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.

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.

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.

Macroscopic Nematic Orientation Dictated by an Orientationally Frustrated Random-Field Surface: Equilibrium Structure and Kinetics.

Liquid crystals subjected to frustrated surfaces with mixed anchoring conditions demonstrate a rich variety of orientational patterns. Particularly, it would trigger either continuous or discontinuous variation of the bulk orientation, i.e., a phenomenon known as the anchoring or orientational transition. Despite its prime importance in developing novel optoelectronic devices, how the surface anchoring patterns dedicate the energy landscape of a system, thus the equilibrium state, still needs to be understood. Here, we designed a simulation to model boundary substrates with two randomly mixed anchoring domains in space, which exhibit planar and homeotropic preferences. We numerically obtain general bulk orientational state diagrams under various surface and electric field conditions, which reveal the roles of each domain's size and surface fraction and anchoring strength on the bulk orientational state. Furthermore, we examine how the external electric field modifies the orientational state diagram and uncovers a field-assisted anchoring transition. We discuss the observed bistability and compare it to experimental evidence.

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.

Polarization patterning in ferroelectric nematic liquids via flexoelectric coupling.

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

Encoding Coacervate Droplets with Paramagnetism for Dynamical Reconfigurability and Spatial Addressability.

It is an ongoing endeavor in chemistry and materials science to regulate coacervate droplets on a physiologically relevant spatiotemporal scale to ultimately match or even surpass living cells' precision, complexity, and functionality. Herein, we develop a magnetic strategy orthogonal to the thermal, pH, light, or chemical counterparts that are commonly employed by biotic or artificial systems; its successful implementation thus adds a missing piece to the current arsenal of manipulative methodologies. Specifically, we paramagnetize the otherwise diamagnetic coacervate droplets by cooperatively combining paramagnetic ingredients (including organic radicals, metal ions, and Fe3O4 nanoparticles) and coacervate ingredients to obtain "MagCoa" droplets. A simple model is derived theoretically to account for migration and division of MagCoa droplets in an uneven magnetic field. Experimentally, we produce an array of compartmentalized and monodispersed droplets using microfluidics and magnetically steer them with uniformity and synchronicity. We design and fabricate spatial magnetic modulators to engineer the landscape of a magnetic field that, in turn, directs the MagCoa droplets into predesigned patterns in a reconfigurable fashion. These programmable liquid patterns can be potentially extended to dynamic assembly and information encryption. We envision that the toolbox established here is of generality and multitudes to serve as a practical guide to control droplets magnetically.

Nontrivial ultraslow dynamics under electric-field in nematics of bent-shaped molecules.

For over decades, nematic liquid crystals have been recognized as highly fluidic materials that respond to electric field on the millisecond scale. In contrast to traditional nematics with fast responsivity, we herein report nontrivial ultraslow electric-driven dynamics in bent-shaped nematic materials. Varying the alkyl chain spacers of bent-shaped cyanobiphenyl dimers (COOm and OCOm) shows a 'transition' in the dynamics behavior between the bent-dimeric and bent-core materials. Interestingly, with short alkyl chain spacers, COO2 exhibits unexpected ultra-slow dynamic pathways, i.e., "quasi-static" electrohydrodynamic convection. A significant observation is that the on/off-electro-switching time of COO2 is 10 000 times higher than that of typical nematic materials, which is the largest value reported ever in the kilo-second range. In addition, the threshold voltage for inducing the reorientation of the nematic director for COO2 is higher than 5 V, which is uncommon in traditional N materials. These properties are distinct from those of traditional nematic materials and discussed in terms of dielectric constants and electrohydrodynamic convection.

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.

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

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.

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.

Nontrivial topological defects of micro-rods immersed in nematics and their phototuning.

Combinations of different geometries and surface anchoring conditions give rise to the diversity of topological structures in nematic colloid systems. Tuning these parameters in a single system offers possibilities for observing the evolution of the topological transformation and for manipulating colloids through topological forces. Here we investigate the nontrivial topological properties of micro-rods dispersed in nematic liquid crystals through experimental observation and computer simulation. The topological variation is driven by photodynamically changing the surface anchoring using azobenzene-based surface-commander molecules, the majority of which are localized on both the substrates and the surface of micro-rods. By comparing experimental and simulation results, we show previously unidentified topological properties of the two-body LC-rod-colloid system. Moreover, unlike the traditional photoresponsive liquid crystal systems, the localization of azobenzene molecules on the surfaces makes it possible to change only the direction of the surface orientation, not disordering of the bulk structures. The results assist in the development of photo-driven micro-robotics in fluids.

Propagating wave in a fluid by coherent motion of 2D colloids.

Just like in living organisms, if precise coherent operation of tiny movable components is possible, one may generate a macroscopic mechanical motion. Here we report that ~1010 pieces of colloidally dispersed nanosheets in aqueous media can be made to operate coherently to generate a propagating macroscopic wave under a non-equilibrium state. The nanosheets are initially forced to adopt a monodomain cofacial geometry with a large and uniform plane-to-plane distance of ~420 nm, where they are strongly correlated by competitive electrostatic repulsion and van der Waals attraction. When the electrostatic repulsion is progressively attenuated by the addition of ionic species, the nanosheets sequentially undergo coherent motions, generating a propagating wave. This elaborate wave in time and space can transport microparticles over a long distance in uniform direction and velocity. The present discovery may provide a general principle for the design of macroscopically movable devices from huge numbers of tiny components.

How Far Can We Push the Rigid Oligomers/Polymers toward Ferroelectric Nematic Liquid Crystals?

The emerging ferroelectric nematic (NF) liquid crystal is a novel 3D-ordered liquid exhibiting macroscopic electric polarization. The combination of the ultrahigh dielectric constant, strong nonlinear optical signal, and high sensitivity to the electric field makes NF materials promising for the development of advanced liquid crystal electroopic devices. Previously, all studies focused on the rod-shaped small molecules with limited length (l) range and dipole moment (µ) values. Here, through the precision synthesis, we extend the aromatic rod-shaped mesogen to oligomer/polymer (repeat unit up to 12 with monodisperse molecular-weight dispersion) and increase the µ value over 30 Debye (D). The NF phase has a widespread existence far beyond our expectation and could be observed in all the oligomer/polymer length range. Notably, the NF phase experiences a nontrivial evolution pathway with the traditional apolar nematic phase completely suppressed, i.e., the NF phase nucleates directly from the isotropic liquid phase. The discovery of thte ferroelectric packing of oligomer/polymer rods not only offers the concept of extending the NF state to oligomers/polymers but also provides some previously overlooked insights in oxybenzoate-based liquid crystal polymer materials.

Spontaneous helielectric nematic liquid crystals: Electric analog to helimagnets.

Recently, a type of ferroelectric nematic fluid has been discovered in liquid crystals in which the molecular polar nature at molecule level is amplified to macroscopic scales through a ferroelectric packing of rod-shaped molecules. Here, we report on the experimental proof of a polar chiral liquid matter state, dubbed helielectric nematic, stabilized by the local polar ordering coupled to the chiral helicity. This helielectric structure carries the polar vector rotating helically, analogous to the magnetic counterpart of helimagnet. The helielectric state can be retained down to room temperature and demonstrates gigantic dielectric and nonlinear optical responses. This matter state opens a new chapter for developing the diverse polar liquid crystal devices.

Photo-reconfigurable twisting structure in chiral liquid crystals triggered by photoresponsive surface.

Shape-transformable molecular additives with photoresponsivity, such as azobenzene or spiropyran, in matter are known to decrease the local order parameter and lead to drastic state variations under light irradiation. For example, a liquid crystalline state can be transformed to an isotropic liquid state by photo-exciting a tiny amount of azobenzene additives from trans- to cis-conformers. On the other hand, structural or shape transformation without changing the phase state is also intriguing since it offers an opportunity for manipulating specific structures. Here, we demonstrate an active control of the topology of chiral particle-like twisting structures, dubbed toron, by light. Interestingly, the individual twisting structure is fully reconfigurable between spherical and unique branched topological states. We reveal that the shape transformation is driven by the free-energy competition between the variation of surface anchoring strength and the elastic energy stored in the twisting structure. The mean-field simulation based on the Landau-de Gennes framework shows that the elastic anisotropy plays the dominant role in modifying the toron topology upon weak anchoring. The results offer a new path for understanding the process of topology-involved shape transformation and fabrication of novel functional materials.

Development of ferroelectric nematic fluids with giant-ε dielectricity and nonlinear optical properties.

Superhigh-ε materials that exhibit exceptionally high dielectric permittivity are recognized as potential candidates for a wide range of next-generation photonic and electronic devices. In general, achieving a high-ε state requires low material symmetry, as most known high-ε materials are symmetry-broken crystals. There are few reports on fluidic high-ε dielectrics. Here, we demonstrate how small molecules with high polarity, enabled by rational molecular design and machine learning analyses, enable the development of superhigh-ε fluid materials (dielectric permittivity, ε > 104) with strong second harmonic generation and macroscopic spontaneous polar ordering. The polar structures are confirmed to be identical for all the synthesized materials. Furthermore, adapting this strategy to high-molecular weight systems allows us to generalize this approach to polar polymeric materials, creating polar soft matters with spontaneous symmetry breaking.