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

Spontaneous helix formation in a polar smectic phase

In soft ferroelectric crystals, the depolarization field can be reduced by a periodic distortion of the polarization direction. In the polar nematic and tilted smectic phases, this process is energetically favored, as it only requires changes in the director orientation. We demonstrate the spontaneous formation of a helical structure in the proper ferroelectric tilted smectic (SmCHP) phase, formed below the heliconical polar nematic (NTBF) phase. The helical pitch in the smectic phase is approximately 600 nm and remains nearly constant across the entire temperature range of the phase. Under weak electric field, the helix reorients while its structure remains largely intact; however, in stronger field the helix is destroyed as the electric polarization aligns along the electric field.

Reactive Fluid Ferroelectrics: A Gateway to the Next Generation of Ferroelectric Liquid Crystalline Polymer Networks

Herein it is reported the first examples of reactive mesogenic materials (RMs) which exhibit fluid ferroelectric order based on the recently discovered ferroelectric nematic (NF) phase. These materials NF RMs and they provide the first steps toward the next generation of ferroelectric liquid crystalline polymer networks is termed. The chemical synthesis and characterization of the liquid crystalline properties of these materials is reported, demonstrating that they have the lowest longitudinal molecular dipole moments (µ) of any reported NF material of 7.39 D. It is go on to demonstrate a potential use case of this new class of reactive material through the polymer stabilization of a matrix which exhibits the NF phase, increasing the phase range of the ferroelectric phase from 75 to 120 °C. The NF RMs reported herein are an exciting step forward in ferroelectric liquid crystal research, demonstrating that reactive NF materials are achievable, allowing for the future development of liquid crystalline ferroelectric networks, elastomers and polymers.

Thermotropic reentrant isotropic symmetry and induced smectic antiferroelectricity in the ferroelectric nematic material RM734

We report a transition from the ferroelectric nematic liquid crystal (NF) phase to a lower-temperature, apolar fluid phase having reentrant isotropic symmetry (IR), in the liquid crystal compound RM734 doped with small concentrations of the ionic liquids 1-Butyl-3-methylimidazolium hexafluorophosphate (BMIM-PF6) or 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI). Even a trace amount of ionic liquid dopant facilitates the kinetic pathway for the transition from the NF to the IR, enabling simple cooling to produce this isotropic fluid phase rather than resulting in immediate crystallization. The IR was also obtained in the absence of specific ionic liquid doping by appropriate temperature cycling in three distinct, as-synthesized-and-purified batches of RM734, two commercial and one from our laboratory. Ionic liquid doping also stabilizes the smectic ZA, an additional birefringent antiferroelectric phase having the director parallel to fluid smectic layers, significantly increasing its temperature range between the paraelectric and ferroelectric nematic phases with increasing BMIM concentration.

Static and hydrodynamic periodic structures induced by ac electric fields in the antiferroelectric SmZ_{A} phase

We report the effect of AC electric fields in the range of 0.1-300 kHz on antiferroelectric SmZ_{A} layers of DIO in the bookshelf geometry. Significant results are (a) primary bifurcation into a quasistationary periodic instability with its voltage threshold U_{c} and wave vector q_{c} along the initial director being, respectively, quadratic and linear functions of f over 10-150 kHz, and with an azimuthal distortion of the director n which changes sign between adjacent stripes, (b) transition from the modulated state to a homogeneous state at higher voltages, and (c) third bifurcation into traveling wave periodic state on further rise in U in the region 10-40 kHz. We interpret these findings as follows. The low voltage instability is very similar to that seen in the higher temperature apolar nematic phase and is the electrohydrodynamic (EHD) instability possibly belonging to the region of dielectric inversion frequency. The azimuthal distortions of n result from an undulatory distortion of the SmZ_{A} layers in the book-shelf geometry. The intermediate homogeneous state of SmZ_{A} in which the periodic structure is absent results from a linear coupling between the layer polarization P and applied field E, giving rise to a scissoring type mutual P reorientation in adjacent layers. Finally, at even higher voltages, the medium goes over to a field-induced transition to the ferroelectric nematic, with the polarization following the AC field, and the periodic EHD instability being similar to that of the dielectric regime. The polar vector symmetry of the medium leads in general to traveling waves.

Antiferroelectric Order in Nematic Liquids: Flexoelectricity Versus Electrostatics

The recent discovery of ferroelectric nematic liquid crystalline phases marks a major breakthrough in soft matter research. An intermediate phase, often observed between the nonpolar and the ferroelectric nematic phase, shows a distinct antiferroelectric response to electric fields. However, its structure and formation mechanisms remain debated, with flexoelectric and electrostatics effects proposed as competing mechanisms. By controlling the magnitude of electrostatic forces through ion addition in two representative ferroelectric nematic materials, it is shown that the primary mechanism for the emergence of antiferroelectric order is the flexoelectric coupling between electric polarization and splay deformation of the nematic director. The addition of ions significantly expands the temperature range over which the antiferroelectric phase is observed, with this range increasing with increasing ion concentration. Polarizing optical microscopy studies and second harmonic generation (SHG) microscopy reveal the splayed structure modulated in 2D, while SHG interferometry confirms its antiferroelectric character. The model previously used to describe pretransitional behavior is extended by incorporating the electrostatic contribution of ions. The model shows qualitative agreement with the experiments, accurately reproducing the phase diagram and temperature-dependent evolution of the modulation period of the observed structure.

Ferroelectric Nematic Liquid Crystals Showing High Birefringence

High birefringence nematic liquid crystals are particularly demanded for adaptive optics applications in the infrared spectrum because it enable a thinner cell gap for achieving fast response time and improved diffraction efficiency. The emerging ferroelectric nematic liquid crystals have attracted widespread interest in soft matter due to their unique combination of ferroelectricity and fluidity. However, the birefringence, which is one of the most important optical parameters in electro-optic devices, is not large enough (<0.25) in most ferroelectric nematic materials. Here, a polar liquid crystal molecule library containing more than 60 molecules with a highly rigid and fluorinated nature is developed. The introduction of triple bonds constructs a long π-electron conjugated mesogen skeleton, significantly improving the birefringence of polar liquid crystal phases. The birefringence and dispersion properties are systematically studied, demonstrating a strong dependence on chemical structures and the type of polar phases. Furthermore, through multi-component mixing, polar liquid crystal mixtures with ultra-wide temperature range and excellent stability at or near room temperature are obtained. They possess much higher birefringence than the existing ferroelectric liquid crystal materials. The unique combination of high birefringence and fluidic ferroelectricity is expected to promote the application of polar liquid crystals in electro-optic technologies.

Macroscopic dynamics of the antiferroelectric smectic Z A phase and its magnetic analog Z M

We analyze the macroscopic dynamics of antiferroelectric smectic Z A and antiferromagnetic smectic Z M liquid crystals. The smectic Z A phase is characterized by antiferroelectric order in one direction in the planes of the smectic layers giving rise to an orthogonal biaxial overall symmetry without polar direction. Thus in sufficiently thick (bulk) samples without externally applied electric fields, globally D 2 h symmetry results. Therefore, the macroscopic dynamics of the smectic Z A is isomorphic to that of the McMillan phase and one can take over the corresponding results in the field-free limit. This also applies to the defect structure in the sense that one can expect the appearance of half-integer defects as they have also been observed for the McMillan phase. Based on the fact that ferromagnetic nematic liquid crystals are known for about a decade, it seems natural to investigate the antiferromagnetic analog of the smectic Z A phase, which we denote as Z M in the present paper. In this phase, one also has an in-plane preferred direction, which is, however, not like a director in an ordinary nematic, but odd under time reversal. It can be characterized by a staggered magnetization, N , just as in a solid antiferromagnet like MnO. As additional macroscopic variables when compared to a usual non-polar smectic A phase, we have the in-plane staggered magnetization and the magnetization M . As a consequence, we find that spin waves (frequently called anti-magnons in solids) become possible. Therefore, we have for the antiferromagnetic smectic phase, Z M , three pairs of propagating modes: first and 'second' sound as in usual smectic A phases and one pair of spin waves. The coupling between 'second' sound and spin waves is also analyzed leading to the possibility to excite spin waves by dynamic layer compressions and, vice versa, to generate 'second' sound by temporally varying magnetic fields. We note, however, that without additional mechanical or magnetic deformations, the coupling between spin waves on the one hand and first and second sound on the other is a higher order effect in the wave vector q . We also analyze the question of antiferroelectricity and antiferromagnetism for nematic liquid crystals.

Fluorination: Simple Change but Complex Impact on Ferroelectric Nematic and Smectic Liquid Crystal Phases

A series of liquid crystal (LC) materials are reported, which form a variety of ferroelectric nematic and smectic phases. The relationship between the number and position of lateral fluorine substituents and the formation of ferroelectric LC phases is investigated. While the addition of fluorine substituents increases the temperature at which ferroelectric order appears, the relationship between fluorination and the LC phase sequence is more complicated. Introducing lateral fluorine substituents can either suppress or promote the formation of ferroelectric smectic phases, depending on their position within the molecule, and the interplay between these trends allows for more exotic ferroelectric phases to appear.

Systematic Fluorination Is a Powerful Design Strategy toward Fluid Molecular Ferroelectrics

Ferroelectric nematic (NF) liquid crystals combine liquid-like fluidity and orientational order of conventional nematics with macroscopic electric polarization comparable in magnitude to solid-state ferroelectric materials. Here, we present a systematic study of twenty-seven homologous materials with various fluorination patterns, giving new insight into the molecular origins of spontaneous polar ordering in fluid ferroelectric nematics. Beyond our initial expectations, we find the highest stability of the NF phase to be in materials with specific fluorination patterns rather than the maximal fluorination, which might be expected based on simple models. We find a delicate balance between polar and apolar nematics, which is entirely dictated by the substitution of the fluorine atoms. Aided by electronic structure calculations, we show this to have its origins in the radial distribution of charge across the molecular surface, with molecules possessing a more oscillatory distribution of electrons across their surfaces and possessing a higher propensity to form polar nematic phases. This work provides a new set of ground rules and design principles that can inform the synthesis of future ferroelectric nematogens.

Thermotropic reentrant isotropy and induced smectic antiferroelectricity in the ferroelectric nematic realm: comparing RM734 and DIO

The current intense study of ferroelectric nematic liquid crystals was initiated by the observation of the same ferroelectric nematic phase in two independently discovered organic, rod-shaped, mesogenic compounds, RM734 and DIO. We recently reported that the compound RM734 also exhibits a monotropic, low-temperature, apolar phase having reentrant isotropic symmetry (the IR phase), the formation of which is facilitated to a remarkable degree by doping with small (below 1%) amounts of the ionic liquid BMIM-PF6. Here we report similar phenomenology in DIO, showing that this reentrant isotropic behavior is not only a property of RM734 but is rather a more general, material-independent feature of ferroelectric nematic mesogens. We find that the reentrant isotropic phases observed in RM734 and DIO are similar but not identical, adding two new phases to the ferroelectric nematic realm. These phases exhibit similar, strongly peaked, diffuse X-ray scattering in the WAXS range (1 < q < 2 Å-1) indicative of a distinctive mode of short-ranged, side-by-side molecular packing. The scattering at small q is, however, quite different in the two materials, with RM734 exhibiting a strong, single, diffuse peak at q ∼ 0.08 Å-1 indicating mesoscale modulation with ∼80 Å periodicity, and DIO a sharper diffuse peak at q ∼ 0.27 Å-1 ∼ (2π/molecular length), with second and third harmonics, indicating that in the reentrant isotropic phase of DIO (which we denote IRlam), short-ranged molecular positional correlation is smectic layer-like. Both reentrant isotropic phases are metastable, eventually generating birefringent crystals.

Freely suspended nematic and smectic films and free-standing smectic filaments in the ferroelectric nematic realm

We show that stable, freely suspended liquid crystal films can be made from the ferroelectric nematic (NF) phase and from the recently discovered polar, lamellar SmZA and SmAF phases. The NF films display two-dimensional, smectic-like parabolic focal conic textures comprising director/polarization bend that are a manifestation of the electrostatic suppression of director splay in the film plane. In the SmZA and SmAF phases, the smectic layers orient preferentially normal to the film surfaces, a condition never found in typical thermotropic or lyotropic lamellar LC phases, with the SmZA films exhibiting focal-conic fan textures mimicking the appearance of typical smectics in glass cells when the layers are oriented normal to the plates, and the SmAF films showing a texture of plaquettes of uniform in-plane orientation where both bend and splay are suppressed, separated by grain boundaries. The SmAF phase can also be drawn into thin filaments, in which X-ray scattering reveals that the smectic layer planes are normal to the filament axis. Remarkably, the filaments are mechanically stable even if they break, forming free-standing, fluid filaments supported only at one end. The unique architectures of these films and filaments are stabilized by the electrostatic self-interaction of the liquid crystal polarization field, which enables the formation of confined, fluid structures that are fundamentally different from those of their counterparts made using previously known liquid crystal phases.

Ferroelectric Smectic C Liquid Crystal Phase with Spontaneous Polarization in the Direction of the Director

In the previous study, the existence of an unidentified ferroelectric smectic phase is demonstrated in the low-temperature region of the ferroelectric smectic A phase, where the layer spacing decreases with decreasing temperature. In the present study, the phase is identified by taking 2D X-ray diffraction images of a magnetically oriented sample while allowing it to rotate and constructed a 3D reciprocal space with the sample rotation angle as the third axis for the whole picture of the reciprocal lattice vectors originating from the smectic structure. Consequently, circular diffraction images are obtained when the reciprocal lattice vectors are evenly distributed on the conical surface at a certain inclination angle in the reciprocal space. This result provides clear evidence that the phase in question is smectic C. The polarization properties also showed that the observed smectic C phase has spontaneous polarization in the direction parallel to the director and is identified as ferroelectric smectic C. These results provide a new type of classification for liquid crystalline phases that has been established over many years and is a significant contribution to the basic science of soft matter research.

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.

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.

Spontaneous symmetry breaking in polar fluids

Spontaneous symmetry breaking and emergent polar order are each of fundamental importance to a range of scientific disciplines, as well as generating rich phase behaviour in liquid crystals (LCs). Here, we show the union of these phenomena to lead to two previously undiscovered polar liquid states of matter. Both phases have a lamellar structure with an inherent polar ordering of their constituent molecules. The first of these phases is characterised by polar order and a local tilted structure; the tilt direction processes about a helix orthogonal to the layer normal, the period of which is such that we observe selective reflection of light. The second new phase type is anti-ferroelectric, with the constituent molecules aligning orthogonally to the layer normal. This has led us to term the phases the Sm C P H and SmAAF phases, respectively. Further to this, we obtain room temperature ferroelectric nematic (NF) and Sm C P H phases via binary mixture formulation of the novel materials described here with a standard NF compound (DIO), with the resultant materials having melting points (and/or glass transitions) which are significantly below ambient temperature. The new soft matter phase types discovered herein can be considered as electrical analogues of topological structures of magnetic spins in hard matter.

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.

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.

Confinement and magnetic-field effect on chiral ferroelectric nematic liquid crystals in Grandjean-Cano wedge cells

We explore the structure and magnetic-field response of edge dislocations in Grandjean-Cano wedge cells filled with chiral mixtures of the ferroelectric nematic mesogen DIO. Upon cooling, the ordering changes from paraelectric in the cholesteric phase N^{*} to antiferroelectric in the smectic SmZ_{A}^{*} and to ferroelectric in the cholesteric N_{F}^{*}. Dislocations of the Burgers vector b equal to the helicoidal pitch P are stable in all three phases, while dislocations with b=P/2 exist only in the N^{*} and SmZ_{A}^{*}. The b=P/2 dislocations split into pairs of τ^{-1/2}λ^{+1/2} disclinations, while the thick dislocations b=P are pairs of nonsingular λ^{-1/2}λ^{+1/2} disclinations. The polar order makes the τ^{-1/2} disclinations unstable in the N_{F}^{*} phase, as they should be connected to singular walls in the polarization field. We propose a model of transformation of the composite τ^{-1/2} line-wall defect into a nonsingular λ^{-1/2} disclination, which is paired up with a λ^{+1/2} line to form a b=P dislocation. The SmZ_{A}^{*} behavior in the in-plane magnetic field is different from that of the N_{F}^{*} and N^{*}: the dislocations show no zigzag instability, and the pitch remains unchanged in the magnetic fields up to 1 T. The behavior is associated with the finite compressibility of smectic layers.

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.

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.

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.

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.

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.

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.