First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics

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.

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.

Extended free-energy functionals for achiral and chiral ferroelectric nematic liquid crystals: theory and simulation

Polar nematic liquid crystals are new classes of condensed-matter states, where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task. Here, we develop a Landau-type mean-field theory for both the achiral and chiral ferroelectric nematics. In the polar nematic states, the inversion symmetry breaking adds three new contributions: an additional odd elastic term (corresponding to the flexoelectricity in symmetry) to the standard Oseen-Frank free energy, electrostatic effect and an additional Landau term relating to the gradient of local polarization. The coupling between the scalar order parameter and polarization order should be considered. In the chiral and polar nematic state, we reveal that the competition between the twist elasticity and polarity dictates effective compressive energy arising from the quasi-layer structure. The polarization gradient is an essential term for describing the ferroelectric nature. Besides, we successfully simulate an experimentally reported structural transition in ferroelectric nematic droplets from a concentric-vortex-like to a line-disclination-mediated topology based on the developed theory. The approaches provide theoretical foundations for testing and predicting polar structures in emerging polar liquid crystals.

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.

An inorganic liquid crystalline dispersion with 2D ferroelectric moieties

Electro-optical effect-based liquid crystal devices have been extensively used in optical modulation techniques, in which the Kerr coefficient reflects the sensitivity of the liquid crystals and determines the strength of the device's operational electric field. The Peterlin-Stuart theory and the O'Konski model jointly indicate that a giant Kerr coefficient could be obtained in a material with both a large geometrical anisotropy and an intrinsic polarization, but such a material is not yet reported. Here we reveal a ferroelectric effect in a monolayer two-dimensional mineral vermiculite. A large geometrical anisotropy factor and a large inherent electric dipole together raise the record value of Kerr coefficient by an order of magnitude, till 3.0 × 10-4 m V-2. This finding enables an ultra-low operational electric field of 102-104 V m-1 and the fabrication of electro-optical devices with an inch-level electrode separation, which has not previously been practical. Because of its high ultraviolet stability (decay <1% under ultraviolet exposure for 1000 hours), large-scale production, and energy efficiency, prototypical displayable billboards have been fabricated for outdoor interactive scenes. This work provides new insights for both liquid crystal optics and two-dimensional ferroelectrics.

Topology of ferroelectric nematic droplets: the case driven by flexoelectricity or depolarization field

The recent discovery of ferroelectric nematics provides new opportunities for exploring polar topology in liquid matter. Here, we report numerous potential polarization topological states (e.g., polar vortex-like and line disclination mediated structures) in confined ferroelectric nematics with similar free-energy levels. In the experiment, they appear according to the confinement size and surface anchoring conditions. Based on a minimal analytical approach, we reveal that the topological transformation is balanced among the nematic elasticity, the polarization gradient, the flexoelectric and the depolarization interactions.

Response of helielectric nematics under an in-plane electric field

In traditional chiral nematic liquid crystals, the apolar cholesterics, the dielectric effect is the main driving force for responding to an electric field. The emerging polar chiral nematics, dubbed helielectric nematics, are the polar counterparts of the cholesterics. The head-to-tail symmetry breaking of the new matter state enables it to respond sensitively to the polarity of an electric field. Here, we report on the observation of a sequential polar winding/unwinding process of polarization helices under an electric field applied perpendicular to the helical axes, which behaves distinctly from the unwinding of the apolar cholesteric helices. Understanding the helix-unwinding behaviors provides insights for developing switchable devices based on helielectric nematics.

Exploring the Impact of Linkage Structure in Ferroelectric Nematic and Smectic Liquid Crystals

The liquid crystal molecule 3-fluoro-4-(3,4,5-trifluorophenyl)phenyl 2,6-difluoro-4-(trans-5-n-propyl-1,3-dioxane-2-yl)benzoate (DIO) has attracted considerable interest owing to its unique ferroelectric nematic phase and extraordinarily high dielectric constant. To expand the DIO series, novel analogs with 1,3-dioxane units converted to ester units (EST analogs) were synthesized, and their physical properties were characterized. The EST analogs exhibited ferroelectric phases similar to those of the corresponding DIO analogs. Interestingly, an EST analogue featuring a defluorinated benzoate unit exhibited a ferroelectric smectic A phase, despite its smaller longitudinal dipole moment of 6.9 D. This result diverges from the common knowledge that the formation of large longitudinal dipoles is traditionally effective in the emergence of ferroelectric phases. Unlike the DIO series, the EST analogs can be readily obtained without the formation of undesired geometric isomers, which is advantageous for practical applications. The results of this study provide valuable insights into the design of liquid-crystalline materials expressing ferroelectric phases.

Fluid fibers in true 3D ferroelectric liquids

We demonstrate an exceptional ability of a high-polarization 3D ferroelectric liquid to form freely suspended fluid fibers at room temperature. Unlike fluid threads in modulated smectics and columnar phases, where translational order is a prerequisite for forming liquid fibers, recently discovered ferroelectric nematic forms fibers with solely orientational molecular order. Additional stabilization mechanisms based on the polar nature of the mesophase are required for this. We propose a model for such a mechanism and show that these fibers demonstrate an exceptional nonlinear optical response and exhibit electric field-driven instabilities.

Chiral ground states of ferroelectric liquid crystals

Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Their three-dimensional orientational order is described as unidirectionally polar. We demonstrate that the ground state of a flat slab of a ferroelectric nematic unconstrained by externally imposed alignment directions is chiral, with left- and right-handed twists of polarization. Although the helicoidal deformations and defect walls that separate domains of opposite handedness increase the elastic energy, the twists reduce the electrostatic energy and become weaker when the material is doped with ions. This work shows that the polar orientational order of molecules could trigger chirality in soft matter with no chemically induced chiral centers.

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.

New examples of ferroelectric nematic materials showing evidence for the antiferroelectric smectic-Z phase

We present a new ferroelectric nematic material, 4-((4'-((trans)-5-ethyloxan-2-yl)-2',3,5,6'-tetrafluoro-[1,1'-biphenyl]-4-yl)difluoromethoxy)-2,6-difluorobenzonitrile (AUUQU-2-N) and its higher homologues, the molecular structures of which include fluorinated building blocks, an oxane ring, and a terminal cyano group, all contributing to a large molecular dipole moment of about 12.5 D. We observed that AUUQU-2-N has three distinct liquid crystal phases, two of which were found to be polar phases with a spontaneous electric polarization Ps of up to 6 µC cm-2. The highest temperature phase is a common enantiotropic nematic (N) exhibiting only field-induced polarization. The lowest-temperature, monotropic phase proved to be a new example of the ferroelectric nematic phase (NF), evidenced by a single-peak polarization reversal current response, a giant imaginary dielectric permittivity on the order of 103, and the absence of any smectic layer X-ray diffraction peaks. The ordinary nematic phase N and the ferroelectric nematic phase NF are separated by an antiferroelectric liquid crystal phase which has low permittivity and a polarization reversal current exhibiting a characteristic double-peak response. In the polarizing light microscope, this antiferroelectric phase shows characteristic zig-zag defects, evidence of a layered structure. These observations suggest that this is another example of the recently discovered smectic ZA (SmZA) phase, having smectic layers with the molecular director parallel to the layer planes. The diffraction peaks from the smectic layering have not been observed to date but detailed 2D X-ray studies indicate the presence of additional short-range structures including smectic C-type correlations in all three phases-N, SmZA and NF-which may shed new light on the understanding of polar and antipolar order in these phases.

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.

Mixing twist-bend and ferroelectric nematic liquid crystals

Twist-bend (N_{tb}) and ferroelectric (N_{F}) nematic liquid crystals exhibit several novel effects and new physical properties. Here, we report experimental studies on the phase diagram and some physical properties of binary mixtures of CB9CB and RM734 mesogens. Both N-N_{tb} and N-N_{F} phase transition temperatures and the corresponding enthalpies decrease significantly and, eventually, these transitions disappear at some intermediate compositions, stabilizing wide nematic phase (N). Temperature-dependent birefringence several degrees above the N-N_{tb} phase transition shows strong director tilt fluctuations. The critical range of the fluctuations increases with the nematic range and the critical exponent is consistent with the mean field. The spontaneous polarization of RM734 decreases drastically with the addition of CB9CB mesogen. The temperature dependence of the splay elastic constant of the mixtures' high-temperature nematic (N) phase strikingly differs from that of the pristine CB9CB and RM734 mesogens. The study shows that a small inclusion of either compound has a substantial effect on the phase diagram and physical properties.

Room-temperature ferroelectric nematic liquid crystal showing a large and diverging density

The ferroelectric nematic phase (NF) is a recently discovered phase of matter in which the orientational order of the conventional nematic liquid crystal state is augmented with polar order. Atomistic simulations suggest that the polar NF phase would be denser than conventional nematics owing to contributions from polar order. Using an oscillating U-tube densitometer, we obtain detailed temperature-dependent density values for a selection of conventional liquid crystals with excellent agreement with earlier reports. Having demonstrated the validity of our method, we then record density as a function of temperature for M5, a novel room-temperature ferroelectric nematic material. We present the first experimental density data for a NF material as well as density data for a nematic that has not previously been reported. We find that the room-temperature NF material shows a large (>1.3 g cm-3) density at all temperatures studied, notably including phases without polar order. An increase in density at phase transitions is observed. The magnitude of the increase for the intermediate-to-ferroelectric nematic (NX-NF) transition is an order of magnitude smaller than the isotropic-nematic (I-N) transition. We then probe potential consequences that may result from an elevated density through measurement of the refractive indices (no and ne). The navg of M5 is compared with 5CB and polar smectic liquid crystals. We observe how the highly polar nature of the system counteracts the effects of an increase in density. With knowledge of experimental density, we are able to derive an approximation that yields the polar order parameter, 〈P1〉, from polarisation measurements. Present results may be typical of ferroelectric nematic materials, potentially guiding material development, and is especially relevant for informing ongoing studies into this emerging class of materials.

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.

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.

Enantiotropic ferroelectric nematic phase in a single compound

The ferroelectric nematic phase became the centre of interest of scientists because of its unique physical properties. The uniqueness of this particular phase results in its monotropic character in all known NF materials. Here we present the very first example of a compound with an enantiotropic ferroelectric nematic phase. Compound 3JK is complementary with already well known NF materials, i.e. RM734 and DIO and is characterized by moderately high dielectric anisotropy.

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.

Second harmonic generation in anisotropic stratified media: a generalization of the Berreman method and its application to photonic materials

We have developed a numerical method for calculating the second-harmonic generation (SHG) generated by an anisotropic material whose optical properties present an arbitrary modulation in one dimension. The method is based on the Berreman 4 × 4 matrix formalism, which is generalized to include nonlinear optical phenomena. It can be used under oblique incidences of the input beam, and is valid even when the SHG frequency is close to photonic bands, where the usual slowly-varying-amplitude approximation breaks down. As an example of application, we have studied the SHG performance of ferroelectric and helielectric fluids. The obtained results indicate that the present procedure may contribute to improving the structural design and enlarging the variety of nonlinear optical materials for application in optical devices.

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.

To Be or Not To Be Polar: The Ferroelectric and Antiferroelectric Nematic Phases

We report two new series of compounds that show the ferroelectric nematic, NF, phase in which the terminal chain length is varied. The longer the terminal chain, the weaker the dipole-dipole interactions of the molecules are along the director and thus the lower the temperature at which the axially polar NF phase is formed. For homologues of intermediate chain lengths, between the non-polar and ferroelectric nematic phases, a wide temperature range nematic phase emerges with antiferroelectric character. The size of the antiparallel ferroelectric domains critically increases upon transition to the NF phase. In dielectric studies, both collective ("ferroelectric") and non-collective fluctuations are present, and the "ferroelectric" mode softens weakly at the N-NX phase transition because the polar order in this phase is weak. The transition to the NF phase is characterized by a much stronger lowering of the mode relaxation frequency and an increase in its strength, and a typical critical behavior is 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.

Spontaneous periodic polarization wave in helielectric fluids

By analogy with spin waves in ferromagnetic systems, the polarization (or dipole) wave is the electric counterpart that remains elusive. Here, we discover that the helielectricity, i.e. a polarization field with helicoidal helices that corresponds to a quasi-layered chiral nematic environment, causes a spontaneous formation of large-scale polarization waves in the form of the sinusoidal function. Both experimental and theoretical analyses reveal that the polarization ordering over a threshold polarization strength violates the inherent periodicity of the polarization helices, thus penalizing the compression energy. It drives a second-order structural transition to a periodically modulated polarization wave state. The roles of chirality and confinement condition are discussed.

Metasurface-enabled polarization-independent LCoS spatial light modulator for 4K resolution and beyond

With the distinct advantages of high resolution, small pixel size, and multi-level pure phase modulation, liquid crystal on silicon (LCoS) devices afford precise and reconfigurable spatial light modulation that enables versatile applications ranging from micro-displays to optical communications. However, LCoS devices suffer from a long-standing problem of polarization-dependent response in that they only perform phase modulation on one linear polarization of light, and polarization-independent phase modulation-essential for most applications-have had to use complicated polarization-diversity optics. We propose and demonstrate, for the first time, an LCoS device that directly achieves high-performance polarization-independent phase modulation at telecommunication wavelengths with 4K resolution and beyond by embedding a polarization-rotating metasurface between the LCoS backplane and the liquid crystal phase-modulating layer. We verify the device with a number of typical polarization-independent application functions including beam steering, holographical display, and in a key optical switching element - wavelength selective switch (WSS), demonstrating the significant benefits in terms of both configuration simplification and performance improvement.

Ferroelectric Nematic-Isotropic Liquid Critical End Point

A critical end point above which an isotropic phase continuously evolves into a polar (ferroelectric) nematic phase with an increasing electric field is found in a ferroelectric nematic liquid crystalline material. The critical end point is approximately 30 K above the zero-field transition temperature from the isotropic to nematic phase and at an electric field of the order of 10  V/μm. Such systems are interesting from the application point of view because a strong birefringence can be induced in a broad temperature range in an optically isotropic phase.

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.

Fluorination Enables Dual Ferroelectricity in Both Solid- and Liquid-Crystal Phases

Ferroelectric materials are a special type of polar substances, including solids or liquid crystals. However, obtaining a material to be ferroelectric in both its solid crystal (SC) and liquid crystal (LC) phases is a great challenge. Moreover, although cholesteric LCs inherently possess the advantage of high fluidity, their ferroelectricity remains unknown. Here, through the reasonable H/F substitution on the fourth position of the phenyl group of the parent nonferroelectric dihydrocholesteryl benzoate, we designed ferroelectric dihydrocholesteryl 4-fluorobenzoate (4-F-BDC), which shows ferroelectricity in both SC and cholesteric LC phases. The fluorination induces a lower symmetric polar P1 space group and a new solid-to-solid phase transition in 4-F-BDC. Beneficial from fluorination, the SC and cholesteric LC phases of 4-F-BDC show clear ferroelectricity, as confirmed by well-shaped polarization-voltage hysteresis loops. The dual ferroelectricity in both SC and cholesteric LC phases of a single material was rarely found. This work offers a viable case for the exploration of the interplay between ferroelectric SC and LC phases and provides an efficient approach for designing ferroelectrics with dual ferroelectricity and cholesteric ferroelectric liquid crystals.

Theoretical models of modulated nematic phases

Novel modulated nematic phases, such as twist-bend nematics, splay-bend nematics and splay nematics, are an important subject of research in the field of liquid crystals. In this article fundamental information about the discovery, structure and properties of these phases is presented. Various theoretical models of elastic properties are compared, especially the proposed formulae for the free energy density of modulated nematic phases and the conditions for their stability. The emphasis is put on the variety of material parameters and variables in the mathematical description of the structures. The elastic models are classified according to a few criteria. Flexopolarisation is indicated as a main phenomenon responsible for the formation of modulated nematic phases. The elastic models are used for analysing the deformations of the twist-bend nematic structure in external fields. Dielectric, flexoelectric, ferroelectric and magnetic effects are considered. Two types of distortions are distinguished: microscopic (connected with the deformation of the director distribution) and macroscopic (related to the change of the optic axis direction). This review can be a starting point for further studies, for example computer simulations of modulated phases and design of liquid crystalline devices.

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.

Walking Ferroelectric Liquid Droplets with Light

The motion of ferroelectric liquid sessile droplets deposited on a ferroelectric lithium niobate substrate can be controlled by a light beam of moderate intensity irradiating the substrate at a distance of several droplet diameters from the droplet itself. The ferroelectric liquid is a nematic liquid crystal, in which almost complete polar ordering of the molecular dipoles generates an internal macroscopic polarization locally collinear to the mean molecular long axis. Upon entering the ferroelectric phase, droplets are either attracted toward the center of the beam or repelled, depending on the side of the lithium niobate exposed to light irradiation. Moreover, moving the beam results in walking the ferroelectric droplet over long distances on the substrate. This behavior is understood as due to the coupling between the polarization of the ferroelectric droplet and the polarization photoinduced in the irradiated region of the lithium niobate substrate. Indeed, the effect is not observed in the conventional nematic phase, suggesting the crucial role of the ferroelectric liquid crystal polarization.

The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

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.

Shape Morphing by Topological Patterns and Profiles in Laser-Cut Liquid Crystal Elastomer Kirigami

Programming shape changes in soft materials requires precise control of the directionality and magnitude of their mechanical response. Among ordered soft materials, liquid crystal elastomers (LCEs) exhibit remarkable and programmable shape shifting when their molecular order changes. In this work, we synthesized, remotely programmed, and modeled reversible and complex morphing in monolithic LCE kirigami encoded with predesigned topological patterns in its microstructure. We obtained a rich variety of out-of-plane shape transformations, including auxetic structures and undulating morphologies, by combining different topological microstructures and kirigami geometries. The spatiotemporal shape-shifting behaviors are well recapitulated by elastodynamics simulations, revealing that the complex shape changes arise from integrating the custom-cut geometry with local director profiles defined by topological defects inscribed in the material. Different functionalities, such as a bioinspired fluttering butterfly, a flower bud, dual-rotation light mills, and dual-mode locomotion, are further realized. Our proposed LCE kirigami with topological patterns opens opportunities for the future development of multifunctional devices for soft robotics, flexible electronics, and biomedicine.

Phase Equilibria and Critical Behavior in Nematogenic MBBA-Isooctane Monotectic-Type Mixtures

The transition from the isotropic (I) liquid to the nematic-type (N) uniaxial phase appearing as the consequence of the elongated geometry of elements seems to be a universal phenomenon for many types of suspensions, from solid nano-rods to biological particles based colloids. Rod-like thermotropic nematogenic liquid crystalline (LC) compounds and their mixtures with a molecular solvent (Sol) can be a significant reference for this category, enabling insights into universal features. The report presents studies in 4'-methoxybenzylidene-4-n-butylaniline (MBBA) and isooctane (Sol) mixtures, for which the monotectic-type phase diagram was found. There are two biphasic regions (i) for the low (TP1, isotropic liquid-nematic coexistence), and (ii) high (TP2, liquid-liquid coexistence) concentrations of isooctane. For both domains, biphasic coexistence curves' have been discussed and parameterized. For TP2 it is related to the order parameter and diameter tests. Notable is the anomalous mean-field type behavior near the critical consolute temperature. Regarding the isotropic liquid phase, critical opalescence has been detected above both biphasic regions. For TP2 it starts ca. 20 K above the critical consolute temperature. The nature of pretransitional fluctuations in the isotropic liquid phase was tested via nonlinear dielectric effect (NDE) measurements. It is classic (mean-field) above TP1 and non-classic above the TP2 domain. The long-standing problem regarding the non-critical background effect was solved to reach this result.

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.

Fluctuations of cell geometry and their nonequilibrium thermodynamics in living epithelial tissue

We measure different contributions to entropy production in a living functional epithelial tissue. We do this by extracting the functional dynamics of development while at the same time quantifying fluctuations. Using the translucent Drosophila melanogaster pupal epithelium as an ideal tissue for high-resolution live imaging, we measure the entropy associated with the stochastic geometry of cells in the epithelium. This is done using a detailed analysis of the dynamics of the shape and orientation of individual cells which enables separation of local and global aspects of the tissue behavior. Intriguingly, we find that we can observe irreversible dynamics in the cell geometries but without a change in the entropy associated with those degrees of freedom, showing that there is a flow of energy into those degrees of freedom. Hence, the living system is controlling how the entropy is being produced and partitioned into its different parts.

Smectic C Self-Assembly in Mesogen-Free Liquid Crystalline Chiral Polyethers with Sulfonylated Methyl-Branched Side Chains

To realize advanced electrical applications for ferroelectric liquid crystalline polymers, high spontaneous polarization (P_s ) is highly desired. However, current ferroelectric liquid crystalline polymers usually exhibit a low P_s . In this work, mesogen-free, chiral polyethers containing sulfonylated methyl-branched alkyl side chains with a (CH₂ )₃ O spacer between the sulfonyl and the branched alkyl groups are designed and synthesized. In contrast to the linear n-alkyl side chains, the methyl-branched alkyl side chains induce chain tilting in the smectic layers. When double chirality exists in both the main chain and the side chains, a crystalline structure is observed after mechanical stretching. Intriguingly, when single chirality exists in either the backbone or the side chains, a liquid crystalline smectic C phase is obtained. The electric displacement-electric field study, however, does not show typical ferroelectric switching, although the dielectric constants are relatively high for these liquid crystalline polymers. This is likely because the dipole-dipole interactions among neighboring sulfonyl groups along the main chain are so strong that the ferroelectric switching is hindered in the samples. For the future work, it is desired to weaken the dipole-dipole interaction to achieve ferroelectricity in these mesogen-free liquid crystalline polymers.

Spontaneous electric-polarization topology in confined ferroelectric nematics

Topological textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially-distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures, which appear during the emergence and growth of quasi-2D ferroelectric nematic domains. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Both experimental and an extended mean-field modelling reveal that the polarization strength plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.

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.