Theory for the evolution of ferroelectric, antiferroelectric, and ferrielectric smectic phases in the electric field

Transformation of polar nematic phases in the presence of an electric field

Only a few years have passed since the discovery of polar nematics, and now they are becoming the most actively studied liquid-crystal materials. Despite numerous breakthrough findings made recently, a theoretical systematization is still lacking. In the present paper, we take a step toward systematization. The powerful technique of molecular-statistical physics has been applied to an assembly of polar molecules influenced by electric field. Three polar nematic phases were found to be stable at various conditions: the double-splay ferroelectric nematic N_{F}^{2D} (observed in the lower-temperature range in the absence of or at low electric field), the double-splay antiferroelectric nematic N_{AF} (observed at intermediate temperature in the absence of or at low electric field), and the single-splay ferroelectric nematic N_{F}^{1D} (observed at moderate electric field at any temperature below transition into paraelectric nematic N and in the higher-temperature range (also below N) at low electric field or without it. A paradoxical transition from N_{F}^{1D} to N induced by application of higher electric field has been found and explained. A transformation of the structure of polar nematic phases at the application of electric field has also been investigated by Monte Carlo simulations and experimentally by observation of polarizing optical microscope images. In particular, it has been realized that, at planar anchoring, N_{AF} in the presence of a moderate out-of-plane electric field exhibits twofold splay modulation: antiferroelectric in the plane of the substrate and ferroelectric in the plane normal to the substrate. Several additional subtransitions related to fitting the confined geometry of the cell by the structure of polar phases were detected.

Emergence of paraelectric, improper antiferroelectric, and proper ferroelectric nematic phases in a liquid crystal composed of polar molecules

We have elaborated a theoretical approach for the description of polar nematic phases observed by Nishikawa et al. [Adv. Mater. 29, 1702354 (2017)0935-964810.1002/adma.201702354], their structures, and transitions between them. Specific symmetry contributions to the pair molecular potentials provide the molecular mechanisms responsible for the formation of proper and improper polarity on the macroscopic level. An improper antiferroelectric nematic M2 phase can arise between paraelectric nematic M1 and proper ferroelectric nematic MP in the temperature scale. The local polarization in M2 arises mostly due to the local splay deformation. The director distribution in M2 represents the conjugation of cylindrical waves with opposite splay and polarization signs. The director and polarization are parallel to the cylindrical domain axes in the middle of each cylinder but exhibit considerable (mostly radial) deformation on the periphery of each cylinder. Polarization vectors are mostly stacked antiparallel on the borders between the domains without the director disruption. The domain size decreases with the decreasing temperature, the percentage of the antiferroelectric decouplings increases, and M2 exhibits the first-order phase transition into proper ferroelectric MP. With the increasing temperature the domain size in the M2 phase increases, the domination of particular polar orientation of molecules reduces, and finally, the domain size diverges at particular temperature corresponding to the second-order phase transition from M2 to paraelectric M1. Variations of the polar and nonpolar orientational order parameters are estimated within each phase and between the phases. Our experimental and computer simulation results (also presented in the paper) fully support our theoretical findings.

Molecular origin of the heterogeneity in the nematic and smectic liquid crystals: Elastic constants, gradients of order parameters, and visualization of small objects

The formation of heterogeneous nematic and smectic liquid crystals in the general case of an arbitrary geometry is investigated in the framework of molecular-statistical approach [Emelyanenko and Khokhlov, J. Chem. Phys. 142, 204905 (2015)JCPSA60021-960610.1063/1.4921684]. The molecular aspects of the orientational and translational orderings at the curved surfaces of small solid objects dispersed in liquid crystal are considered, and the differential equations for gradients of the order parameters in vicinities of the small objects are presented in the general form. The five elastic constants are obtained within the same approach, from which we were able to predict that a significant space variations of the order parameters can be observed within the 0.5-0.8μm area around any small object, almost independently of its own dimension. Therefore, the liquid crystals can be a simple tool for the optical visualization of nano-objects. It is also demonstrated that the kind of molecular self-organization (smectic, nematic or conventionally isotropic) at the surfaces of small solid objects can be different from that in the bulk of mesogenic material. Totally we predict eight various combinations of simple states at the surfaces and in the bulk depending on the solid objects' size and temperature. It is also shown that the surfaces of 10μm-size solid objects and larger act almost as flat surfaces, while the surfaces of 1μm-size solid objects and smaller act almost as point defects.

Inverse "guest-host" effect: ferroelectric nanoparticles mediated switching of nematic liquid crystals

Liquid crystals are widely used as a host matrix to embed different materials: dyes, fullerenes, carbon nanotubes, various nanoparticles (metallic, semiconductor, ferromagnetic, ferroelectric). The usual approach is related to the so called "guest-host" effect: external electric (or magnetic) fields drive liquid crystals (host), and liquid crystals reorient embedded particles (guest). In this paper we report an experimental observation of the effect that is completely opposite to the classical "guest-host" phenomenon: ferroelectric nanoparticles being switched by an external field mediate the switching of liquid crystals. Our experiments show that ferroelectric nanoparticles reorient and hold liquid crystal molecules in a direction of the ferroelectric nanoparticles orientation even when an external electric field attempts to orient a liquid crystal in an orthogonal direction.

Molecular–Statistical Theory for the Description of Re-Entrant Ferroelectric Phase

The re-entrant ferroelectric phase (Sm- C re * ) is investigated in the framework of a molecular–statistical approach. It was found that anticlinic synpolar along the smectic layer normal phase can arise below the antiferroelectric phase (Sm- C A * ) in the temperature scale, and we suggest this phase to be Sm- C re * . We have shown that in the vicinity of Sm- C A * –Sm- C re * phase transition temperature, a very small electric field can cause a transition into the bidomain synclinic phase, where the helical pitch is unwound and the tilt planes have contributions either along or against the electric field. The helical rotation, elasticity and deformation of the Sm- C * , Sm- C A * and Sm- C re * structures without electric field or in the presence of electric field, as well as the dielectric response, are investigated. It is shown that Sm- C re * can arise solely due to the dipole–dipole interaction, and thus, in contrast to the conventional (improper) ferroelectric Sm- C * , appears to be the proper ferroelectric phase.

Multistability in the mixtures of smectic-C^{*} materials with compensated twisting power

The effect of multistability in the mixtures of smectic-C^{*} materials with compensated twisting power, i.e., the existence of a large number of almost equiprobable states in the same mixture under the same conditions, is analyzed in the framework of elastic continuum theory. A simple molecular model is also considered. It is shown that multistability can follow from the bulk properties of the smectic-C^{*} materials with compensated twisting power, but with high spontaneous polarization. Multistability leads to the formation of ferroelectric domains, in which the director oscillates in space. The length and amplitude of this oscillation is tunable smoothly by an electric field. Theoretical results for the domain length agree completely with the experimental data. A suggestion is made as to why each domain structure is remembered without the energy consumption, when the electric field is abruptly switched off. The structural dependence on material parameters, such as the spontaneous polarization, the elastic constant, and the equilibrium wave number, is predicted.

Effective long-range interlayer interactions and electric-field-induced subphases in ferrielectric liquid crystals

Microbeam resonant x-ray scattering experiments recently revealed the sequential emergence of electric-field-induced subphases (stable states) with exceptionally large unit cells consisting of 12 and 15 smectic layers. We explain the emergence of the field-induced subphases by the quasimolecular model based on the Emelyanenko-Osipov long-range interlayer interactions (LRILIs) together with our primitive way of understanding the frustration in clinicity using the q_{E} number defined as q_{E}=|[R]-[L]|/([R]+[L]); here [R] and [L] refer to the numbers of smectic layers with directors tilted to the right and to the left, respectively, in the unit cell of a field-induced subphase. We show that the model actually stabilizes the field-induced subphases with characteristic composite unit cells consisting of several blocks, each of which is originally a ferrielectric three-layer unit cell stabilized by the LRILIs, but some of which would be modified to become ferroelectric by an applied electric field. In a similar line of thought, we also try to understand the puzzling electric-field-induced birefringence data in terms of the LRILIs.

Systems with competing interlayer interactions and modulations in one direction: finding their structures

Complex structures in polar smectic systems can be studied within framework of discrete phenomenological models. Considered interactions are usually described by nonlinear trigonometric functions that do not allow for a straightforward search for solutions. The review of three methods reported in the literature are presented and their appropriateness, advantages and disadvantages are discussed. Examples are given as an illustration for each method.

Effect of an external electric field on the smectic-Ctilted* phases

We are interested in the chiral tilted smectic subphases, smectic-C(tilted)(*), including commensurate structures as well as the incommensurate smectic-C(α)(*) one. The continuum theory defines two scalar order parameters I and J, which can be coupled with an external electric field through a linear term I × E and a dielectric term J × E(2). We have calculated the changes due to these terms in the phase diagrams in the (α,η) plane, where α comes from the spontaneous twist and η measures the strength of the biaxial order. The coupling with an external electric field induces the expansion of the areas with spontaneous polarization and the appearance of an electroazimuthal effect.

Electric-field-induced transition from helical to planar smectic structures without helix unwinding

Previously electric-field-induced transitions from helical to planar structures in bulk liquid crystals were considered to take place with unwinding of helix. We show that the transition to the planar structure in polar smectic with frustrating interlayer interaction can occur without unwinding but through the formation of a periodic modulated structure with successive left-hand and right-hand sense of rotation in every half period. With field the amplitude of the left-right rotation decreases and a planar structure is formed. This mechanism of transition can take place in the short-pitch SmC(α)(*) phase formed as a result of frustrating interaction.

Effect of intralayer inhomogeneity on helical superstructures of liquid crystals

A mechanism to form distorted helical structures in ferroelectric liquid crystals is presented. It is shown that the deformation of helical interlayer structures of thin smectic systems can be considered as a direct consequence of the surface-induced spatial inhomogeneity in the distribution of the azimuthal molecular orientation within smectic layers. The intralayer azimuthal nonuniformity occurring in helical phases is argued to generate a local depolarizing electric field of the strength varying not only in smectic layers but also between the layers. The resulting modulation of the depolarization level in the direction of helical axes is shown to lead to a distortion of helices. Using a simple model, including the depolarization interaction, it is demonstrated that the degree of the helix deformation strongly varies as parameters of the model are changed. It is also shown that strong deformations of extremely short helices, found for appropriate values of the parameters, reflect nonuniformity of helicoidal superstructures of respective smectic subphases in real liquid crystalline systems.