A general phenomenological description and a simple molecular model is proposed for the "discrete" flexoelectric effect in tilted smectic liquid crystal phases. This effect defines a polarization in a smectic layer induced by a difference of director orientations in the two smectic layers adjacent to it. It is shown that the "discrete" flexoelectric effect is determined by electrostatic dipole-quadrupole interaction between positionally correlated molecules located in adjacent smectic layers, while the corresponding dipole-dipole interaction is responsible for a coupling between polarization vectors in neighboring layers. It is shown that a simple phenomenological model of a ferrielectric smectic liquid crystal, which has recently been proposed in the literature, can be used to describe the whole sequence of intermediate chiral smectic C* phases with increasing periods, and to determine the nonplanar structure of each phase without additional assumptions. In this sequence the phases with three- and four-layer periodicities have the same structure, as observed in the experiment. The theory predicts also the structure of intermediate phases with longer periods that have not been studied experimentally so far. The structures of intermediate phases with periodicities of up to nine layers are presented together with the phase diagrams, and a relationship between molecular chirality and the three-dimensional structure of intermediate phases is discussed. It is considered also how the coupling between the spontaneous polarization determined by molecular chirality and the induced polarization determined by the discrete flexoelectric effect stabilizes the nonplanar structure of intermediate phases.

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A molecular theory of the helical twisting in chiral liquid crystals is developed, which provides an explanation for the experimentally observed helical sense inversion induced by a change of concentration in binary mixtures of chiral and nonchiral nematic liquid crystals. The theory also describes the sense inversion induced by a change of temperature observed in some single component nematics. The theory present is based on a simple model of a chiral rigid molecule, composed of several equivalent nonchiral sites, which are arranged in the molecule to form a chiral configuration. The macroscopic helical pitch in the chiral nematic phase, twist elastic constant, and nematic order parameters are calculated using the same molecular model. It is shown that the helical sense inversion can be determined by a large biaxiality of chiral molecules. It is also demonstrated that the biaxiality is important in determining the variation of the helical pitch with temperature and concentration.

The electric-field-induced birefringence has been investigated by using a photoelastic modulator, with a view to obtaining a molecular model for the subphases produced by the frustration between ferroelectricity and antiferroelectricity in the chiral smectic liquid crystals. It has been found that even in the bulk, there exist two subphases in the smectic-C(alpha)* (Sm-C(alpha)*) temperature range. By extending the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)] to include the temperature dependence of the tilt angle, we have alluded to a possible lifting of the degeneracy at the frustration point P(alpha) , where Sm-C(A)*, Sm-C*, and Sm-A have the same free energy. This leads to the appearance of uniaxial Sm-C(alpha)* characterized by short-pitch helical structures and consequently with a pitch much lower than the optical wavelength. The numerical calculations indicate that the short pitch may generally increase or decrease monotonically with temperature. Depending on the parameter value that represents the relative strength of ferroelectricity and antiferroelectricity, the short-pitch temperature variation may abruptly change from increase to decrease at a temperature; this can be assigned to the observed phase transition between the two Sm-C(alpha)* subphases.

Optical textures and appropriate orientational structures have been studied within droplets of chiral nematic dispersed in polymer assigning the homeotropic anchoring. The helix axis of the chiral structure inside droplets forms the bipolar configuration. The optical droplet textures were analysed in the unpolarised light, analyser switching-off scheme and in crossed polarisers. The twisted loop defect reveals itself convincingly in all schemes. Its appearance at the optical patterns of the chiral nematic droplets has been examined depending on their size and the aspect direction. The existence of the defect has been verified by the structural and optical calculations. The effect of an electric field on both the defect line shape and the orientational structure of chiral nematic has been studied.

The dependency of orientational structures in cholesteric droplets with homeotropic surface anchoring on the helicity parameter has been studied by experiment and simulations.

We consider the structure transitions in oblate supramicrometer nematic droplets related to reorientation of the line defect in the electric field. These transitions can be used in optical devices based on polymer dispersed liquid crystal materials with high contrast ratio. We suggest a simple method for determination of director distribution in nematic droplets of an arbitrary shape with surface interaction and in the presence of constant electric field. Point and linear defects are taken into account. This method does not require any presuppositions about symmetry of the director distribution. The elasticity continuum theory is treated with Monte Carlo annealing on a simple lattice. A special triangulation-based technique is applied for accurate representation of the droplet boundaries. The method is tested on 5CB material.

The subphase for the temperature range that lies in between Sm-C A * and the three-layer Sm-C A * ͑1/3͒ subphase has been confirmed to exist using the measurements of electric-field-induced birefringence, optical rotation, and the characteristic reflection bands in the antiferroelectric liquid-crystalline compound, 1-trifluoromethylundecyl-4-͑4Ј-dodecyloxybiphenyl-4-yl-carbonyloxy͒-3-fluorobenzoate ͑12BIMF10͒. The measurements of electric-field-induced birefringence and optical rotatory power are made on 25-m-thick homeotropic cells, and the characteristic reflection bands are observed in free-standing films of thicknesses ranging from 30 to 50 m. Several binary mixtures have been prepared by mixing ͑S͒-12BIMF10 with ͑S͒-4-͑1-methylheptyloxycarbonyl͒-phenyl-4Ј-octylbiphenyl-4-carboxylate ͑MHPBC͒, and the effect of racemization of the compound on the character of the biaxial subphase ͑other than three and four layers͒ is also discussed. The results are interpreted in terms of the Emelyanenko-Osipov model ͓Phys. Rev. E 68, 051703 ͑2003͔͒; the effective long-range couplings between the director orientations in separated smectic layers emerge after the minimization of free energy with respect to the total ͑ordinary spontaneous and discrete flexoelectric͒ polarizations, lifting the degeneracy and producing the nonplanar structures of the subphases.