Mosaics of topological defects in micropatterned liquid crystal textures

On-Demand Tunable Electrical Conductance Anisotropy in a MOF-Polymer Composite

Property optimization through orientation control of metal-organic framework (MOF) crystals that exhibit anisotropic crystal structures continues to garner tremendous interest. Herein, an electric field is utilized to post-synthetically control the orientation of conductive layered Cu3(HHTP)2 (HHTP = 2,3,6,7,10,11-hexahydroxytriphenylene) crystals dispersed in an electronically insulating poly(ethylene glycol) diacrylate (PEGDA) oligomer matrix. Optical and electrical measurements are performed to investigate the impact of the electric field on the alignment of Cu3(HHTP)2 crystals and the formation of aggregated microstructures, which leads to an ≈5000-fold increase in the conductivity of the composite. Notably, the composite thin-films containing aligned Cu3(HHTP)2 crystals exhibit significant conductivity of ≈10-3 S cm-1 despite the low concentration (≈1 wt.%) of conductive Cu3(HHTP)2. The use of an electric field to align Cu3(HHTP)2 crystals can rapidly generate various desired patterns that exhibit on-demand tunable collective charge transport anisotropy. The findings provide valuable insights toward the manipulation and utilization of conductive MOFs with anisotropic crystal structures for various applications such as adhesive electrical interconnects and microelectronics.

Tunable templating of photonic microparticles via liquid crystal order-guided adsorption of amphiphilic polymers in emulsions

Multiple emulsions are usually stabilized by amphiphilic molecules that combine the chemical characteristics of the different phases in contact. When one phase is a liquid crystal (LC), the choice of stabilizer also determines its configuration, but conventional wisdom assumes that the orientational order of the LC has no impact on the stabilizer. Here we show that, for the case of amphiphilic polymer stabilizers, this impact can be considerable. The mode of interaction between stabilizer and LC changes if the latter is heated close to its isotropic state, initiating a feedback loop that reverberates on the LC in form of a complete structural rearrangement. We utilize this phenomenon to dynamically tune the configuration of cholesteric LC shells from one with radial helix and spherically symmetric Bragg diffraction to a focal conic domain configuration with highly complex optics. Moreover, we template photonic microparticles from the LC shells by photopolymerizing them into solids, retaining any selected LC-derived structure. Our study places LC emulsions in a new light, calling for a reevaluation of the behavior of stabilizer molecules in contact with long-range ordered phases, while also enabling highly interesting photonic elements with application opportunities across vast fields.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Simultaneous detection of polarization states and wavefront by an angular variant micro-retarder-lens array

We have demonstrated simultaneous detection of the polarization states and wavefront of light using a 7 × 7 array of angular variant micro-retarder-lenses. Manipulating the angular variant polarization with our optical element allows us to determine the two-dimensional distribution of polarization states. We have also proposed a calibration method for polarization measurements using our micro-retarder-lens array, allowing accurate detection of polarization states with an ellipticity of ± 0.01 and an azimuth of ± 1.0°. We made wavefront measurements using the micro-retarder-lens array, achieving a resolution of 25 nm. We conducted simultaneous detection of the polarization states and wavefront on four types of structured beam as samples. The results show that the two-dimensional distributions of the polarization states and wavefront for the four types of structured light are radially and azimuthally polarized beams, as well as left- and right-hand optical vortices. Our sensing technology has the potential to enhance our understanding of the nature of light in the fields of laser sciences, astrophysics, and even ophthalmology.

Electrical tuning of branched flow of light

Branched flows occur ubiquitously in various wave systems, when the propagating waves encounter weak correlated scattering potentials. Here we report the experimental realization of electrical tuning of the branched flow of light using a nematic liquid crystal (NLC) system. We create the physical realization of the weakly correlated disordered potentials of light via the inhomogeneous orientations of the NLC. We demonstrate that the branched flow of light can be switched on and off as well as tuned continuously through the electro-optical properties of NLC film. We further show that the branched flow can be manipulated by the polarization of the incident light due to the optical anisotropy of the NLC film. The nature of the branched flow of light is revealed via the unconventional intensity statistics and the rapid fidelity decay along the light propagation. Our study unveils an excellent platform for the tuning of the branched flow of light which creates a testbed for fundamental physics and offers a new way for steering light.

Planar Spin Glass with Topologically Protected Mazes in the Liquid Crystal Targeting for Reconfigurable Micro Security Media

The planar spin glass pattern is widely known for its inherent randomness, resulting from the geometrical frustration. As such, developing physical unclonable functions (PUFs)-which operate with device randomness-with planar spin glass patterns is a promising candidate for an advanced security systems in the upcoming digitalized society. Despite their inherent randomness, traditional magnetic spin glass patterns pose considerable obstacles in detection, making it challenging to achieve authentication in security systems. This necessitates the development of facilely observable mimetic patterns with similar randomness to overcome these challenges. Here, a straightforward approach is introduced using a topologically protected maze pattern in the chiral liquid crystals (LCs). This maze exhibits a comparable level of randomness to magnetic spin glass and can be reliably identified through the combination of optical microscopy with machine learning-based object detection techniques. The "information" embedded in the maze can be reconstructed through thermal phase transitions of the LCs in tens of seconds. Furthermore, incorporating various elements can enhance the optical PUF, resulting in a multi-factor security medium. It is expected that this security medium, based on microscopically controlled and macroscopically uncontrolled topologically protected structures, may be utilized as a next-generation security system.

Formation of topological defects at liquid/liquid crystal interfaces in micro-wells controlled by surfactants and light

Topological defects, the fundamental entities arising from symmetry-breaking, have captivated the attention of physicists, mathematicians, and materials scientists for decades. Here we propose and demonstrate a novel method for robust control of topological defects in a liquid crystal (LC), an ideal testbed for the investigation of topological defects. A liquid layer is introduced on the LC in microwells in a microfluidic device. The liquid/LC interface facilitates the control of the LC alignment thereby introducing different molecules in the liquid/LC phase. A topological defect is robustly formed in a microwell when the liquid/LC interface and the microwell surface impose planar and homeotropic alignment, respectively. We also demonstrate the formation/disappearance of topological defects by light illumination, realized by dissolving photo-responsive molecules in the LC. Our platform that facilitates the control of LC topological defects by the introduction of different molecules and external stimuli could have potential for sensor applications.

Utilization of Physical Anisotropy in Metal-Organic Frameworks via Postsynthetic Alignment Control with Liquid Crystal

Metal-organic frameworks (MOFs) represent crystalline materials constructed from combinations of metal and organic units to often yield anisotropic porous structures and physical properties. Postsynthetic methods to align the MOF crystals in bulk remain scarce yet tremendously important to fully utilize their structure-driven intrinsic properties. Herein, we present an unprecedented composite of liquid crystals (LCs) and MOFs and demonstrate the use of nematic LCs to dynamically control the orientation of MOF crystals with exceptional order parameters (as high as 0.965). Unique patterns formed through a facile multidirectional alignment of MOF crystals exhibit polarized fluorescence with the fluorescence intensity of a pattern dependent on the angle of a polarizer, offering potential use in various optical applications such as an optical security label. Further, the alignment mechanism indicates that the method is applicable to numerous combinations of MOFs and LCs, which include UV polymerizable LC monomers used to fabricate free-standing composite films.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Patterned Hydrophobic Liquid Crystalline Fibers Fabricated from Defect Arrays of Reactive Mesogens via Electric Field Modulation

We have fabricated patterned fibers using a small-molecular-weight liquid crystal (LC) and reactive mesogens (RMs) under controlled electric fields in which defect arrays are generated depending on the electrode configuration. For this, the AC electric field with interdigitated electrodes is used to develop versatile defect structures of the LC phase. Hydrophobic LC network (LCN) fibers exhibiting porous morphologies have been made by removing the LC part after the polymerization of RM. The resulting LCN fibers show a surface tension reduction characteristic compared to the neat RM film and a sticky characteristic with the water droplet, suggesting a facile way to fabricate the hydrophobic surface that can be used in microdroplet transport.

Self-assembled liquid crystal architectures for soft matter photonics

Self-assembled architectures of soft matter have fascinated scientists for centuries due to their unique physical properties originated from controllable orientational and/or positional orders, and diverse optic and photonic applications. If one could know how to design, fabricate, and manipulate these optical microstructures in soft matter systems, such as liquid crystals (LCs), that would open new opportunities in both scientific research and practical applications, such as the interaction between light and soft matter, the intrinsic assembly of the topological patterns, and the multidimensional control of the light (polarization, phase, spatial distribution, propagation direction). Here, we summarize recent progresses in self-assembled optical architectures in typical thermotropic LCs and bio-based lyotropic LCs. After briefly introducing the basic definitions and properties of the materials, we present the manipulation schemes of various LC microstructures, especially the topological and topographic configurations. This work further illustrates external-stimuli-enabled dynamic controllability of self-assembled optical structures of these soft materials, and demonstrates several emerging applications. Lastly, we discuss the challenges and opportunities of these materials towards soft matter photonics, and envision future perspectives in this field.

The fate of liquid crystal topological defects on chemically patterned surfaces during phase transitions

Controlling topological defects in liquid crystals (LCs) is an essential element in the development of areas such as directed self-assembly and micropatterning materials. However, during the phase transition on confined patterned surfaces, how the morphologies in one liquid crystalline phase change from deformations or defects into another phase is much less known. Here, we examine the fate of defects in a LC confined on a patterned surface during smectic-A-nematic and nematic-isotropic phase transitions, using experiments and simulation analyses. Upon heating from smectic-A to nematic, a Toric focal conical domain (TFCD) melts into a +1 converging boojum defect, which then transitioned into a concentric configuration as temperature increases, attributed to a steeper decrease of the bend and twist modulus compared to splay modulus. During cooling, TFCDs are developed from two distinct pathways depending on the cooling rates. Our continuum simulation recapitulates these transformations and provides elastic constant-based explanations for the two pathways. Although the phase transition pathways of defects are independent of the geometry of the confined patterns, the arrangement of FCDs is highly dependent on the size and shape of the patterns. Taken together, this simple approach offers promising opportunities for tuning the micro- or nano-patterning of topological defects in liquid crystals.

Fabrication of Arrays of Topological Solitons in Patterned Chiral Liquid Crystals for Real-Time Observation of Morphogenesis

Topological solitons have knotted continuous field configurations embedded in a uniform background, and occur in cosmology, biology, and electromagnetism. However, real-time observation of their morphogenesis and dynamics is still challenging because their size and timescale are enormously large or tiny. Liquid crystal (LC) structures are promising candidates for a model-system to study the morphogenesis of topological solitons, enabling direct visualization due to the proper size and timescale. Here, a new way is found to rationalize the real-time observation of the generation and transformation of topological solitons using cholesteric LCs confined in patterned substrates. The experimental demonstration shows the topologically protected structures arise via the transformation of topological defects. Numerical modeling based on minimization of free energy closely reconstructs the experimental findings. The fundamental insights obtained from the direct observations pose new theoretical challenges in understanding the morphogenesis of different types of topological solitons within a broad range of scales.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

Oblique light incidence method to study topological defects in nematic layers with conical boundary conditions

A polarization microscopy method to investigate the orientational structures and boojums formed in the chiral and achiral nematic layers under conical (tilted) boundary conditions has been developed. Oblique light incidence on nematic layer is used, due to which the phase difference between the ordinary and extraordinary waves depends on the director's azimuthal angle. The phase difference gets maximal when the director azimuthal angle of achiral nematic [Formula: see text] and an azimuthal angle at the center of the chiral nematic layer [Formula: see text] independently of the total twist angle [Formula: see text]. It has been found that the [Formula: see text] boojums with the phase [Formula: see text] and [Formula: see text] are formed in achiral and chiral nematics, respectively, at the director tilt angle [Formula: see text] at the interface. In addition, the defectless structure of chiral nematic with the periodically variable azimuthal director angle on the substrates has been studied.

Role of Stimuli on Liquid Crystalline Defects: From Defect Engineering to Switchable Functional Materials

Achieving tunable physical properties is currently one of the most exciting research topics. In order to realize this goal, a medium that is responsive to external stimuli and can undergo a change in its physical property is required. Liquid crystal (LC) is a prominent candidate, as its physical and optical properties can be easily manipulated with various stimuli, such as surface anchoring, rubbing, geometric confinement, and external fields. Having broken away from the past devotion to obtaining a uniform domain of LCs, people are now putting significant efforts toward forming and manipulating ordered and oriented defect structures with a unique arrangement within. The complicated molecular order with tunability would benefit the interdisciplinary research fields of optics, physics, photonics, and materials science. In this review, the recent progress toward defect engineering in the nematic and smectic phases by controlling the surface environment and electric field and their combinational methods is introduced. We close the review with a discussion of the possible applications enabled using LC defect structures as switchable materials.

Periodic Arrays of Chiral Domains Generated from the Self-Assembly of Micropatterned Achiral Lyotropic Chromonic Liquid Crystal

Achiral building blocks forming achiral structures is a common occurrence in nature, while chirality emerging spontaneously from an achiral system is usually associated with important scientific phenomena. We report on the spontaneous chiral symmetry-breaking phenomena upon the topographic confinement of achiral lyotropic chromonic liquid crystals in periodically arranged micrometer scale air pillars. The anisotropic fluid arranges into chiral domains that depend on the arrangement and spacing of the pillars. We characterize the resulting domains by polarized optical microscopy, support their reconstruction by numerical calculations, and extend the findings with experiments, which include chiral dopants. Well-controlled and addressed chiral structures will be useful in potential applications like programmable scaffolds for living liquid crystals and as sensors for detecting chirality at the molecular level.

Topological-Defect-Induced Surface Charge Heterogeneities in Nematic Electrolytes

We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In particular, the location and type of the defect encodes the precise distribution of surface charges and the effect is enhanced when the liquid crystal is flexoelectric. We demonstrate the principle for patterned surfaces and charged colloidal spheres. More generally, our results indicate an interesting approach to control surface charges on external surfaces without changing the surface chemistry.

Fiber Lithography: A Facile Lithography Platform Based on Electromagnetic Phase Modulation Using a Highly Birefringent Electrospun Fiber

Lithography plays a key role in advancing manufacturing as well as the semiconductor industry. However, the currently available state-of-the-art lithography methods still require access to expensive tools and facilities. Herein, we suggest a novel lithography method based on electromagnetic phase modulation of ultraviolet using a highly birefringent electrospun fiber to overcome such limitations. The optical birefringent effect, by which the phase of incident ultraviolet electromagnetic fields is retarded when passing through optically anisotropic media, is combined with semicrystalline poly(ethylene oxide) (PEO)-poly(ethylene glycol) (PEG) polymeric microfibers patterned in a programmable form using near-field electrospinning. By positioning the mask between two linear polarizers that are perpendicular to each other, only the UV waves that are passing through the fibers can be selectively utilized to exhibit lithographic property. Therefore, the UV intensity on the photoresist (PR) surface follows the shape of the fiber pattern, enabling precisely controlled patterning of the photoresist. Zero- to two-dimensional key features of lithography are achieved, including straight, curved, array, and isolated patterns. Facile optical alignments without using dedicated alignment marks are successfully demonstrated, as well as various applications including micro- to macroscale serpentine, tree, and antenna circuit patterns on a flexible substrate. The presented approach, packed in a table-top scale, is expected to provide a practical and affordable lithography solution by leveraging the direct-writing capability and tunable optical functionality of polymers, scalability, and the simple optical alignment method.

Topological Defect Arrays in Nematic Liquid Crystals Assisted by Polymeric Pillar Arrays: Effect of the Geometry of Pillars

Topological defects that spontaneously occur in condensed matter and structured fluids such as liquid crystals are useful for their elastic and optical properties, but often the applicability of defect arrays to optics and photonic devices relies on the regularity and tunability of the system. In our recent work [Adv. Opt. Mater. 8, 1900991 (2020)], we showed the formation of regular, reconfigurable, and scalable patterns by exploiting the elastic response of a defect array in liquid crystals in the presence of a polymeric pillar array. In this work, we experimentally investigate the role of size and shape of the pillars on the defect array. We find that the pillar size and geometry provide additional means to regulate the response time, the threshold voltage for the defects’ formation, and the spatial arrangement of the defects.

Self-Assembled Asymmetric Microlenses for Four-Dimensional Visual Imaging

Visual imaging that can extract three-dimensional (3D) space or polarization information on the target is essential in broad sciences and technologies. The simultaneous acquisition of them usually demands expensive equipment and sophisticated operations. Therefore, it is of great significance to exploit convenient approaches for four-dimensional (3D and polarization) visual imaging. Here, we present an efficient solution based on self-assembled asymmetric liquid crystal microlenses, with freely manipulated phase profiles and symmetry-breaking properties. Accordingly, characteristics of multifocal functionality and polarization selectivity are exhibited, along with the underlying mechanisms. Moreover, with a specific sample featured by radially increased unit sizes and azimuthally varied domain orientations, the discriminability of four-dimensional information is extracted in a single snapshot, via referring to the coordinates of the clearest images. Demultiplexing of depth/polarization information is also demonstrated. This work will unlock a variety of revolutionary apparatuses and lighten extensive applications.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Artificial colloidal liquid metacrystals by shearing microlithography

Meta-periodicity beyond intrinsic atomic and molecular order, such as metacrystalline and quasicrystalline lattices, exists in solids, but is usually elusive in lyotropic liquid crystals for its energetic instability. The stable meta-periodicity in lyotropic liquid crystals in the absence of external stimuli remains unexplored, and how to achieve it keeps a great challenge. Here we create lyotropic liquid crystals with stable meta-periodicity in a free state, coined as liquid metacrystals, in colloidal systems by an invented shearing microlithography. The meta-periodicity is dynamically stabilized by the giant molecular size and strong excluded volume repulsion. Liquid metacrystals are designed to completely cover a library of symmetries, including five Bravais and six quasicrystalline lattices. Liquid metacrystal promises an extended form of liquid crystals with rich meta-periodicity and the shearing microlithography emerges as a facile technology to fabricate liquid meta-structures and metamaterials, enabling the digital design of structures and functionalities of liquid crystalline materials.

Stable periodic structures can be difficult to obtain in a liquid crystal compared to a solid due to the energetic instability of the former. Here the authors present a technique to fabricate quasicrystalline structures of graphene oxide liquid crystals which have high stability.

Topological defects and geometric memory across the nematic-smectic A liquid crystal phase transition

We study transformations of self-organised defect arrays at the nematic-smectic A liquid crystal phase transition, and show that these defect configurations are correlated, or "remembered", across the phase transition. A thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an air interface and a water substrate, and viewed under polarised optical microscopy. Upon heating from smectic-A to nematic, a packing of focal conic domains melts into a dense array of boojums-nematic surface defects-which then coarsens by pair-annihilation. With the aid of Landau-de Gennes numerical modeling, we elucidate the topological and geometrical rules underlying this transformation. In the transition from nematic to smectic-A, we show that focal conic domain packings are organised over large scales in patterns that retain a geometric memory of the nematic boojum configuration, which can be recovered with remarkable fidelity.