Ferroelectric nematic liquid-crystalline phases

Electrically activated ferroelectric nematic microrobots

Ferroelectric nematic liquid crystals are fluids exhibiting spontaneous electric polarization, which is coupled to their long range orientational order. Due to their inherent property of making bound and surface charges, the free surface of ferroelectric nematics becomes unstable in electric fields. Here we show that ferroelectric liquid bridges between two electrode plates undergo distinct interfacial instabilities. In a specific range of frequency and voltage, the ferroelectric fluid bridges move as active interacting particles resembling living organisms like swarming insects, microbes or microrobots. The motion is accompanied by sound emission, as a consequence of piezoelectricity and electrostriction. Statistical analysis of the active particles reveals that the movement can be controlled by the applied voltage, which implies the possible application of the system in new types of microfluidic devices.

Emergent Ferroelectric Nematic and Heliconical Ferroelectric Nematic States in an Achiral "Straight" Polar Rod Mesogen

Ferroelectric nematic liquid crystals (NFLCs) are distinguished by their remarkable polarization characteristics and diverse physical phenomena, sparking significant interest and excitement within the scientific community. To date, over 150 NFLC molecules are developed; however, there are no reports regarding straight linear polar molecules with a parallel alignment of the permanent dipole moment and the molecular axis. The straight polar mesogen nBOE exhibits an enantiotropic NF phase with a wide temperature window (up to 100 K) despite having a longer alkyl chain (up to n = 6) than the critical alkyl chain length of conventional models. Interestingly, nBOE with a medium-length alkyl chain displays an exotic phase sequence of NF-HCNF-SmXF during the elimination of positional displacement among adjacent molecules. Furthermore, the reflective color modulation of the HCNFLC over the entire VIS-NIR spectral regime by ultralow E-field (up to 0.14 V µm-1) is demonstrated.

Dynamic flexoelectric instabilities in nematic liquid crystals

Electrohydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of the physical community in out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity, and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigenvalues of the evolution matrix for a period of the external alternating electric field. These eigenvalues determine the amplification factors for the modes during the period. The instability occurs when the principal eigenvalue of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space-modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works. We formulate conditions needed for the scenario to be realized. We hope that the results of our work will open the door to a broad range of further studies. Of especial importance would be a comprehensive understanding of the role of various material parameters and nonlinear effects which is a key step for the rational design of NLCs exhibiting the predicted in this publication multidimensional oscillating in time patterns.

Dielectric Properties of a Ferroelectric Nematic Material: Quantitative Test of the Polarization-Capacitance Goldstone Mode

The recently discovered ferroelectric nematic (N_{F}) liquid crystals (LC) have been reported to show an extraordinarily large value of the real part of the dielectric constant (ϵ^{'}>10^{3}) at low frequencies. However, it was argued by Clark et al. in Phys. Rev. Res. 6, 013195 (2024)PPRHAI2643-156410.1103/PhysRevResearch.6.013195 that what was measured was the capacitance of the insulating layer at LC or electrode surface and not that of the liquid crystal. Here we describe the results of dielectric spectroscopy measurements of an N_{F} material in cells with variable thickness of the insulating layers. Our measurements quantitatively verify the model by Clark et al. Additionally, our measurements in cells with bare conducting indium tin oxide surface provide a crude estimate of ϵ_{⊥}∼10^{2} in the N_{F} phase.

Revealing the antipolar order in the antiferroelectric SmZA phase by means of circular alignment

Many ferroelectric nematic liquid crystals, like one of the archetype materials, DIO, do not have a direct paraelectric N to ferroelectric NF phase transition, but exhibit yet another phase between N and NF. This phase has recently been proposed to be antiferroelectric, with a layered structure of alternating polarization normal to the average director and is sometimes referred to as Smectic ZA (SmZA). We have examined the SmZA phase in circularly rubbed (CR) cells, known to discriminate between the polar NF and the non-polar N phase from the configuration of disclination lines formed. We find that the ground state of SmZA has the same disclination configuration as the non-polar N phase, demonstrating that the SmZA phase is also non-polar, i.e., it has no net ferroelectric polarization. At the same time, the SmZA texture generally has a grainy appearance, which we suggest is partly a result of the frustration related to layered order combined with the imposed twist in CR cells. We discuss possible orientations of the smectic layers, depending on the alignment conditions. While a horizontal SmZA layer structure is always compatible with surface-induced twist, a vertical layer structure would tend to break up in a twisted bookshelf structure to match non-parallel alignment directions at the two surfaces.

Tunable entangled photon-pair generation in a liquid crystal

Liquid crystals, with their ability to self-assemble, strong response to an electric field and integrability into complex systems, are key materials in light-beam manipulation1. The recently discovered ferroelectric nematic liquid crystals2,3 also have considerable second-order optical nonlinearity, making them a potential material for nonlinear optics4,5. Their use as sources of quantum light could considerably extend the boundaries of photonic quantum technologies6. However, spontaneous parametric down-conversion, the basic source of entangled photons7, heralded single photons8 and squeezed light9, has so far not been observed in liquid crystals-or in any liquids or organic materials. Here we implement spontaneous parametric down-conversion in a ferroelectric nematic liquid crystal and demonstrate electric-field tunable broadband generation of entangled photons, with an efficiency comparable to that of the best nonlinear crystals. The emission rate and polarization state of photon pairs is markedly varied by applying a few volts or twisting the molecular orientation along the sample. A liquid-crystal source enables a special type of quasi-phase matching10, which is based on the molecular twist structure and is therefore reconfigurable for the desired spectral and polarization properties of photon pairs. Such sources promise to outperform standard nonlinear optical materials in terms of functionality, brightness and the tunability of the generated quantum state. The concepts developed here can be extended to complex topological structures, macroscopic devices and multi-pixel tunable quantum light sources.

Calorimetric evidence for the existence of an intermediate phase between the ferroelectric nematic phase and the nematic phase in the liquid crystal RM734

The idea that rodlike molecules possessing an electric dipole moment could exhibit a ferroelectric nematic phase was suggested more than a century ago. However, only recently such a phase has been reported for two quite different liquid crystals: RM734 [4-[(4-nitrophenoxy)carbonyl)]phenyl 2,4-dimethoxybenzoate] and DIO [2.3',4',5'-tetrafluoro[1,1'-biphenyl]-4-yl 2.6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate]. For RM734 a direct ferroelectric nematic (N_{F}) to classical nematic N transition was reported, whereas for DIO an intermediate phase N_{x} was discovered between the N_{F} and the N phases. Here we present high-resolution calorimetric evidence that an intermediate N_{x} phase also exists in RM734 along a narrow temperature range between the N_{F} and the N phases.

Fluid jets and polar domains, on the relationship between electromechanical instability and topology in ferroelectric nematic liquid crystal droplets

Ferroelectric nematic liquid crystals are a class of recently discovered fluid materials formed by highly polar molecules that spontaneously align along a common direction, giving rise to a macroscopic polarization P. Since the polarization vector is locally collinear to the optical axis n, the study of the spatial patterns of n enables deducing the structure of P. We have carried on such topological study on ferroelectric nematic droplets confined between two solid ferroelectric substrates both when the droplet is in equilibrium and during a jet-emission phase that takes place when the solid surfaces become sufficiently charged. We find that in equilibrium the droplet splits in striped domains in which P has alternating directions. When these domains extend close to the droplets' perimeter, P adopts a π-twisted structure to minimize accumulation of polarization charges. As the substrate surface charge is increased above threshold, fluid jets are emitted with a quasi-periodic pattern, a behaviour suggesting that their location is governed by an electrofluidic instability on the droplets' rim, in turn indicating the absence of specific trigger points. Soon after their emission, the jet periodicity is lost; some jets retract while other markedly grow. In this second regime, jets that grow are those that more easily connect to polar domains with P along the jet axis. Occasionally, ejection of isolated spikes also occurs, revealing locations where polarization charges have accumulated because of topological patterns extending on length scales smaller than the typical domain size.

The past 10 years of molecular ferroelectrics: structures, design, and properties

Ferroelectricity, which has diverse important applications such as memory elements, capacitors, and sensors, was first discovered in a molecular compound, Rochelle salt, in 1920 by Valasek. Owing to their superiorities of lightweight, biocompatibility, structural tunability, mechanical flexibility, etc., the past decade has witnessed the renaissance of molecular ferroelectrics as promising complementary materials to commercial inorganic ferroelectrics. Thus, on the 100th anniversary of ferroelectricity, it is an opportune time to look into the future, specifically into how to push the boundaries of material design in molecular ferroelectric systems and finally overcome the hurdles to their commercialization. Herein, we present a comprehensive and accessible review of the appealing development of molecular ferroelectrics over the past 10 years, with an emphasis on their structural diversity, chemical design, exceptional properties, and potential applications. We believe that it will inspire intense, combined research efforts to enrich the family of high-performance molecular ferroelectrics and attract widespread interest from physicists and chemists to better understand the structure-function relationships governing improved applied functional device engineering.

Macroscopic dynamics of ferromagnetic smectic-A

We derive the macroscopic dynamic equations for ferromagnetic smectic-A liquid crystals for which the spontaneous magnetization is parallel to the layer normal of the layering. As additional macroscopic variables when compared to simple fluids, we have the layer displacement u, familiar from smectic liquid crystals, and the magnetization density M. We find a number of reversible and dissipative cross-coupling terms to the additional macroscopic variables and discuss possible experiments to detect them. Among other effects, we point out that the velocity of first sound becomes anisotropic due to the influence of the modulus of the magnetization, while the magnitude of the velocity of second sound is modified. As for the static behavior, we find cross-coupling terms between the magnitude of the magnetization, on the one hand, and layer compression as well as osmotic pressure, on the other hand. In addition, we point out that as a dissipative effect, temperature gradients can induce gradients in the magnetization parallel to the layer normal, mediated by layer compressions.

The Emergence of a Polar Nematic Phase: A Chemist's Insight into the Ferroelectric Nematic Phase

The discovery of a new polar nematic phase; the ferroelectric nematic, has generated a great deal of excitement in the field of liquid crystals. To date there have been around 150 materials reported exhibiting the ferroelectric nematic phase, in general, following three key archetypal structures with these compounds known as RM734, DIO and UUQU-4N. In this review, the relationship between the molecular structure and the stability of the ferroelectric nematic, NF, phase will be described from a chemist's perspective. This will look to highlight the wide variety of functionalities which have been incorporated into these archetypal structures and how these changes influence the transition temperatures of the mesophases present. The NF phase appears to be stabilised particularly by reducing the length of terminal alkyl chains present and adding fluorines laterally along the length of the molecular backbone. This review will look to introduce the background of the ferroelectric nematic phase before then showing the molecular structures of a range of materials which exhibit the phase, describing their structure-property relationships and therefore giving an up-to-date account of the literature for this fascinating new mesophase.

Fluid Ferroelectric Filaments

Freestanding slender fluid filaments of room-temperature ferroelectric nematic liquid crystals are described. They are stabilized either by internal electric fields of bound charges formed due to polarization splay or by external voltage applied between suspending wires. The phenomenon is similar to those observed in dielectric fluids, such as deionized water, except that in ferroelectric nematic materials the voltages required are three orders of magnitudes smaller and the aspect ratio is much higher. The observed ferroelectric fluid threads are not only unique and novel but also offer measurements of basic physical quantities, such as the ferroelectric polarization and viscosity. Ferroelectric nematic fluid threads may have practical applications in nano-fluidic micron-size logic devices, switches, and relays.

Polar Self-Organization of Ferroelectric Nematic-Liquid-Crystal Molecules on Atomically Flat Au(111) Surface

Understanding nanoscale mechanisms responsible for the recently discovered ferroelectric nematics can be helped by direct visualization of self-assembly of strongly polar molecules. Here, we report on scanning tunneling microscopy studies of monomolecular layers of a ferroelectric nematic liquid crystal on a reconstructed Au(111) surface. The monolayers are obtained by deposition from a solution at ambient conditions. The adsorbed ferroelectric nematic molecules self-assemble into regular rows with tilted orientation, resembling a layered structure of a smectic C. Remarkably, each molecular dipole in this architecture is oriented along the same direction giving rise to polar ferroelectric ordering.

Macroscopic dynamics of the ferroelectric smectic [Formula: see text] phase with [Formula: see text] symmetry

We present the macroscopic dynamics of ferroelectric smectic A, smectic [Formula: see text], liquid crystals reported recently experimentally by three groups. In this fluid and orthogonal smectic phase, the macroscopic polarization, [Formula: see text], is parallel to the layer normal thus giving rise to [Formula: see text] overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to non-polar smectic A phases, we find a static cross-coupling between compression of the layering and bending of the layers, which does not lead to elastic forces, but to elastic stresses. In addition, it turns out that a reversible cross-coupling between flow and the magnitude of the polarization modifies the velocities of both, first and second sound. At the same time, the relaxation of the polarization gives rise to dissipative effects for second sound at the same order of the wavevector as for the sound velocity. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Apparently this type of terms has never been considered before for smectic phases. The question how the linear [Formula: see text] coupling in the energy alters the macroscopic response behavior when compared to usual non-polar smectic A phases is also addressed.

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.

Dipole-dipole correlations in the nematic phases of symmetric cyanobiphenyl dimers and their binary mixtures with 5CB

We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1'',9''-bis(4-cyanobiphenyl-4'-yl)nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence measurements are used to estimate the temperature dependence of the tilt between the axis defining the nanoscale helical modulation of the low temperature nematic phase with the (local) direction of the maximal alignment of the cyanobiphenyl units. Planar as well as magnetically and/or electrically aligned samples are used to measure the perpendicular and parallel components of the dielectric permittivity in both nematic phases. A self-consistent molecular field theory that takes into account flexibility and symmetry of the constituent mesogens is introduced for the calculation of order parameters and intra-molecular orientational dipolar correlations of the flexible dimers as a function of temperature/concentration. Utilising the tilt angle, as calculated from the birefringence measurements, and the predictions of the molecular theory, dielectric permittivity is modelled in the framework of the anisotropic version of the Kirkwood-Fröhlich theory. Using the inter-molecular Kirkwood correlation factors as adjustable parameters, excellent agreement between theory and permittivity measurements across the whole temperature range and composition of the mixtures is obtained. The importance of the orientational, intra- and inter-molecular, dipolar correlations, their relative impact on the static dielectric properties, as well as their connection with the local structure of the nematic phases of bent-shaped bimesogens, is discussed.

Lateral electric field switching in thin ferroelectric nematic liquid crystal cells

This study shows that, in cells with small thicknesses, the permanent polarization in the ferroelectric nematic phase of RM734 is aligned in the direction opposite to the rubbing direction. The electrode configuration induces an in-plane field near one substrate and a normal field near the other substrate. At low voltages, the permanent polarization rotates parallel to the substrate plane when its original orientation is at an angle with the electric field. The rotation occurs over a distance of more than 100 μm, where the applied electric field is very small. At higher voltages, the polarization aligns perpendicularly to the substrates under the influence of the transverse electric field. After removing the voltage, sometimes a slow reorientation of the polarization can be observed, which is ascribed to the slow release of ionic species. The results provide insight into the complex mechanisms that are involved in the switching of ferroelectric nematic liquid crystals.

Collective and non-collective molecular dynamics in a ferroelectric nematic liquid crystal studied by broadband dielectric spectroscopy

A great deal of effort has been recently devoted to the study of dielectric relaxation processes in ferroelectric nematic liquid crystals, yet their interpretation remains unclear. In this work, we present the results of broadband dielectric spectroscopy experiments of a prototypical ferroelectric nematogen in the frequency range 10 Hz-110 MHz at different electrode separations and under the application of DC bias fields. The results evidence a complex behavior in all phases due to the magnitude of polar correlations in these systems. The observed modes have been assigned to different relaxation mechanisms based on existing theoretical frameworks.

Splay-induced order in systems of hard tapers

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Splay and polar order in a system of hard pear-like molecules: confrontation of Monte Carlo numerical simulations with density functional theory calculations

Recent experimental discoveries of novel nematic types with polar order, including ferroelectric nematic and splay nematic, have brought the resurgence of the interest in polar and modulated phases. One of the most important factors that is widely believed to be crucial for the formation of new phases is the pear-like shape of mesogenic molecules. Such molecules were treated using second-virial density functional theory in [De Gregorio, P et al., Soft Matter, 2016, 12(23), 5188-5198], where the authors showed that the K11 splay elastic constant can become negative due to solely entropic reasons leading to long-range splay and polar correlations. To verify whether the predictions are correct, we performed Monte Carlo simulations of the same hard-core molecules used in the DFT study. As our results suggest, no polar or modulated liquid crystalline phases emerge; polar and splay correlations are either at most short-range or completely absent. On the other hand, a polar ferroelectric splay crystal was observed.

Solid-Liquid Crystal Biphasic Ferroelectrics with Tunable Biferroelectricity

Ferroelectricity has been separately found in numerous solid and liquid crystal materials since its first discovery in 1920. However, a single material with biferroelectricity existing in both solid and liquid crystal phases is very rare, and the regulation of biferroelectricity has never been studied. Here, solid-liquid crystal biphasic ferroelectrics, cholestanyl 4-X-benzoate (4X-CB, X = Cl, Br, and I), which exhibits biferroelectricity in both the solid and liquid crystal phases, is presented. It is noted that the ferroelectric liquid crystal phase of 4X-CB is a cholesteric one, distinct from the ordinary chiral smectic ferroelectric liquid crystal phase. Moreover, 4X-CB shows solid-solid and solid-liquid crystal phase transitions, of which the transition temperatures gradually increase from Cl to Br to I substitution. The spontaneous polarization (Ps ) of 4X-CB in both solid and liquid crystal phases can also be regulated by different halogen substitutions, where the 4Br-CB has the optimal Ps because of the larger molecular dipole moment. To the authors' knowledge, 4X-CB is the first ferroelectric with tunable biferroelectricity, which offers a feasible case for the performance optimization of solid-liquid crystal biphasic ferroelectrics.

Polarization patterning in ferroelectric nematic liquids via flexoelectric coupling

The recently discovered ferroelectric nematic liquids incorporate to the functional combination of fluidity, processability and anisotropic optical properties of nematic liquids, an astonishing range of physical properties derived from the phase polarity. Among them, the remarkably large values of second order optical susceptibility encourage to exploit these new materials for non-linear photonic applications. Here we show that photopatterning of the alignment layer can be used to structure polarization patterns. To do so, we take advantage of the flexoelectric effect and design splay structures that geometrically define the polarization direction. We demonstrate the creation of periodic polarization structures and the possibility of guiding polarization by embedding splay structures in uniform backgrounds. The demonstrated capabilities of polarization patterning, open a promising new route for the design of ferroelectric nematic based photonic structures and their exploitation.

Molecular Shape, Electronic Factors, and the Ferroelectric Nematic Phase: Investigating the Impact of Structural Modifications

The synthesis and characterisation of two series of low molar mass mesogens, the (4-nitrophenyl) 2-alkoxy-4-(4-methoxybenzoyl)oxybenzoates (NT3.m) and the (3-fluoro-4-nitrophenyl) 2-alkoxy-4-(4-methoxybenzoyl)oxybenzoates (NT3F.m), are reported in order to investigate the effect of changing the position of a lateral alkoxy chain from the methoxy-substituted terminal ring to the central phenyl ring in these two series of materials based on RM734. All members of the NT3.m series exhibited a conventional nematic phase, N, which preceded the ferroelectric nematic phase, NF , whereas all the members of the NT3F.m series exhibited direct NF -I transitions except for NT3F.1 which also exhibited an N phase. These materials cannot be described as wedge-shaped, yet their values of the ferroelectric nematic-nematic transition temperature, TN F N ${{_{{\rm N}{_{{\rm F}}}{\rm N}}}}$ , exceed those of the corresponding materials with the lateral alkoxy chain located on the methoxy-substituted terminal ring. In part, this may be attributed to the effect that changing the position of the lateral alkoxy chain has on the electronic properties of these materials, specifically on the electron density associated with the methoxy-substituted terminal aromatic ring. The value of TNI decreased with the addition of a fluorine atom ortho to the nitro group in NT3F.1, however, the opposite behaviour was found when the transition temperatures of the NF phase were compared which are higher for the NT3F.m series. This may reflect a change in the polarity and polarizability of the NT3F.m series compared to the NT3.m series. Therefore, it is suggested that, rather than simply promoting a tapered shape, the role of the lateral chain in inhibiting anti-parallel associations and its effect on the electronic properties of the molecules are the key factors in driving the formation of the NF phase.

Ferroelectricity in a nematic liquid crystal under a direct current electric field

We investigated the electrical properties of the liquid crystal compound 4-(4-nitrophenoxycarbonyl)phenyl 2,4-dimethoxybenzoate, known as RM734, exhibiting a ferroelectric nematic phase. The influence of alternating (AC) and direct (DC) current electric fields on the switching process of the polarization vector and dielectric constant of planarly aligned ferronematic and nematic phases were examined. The decrease of the real part of electric permittivity in the ferronematic phase and the creation of a ferroelectric order in the nematic phase under a DC field were demonstrated. The analysis of the results reveals the latching of the ferroelectric state. The applied DC field created a ferroelectric mode in the nematic phase. A new model of collective and molecular relaxations considering the domain structure of the ferronematic phase was proposed. The temperature and DC field dependence of dielectric properties was shown. Spontaneous polarization was measured using the field reversal technique. The spontaneous polarization value reaches the maximum at a fixed temperature.

Electric field-induced interfacial instability in a ferroelectric nematic liquid crystal

Studies of sessile droplets and fluid bridges of a ferroelectric nematic liquid crystal in externally applied electric fields are presented. It is found that above a threshold, the interface of the fluid with air undergoes a fingering instability or ramification, resembling to Rayleigh-type instability observed in charged droplets in electric fields or circular drop-type instabilities observed in ferromagnetic liquids in magnetic field. The frequency dependence of the threshold voltage was determined in various geometries. The nematic director and ferroelectric polarization direction was found to point along the tip of the fingers that appear to repel each other, indicating that the ferroelectric polarization is essentially parallel to the director. The results are interpreted in connection to the Rayleigh and circular drop-type instabilities.

Alignment properties of a ferroelectric nematic liquid crystal on the rubbed substrates

The orientation characteristics of FNLC-919, a new material with a ferroelectric nematic phase at room temperature, were investigated. Its alignment characteristics varied greatly depending on the relative rubbing direction on both substrates of a liquid crystal cell. In a cell where the two substrates were rubbed in the same direction, they were arranged homogeneously along the rubbing direction without domains or defects in the ferroelectric nematic phase. In a cell where the two substrates were rubbed in the anti-parallel direction, the two domains were twisted in the opposite direction. We quantitatively obtained the twisted direction and angle by matching the experimental data and calculation results using Jones matrix calculations. From the electro-optical experiment, it was confirmed that the polarization direction was opposite to the rubbing direction. In addition, the wavelength and temperature dependence of birefringence was measured for FNLC-919. In a cell where the rubbing direction between two substrates was 90°, two domains of opposite directions were observed in the nematic phase. When it becomes a ferroelectric nematic phase on cooling, the twist is determined to be only in one direction. The twist direction and angle were quantitatively obtained in the nematic and ferroelectric nematic phases. It was twisted more in the ferroelectric nematic phase than in the nematic phase.

Spontaneous mirror symmetry breaking and chiral segregation in the achiral ferronematic compound DIO

An achiral compound, DIO, known to exhibit three nematic phases namely N, N_X and N_F, is studied by polarizing microscopy and electro-optics for different surface conditions in confinement. The high temperature N phase assigned initially as a conventional nematic phase, shows two additional unusual features: the optical activity and the linear electro-optic response related to the polar nature of this phase. An appearance of chiral domains is explained by the spontaneous symmetry breaking arising from the saddle-splay elasticity and followed by the formation of helical domains of the opposite chirality. This is the first example of helical segregation observed in calamitic non-chiral molecules in the nematic phase. As reported previously, the ferronematic N_F shows strong polar azimuthal surface interaction energy which stabilizes a homogeneous structure in planar aligned LC cells rubbed parallel and exhibits a twisted structure in cells with antiparallel buffing. The transmission spectra are simulated using Berreman's 4 × 4 matrix method. The observed agreement between the experimental and the simulated spectra quantitatively confirms the presence of twisted structures in antiparallel rubbed cells.

Ferroelectric nematic liquids with conics

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (N_F) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

Ferroelectric nematic droplets in their isotropic melt

The isotropic to ferroelectric nematic liquid transition was theoretically studied over one hundred years ago, but its experimental studies are rare. Here we present experimental results and theoretical considerations of novel electromechanical effects of ferroelectric nematic liquid crystal droplets coexisting with the isotropic melt. We find that the droplets have flat pancake-like shapes that are thinner than the sample thickness as long as there is room to increase the lateral droplet size. In the center of the droplets a wing-shaped defect with low birefringence is present that moves perpendicular to a weak in-plane electric field, and then extends and splits in two at higher fields. Parallel to the defect motion and extension, the entire droplet drifts along the electric field with a speed that is independent of the size of the droplet and is proportional to the amplitude of the electric field. After the field is increased above 1 mV μm^-1 the entire droplet gets deformed and oscillates with the field. These observations led us to determine the polarization field and revealed the presence of a pair of positive and negative bound electric charges due to divergences of polarization around the defect volume.

Phase transitions study of the liquid crystal DIO with a ferroelectric nematic, a nematic, and an intermediate phase and of mixtures with the ferroelectric nematic compound RM734 by adiabatic scanning calorimetry

High-resolution calorimetry has played a significant role in providing detailed information on phase transitions in liquid crystals. In particular, adiabatic scanning calorimetry (ASC), capable of providing simultaneous information on the temperature dependence of the specific enthalpy h(T) and on the specific heat capacity c_{p}(T), has proven to be an important tool to determine the order of transitions and render high-resolution information on pretransitional thermal behavior. Here we report on ASC results on the compound 2,3',4',5'-tetrafluoro[1,1'-biphenyl]-4-yl 2,6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate (DIO) and on mixtures with 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). Both compounds exhibit a low-temperature ferroelectric nematic phase (N_{F}) and a high-temperature paraelectric nematic phase (N). However, in DIO these two phases are separated by an intermediate phase (N_{x}). From the detailed data of h(T) and c_{p}(T), we found that the intermediate phase was present in all the mixtures over the complete composition range, albeit with strongly decreasing temperature width for that phase with decreasing mole fraction of DIO (x_{DIO}). The x_{DIO} dependence on the transition temperatures for both transitions could be well described by a quadratic function. Both these transitions were weakly first order. The true latent heat of the N_{x}-N transition of DIO was as low as L=0.0075±0.0005J/g and L=0.23±0.03J/g for the N_{F}-N_{x} transition, which is about twice the previously reported value of 0.115 J/g for the N_{F}-N transition in RM734. In the mixtures both transition latent heats decrease gradually with decreasing x_{DIO}. At all the N_{x}-N transitions pretransition fluctuation effects are absent and these transitions are purely but very weakly first order. As in RM734 the transition from the N_{F} to the higher-temperature phase exhibits substantial pretransitional behavior, in particular, in the high-temperature phase. Power-law analysis of c_{p}(T) resulted in an effective critical exponent α=0.88±0.1 for DIO and this value decreased in the mixtures with decreasing x_{DIO} toward α=0.50±0.05 reported for RM734. Ideal mixture analysis of the phase diagram was consistent with ideal mixture behavior provided the total transition enthalpy change was used in the analysis.

Polarisation-driven magneto-optical and nonlinear-optical behaviour of a room-temperature ferroelectric nematic phase

Nematics with a broken polar symmetry are one of the fascinating recent discoveries in the field of soft matter. High spontaneous polarisation and the fluidity of the ferroelectric nematic N_F phase make such materials attractive for future applications and interesting for fundamental research. Here, we explore the polar and mechanical properties of a room-temperature ferroelectric nematic and its behaviour in a magnetic field. We show that N_F is much less susceptible to the splay deformation than to the twist. The strong splay rigidity can be attributed to the electrostatic self-interaction of polarisation avoiding the polarisation splay.

Emerging Ferroelectric Uniaxial Lamellar (Smectic AF) Fluids for Bistable In-Plane Polarization Memory

The emerging matter category of liquid-matter ferroelectrics, i.e., ferroelectric nematics, demonstrates an unprecedented combination of fluidity and spontaneous polarization. However, unlike traditional ferroelectrics, the field-switched polarization at zero-field cannot be conserved, so the memory effect remains challenging. Here we report another new type of ferroelectric liquid crystal state, dubbed the ferroelectric smectic A phase, where the polarization is longitudinally coupled to the smectic quasi-layer order. With higher packing density, the phase exhibits higher values of refractive anisotropy and spontaneous polarization compared to the ferroelectric nematics. A delicate balance between the liquid crystal elasticity and flow viscosity enables both the switching and memory of the polarization field, thus opening the door toward realizing liquid-matter ferroelectric memory devices.