Ferrielectricity in smectic-C

Recent experiments probing a new ferroelectric liquid crystal (CLF08) confined in cells with planar alignment have shown dielectric and optic anomalies suggesting the onset of ferrielectric ordering within the surface lattice of dechiralization lines. We present a phenomenological theory describing the corresponding phase transition sequence SmA→SmC^{*}→Ferri. Phase diagrams and thermodynamic, dielectric, and optic properties are worked out and compared with experiments. The anomalies are related to the predicted tristability of the experimental cells under applied electric field. The order parameters of Landau theory are reinterpreted in terms of line positions, allowing description of the entrance and exit line behavior, and yielding the prediction and identification of new limit phases within a nonconventional Landau approach.

Directional magnetoelectric effects in MnWO4: magnetic sources of the electric polarization.

The ferroelectric order and magnetic field induced effects observed in the spiral phase of MnWO4 are described theoretically. It is demonstrated explicitly that the Dzyaloshinskii-Moriya antisymmetric interactions contribute to the correlation between spins and electric dipoles in the incommensurate and commensurate ferroelectric phases of magnetic multiferroics. However, other single-site symmetric interactions are shown to be involved in the magnetoelectric process, suggesting the possible existence of an electric polarization originating from purely symmetric effects.

Theory of two- and three-dimensional bent-core mesophases.

An extension of the vector-wave theory of antiferroelectric bent-core liquid crystals to columnar and soft-crystalline mesophases is presented. We enumerate and describe the phases resulting from the condensation of one, two, and three vector waves in the isotropic liquid of bent-core molecules. Beside the one-dimensional B2 and smectic- CP phases, 24 columnar and soft-crystalline orthorhombic, monoclinic, and triclinic phases can be stabilized when two or three waves have nonparallel wave vectors. Their symmetry groups, molecular arrangements, and phase diagrams are worked out and used to identify the structures of the main observed bent-core phases and their various subphases.

Macroscopic and molecular symmetries of unconventional nematic phases.

The effects of the molecular symmetry on macroscopic properties of conventional and unconventional nematic phases are investigated theoretically. These effects concern: (1) the form of the molecular orientation fluctuations, (2) the thermodynamic behavior and the list of stable ordered phases, (3) the effective symmetry of the molecules in the ordered phases. The order-parameter consists of tensors forming the main harmonics of the fluctuation distribution. In conventional models (valid for uniaxial molecules) a single tensor is sufficient while unconventional models (valid for less symmetric molecules) need several tensors with the same rank. We analyze the qualitative differences arising when the number of equivalent tensors varies. We show how to work out complete models in the general case, and to calculate the sequences of stable phases and the corresponding effective molecular symmetries. This yields, for each molecular group and each tensor rank, a complete classification and a deep insight into the structure of thermotropic nematics. This work generalizes the approach we have applied to polar nematics recently observed in polyester compounds and to unconventional uniaxial and biaxial phases of bent-core materials.

Theory of the cooperative evaporation of volatile droplets.

A theoretical approach to the cooperative process of evaporation of volatile liquid droplet arrays is proposed which combines the equation of the liquid-gas interface with a Landau-type description. The spatial and temporal behaviors of the process are shown to be governed by the spontaneous symmetry breaking mechanism of a parent droplet configuration. The applicability of the approach is illustrated by the theoretical description of recent experiments in closed and open systems.

Theory of uniaxial and biaxial nematic phases in bent-core systems.

We present a phenomenological theory of the uniaxial and biaxial nematic phases recently observed in bent-core mesogenic systems. To take into account the molecular anisotropy we introduce two types of symmetry transformation: "external" rotations which turn the molecules with respect to the laboratory axes and "internal" rotations which turn them with respect to the molecular axes. We show then that the description of bent-core nematic phases involves two isomorphic copies of the conventional tensor order parameter instead of one for conventional rod like and disk like molecules. The second tensor stabilizes additional monoclinic and triclinic phases and merges the calamitic and diskotic uniaxial states into a single phase. The uniaxial and biaxial phases can appear, respectively, in six and 21 distinct configurations according to the molecular axis that dominates the ordering process. We predict a number of isostructural transitions between these configurations within a thermodynamic Landau-type approach. Because bent-core molecules have the same microscopic behavior as orthorhombic micelles, the biaxial phase can be stabilized in both systems.

Theory of chiral periodic mesophases formed from an achiral liquid of bent-core molecules.

The theory of unconventional one-dimensional periodic mesophases forming in a liquid of achiral bent-core molecules is presented. The order parameter is a polarization wave. Three distinct phases which can be stabilized directly from the isotropic liquid phase are associated with linear, circular, and elliptic polarizations of the wave. The elliptic polarization leads to the structure of the commonly studied B2 "bent-core" mesophase whereas the recently discovered C(p) phase may be assigned to the linear polarization. We present the molecular configurations and macroscopic properties of the stable states. Their behavior under chiral doping and electric field application are investigated and the corresponding phase diagrams are calculated.

Theory of the incommensurate smectic-A phases in dimesogenic liquid crystals.

A mechanism assuming a mismatch between the basic smectic periodicity and the amplitude and phase modulations periods of the mass density wave order parameter is proposed, for describing the incommensurate smectic-A structure found in dimesogenic liquid crystals. The different sequences of phases found in this family of compounds are described theoretically.

Theory of the anticlinic pretilted surface phase in tilted chiral smectic films.

In freely suspended chiral smectic films, the molecules tilt at the surfaces above the bulk ferroelectric transition temperature. The tilt angle at the two surfaces can be either equal (synclinic surface phase) or opposite (anticlinic surface phase) on each surface of the film. We propose a realistic theoretical model accounting for the stability and properties of these two structures, based on competing surface interactions. The anticlinic phase is stable for sufficiently thin samples and high temperatures. We predict a reentrant SmA phase merging with the surface phases at a three-phase point.