Spontaneous helielectric nematic liquid crystals: Electric analog to helimagnets

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.

Advancing interactive systems with liquid crystal network-based adaptive electronics

Achieving adaptive behavior in artificial systems, analogous to living organisms, has been a long-standing goal in electronics and materials science. Efforts to integrate adaptive capabilities into synthetic electronics traditionally involved a typical architecture comprising of sensors, an external controller, and actuators constructed from multiple materials. However, challenges arise when attempting to unite these three components into a single entity capable of independently coping with dynamic environments. Here, we unveil an adaptive electronic unit based on a liquid crystal polymer that seamlessly incorporates sensing, signal processing, and actuating functionalities. The polymer forms a film that undergoes anisotropic deformations when exposed to a minor heat pulse generated by human touch. We integrate this property into an electric circuit to facilitate switching. We showcase the concept by creating an interactive system that features distributed information processing including feedback loops and enabling cascading signal transmission across multiple adaptive units. This system responds progressively, in a multi-layered cascade to a dynamic change in its environment. The incorporation of adaptive capabilities into a single piece of responsive material holds immense potential for expediting progress in next-generation flexible electronics, soft robotics, and swarm intelligence.

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.

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.

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.

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.

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.

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.

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.

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.

The effect of a lateral alkyloxy chain on the ferroelectric nematic phase

The synthesis and characterisation of two series of low molar mass liquid crystals, the 4-[(4-nitrophenoxy)carbonyl]phenyl 2-alkoxy-4-methoxybenzoates (series 5-m) and the 4-[(3-fluoro-4-nitrophenoxy)carbonyl]phenyl 2-alkoxy-4-methoxybenzoates (series 6-m) are reported in order to explore the effects of a lateral alkyloxy chain on the formation and stability of the recently discovered ferroelectric nematic phase. In both series m, the number of carbon atoms in the lateral chain, is varied from one to nine. The two series differ by the addition of a fluorine substituent in the 6-m series. 5-1 is the extensively studied ferroelectric nematogen RM734. All the members of the 5-m series exhibited both a conventional nematic, N, and ferroelectric nematic, N_F, phase, whereas all the members of the 6-m series exhibit a direct N_F-I transition with the exception of 6-1 that also exhibits a N phase. The replacement of a hydrogen atom by a fluorine atom reduces the nematic-isotropic transition temperature, T _NI, whereas the ferroelectric nematic-nematic, or isotropic, transition temperature, T _NFN/I, increases. This is interpreted in terms of the reduced structural anisotropy associated with the larger fluorine atom whereas the increase in the stability of the N_F phase reflects changes in polarity and polarizability. The dependence of T _NI and T _NFN/I on m in both series is similar, and these initially decrease on increasing m but converge to limiting values on further increasing m. This suggests that the lateral alkyloxy chain may adopt conformations in which it lies along the major axis of the mesogenic unit.

Fluid Layered Ferroelectrics with Global C∞v Symmetry

Ferroelectricity in fluid materials, which allows free rotation of molecules, is an unusual phenomenon raising cutting-edge questions in science. Conventional ferroelectric liquid crystals have been found in phases with low symmetry that permit the presence of spontaneous polarization. Recently, the discovery of ferroelectricity with high symmetry in the nematic phase has attracted considerable attention. However, the physical mechanism and molecular origin of ferroelectricity are poorly understood and a large domain of macroscopically oriented spontaneous polarization is difficult to fabricate in the ferroelectric nematic phase. This study reports new fluid layered ferroelectrics with the C_∞v symmetry in which nearly complete orientation of the spontaneous polarization remains stable under zero electric field without any orientation treatment. These ferroelectrics are obtained by simplifying the molecular structure of a compound with a known ferroelectric nematic phase, although the simplification reduced the dipole moment. The results provide useful insights into the mechanism of ferroelectricity due to dipole-dipole interactions in molecular assemblies. The new ferroelectric materials are promising for a wide range of applications as soft ferroelectrics.

Ferroelectric nematic liquid-crystalline phases

Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these phases, guided by their fundamental and applicative interest. In this Perspective, we give an overview of this emerging field by linking history and theoretical predictions to a general outlook of the development and properties of the materials exhibiting ferroelectric nematic phases. We will highlight the most relevant observations to date, e.g., giant dielectric permittivity values, polarization values an order of magnitude larger than in classical ferroelectric liquid crystals, and nonlinear optical coefficients comparable with several ferroelectric solid materials. Key observations of anchoring and electro-optic behavior will also be examined. The collected contributions lead to a final discussion on open challenges in materials development, theoretical description, experimental explorations, and possible applications of the ferroelectric phases.

Nontrivial phase matching in helielectric polarization helices: Universal phase matching theory, validation, and electric switching

Nonlinear three-wave mixing is a fundamental physical pathway in nonlinear optical materials, providing a route for producing a high-energy photon through two input photons. This report proposes a generalized phase-matching theory that evaluates second-order nonlinear optical properties for arbitrary polarization structures. It predicts light amplification pathways by using polarization helices, which are justified by experiments based on spontaneous helielectric nematic fluids. The unique polar electric field switching of the helielectrics enables the dynamic tuning of the emitted nonlinear light. The discovery not only introduces a general principle for nonlinear optical calculation but also contributes to a significant advance in diversifying the category and structure of polar materials.

Second-order optical nonlinearity is the essential concept for realizing modern technologies of optical wavelength conversion. The emerging helical polarization fluid, dubbed helielectric nematic, now makes it possible to design and easily fabricate various polarization structures and control their optical responses. The matter family is demonstrated as an ideal liquid platform for nonlinear optical conversion and amplification with electric-reconfigurable tunability. We here develop a universal phase matching theory and reveal a nonclassic chirality-sensitive phase-matching condition in the polarization helices through both the numerical calculation and the experimental validations. The nonlinear optical amplification can be dramatically modulated with a contrast ratio of >100:1 by an in-plane electric field. Furthermore, we employ the director relaxation under electric fields coupled with nonlinear optical simulation to clarify the topology–light interactions.

A new order of liquids: polar order in nematic liquid crystals

Given the widespread adoption of display technology based on nematic liquid crystals, the discovery of new nematic phases at thermodynamic equilibrium, although extremely rare, generates much excitement. The remarkable discovery polar order and giant ferroelectric polarisation in a nematic fluid is a watershed moment in soft matter research, and is one of the most important discoveries in the 150 year history of liquid crystals. After a brief introduction to this emerging field, we present the current state-of-the art in terms of understanding the molecular origins of this phase, before exploring how molecular structure underpins the incidence of this phase, as well as exploring future directions.

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

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

Development of emergent ferroelectric nematic liquid crystals with highly fluorinated and rigid mesogens

The emerging ferroelectric nematic liquid crystals have been attracting broader interests in new liquid crystal physics and their unique material properties. One big challenge for the ferroelectric nematic research is to enrich the material choice, which is now limited to RM734 and DIO families as representatives, in sharp contrast to the enormously diverse variety of the traditional apolar nematic liquid crystals. Here, we report a design of novel ferroelectric nematic materials with highly fluorinated and rigid mesogens. Noteworthily, they show distinct chemical structural features compared with previous aromatic ester-based molecules. The ferroelectric nematic phase was identified and confirmed through rigorous experiments. The bulk polarization was found to become purely along the long axis director, creating giant dielectric anisotropy. This work demonstrates a great potential for expanding ferroelectric nematic material diversity and will accelerate the corresponding application research and technology innovation.

Revealing the polar nature of a ferroelectric nematic by means of circular alignment

The recent discovery of spontaneously polar nematic liquid crystals-so-called ferroelectric nematics-more than a century after the first discussions about their possible existence-has attracted large interest, both from fundamental scientific and applicational points of view. However, the experimental demonstration of such a phase has, so-far, been non-trivial. Here I present a direct method for the experimental verification of a ferroelectric nematic liquid crystal phase. The method utilizes a single sample cell where the two substrates are linearly and circularly rubbed, respectively, and the ferroelectric nematic phase (N_F) is revealed by the orientation of the resulting disclination lines in the cell.