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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 Z A ," 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-SmZ A -ferroelectric nematic phase sequence.

We report the observation of the smectic A F , a liquid crystal phase of the ferroelectric nematic realm. The smectic A F is a phase of small polar, rod-shaped molecules that form two-dimensional fluid layers spaced by approximately the mean molecular length. The phase is uniaxial, with the molecular director, the local average long-axis orientation, normal to the layer planes, and ferroelectric, with a spontaneous electric polarization parallel to the director. Polarization measurements indicate almost complete polar ordering of the ∼10 Debye longitudinal molecular dipoles, and hysteretic polarization reversal with a coercive field ∼2 × 10 5 V / m is observed. The SmA F phase appears upon cooling in two binary mixtures of partially fluorinated mesogens: 2N/DIO, exhibiting a nematic (N)-smectic Z A (SmZ A )-ferroelectric nematic (N F )-SmA F phase sequence, and 7N/DIO, exhibiting an N-SmZ A -SmA F phase sequence. The latter presents an opportunity to study a transition between two smectic phases having orthogonal systems of layers.

The success of nematic liquid crystals in displays and optical applications is due to the combination of their optical uniaxiality, fluidity, elasticity, responsiveness to electric fields and controllable coupling of the molecular orientation at the interface with solid surfaces. The discovery of a polar nematic phase opens new possibilities for liquid crystal-based applications, but also requires a new study of how this phase couples with surfaces. Here we explore the surface alignment of the ferroelectric nematic phase by testing different rubbed and unrubbed substrates that differ in coupling strength and anchoring orientation and find a variety of behaviors - in terms of nematic orientation, topological defects and electric field response - that are specific to the ferroelectric nematic phase and can be understood as a consequence of the polar symmetry breaking. In particular, we show that by using rubbed polymer surfaces it is easy to produce cells with a planar polar preferential alignment and that cell electrostatics ( e.g. grounding the electrodes) has a remarkable effect on the overall homogeneity of the ferroelectric ordering.

We show that surface interactions can vectorially structure the three-dimensional polarization field of a ferroelectric fluid. The contact between a ferroelectric nematic liquid crystal and a surface with in-plane polarity generates a preferred in-plane orientation of the polarization field at that interface. This is a route to the formation of fluid or glassy monodomains of high polarization without the need for electric field poling. For example, unidirectional buffing of polyimide films on planar surfaces to give quadrupolar in-plane anisotropy also induces macroscopic in-plane polar order at the surfaces, enabling the formation of a variety of azimuthal polar director structures in the cell interior, including uniform and twisted states. In a π-twist cell, obtained with antiparallel, unidirectional buffing on opposing surfaces, we demonstrate three distinct modes of ferroelectric nematic electro-optic response: intrinsic, viscosity-limited, field-induced molecular reorientation; field-induced motion of domain walls separating twisted states of opposite chirality; and propagation of polarization reorientation solitons from the cell plates to the cell center upon field reversal. Chirally doped ferroelectric nematics in antiparallel-rubbed cells produce Grandjean textures of helical twist that can be unwound via field-induced polar surface reorientation transitions. Fields required are in the 3-V/mm range, indicating an in-plane polar anchoring energy of w P ∼3 × 10 -3 J/m 2 ., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm 2 , the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction., Competing Interests: Competing interest statement: D.B. is one of the coowners of Wasatch Molecular Inc., which distributes the APPLE&P database., (Copyright © 2020 the Author(s). Published by PNAS.)

The helical nanofilament (HNF) and low-temperature dark conglomerate (DC) liquid-crystal (LC) phases of bent-core molecules show the same local layer structure but present different bulk morphologies. The DC phase is characterized by the formation of nanoscale toric focal conics, whereas the HNF phase is constructed of bundles of twisted layers. Although the local layer structure is similar in both phases, materials that form these phases tend to form one morphology in preference to the other. Targeted control of the nanostructures would provide pathways to potential applications and insight into how conditions drive a specific phase formation. Here, W624, a compound known to form the DC phase is confined in nanometer scale channels of porous anodized aluminum oxide (AAO) membranes. Within each nanochannel, the DC phase is suppressed forming the HNF structure instead, indicating the nanoscale spatial limitation can control the phase structure of the DC phase., (© 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We have previously reported the first realization of an orthogonal ferroelectric bent-core SmAP F phase by directed design in mesogens with a single tricarbosilane-terminated alkoxy tail. Given the potentially useful electrooptic properties of this phase, including analog phase-only electrooptic index modulation with optical latching, we have been exploring its "structure space", searching for novel SmAP F mesogens. Here, we report two classes of these-the first designed to optimize the dynamic range of the index modulation in parallel-aligned cells by lowering the bend angle of the rigid core, and the second expanding the structure space of the phase by replacing the tricarbosilane-terminated alkyl tail with a polyfluorinated polyethylene glycol oligomer., Competing Interests: The authors declare no conflict of interest.

A lamellar liquid crystal (LC) phase of certain bent-core mesogenic molecules can be grown in a manner that generates a single chiral helical nanofilament in each of the cylindrical nanopores of an anodic aluminum oxide (AAO) membrane. By introducing guest molecules into the resulting composite chiral nanochannels, we explore the structures and functionality of the ordered guest/host LC complex, verifying the smectic-like positional order of the fluidic nematic LC phase, which is obtained by the combination of the LC organization and the nanoporous AAO superstructure. The guest nematic LC 4'- n -pentyl-4-cyanobiphenyl is found to form a distinctive fluid layered ordered LC complex at the nanofilament/guest interface with the host 1,3-phenylene bis[4-(4-nonyloxyphenyliminomethyl)benzoate], where this interface contacts the AAO cylinder wall. Filament growth form is strongly influenced by mixture parameters and pore dimensions.

We investigated a controlled helical nanofilament (HNF: B4) phase under topographic confinement with airflow that can induce a shear force and temperature gradient on the sample. The resulting orientation and ordering of the B4 phase in this combinational effort was directly investigated using microscopy. The structural freedom of the complex B7 phase, which is a higher temperature phase than the B4 phase, can result in relatively complex microscopic arrangements of HNFs compared with the B4 phase generated from the simple layer structure of the B2 phase. This interesting chiral/polar nanofilament behaviour offers new opportunities for further exploration of the exotic physical properties of the B4 phase.

The B4 helical nanofilament (HNF) liquid crystal (LC) phase is a three-dimensional (3D) helical structure composed of 2D smectic layers. Because of the complex shape of the HNF phase, it is difficult to understand the generation mechanism of HNFs in the bulk as well as in the thin-film condition. Here, we directly investigated the nucleation and growth of HNFs in nanobowls. A combination of electron microscopy and X-ray diffraction was used to reveal the transitional surface structures, in which barrel-like structures as well as short HNFs with random handedness were observed, depending on the LC film thickness. These results will be useful in achieving a better understanding of thin film structures of complex chiral structures in soft matter.

In many technologies used to achieve separation of enantiomers, chiral selectors are designed to display differential affinity for the two enantiomers of a chiral compound. Such complexes are diastereomeric, differing in structure and free energy for the two enantiomers and enabling chiral discrimination. Here we present evidence for strong diastereomeric interaction effects at the mesoscale, manifested in chiral liquid crystal guest materials confined in a chiral, nanoporous network of semi-crystalline helical nanofilaments. The nanoporous host is itself an assembly of achiral, bent-core liquid crystal molecules that phase-separate into a conglomerate of 100 micron-scale, helical nanofilament domains that differ in structure only in the handedness of their homogeneous chirality. With the inclusion of a homochiral guest liquid crystal, these enantiomeric domains become diastereomeric, exhibiting unexpected and markedly different mesoscale structures and orientation transitions producing optical effects in which chirality has a dominant role.

We have investigated the various morphological changes of helical nanofilament (HNF; B4) phases in multiscale nanochannels made of porous anodic aluminum oxide (AAO) film. Single or multihelical structures could be manipulated depending on the AAO pore size and the higher-temperature phase of each molecule. Furthermore, the nanostructures of HNFs affected by the chemical affinity between the molecule and surface were drastically controlled in surface-modified nanochannels. These well-controlled hierarchical helical structures that have multidimensions can be a promising tool for the manipulation of chiral pores or the nonlinear optical applications.

A series of simple hierarchical self-assembly steps achieve self-organization from the centimeter to the subnanometer-length scales in the form of square-centimeter arrays of linear nanopores, each one having a single chiral helical nanofilament of large internal surface area and interfacial interactions based on chiral crystalline molecular arrangements.

Azobenzene-based molecules forming a self-assembled monolayer (SAM) tethered to a glass surface are highly photosensitive and readily reorient liquid crystals in contact with them when illuminated with polarized actinic light. We probe the coupling of such monolayers to nematic liquid crystal in a hybrid cell by studying the dynamics of liquid crystal reorientation in response to local orientational changes of the monolayer induced by a focused actinic laser with a rotating polarization. The steady increase in the azimuth of the mean molecular orientation of the SAM around the laser beam locally reorients the nematic, winding up an extended set of nested rings of splay-bend nematic director reorientation until the cumulative elastic torque exceeds that of the surface coupling within the beam, after which the nematic director starts to slip. Quantitative analyses of the ring dynamics allow measurements of the anchoring strength of the azo-SAM and its interaction with the nematic liquid crystal.

Smectic layers of tilted, bent-core liquid crystals have a tendency to exhibit spontaneous saddle-splay curvature, a mechanical response that relieves the internal strain of the layers. When this tendency is strong enough, the smectic layers form complex, equilibrium, non-planar structures such as the helical nanofilaments in the B4 phase and the disordered focal conics in the chiral dark conglomerate (DC) phase. The DC phase is usually observed on cooling directly from the isotropic phase, with the disordered focal conics analogous to the disordered sponge phase found in lyotropic systems. We report a DC phase observed below a B2 phase that is stable down to room temperature. In mixtures with the calamitic liquid crystal 8CB, the low-temperature DC phase forms a more ordered, bicontinuous structure, resembling the cubic phase observed in the lyotropic systems, which is attributed to the enhanced intralayer ordering of the bent-core molecules in the mixtures., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

We have identified a metastable liquid-crystal (LC) structure in the de Vries smectic-A* phase (de Vries Sm-A*) formed by silicon-containing molecules under certain boundary conditions. The phase transition with the metastable structure was observed in a LC droplet placed on a planar aligned substrate and LCs confined in the groove of a silicon microchannel. During the rapid cooling step, a batonnet structure was generated as an intermediate and metastable state prior to the transition that yielded the thermodynamically stable toric focal conic domains. This distinctive behavior was characterized using depolarized reflection light microscopy and grazing incidence x-ray diffraction techniques. We concluded that the silicon groups in the molecules that formed the de Vries phase induced the formation of layered clusters called cybotactic structures. This observation is relevant to an exploration of the physical properties of cybotactic de Vries phases and gives a hint as to their optoelectronic applications.

Freeze-fracture transmission electron microscopy study of the nanoscale structure of the so-called "twist-bend" nematic phase of the cyanobiphenyl (CB) dimer molecule CB(CH2)7CB reveals stripe-textured fracture planes that indicate fluid layers periodically arrayed in the bulk with a spacing of d ~ 8.3 nm. Fluidity and a rigorously maintained spacing result in long-range-ordered 3D focal conic domains. Absence of a lamellar X-ray reflection at wavevector q ~ 2π/d or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic rather than smectic molecular ordering. A search for periodic ordering with d ~ in CB(CH2)7CB using atomistic molecular dynamic computer simulation yields an equilibrium heliconical ground state, exhibiting nematic twist and bend, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer. We measure the director cone angle to be θ(TB) ~ 25° and the full pitch of the director helix to be p(TB) ~ 8.3 nm, a very small value indicating the strong coupling of molecular bend to director bend.

We report a bent-core liquid crystal (LC) compound exhibiting two fluid smectic phases in which two-dimensional, polar, orthorhombic layers order into three-dimensional ferroelectric states. The lower-temperature phase has a uniform polarization field which responds in an analog fashion to applied electric field. The higher-temperature phase is a new smectic state with periodic undulation of the polarization, structurally modulated layers, and a bistable response to applied electric field which originates in the periodically splay-modulated bulk of the LC rather than by surface stabilization at the cell boundaries.

We describe the unusual electro-optic response of a biaxial bent-core liquid crystal molecule that exhibits an anticlinic, antiferroelectric smectic phase (Sm-C(A)P(A)) with a molecular tilt angle close to 45°. In the ground state, the sample shows very low birefringence. A weak applied electric field distorts the antiferroelectric ground state, inducing a small azimuthal reorientation of the molecules on the tilt cone. This results in only a modest increase in the birefringence but an anomalously large (∼40°) analog rotation of the extinction direction. This unusual electro-optic response is shown to be a consequence of the molecular biaxiality.

The B4 liquid crystal phase of bent-core molecules, a smectic phase of helical nanofilaments, is one of the most complex hierarchical self-assemblies in soft materials. We describe the layer topology of the B4 phase of mesogens in the P-n-OPIMB homologous series near the liquid crystal/glass interface. Freeze-fracture transmission electron microscopy reveals that the twisted layer structure of the bulk is suppressed, the layers instead forming a structure with periodic layer undulations, with the topography depending on the distance from the glass. The surface layer structure is modeled as parabolic focal conic arrays generated by equidistant parabolas whose foci are defect lines along the glass surface. Nucleation and growth of toric focal conics near the glass substrate is also observed. Although the growth of twisted nanofilaments, the usual manifestation of structural chirality in the B4 phase, is suppressed near the surface, the smectic layers are intrinsically chiral, and the helical filaments that form on top of them grow with specific handedness., (Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The growth of helical filaments in the B4 liquid-crystal phase was investigated in mixtures of the bent-core and calamitic mesogens NOBOW and 8CB. Freezing-point depression led to nucleation of the NOBOW B4 phase directly from the isotropic phase in the mixtures, forming large left- and right-handed chiral domains that were easily observed in the microscope. We show that these domains are composed of homochiral helical filaments formed in a nucleation and growth process that starts from a nucleus of arbitrary chirality and continues with chirality-preserving growth of the filaments. A model that accounts for the observed local homochirality and phase coherence of the branched filaments is proposed. This model will help in providing a better understanding of the nature of the B4 phase and controlling its growth and morphology for applications, such as the use of the helical nanophase as a nanoheterogeneous medium.

A smectic-A (SmA) liquid crystal phase of fluid layers with in-plane polarization P is shown to exhibit effective conductivity in the semiconducting range during electric-field-induced polarization reorientation, but becomes insulating once the polarization is aligned with the field. Such fluid ferroelectrics sandwiched between highly insulating layers enable electro-optic devices with long-term dc electrostatic control of polarization and optic axis orientation.

Self-assembled monolayers (SAMs) were prepared from solutions with different proportions of a photoactive, azobenzene-based, silanized derivative of disperse red one (dDR1), and octyltriethoxysilane (OTE), a shorter, nonphotoactive molecule. The in-plane photoinduced orientational ordering of the resulting two component monolayers was monitored via precision measurement of in-plane birefringence using a dedicated high-extinction polarimeter. Measurements of contact angle, absorption, and birefringence show that introduction of OTE into the dDR1 deposition solution produces a continuous reduction of the surface density of dDR1 in the SAM, enabling the study of photowriting and relaxation dynamics in monolayers ranging from 100% dDR1 to samples where the dDR1 coverage is about 35%. The orientational dynamics depend strongly on the areal density of dDR1. As the fractional area of dDR1 is reduced, the rates of photowriting, photoerasing, and thermal relaxation increase, and the local orientational confinement of the molecules becomes more heterogeneous.

Macroscopic polarization density, characteristic of ferroelectric phases, is stabilized by dipolar intermolecular interactions. These are weakened as materials become more fluid and of higher symmetry, limiting ferroelectricity to crystals and to smectic liquid crystal stackings of fluid layers. We report the SmAP(F), the smectic of fluid polar orthorhombic layers that order into a three-dimensional ferroelectric state, the highest-symmetry layered ferroelectric possible and the highest-symmetry ferroelectric material found to date. Its bent-core molecular design employs a single flexible tail that stabilizes layers with untilted molecules and in-plane polar ordering, evident in monolayer-thick freely suspended films. Electro-optic response reveals the three-dimensional orthorhombic ferroelectric structure, stabilized by silane molecular terminations that promote parallel alignment of the molecular dipoles in adjacent layers.

Mixtures of 8CB (a calamitic mesogen) and NOBOW (P-9-O-PIMB, a bent-core mesogen) have been investigated using differential scanning calorimetry, nuclear magnetic resonance spectroscopy, and freeze fracture transmission electron microscopy. On cooling the isotropic mixture, the NOBOW component phase separates, forming a dilute, random network of helical nanofilaments in the B4 phase with isotropic 8CB material filling the interstitial volume. At lower temperature, but still far above the bulk isotropic-nematic transition of pure 8CB, a significant fraction of the 8CB becomes prealigned on the filament surfaces. We propose that this pretransitional ordering is induced by short-range interactions of the polar 8CB molecules with the NOBOW filaments, leading to the formation of an adsorbed film of orientationally frozen 8CB around each filament.

Among the condensed phases, those of lowest point group symmetry are the triclinic crystals, which have only the identity element or the identity and inversion elements. Such low symmetry is stabilized by the specificity of molecular interaction, which is weakened with increasing disorder, so that known phases with fluid degrees of freedom are more symmetric. Here we report triclinic order, appearing as a broken symmetry in a single, isolated, fluid smectic liquid crystal layer freely suspended in air, showing that none of its principal dielectric axes lies either normal or parallel to the layer plane.

W415 is a chiral smectic compound with a remarkably weak temperature dependence of its giant electroclinic effect in the liquid crystalline smectic A* phase. Furthermore it possesses a high spontaneous polarization in the smectic C* phase. The origin of this striking electroclinic effect is the co-occurrence of a de Vries-type ordering with a weak first-order tilting transition (see the synchroton X-ray scattering profiles).

We describe a new type of optically controlled liquid crystal alignment layer that demonstrates unprecedented performance. It consists of an aminoazobenzene-type material with a very simple molecular structure, which is derived from methyl red by a one-step synthesis. We have devised a method of forming covalently attached monolayers of this material on glass by an amine-assisted condensation reaction involving the triethoxysilane end of the molecule. A nematic liquid crystal (LC) cell made with the monolayer and a rubbed polymer layer was switched from a uniform state to a twisted state with a polarized 450 nm control beam having a dose of 5.5 mJ/cm(2). This is equivalent to an average of only one absorbed photon per azobenzene group. Through atomic force microscopy, absorption spectroscopy, spectroscopic ellipsometry, and second harmonic generation experiments, we have confirmed that layers of this type are smooth and uniform with a surface coverage consistent with a monolayer and that the azobenzene groups are tilted, on average, 55 degrees with respect to the surface normal. These characteristics lead to a large interaction energy density between the layer and LC. The monolayer's rapid response in developing anisotropy in this property can be attributed to a large absorption cross section, as well as the favorable tilt angle, which allows for sufficient photoisomerization free volume in a dense layer.

The SmC phase of 4'-octyloxyphenyl-4-octyloxybenzoate has been examined in light of recent reports that this phase is chiral. The results suggest that two varieties of chiral domains in LC cells of the phenylbenzoate are indeed formed, driven by interactions with surfaces. Application of sensitive probes for chirality and polarity in the absence of such interfacial influences failed to find any. Currently, there is no evidence that the subject SmC phase is chiral.