliminary studies showed that these cells can be used as polarization gratings. Here we present a theoretical description of the formation of a two-dimensionally modulated structure. By considering the N_{TB} phase as a pseudolayer medium, a threshold condition for the onset of a modulated structure is calculated for weak and strong boundary conditions in the case of initially bookshelf or pretilt alignment of pseudolayers. Based on the modeled structure we determine spatial variation of the optic axis and calculate properties of the transmitted diffracted light. Results of the beam propagation method (BPM) and transfer matrix method are compared and it is shown that a more complex BPM gives better agreement with experimental results, meaning that even in thin cells the diffraction of light inside the grating should not be neglected.

Thermotropic cubic and tetragonal phases made of rod-like molecules.

Systematic studies on three dimensionally ordered liquid crystalline phases of different cubic and tetragonal symmetries are presented. The structures of the phases are determined by reconstruction of the electron density distribution from the X-ray diffraction patterns. The known models for electron densities in cubic structures were used whereas a new theoretical model for the structure of the tetragonal phase, which shows good agreement with the experimentally obtained electron densities, was proposed. For the first time a continuous phase transition between three dimensional phases with tetragonal and monoclinic symmetries was observed for an optically pure compound.

Effect of a bias electric field on the structure and dielectric response of the ferroelectric smectic-A liquid crystal in thin planar cells.

The phenomenological continuum model is used to study the director structure and dielectric response of the ferroelectric smectic-A phase in thin planar cells. The frequency of the phase mode and the dielectric permittivity are calculated numerically as a function of the bias external DC electric field, cell thickness, the strength of polar surface anchoring, and the ratio between the bend and splay elastic constants. The theoretically obtained dependencies are in agreement with the recently reported experimental measurements, which show that in thin planar cells both the phase mode frequency and the dielectric permittivity decrease with increasing external bias electric field.

Polar and apolar columnar phases made of bent-core mesogens.

Structural studies of two-dimensionally ordered phases made of bent-core mesogens are presented, with the emphasis on the X-ray studies of the columnar phases built of smectic layer fragments. We present the evidence for two types of packing of layer fragments: the B1-type structures where the layers are broken into blocks arranged into the orthogonal body centered lattice and the B1rev-type structures made of slightly deformed layers, where the primitive crystallographic unit cell is in general oblique. In some cases two-dimensional structures made of bilayers are observed. Bilayers are characteristic for the general tilt phases, which possess a longitudinal polarization component, in the direction perpendicular to the smectic layer fragment. We also outline the theoretical model predicting and describing the observed structures and present a model which enables the calculation of the electron density maps from the X-ray diffraction data.

Structure studies of the nematic phase formed by bent-core molecules.

In recent years there are several reports showing that bent-core mesogenic molecules are able to form biaxial nematic phase in which molecular rotation around the long molecular axis is strongly hindered. The x-ray pattern with azimuthally split signals at low angle region of diffraction is usually given as evidence for the biaxial nematic phase. We show experimentally and theoretically that such x-ray pattern is due to the local smectic- C fluctuations ("cybotactic" groups) in the uniaxial nematic phase.

Reentrant ferroelectricity in liquid crystals.

The ferroelectric (Sm C*)-antiferroelectric (Sm C*A)-reentrant ferroelectric (re Sm C*) phase temperature sequence was observed for systems with competing synclinic-anticlinic interactions. The basic properties of this system are as follows: (i) the Sm C* phase is metastable in the temperature range of the Sm C*A; (ii) the helix handedness inverts at both Sm C*-Sm C*A and Sm C*A-re-Sm C* phase transitions; (iii) the threshold electric field that is necessary to induce synclinic ordering in the Sm C*A phase decreases near both Sm C*A-Sm C* and Sm C*A-re-Sm C* phase boundaries. All these properties are properly described by a simple Landau model that accounts for nearest neighboring layer steric interactions and quadrupolar ordering only.

Influence of an external electric field on structure in surface-stabilized smectic-C chevron cells

We use a Landau-de Gennes model to study the effect of static external electric fields on the director and layer structure and switching in surface stabilized smectic-C cells with uniform chevron structure. We consider uniform switching of the whole cell and find the threshold electric field needed to switch the director from one stable state to the other stable state. The effect of temperature and cell thickness on the value of the threshold electric field is studied. We also find the switching time as a function of the strength of the applied electric field and study the director and layer structure during the switch.