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.

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 subphase for the temperature range that lies in between $\mathrm{Sm}\text{−}{C}_A^{*}$ and the three-layer $\mathrm{Sm}\text{−}{C}_A^{*}(1∕3)$ 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-($4^{\prime }$-dodecyloxybiphenyl-4-yl-carbonyloxy)-3-fluorobenzoate (12BIMF10). The measurements of electric-field-induced birefringence and optical rotatory power are made on $25\text{−}\mu \mathrm{m}$-thick homeotropic cells, and the characteristic reflection bands are observed in free-standing films of thicknesses ranging from $30\text{to}50\mu \mathrm{m}$. Several binary mixtures have been prepared by mixing $\left(S\right)$-12BIMF10 with $\left(S\right)$-4-(1-methylheptyloxycarbonyl)-phenyl-$4^{\prime }$-octylbiphenyl-4-carboxylate (MHPBC), and the effect of racemization of the compound on the character of the biaxial subphase (other than three and four layers) is also discussed. The results are interpreted in terms of the Emelyanenko-Osipov model [Phys. Rev. E 68, 051703 (2003)]; 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 flexoelectric) polarizations, lifting the degeneracy and producing the nonplanar structures of the subphases.

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 wavelenth. 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.

A molecular-statistical theory for the entire sequence of the chiral tilted smectic phases is derived. Uniaxial and biaxial subphases were found to be stable in different temperature ranges depending on the molecular parameters. The model of a chiral molecule possessing a strong transverse terminal dipole moment and a quadrupole moment located in the molecular core was used. Direct dispersion and electrostatic interactions (modulated by shape) between molecules located in the same or in the neighboring smectic layers are taken into account. An effective long-range interaction arises after the minimization of the free energy with respect to polarization vectors. If the molecular quadrupole moment is small, only uniaxial phases with different periodicities arise. Their periodicity may be tens and hundreds of layers $\left(\mathrm{Sm}\text{−}{C}^{*}\right)$, or approximately two layers $\left(\mathrm{Sm}\text{−}{C}_A^{*}\right)$, or several layers $\left(\mathrm{Sm}\text{−}{C}_{\alpha }^{*}\right)$. In the presence of the nonpolar biaxial ordering (in addition to polarization) there is a cap-shaped border in the phase diagram that separates $\mathrm{Sm}\text{−}{C}_A^{*}$, $\mathrm{Sm}\text{−}{C}^{*}$, and $\mathrm{Sm}\text{−}{C}_{\alpha }^{*}$. If the molecules are nonchiral, $\mathrm{Sm}\text{−}{C}_A$, $\mathrm{Sm}\text{−}C$, and the de Vries’s phases arise instead of the three phases mentioned above. If the molecular quadrupole moment is large, the left “arm” of the border breaks into two lines, and a sequence of biaxial subphases arises in the area between these two lines. Among these biaxial subphases, the one with periodicity of three smectic layers appears to be the broadest in the temperature range. In addition, the subphases with different periodicities were found to be stable in narrow temperature ranges. The long helical rotation in every biaxial subphase is calculated. It is found to change sign between the three-layer subphase and $\mathrm{Sm}\text{−}{C}^{*}$, and may diverge in the four-layer subphase if it arises. All calculations are done with help of (A)FLC Phase Diagram Plotter software developed by the first author and available at his web-page.

Mono- and bis-rhodamine derivatives appended with amino (RhB1) and imino (BRI) groups, respectively, have been designed as fluorescent sensors for Pd²⁺ions.