Two-dimensional Liquid Crystal Research Articles

An Electro-Optical Kerr Device Based on 2D Boron Nitride Liquid Crystals for Solar-Blind Communications.

Achieving light modulation in the spectral range of 200-280 nm is a prerequisite for solar-blind ultraviolet communication, where current technologies are mainly based on the electro-luminescent self-modulation of the ultraviolet source. External light modulation through the electro-birefringence control of liquid crystal (LC) devices has shown success in the visible-to-infrared regions. However, the poor stability of conventional LCs against ultraviolet irradiation and their weak electro-optical response make it challenging to modulate ultraviolet light. Here, an external ultraviolet light modulator is demonstrated using two-dimensional boron nitride LC. It exhibits robust ultraviolet stability and a record-high specific electro-optical Kerr coefficient of 5.1×10⁻2 m V-2, being three orders of magnitude higher than those of other known electro-optical media that are transparent (or potentially transparent) in the ultraviolent spectral range. The sensitive response enables fabricating transmissive and stable ultraviolet-C electro-optical Kerr modulators for solar-blind ultraviolet light. An M-ary coding array with high transmission density is also demonstrated for solar-blind ultraviolet communication.

A blow-up criterion for the strong solutions to the two-dimensional non-isothermal inhomogeneous liquid crystal flow with density-dependent viscosity

A blow-up criterion for the strong solutions to the two-dimensional non-isothermal inhomogeneous liquid crystal flow with density-dependent viscosity

A high-haze liquid crystal grating device with asymmetric anchoring energies

We present the development of a novel two-dimensional (2-D) liquid crystal (LC) grating device with asymmetric surface anchoring. By employing a waffle-shaped electrode on one substrate, a 2-D electric field is generated. The introduction of weak anchoring energy on one of the substrates enables easier rotation of LC molecules between the electrodes upon voltage application in an asymmetrically anchored device. As a result, the proposed grating device exhibits a significant spatial phase difference in any direction, leading to a high-haze value in the opaque state (94.36%). Furthermore, it offers notable advantages such as enhanced fabricability, simplified driving mechanism, and reduced operating voltage requirements.

Orientational ordering of polydisperse nanorods on a flat surface

The use of two-dimensional liquid crystals (2D LCs) made of carbon nanorods has become increasingly popular in electronic, optical, and energy applications due to their unique properties. However, the orientational ordering of such liquid crystals remains poorly understood. Here, we model of 2D LCs using the length polydisperse hard needle model and apply theOnsager theory to explore the impact of length polydispersity on nematic ordering. Our results show that length polydispersity plays a crucial rolein stabilizing the nematic phase over the isotropic phase, albeit at the expense of weaker orientational ordering. Longer rods, in particular, contribute to the stabilization of the nematic phase, whereas shorter rods result in weaker nematic ordering. To achieve a highly ordered 2D nematic phase, the polydispersity of the nanorods must be reduced.

Droplet Formation in Dynamic Stratified Liquid–Liquid Systems for Solution-Based Deposition Methods

Abstract The assembly of a two-dimensional (2D) nematic liquid crystal at an interface between two liquids can be exploited to assemble densely packed and highly aligned arrays of rod-like nanoparticles. This method is especially relevant to creating arrays of semiconducting carbon nanotubes (CNTs) for high-performance electronics. When a dense solvent containing CNTs flows over a less dense water subphase in a confined channel, the locally aligned arrays of nanoparticles align globally with the flow direction and can be transferred to the substrate. For large substrates and long channels, the dense solvent tends to slow and create a pool, which then drops through the interface and disturbs the delicate deposition process. Understanding this phenomenon is critical to improving and scaling up similar manufacturing processes. Here, data are collected, and an empirical model is developed to understand and predict the pooling behavior of a suspended fluid flowing over a less dense subphase. The model is demonstrated with two different solvents and proves to be accurate within +/− 15%. With a better understanding of the physics governing the system, the model is then used to suggest methods for minimizing pooling behavior.

Flow patterns and defect dynamics of active nematic liquid crystals under an electric field.

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics with simultaneous creation of two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.

P‐12.1: Two‐dimensional Edge Detection Implementation of Liquid Crystal Computing Metasurfaces

Computing metasurfaces have received widespread attention since they were proposed, and the ability to realize mathematical operations has enabled real time image processing with new breakthroughs, such as optical edge detection. In this paper, a new method for two-dimensional edge detection is presented, and the two-dimensional liquid crystal polarization grating is designed from the theoretical derivation. The gratings with different periods are fabricated by photoalignment technology. The one-dimensional and two-dimensional imaged edge detection are experimental realized in this work. By measuring the displacement of edge detection, the experimental results with different periods are in line with theoretical formula. The low cost and easily fabricated photoaligned liquid crystal polarization gratings achieved the real time optical computation with broadband and adjustable, which can be further applied in biological image edge and other optical display related fields.

Active nematic fluid films

Coupling surface deformations with active stresses in two-dimensional nematic liquid crystal films leads to a rich area of investigation, particularly in biological fluid mechanics across multiple scales from tissue mechanics to cell membrane mechanics. In Al-Izzi & Morris (J. Fluid Mech., vol. 957, 2023, A4), the authors derive the complete set of governing equations for such systems. Their results provide an extended theoretical framework with which active nematic fluid films with in-plane flow and out-of-plane deformation can be analysed. To illustrate the potential applications of this framework, a few specific biologically inspired examples are discussed.

Hydrodynamic Enhancement of p-atic Defect Dynamics.

We investigate numerically and analytically the effects of hydrodynamics on the dynamics of topological defects in p-atic liquid crystals, i.e., two-dimensional liquid crystals with p-fold rotational symmetry. Importantly, we find that hydrodynamics fuels a generic passive self-propulsion mechanism for defects of winding number s=(p-1)/p and arbitrary p. Strikingly, we discover that hydrodynamics always accelerates the annihilation dynamics of pairs of ±1/p defects and that, contrary to expectations, this effect increases with p. Our Letter paves the way toward understanding cell intercalation and other remodeling events in epithelial layers.

Laminar and turbulent flow development study in a rectangular duct with 180° sharp bend by using stereo particle image velocimetry and liquid crystal thermography measurements

This work presents a detailed insight into the flow progression and surface heat transfer distribution across the sharp 180° bend of a two-pass rectangular duct for laminar (Re = 800) and turbulent (Re = 6500) in-flow conditions. Stereoscopic particle image velocimetry (stereo PIV) as well as two-dimensional and two-component PIV measurements and liquid crystal thermography techniques are appropriately used for flow and heat transfer characterization across the complete sharp 180° bend. The centrifugal instabilities arise due to the sharp bend, which induces the secondary flows in the form of counter-rotating vortex pairs commonly known as Dean vortices. These secondary vortices play a significant role in the localized laminar–turbulent transition and turbulence augmentations for laminar and turbulent inflow conditions. Subsequently, quantitative analysis shows that complete 180° turning of flow resulted in intense augmentation of spatially averaged turbulence quantities. Root mean square (RMS) fluctuations in the transverse direction V¯T|rms increase by 298% and 186% for respective flow conditions. Augmentation of ∼ 287% (laminar) and 260% (turbulent) in the wall-normal RMS fluctuations (V¯N|rms) are observed. These augments in transverse and wall-normal velocity fluctuations result in a very sharp amplification of spatially averaged turbulent kinetic energy (k¯), that is, 1825% for inlet laminar and 928% for inlet turbulent flow regimes.

Continuous structural deformation of graphene oxide liquid crystal colloids under shear for hydrogel films

In the processing of two-dimensional (2D) liquid crystal (LC), the microstructure of 2D LC colloids is continuously deformed by shearing, which ultimately determines their physical properties. However, it is experimentally difficult to investigate and visualize how the microstructure continuously changes during processing involving shear stress. Thus, controlling the microstructure of 2D LCs using shear forces remains a more difficult problem.Herein, we report the in-situ analysis of structural deformation for 2D colloids liquid crystals focused on the reorientation of the liquid crystal (LC) under oscillatory shear. Graphene oxide (GO) was employed as a model system for 2D LC colloids, and polymers were added to control the 2D colloidal interactions. We found that the GO structure deforms in two steps: The first step is the transition to multi-domains of GO LC and the second transition brings the macroscopic alignment of GO. We additionally found that the added polymer causes the earlier disappearance of multiple GO LC domains and provides a better macroscopic alignment at the same shear condition. The study will be of great interest in the 2D colloidal process accompanying yielding behavior, providing an effective strategy to control the domain orientation and the resulting properties.

Graphene Oxide Liquid Crystals Aligned in a Confined Configuration: Implications for Optical Materials

Orientation control of two-dimensional (2D) colloidal liquid crystals in both microscopic and macroscopic scales holds massive promise for improved multifield applications. In this respect, graphene oxide (GO) is used as a platform substance for 2D carbon-based lyotropic liquid crystal (LC) materials. Here, we design the directed alignment of aqueous GO-LC dispersion confined in a rectangular capillary tube. The isotropic GO dispersion is loaded into a horizontal capillary and subsequently concentrated to the LC phase by slow water evaporation at open ends of the tube. An obtained surprising result, GO layers organize normal to the inner surfaces of the capillary with a highly ordered orientation of the optic axis over tens of millimeters. Such transverse orientation of GO layers originates from the meniscus region and then moves toward the center, caused by the interfacial effect and the sequential isotropic-to-nematic transition. This aligned mesomorphic system is characterized via optical retardation, nematic order parameter, absorption, and modified Cauchy’s transmission equation about the dependency of both birefringence and wavelength with concentration. Finally, the aligned GO-LC layers are preserved in a polymer composite matrix by photopolymerizing the evaporation-aligned GO/acrylamide-LC dispersion confined in a capillary. This composite shows higher thermal stability than polyacrylamide until 500 °C of about 6.1%. Our experimental findings provide efficient advantages for controlling the orientation of GO-LC and 2D materials, beneficial for diverse optical applications due to their directional ordering.

Defect absorption and emission for p-atic liquid crystals on cones.

We investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle β, the apex develops an effective topological charge of -χ, where 2πχ=2π(1-sinβ) is the deficit angle of the cone, and a topological defect of charge σ behaves as if it had an effective topological charge Q_{eff}=(σ-σ^{2}/2) when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. For total topological defect charge 1, e.g., imposed by tangential boundary conditions at the edge, we find that for a disk the ground-state configuration consists of p defects each of charge +1/p lying equally spaced on a concentric ring of radius d=(p-1/3p-1)^{1/2p}R, where R is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground-state configurations as a function of cone angle: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on p and the deficit angle, which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

Liquid crystal behaviors of micron and submicron-sized black phosphorus nanosheets

In this study, liquid crystal behaviors of black phosphorus (BP) nanosheets were investigated. A birefringence of approximately 10−4 was achieved for BP owing to its anisotropy, compared to that of 10−5 for graphene oxide. The submicron-sized BP nanosheets (S-BPNS) showed larger birefringence than the micron-sized BP nanosheets (M-BPNS) in blue–green light. The birefringence of both types increased with the incident wavelength; however, that of the S-BPNS remained a constant of approximately 3.8 × 10−4 near 672 nm, whereas that of the M-BPNS reached 4.8 × 10−4 before 753 nm. This inversion in red–yellow light was caused by the layer-dependent bandgap of BP. The anisotropy and tunable bandgap endow BP unique two-dimensional liquid crystal behaviors.

Hydrodynamic theory of p-atic liquid crystals.

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic p-fold rotational symmetry, also known as p-atics, of which nematics (p=2) and hexatics (p=6) are the two best known examples. Previous hydrodynamic theories of p-atics are characterized by continuous O(2) rotational symmetry, which is higher than the discrete rotational symmetry of p-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for p>2. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any p-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates.

Long-Ranged Order and Flow Alignment in Sheared p-atic Liquid Crystals.

We formulate a hydrodynamic theory of p-atic liquid crystals, namely, two-dimensional anisotropic fluids endowed with generic p-fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of p-atic phases, allows us to unveil several unknown aspects of flowing p-atics, that previous theories, characterized by O(2) rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

Fractional defect charges in liquid crystals with p-fold rotational symmetry on cones.

Conical surfaces, with a δ function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry p. We find that these states are characterized by a set of fractional defect charges at the apex and that the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our predictions for the ground-state energies numerically for a set of commensurate cone angles (corresponding to a set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as a perfect triangular or square mesh, and find excellent agreement with our theoretical predictions.

Defect patterns of two-dimensional nematic liquid crystals in confinement.

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.

Patterned Photoalignment-Based One- and Two-Dimensional Liquid Crystal Forked Gratings

Based on the technology of patterned photoalignment of polymerizable nematic liquid crystal, one- and two-dimensional fork-dislocation gratings which enable formation of singular light beams (optical vortices) have been fabricated and examined. The proposed approach to the formation of a two-dimensional optical structure presents itself a combination of two one-dimensional gratings with mutually orthogonal orientations of the grooves. Phase structures of the formed singular beams as well as their spatial and polarization characteristics have been studied experimentally. The obtained results offer new potentialities in design of optical devices and systems for transformation of phase and polarization structures of light beams.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems.

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (as) but fixed the substrate strength. We observed that with a small value of as, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of as, the system melts and transitions to a modulate-smectic. Finally, with a further increase in as, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.