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Guiding and dynamically modulating topological defects are critical challenges in defect engineering of liquid crystals. Here, we employ molecular dynamics simulations to investigate the transition dynamics and relative kinetic stability of defect patterns in two-dimensional nematic Gay–Berne liquid crystals confined within rectangular geometries. We observe the formation of various defect patterns including long-axis, diagonal, X-shaped, composite, and bend configurations under different confinement conditions. The competition between boundary effects and the uniformity of nematic orientation induces the continuous realignment of liquid crystal molecules, facilitating the spatially continuous transformation of defect patterns over time. This transition involves changes in both defect types and their locations, typically initiating from defect regions. Furthermore, we demonstrate that the relative stability of these defect patterns can be effectively controlled by adjusting confinement parameters and external field conditions. Our findings provide fundamental insights into the transition kinetics of defect patterns in confined nematic liquid crystals, thereby enhancing our ability to manipulate topological defects for advanced applications. [ABSTRACT FROM AUTHOR]

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones, and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation. [ABSTRACT FROM AUTHOR]

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global strong solution for initial data close to constant equilibria. The proof of the global strong solution relies on a new splitting method for the director in a mean value zero and average part. [ABSTRACT FROM AUTHOR]

The development of straightforward and effective methods to determine the topological charge of phase singular beams is crucial for broadening the applications of optical vortices. Here, a straightforward and elegant method for determining the topological charge of an optical vortex using an innovative switchable achromatic nematic liquid crystal Fresnel lens is proposed. The approach allows for the unambiguous determination of both the absolute value and the sign of the topological charge of a singular beam across a wide range of the visible spectrum, as demonstrated both experimentally and theoretically. The research outcomes are promising for applications in optical information transmission systems, cryptography, and quantum computing. [ABSTRACT FROM AUTHOR]

Using liquid crystals in near-infrared applications suffers from effects related to processes like parasitic absorption and high sensitivity to UV-light exposure. One way of managing these disadvantages is to use deuterated systems. The combined 1H and 2H nuclear magnetic resonance relaxometry method (FFC NMR), dielectric spectroscopy (DS), optical microscopy (POM), and differential scanning calorimetry (DSC) approach was applied to investigate the influence of selective deuteration on the molecular dynamics, thermal properties, self-organization, and electric-field responsiveness to a 4′-pentyl-4-biphenylcarbonitrile (5CB) liquid crystal. The NMR relaxation dispersion (NMRD) profiles were analyzed using theoretical models for the description of dynamics processes in different mesophases. Obtained optical textures of selectively deuterated 5CB showed the occurrence of the domain structure close to the I/N phase transition. The dielectric measurements showed a substantial difference in switching fields between fully protonated/deuterated 5CB and selectively deuterated molecules. The DSC thermograms showed a more complex phase transition sequence for partially deuterated 5CB with respect to fully protonated/deuterated molecules. [ABSTRACT FROM AUTHOR]

Nonlinear electrophoresis in complex fluids like nematic liquid crystals provides new pathways toward achieving precisely controlled motion and assembly of microscopic objects. The nematic host introduces a paradigm shift in the mechanism of electrophoretic transport by generating unbalanced electro-osmotic flows around the colloidal particle due to symmetry breaking of the medium caused by the induced topological defects. Rationally designed particles, which induce various types of defects and asymmetries, provide new opportunities in this regard. In this Perspective article, we discuss how the asymmetry in the shape and interfacial properties help in piloting the particles using an AC electric field. Finally, we propose some feasible strategies to achieve navigational control using magnetic and photo-responsive particles, guided by orthogonal electric, magnetic fields, and light, respectively. [ABSTRACT FROM AUTHOR]

We give a homotopy classification of the global defects in ordered media and explain it via the example of biaxial nematic liquid crystals, that is, systems where the order parameter space is the quotient of the three-sphere S3 by the quaternion group Q. As our mathematical model, we consider continuous maps from complements of spatial graphs to the space S3/Q modulo a certain equivalence relation and find that the equivalence classes are enumerated by the six subgroups of Q. Through monodromy around meridional loops, the edges of our spatial graphs are marked by conjugacy classes of Q ; once we pass to planar diagrams, these labels can be refined to elements of Q associated with each arc. The same classification scheme applies not only in the case of Q but also to arbitrary groups. [ABSTRACT FROM AUTHOR]

We study the optical and electrowetting (EW) property of polymer-dispersed liquid crystal (PDLC) dielectric. The dielectric films of nematic liquid crystal (LC) dispersed in polymethyl methacrylate matrix were characterized using polarized optical microscope and luminescence spectroscopy. The photoluminescence (PL) spectra show shift in peak emission wavelength due to the variation in refractive index between dispersed LC phase in the polymer matrix. The distribution of optically active LC phase plays a major role in the light scattering process. The LC concentration in polymer matrix varying from 10 to 70 wt % shows enhancement in PL intensity. Also, reduction in the PL peak broadening indicates improvement in optical properties. Finally, electrowetting using saline water on the PDLC dielectric was investigated for ac voltage as well as for dc voltages. The dielectric constant for PDLC obtained from EW response and impedance analyzer is in good agreement. The asymmetry in EW response indicates a trapping of charges in the PDLC dielectric, where magnitude of charge trapping increases with LC concentration. Our results provide insights into the intricate mechanisms influencing optical and EW properties, guiding the development of advanced materials for displays, lenses, and optoelectronics applications. [ABSTRACT FROM AUTHOR]

Orientational ordered soft matter possessing diverse microstructures has become a focal point of scientific research and technological exploration, thanks to its advancements in serving as an indispensable optical platform enabling propagation of light with multidimensional and manipulatable states. Herein, a facile way is developed to manipulate the in‐plane light beam transition dynamics by harnessing a time‐variable nematic liquid crystal (NLC) film through the electrical‐field‐induced topological defects. The results show that the dynamic change of optical branched flow is associated with the growth in the correlation length of optical potential and the reduction in the density of topological defects. The optical branching can continuously transform to deterministic and tunable beam steering at the low‐defect‐density regime through annihilation kinetics of defects. The explored soft matter system provides an excellent planar platform for the fundamental physics of light interacting with topological defects and may offer new perspectives for novel optics elements toward the applications of soft matter photonics. [ABSTRACT FROM AUTHOR]

The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space RN$\mathbb {R}^N$ with N≥3$N\ge 3$. In our work, we suppose the initial condition v0$v_0$ stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution u∈L∞((0,T);Hs(RN)),∇u∈L2((0,T);Hs(RN)),$$\begin{equation*} \hspace*{60pt}u\in L^\infty ((0,T);H^s(\mathbb {R}^N)),\quad \nabla u\in L^2((0,T);H^s(\mathbb {R}^N)), \end{equation*}$$∇v∈L∞((0,T);Hs(RN)),∇2v∈L2((0,T);Hs(RN))$$\begin{equation*} \hspace*{55pt}\nabla v\in L^\infty ((0,T);H^s(\mathbb {R}^N)),\quad \nabla ^2v\in L^2((0,T);H^s(\mathbb {R}^N)) \end{equation*}$$for s>N2−1$s>\frac{N}{2}-1$, asking low regularity assumptions on u0$u_0$ and v0$v_0$. [ABSTRACT FROM AUTHOR]

In this paper, phase transition temperatures of nematic liquid crystals: 4-n alkoxy benzoic acid (nOBA, where n = 4 and 6) are determined from the Legendre moments of liquid crystal textures. Here, the image analysis technique in conjunction with polarizing optical microscope is used to compute the Legendre moments from the textures of liquid crystals. As a function of temperature, Liquid crystal textures are recorded from the arthroscopic mode of optical microscope. Changes in textural features of the sample with respect to temperature bring the variations in intensity values of liquid crystal textures. The brightness image that is generated from the liquid crystal textural patterns separates the information about fluctuations in intensity. In this approach, Legendre moments are computed from the brightness images of the liquid crystal textures and are plotted as a function of temperature. Significant variations in the brightness Legendre moment curve provide insight into the liquid crystal transition temperatures. Results obtained from the present methodology are compared with gray color textures data and the experimental technique of differential scanning calorimetry and are in good agreement with each other. This method is an objective and quantitative technique whereas POM method is qualitative and subjective. [ABSTRACT FROM AUTHOR]

Direct viscous mechano‐electric response is demonstrated for a room‐temperature ferroelectric nematic liquid, which combines large spontaneous electric polarization with 3D fluidity. The mechano‐electric transduction is observed in the frequency range 1 −200 Hz via a simple demonstrator device. The liquid is placed into a deformable container with electrodes and the electric current induced by both periodic and irregular actuation of the container is examined. The experiments reveal a rich interplay of several distinct viscous mechano‐electric phenomena, where both shape deformations and material flow cause changes in the electric polarization structure of a ferroelectric nematic liquid. The results show that the mechano‐electric features of the material promise a considerable applicative perspective spanning from sensitive tactile sensors to energy harvesting devices. [ABSTRACT FROM AUTHOR]

Entanglement in a soft condensed matter system is enabled in the form of entangled disclination lines by using colloidal particles in nematic liquid crystals. These topological excitations are manifested as colloidal entanglement at equilibrium. How to further utilize nonequilibrium disclination lines to manipulate colloidal entanglement remains a nontrivial and challenging task. In this work, we use experiments and simulations to demonstrate the reconfigurations of nematic colloidal entanglement in light-driven spatiotemporal evolutions of disclination lines. Colloidal entanglement can sense subtle changes in the topological structures of disclination lines and realize chirality conversion. This conversion is manifested as the "domino effect" of the collective rotation of colloids in the disclination lines. By programming the topological patterns and the geometry of the disclination lines, colloidal entanglement can be assembled and split. More remarkably, a double-helix entangled structure can be formed by controlling the changes in the morphology of the disclination lines. Thus, this work will provide opportunities to program colloidal composites for smart materials and micromachines. [ABSTRACT FROM AUTHOR]

We report on a set of experiments directed to a problem of microparticles interaction with a disclination in a nematic liquid crystal matrix. The idea of the study consists in the visualization of the disclination by filling it with particles efficiently scattering light. A θ-cell possessing a topological defect of undetermined twist which can capture micro-sized objects was exploited. The results obtained for samples of different shape can be used as for the understanding of the nature of self-assembling clusters, as for the practical goal of increasing the visibility of a disclination being a dynamic object sensitive to temperature and other external factors and able to move the trapped particles. [ABSTRACT FROM AUTHOR]

Polymer‐dispersed liquid crystals (PDLCs) with nano‐phase‐separated structures, in which nanometer‐sized liquid crystal (LC) domains are dispersed within a polymer matrix (nano‐PDLCs), are transparent solid materials whose optical properties can be modulated by applying an electric field (E‐field). Because the proportion of LC that can respond to an electric field is small, the specific surface area of the phase‐separated interface of nano‐PDLCs is larger than that of conventional PDLCs, resulting in higher drive voltages than those of conventional PDLCs. To lower the driving voltage of nano‐PDLCs, highly polar LCs (C3DIO) are used with a large dielectric anisotropy (>10000), and prepared nano‐PDLCs using DIO mixtures obtained by mixing them with related compounds as the host LC. Nano‐PDLCs employing DIO mixtures exhibit higher E‐field responsivity than those using conventional LC. In addition, the electro‐optical Kerr coefficient at visible wavelength is significantly high, reaching 10−8 m V−2. Furthermore, nano‐PDLCs using the DIO mixture exhibit a memory effect in which the induced birefringence remains even after the removal of the in‐plane E‐field. Memorized birefringence can be erased by heating or applying an E‐field perpendicular to the substrate surface. Nano‐PDLCs using a DIO mixture can be rewritable electro‐birefringence‐responsive materials that can memorize arbitrary birefringence values. [ABSTRACT FROM AUTHOR]

The elastic behavior of nematics is commonly described in terms of the three so-called bulk deformation modes, i.e., splay, twist, and bend. However, the elastic free energy contains also other terms, often denoted as saddle–splay and splay–bend, which contribute, for instance, in confined systems. The role of such terms is controversial, partly because of the difficulty of their experimental determination. The saddle–splay (K24) and splay–bend (K13) elastic constants remain elusive also for theories; indeed, even the possibility of obtaining unambiguous microscopic expressions for these quantities has been questioned. Here, within the framework of Onsager theory with Parsons–Lee correction, we obtain microscopic estimates of the deformation free energy density of hard rod nematics in the presence of different director deformations. In the limit of a slowly changing director, these are directly compared with the macroscopic elastic free energy density. Within the same framework, we derive also closed microscopic expressions for all elastic coefficients of rodlike nematics. We find that the saddle–splay constant K24 is larger than both K11 and K22 over a wide range of particle lengths and densities. Moreover, the K13 contribution comes out to be crucial for the consistency of the results obtained from the analysis of the microscopic deformation free energy density calculated for variants of the splay deformation. [ABSTRACT FROM AUTHOR]

Due to their high anisotropic behavior, liquid crystals possess strong nonlinear optical properties. The RM734 liquid crystal is famous for having high anisotropic behaviors compared to traditional liquid crystals. The present work focused on the evaluation of electronic, charge-transport, nonlinear optical, electro-optical, and thermochemical properties of the RM734 liquid crystal. Furthermore, the effect of halogenation on the above properties of RM734 was investigated and is discussed in depth as halogen substitution on the liquid crystal molecule can alter the quantum mechanical properties of any liquid crystal molecule. Density functional theory combined with B3LYP and dispersion correction were used to calculate the properties of RM734. The 6-311G** basis set was used for the estimation of these properties, whereas def2-TZVPD was used to evaluate the nonlinear optical parameters. Due to the halogenation of RM734, its electronic properties vary significantly. By halogenation, a better electron-transport molecule can be converted into a hole-transport molecule. The electro-optical properties were calculated with the application of an external electric field for all molecules. With the help of the order parameter, the nematic phase was observed for all reported molecules. The variation in the birefringence with respect to the external electric field was investigated and discussed in detail. Therefore, the present study reveals the significant impact of halogenation in terms of the nonlinear optical and thermochemical properties of RM734. [ABSTRACT FROM AUTHOR]

Monodomain liquid crystal elastomers (LCEs) are prepared using liquid crystal block copolymers (LCBCPs) comprised of a nematic liquid crystal (NLC) main‐chain polyester linked to cross‐linkable polymethacrylate (PMA) at both ends. LCBCPs at a PMA weight fraction of ≈30% are doped with a tetra‐thiol compound, stretched in one direction, and then illuminated by UV light, yielding LCBCPs that formed microlamellae consisting of alternate stacking crosslinked PMA blocks and NLC polyester blocks. The LC director lay along the stretching direction (SD). Raising the temperature to the NLC isotropization temperature, the crosslinked LCBCP strips fixed at one end contracted reversibly by a factor of 1.2–1.4 along the SD, deforming the microlamellae. The strips fixed at both ends increased the tensile stress to ≈200 kPa while maintaining the microlamellae undeformed. Regardless of strip fixation at one or both ends, the NLC decreased the orientational order. The contraction amounts and the tensile stress of strips are well associated with decreased NLC orientational order. [ABSTRACT FROM AUTHOR]

The fabrication of liquid crystalline elastomer (LCE) with reversible deformation is promising for development of intelligent materials and equipment. Preparing new liquid crystalline monomer (LCM) and developing novel LCE structures are crucial for the fabrication of advanced LCE. Herein, we design and synthesis a series of side-on nematic epoxy LCM, and then fabricate corresponding LCE with micropillar array via photoinitiated polymerisation of a magnetic induced oriented LCMs with soft lithography patterned structures. 1H NMR, 13C NMR, COSY, FTIR and MS spectra confirm the structures of the LCMs. DSC and POM results demonstrate that the LCMs are nematic liquid crystals. SEM, OM, and POM observations indicate the successful fabrication of LCE micropillars that exhibit reversible contraction and extension during heating and cooling cycles. In addition, the thermal induced reversible deformation of the LCE micropillars is closely related to the structure of the LCM. By using the same method, functional LCE with multi-fold gratings are prepared by using the multi-fold gratings master mask during the fabrication process, providing a material foundation for the construction of intelligent surfaces that can selectively diffract light under external thermal stimuli. [ABSTRACT FROM AUTHOR]

The study looks into magnetically induced orientational transitions in suspensions of goethite nanorods based on a nematic liquid crystal. The study considers magnetically compensated suspension, which is a liquid-crystal analogue of an antiferromagnet. Unlike conventional magnetic particles, goethite nanorods have a remanent magnetic moment directed along the long axis of the particle and also they have negative diamagnetic anisotropy. Thus, it can be claimed that liquid-crystal composites of goethite nanorods have three mechanisms of interaction with an external magnetic field. The first two mechanisms are originally quadrupolar and are related to diamagnetic susceptibility anisotropies of liquid-crystal matrix and impurity goethite nanorods. The third mechanism is a dipolar one and is due to a remanent longitudinal magnetic moment of each dispersed particle. The magnetic-field-induced birefringence is used to show that the presence of three competing orientational mechanisms of interaction with an external magnetic field can both increase and decrease the Fréedericksz transition threshold compared to a pure liquid crystal. Diagrams of orientational phases of the suspension were constructed, and cases of various orientational mechanism predominance were analysed. Besides, a representation of the free energy of the suspension near the Fréedericksz transition in the form of the Landau expansion was obtained. This made it possible to establish that the Fréedericksz transition can occur as a phase transition of both the first and second order. [ABSTRACT FROM AUTHOR]

This paper introduces an origami metastructure (OMST), which realizes the conversion of electromagnetically induced transparency (EIT) to electromagnetically induced absorption (EIA), and realizes the liquid crystal adjustable curvature sensing (CS) function using EIA. The OMST consists of an upper resonator (resonator 1) and a lower resonator (resonator 2). Resonator 1 achieves the EIT phenomenon when 0–2 THz is excited by an electromagnetic wave (EMW), and a transparent window appears at 0.883 THz. When resonator 2 is introduced, the phase of OMST is regulated and the EIT phenomenon changes to EIA. The absorption peak is 0.998 THz, and the peak value is 0.937. OMST uses the flexible material polyimide, and the liquid crystal injected between the resonators 1 and 2 layers is a nematic liquid crystal (HTW114200-100). The metastructure is used on cylindrical surfaces of CS to measure their curvature. In the initial liquid crystal state, when EMW incident, the OMST resonance frequency changes from 0.998 to 1.006 THz, and the corresponding absorptivity changes from 0.937 to 0.650 (from 0.924 to 0.613 in the bias liquid crystal state). Regarding CS, OMST can be used for curvature detection in the micrometer class, with a detection range of 0–0.02 μm. The maximum curvature measurement sensitivity is 32.230 (33.690), and the quality-factor is 41.859 (40.840). Traditional CS is usually made of optical fiber, but because of the fragility of optical fiber sensors, it is difficult to directly apply to the curvature measurement of various objects. However, OMST's design overcomes this shortcoming and is simple to manufacture. OMST has a high detection accuracy and can be used to detect the curvature of small objects, which has a potential application value in flatness detection and intelligent robots. [ABSTRACT FROM AUTHOR]

Topological defects (TDs) manifest in many condensed matter systems. In liquid crystals (LCs), they occur as point or line singularities in the otherwise smooth director profile. Engineered and controllable TDs are of great interest for functional optoelectronic devices; however, the formation mechanism in patterned devices is not fully understood. In this work, electrically addressable TDs in doped mixtures of prototypical n‐alkyl‐cyanobiphenyl LCs 4‐cyano‐4′‐pentylbiphenyl (5CB) and 4‐cyano‐4′‐octylbiphenyl (8CB) are focused on. Doping concentrations of hexadecyltrimethylammonium bromide (CTAB) are varied and the effect of varying the host LC properties (through binary 5CB:8CB mixtures) on defect formation is studied. In the results, a strong correlation between LC "fluidity" and the ease of defect array formation is presented, with 0.5 wt% CTAB‐doped 5CB giving the best controllability/uniformity of TDs at low‐threshold voltages. Furthermore, it is demonstrated that the devices can be utilized as electrically switchable optical diffractive elements. In these findings, directions are mapped out that future studies can take in designing deterministic, electrically or magnetically tunable TD‐based photonic devices using LC systems. [ABSTRACT FROM AUTHOR]

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen's theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen's theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart. [ABSTRACT FROM AUTHOR]

Cellulose nanocrystals (CNCs) are commercially available materials derived from cellulose, the most abundant biopolymer on our planet. Due largely to their high strength, high surface area‐to‐volume ratio, tailorable surface chemistry, and the abundance of biomass feedstocks with which to produce them, CNCs have attracted significant interest in applications spanning the paints and coatings, composites, packaging, and biomedical sectors. However, and perhaps most interestingly, CNCs will self‐assemble (or, as I've teased in the title, organize) to form highly ordered chiral nematic liquid crystal phases when concentrated in suspension. Upon complete solvent evaporation, this chiral nematic order is 'locked', yielding films with structural colour—colour arising not due to chemical pigments, but rather due to the physical structure of a material itself. In the pursuit of novel multi‐functional materials, research interest has shifted recently towards the incorporation of functional additives to form composite chiral nematic films. Along with introducing the basics of liquid crystals and self‐assembly, this review discusses the main approaches used in order to form CNC‐based composite films: co‐assembly, templating, and post‐processing, and highlights exceptional examples in each case. Finally, I give my uniquely Canadian perspective on the current status, future prospects, and major challenges associated with the development of CNC‐based chiral nematic composite materials. [ABSTRACT FROM AUTHOR]

Liquid crystals with high dielectric anisotropy, low operational thresholds, and significant birefringence (Δn) represent a key focus in soft matter research. This work introduces a novel series of hydrogen-bonded liquid crystals (HBLCs) derived from 4-n-alkoxybenzoic, 4-alkoxy-3-fluorobenzoic derivatives (nOBAF), 4-alkoxy-2,3-fluorobenzoic derivatives (nOBAFF), and 2-fluoro-4-nitrobenzoic acid. The HBLCs were characterized using Fourier transform infrared spectroscopy, and their thermal behavior was evaluated via differential scanning calorimetry. Optical observations were conducted using polarized optical microscopy. The results indicate that mixtures containing benzoic acid with a bilateral fluorine substituent exhibit both SmA and SmC phases, while those with a unilateral fluorine substituent exhibit nematic and SmA phases. Moreover, an increase in the length of the alkoxy chain results in an expanded mesophase temperature range. This study demonstrates that the presence of a fluorine substituent and the incorporation of an NO2 group in the molecular structure result in an increase in dielectric permittivity, DC conductivity, dielectric anisotropy, and birefringence. [ABSTRACT FROM AUTHOR]

In this paper, we study the Lipschitz continuous dependence of conservative H\"older continuous weak solutions to a variational wave system derived from a model for nematic liquid crystals. Since the solution of this system generally forms a finite time cusp singularity, the solution flow is not Lipschitz continuous under the Sobolev metric used in the existence and uniqueness theory. We establish a Finsler type optimal transport metric, and show the Lipschitz continuous dependence of the solution on the initial data under this metric. This kind of Finsler type optimal transport metrics was first established in [A. Bressan and G. Chen, Arch. Ration. Mech. Anal., 226 (2017), pp. 1303-1343] for the scalar variational wave equation. This equation can be used to describe the unit direction n of mean orientation of nematic liquid crystals, when n is restricted on a circle. The model considered in this paper describes the propagation of n without this restriction, i.e. n, takes any value on the unit sphere. So we need to consider a wave system instead of a scalar equation. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model describing the movement of a colloidal particle in a fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is governed by the Beris--Edwards model for nematohydrodynamics equations, which couples the incompressible Navier--Stokes equations with a parabolic system. The dynamics of colloidal particle within the nematic liquid crystal is described by the conservation laws of linear and angular momentum. We prove the existence of global weak solutions for the coupled system. [ABSTRACT FROM AUTHOR]

As a way to reduce microplastics or nano-plastics in the ocean, it is of interest to develop biodegradable paper-based drinking straws to replace non-degradable plastic drinking straws. Primary questions to be addressed include how to design suitable coatings for paper drinking straws. Such coatings not only need to resist water. In addition, consumers have high expectations for the strength of a drinking straw. It is proposed here to replace non-biodegradable polypropylene, which is presently the main component of straws, with biodegradable and hydrophobic coating components via an entropy-driven approach. It is further proposed to develop colored paper-based drinking straws with cellulose nematic liquid crystal photonic pigments as a way to make the product stand out visibly, while at the same time mediating the usage of toxic chemical pigments. [ABSTRACT FROM AUTHOR]

Liquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting. [ABSTRACT FROM AUTHOR]

Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen's inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate. [ABSTRACT FROM AUTHOR]

In the 1960s Jerry Ericksen made major contributions to the construction of the continuum theory of nematic liquid crystals. This paper gives a brief summary of his work and the consequent giant impact on the field. [ABSTRACT FROM AUTHOR]

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πRmol, where Rmol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) printing of nematic liquid crystals (LCs) is demonstrated. Miniscule LC droplets, as small as 1 micron, are generated with the EHD printing system and deposited with high precision onto a glass substrate. Herein, we show how the voltage waveform and pulse frequency applied to the print nozzle influences the dynamics of the deposition process and the final landed footprint diameter of the printed spherical‐cap‐shaped LC droplets at the glass substrater. To complement results from high‐speed shadowgraphy imaging, simulations are employed to model the jetting process and the formation of the Taylor cone. Using EHD printing, results for two different printing modes, cone jetting and microdripping, are shown. The benefits and drawbacks of each mode are highlighted, and the paper is concluded with the demonstration of a printed alphanumeric pattern that showcases the capability of EHD printing to deposit very small volumes of nematic LC in order to form well‐defined spatial patterns. [ABSTRACT FROM AUTHOR]

This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) L2 gradient flow for computing energy minimizers of the LdG model, and note a time-step restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite-element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit 'twist.' Furthermore, we perform a computational exploration of the model and present several numerical simulations in three dimensions, on both slab geometries and spherical shells, with our finite-element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction. [ABSTRACT FROM AUTHOR]

This paper presents a novel pentagonal structure dual-core photonic crystal fiber polarizing beam splitter (PS-DC-PCF PBS) filled with a nematic liquid crystal (NLC) in the central hole. Unlike previous designs with symmetric arrangements, the upper and lower halves of the structure have different air hole arrangements. The upper half consists of air holes arranged in a regular quadrilateral pattern, while the lower half features a regular hexagonal arrangement of air holes. By filling the central hole with birefringent liquid crystal, the birefringence of the structure is enhanced, reducing the coupling lengths along the x polarization and y polarization directions. The polarization properties, coupling characteristics, and the influence of different structural parameters on the extinction ratio of the polarizing beam splitter are analyzed using the full-vector finite element method. Simulation results demonstrate that the designed PS-DC-PCF PBS achieves a maximum extinction ratio (ER) of 72.94 dB with a splitting length of only 61.9 μm and a wide operating bandwidth of 423 nm (1.324–1.747 μm), covering most of the O, E, S, C, L, and U communication bands. It exhibits not only ultra-short splitting lengths and ultra-wide splitting bandwidth but also good manufacturing tolerances and anti-interference capabilities. The designed PS-DC-PCF PBS could provide crucial device support for future all-optical communication systems and has potential applications in fiber optic communication or fiber laser systems. [ABSTRACT FROM AUTHOR]

Self-assemblies of anisotropic colloidal particles into colloidal liquid crystals and well-defined superlattices are of great interest for hierarchical nanofabrications that are applicable for various functional materials. Inorganic nanosheets obtained by exfoliation of layered crystals have been highlighted as the intriguing colloidal units; however, the size polydispersity of the nanosheets has been preventing precise design of the assembled structures and their functions. Here, we demonstrate that the anionic titanate nanosheets with monodisperse size reversibly form very unusual superstructured mesophases through finely tunable weak attractive interactions between the nanosheets. Transmission electron microscopy, polarizing optical microscopy, small-angle x-ray scattering, and confocal laser scanning microscopy clarified the reversible formation of the mesophases (columnar nanofibers, columnar nematic liquid crystals, and columnar nanofiber bundles) as controlled by counter cations, nanosheet concentration, solvent, and temperature. [ABSTRACT FROM AUTHOR]

Just as nematic liquid crystals are widespread in display technology, a small number of building blocks find widespread use in the design and synthesis of liquid crystalline materials. This review explores the intricate relationship between the molecular structure of thermotropic liquid crystals (LCs) and their phase behaviour, emphasising the role of specific structural fragments in determining LC properties. We also detail into the impact of non-conventional building blocks on LC properties by comparing families of materials differentiated by only a single structural variation, allowing us to probe the extent to which deviations from traditional structures can maintain liquid crystallinity. This comprehensive overview not only underscores the importance of specific molecular fragments in LC design but also opens avenues for the innovative use of non-traditional building blocks in the development of new LC materials. Just as the ubiquity of 1,4-disubstituted benzene rings has its genesis (partly) in the extremely robust and predictable synthesis of such systems through cross-coupling chemistry; we consider that, the rapid progress in coupling sp3 fragments, coupled with the growing availability of suitable building blocks, makes the inclusion of said fragments ever more practical and attractive for use in liquid crystalline systems. [ABSTRACT FROM AUTHOR]

Liquid crystal-forming cyanobiphenyls are truly extraordinary molecules that have had an enormous impact on liquid crystal research and applications since they were first synthesised. This impact is, on the one hand, due to the exceptionally convenient physical properties of the main characters, 5CB and 8CB, allowing easy experiments at room temperature, as well as their commercial availability at reasonable cost. On the other hand, the cyanobiphenyl chemical structure leads to some quite peculiar characteristics in terms of organisation at the molecular scale, which are sometimes well recognised and even utilised, but often the awareness of these peculiarities is not strong. This perspective article reviews the use of cyanobiphenyls in making liquid crystal shells and liquid crystal core fibres, in sensing, as a medium for simultaneously aligning and dispersing carbon nanotubes, and as highly useful solvents for reactive mesogens that can be polymerised into anisotropic networks. This choice is very much motivated by how cyanobiphenyls have impacted our group's research throughout the years, which is the basis for the examples I provide. Nevertheless, I believe they serve well to illustrate the immense usefulness of cyanobiphenyls in innovating research and applications related to liquid crystals. [ABSTRACT FROM AUTHOR]

Graphene oxide is hydrophilic due to its oxygen functionality, making it easy to disperse in liquid crystalline media. The nanocomposites of graphene oxide and reduced graphene oxide have been prepared in a nematic liquid crystal. Results reveal rising transition temperatures, enthalpies, and order parameters for graphene oxide dispersed nanocomposites. UV-Vis spectroscopy results show an increase of the optical band gap for graphene oxide whereas decrease for reduced graphene oxide dispersed system. Impedance spectroscopy is used for the determination of various parameters such as permittivity, dielectric anisotropy, conductivity, relaxation frequency and activation energy. Results show that the dielectric anisotropy is increased for graphene oxide dispersed nanocomposite, however, reduced graphene oxide dispersed system demonstrates the opposite property. Relaxation frequency has increased for graphene oxide dispersed system while unchanged for reduced graphene oxide dispersed system. Conductivity of reduced graphene oxide dispersed nanocomposite has increased by three orders of magnitude but for graphene oxide dispersed system, it has decreased as compared to that of the pure sample. We observed decrease in threshold voltage, elastic constant, and rotational viscosity for both GO/rGO dispersed systems. The outcome for the graphene oxide dispersed nanocomposite looks to be more effective due to the system's enhanced molecular polarisability. [ABSTRACT FROM AUTHOR]

Calamitic molecules consisting of pentabromophenol tethered to cyanobiphenyl via a flexible alkyl chain were synthesised and characterised for their mesomorphic properties. New chemical structures differing in the length of the spacer (6a–f) were confirmed by FT-IR, 1H-NMR and 13C-NMR spectroscopies, and by elemental analysis. Compounds having six, eight, nine and ten methylene units in the spacer show room-temperature nematic liquid crystalline phases and the other derivatives are soft solids. The mesomorphic behaviour and thermal stability of all compounds have been investigated by polarised optical microscopy, differential scanning calorimetry and thermal gravimetric analysis, respectively. [ABSTRACT FROM AUTHOR]

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model. [ABSTRACT FROM AUTHOR]

We present and demonstrate a method to produce quantitative and qualitative descriptions of transient dynamics from empirical data, with the purpose of analyzing a novel transient discovered in liquid crystal electroconvection. By constructing a tensor bundle around an exemplar transient and creating a chart at every step aligned with the direction of propagation, we show that the Jacobian estimation problem can be reduced by a single dimension, relaxing data requirements and clarifying results. We apply this analysis to identify the onset of a boundary crisis in a predator–prey model. The resulting tensor bundle estimated from image data taken during a dynamical phase transition in a nematic liquid crystal details the behavior of the system along that trajectory, allowing topological analysis. Using this method, we quantify a saddle point in the phase space that drives the initial dynamics during a sudden increase in the driving voltage. [ABSTRACT FROM AUTHOR]

The presence of a polymer network and/or the addition of ferroelectric nanoparticles to a nematic liquid crystal are found to lower transition temperatures and birefringence, which indicates reduced orientational order. In addition, the electro-optic switching voltage is considerably increased when a polymer network is formed by in situ polymerization in the nematic state. However, the resulting polymer network liquid crystal switches at similar voltages as the neat liquid crystal when polymerization is performed at an elevated temperature in the isotropic state. When nanoparticle dispersions are polymerized at an applied DC voltage, the transition temperatures and switching voltages are reduced, yet they are larger than those observed for polymer network liquid crystals without nanoparticles polymerized in the isotropic phase. [ABSTRACT FROM AUTHOR]

Optoelectronic and spinoptronic technologies benefit from flexible and tunable coherent light sources combining the best properties of nano- and material-engineering to achieve favorable properties such as chiral lasing and low threshold nonlinearities. In this work we demonstrate an electrically wavelength- and polarization-tunable room temperature polariton laser due to emerging photonic spin–orbit coupling. For this purpose, we design an optical cavity filled with both birefringent nematic liquid crystal and an inorganic perovskite. Our versatile growth method of single CsPbBr3 inorganic perovskite crystals in polymer templates allows us to reach strong light–matter coupling and pump-induced condensation of exciton–polaritons resulting in coherent emission of light. The sensitivity of the liquid crystal to external voltage permits electrical tuning of the condensate energy across 7 nm; its threshold power, allowing us to electrically switch it on and off; and its state of polarization sweeping from linear to locally tilted circularly polarized emission. [ABSTRACT FROM AUTHOR]

Thermotropic liquid crystals are versatile optical materials that exhibit a state of matter intermediate between liquids and solids. Their properties can change significantly with temperature, pressure, or other external factors, leading to different phases. The transport properties within these materials in different phases are still largely unexplored, and their understanding would enable exciting prospects for innovative technological advancements. High-order harmonic spectroscopy proved to be a powerful spectroscopic tool for investigating the electronic and nuclear dynamics in matter. Here, we report the first experimental observation of high-order harmonic generation in thermotropic liquid crystals in two different phase states, nematic and isotropic. We found the harmonic emission in the nematic phase to be strongly dependent on the relative orientation of the driving field polarization with respect to the liquid crystal alignment. Specifically, the harmonic yield has a maximum when the molecules are aligned perpendicularly to the polarization of the incoming radiation. Our results establish the first step for applying high-order harmonic spectroscopy as a tool for resolving ultrafast electron dynamics in liquid crystals with unprecedented temporal and spatial resolution. [ABSTRACT FROM AUTHOR]

We use the Landau-de Gennes energy to describe a particle immersed into nematic liquid crystals with a constant applied magnetic field. We derive a limit energy in a regime where both line and point defects are present, showing quantitatively that the close-to-minimal energy is asymptotically concentrated on lines and surfaces nearby or on the particle. We also discuss regularity of minimizers and optimality conditions for the limit energy. [ABSTRACT FROM AUTHOR]

The liquid crystal display (LCD) continues to hold a prominent position in the display industry. These years' key research topic is the fringe field effect, which aims to improve the LCD's performance. A new LCD structure utilizing the fringe field effect has been identified as a promising solution. This structure allows for the control of the electromagnetic field of the liquid crystal cell by regulating the voltage of the ring‐shaped and circular‐patch cell (RCC). This innovative structure is comprised of nematic liquid crystals (LCs) with negative dielectric anisotropy, a two‐electrode system consisting of a ring‐shaped ITO structure on the top layer and a circular patch structure on the bottom layer, and a SiO2 porous structure. Finite element simulation tests have verified the electric field strength, transmittance, and contrast of the cell and the 2x2 matrix structure, meeting the design objectives. This breakthrough has significant potential for application in the display field. [ABSTRACT FROM AUTHOR]

Most of the current highly polar rod-shaped molecules that form ferroelectric nematic (NF) phase do so only at elevated temperatures and multicomponent mixtures are generally needed to obtain a broad and room temperature range NF phase. In this work, we describe the synthesis, phase characterisation and measurement of various physical properties of a new ferroelectric nematic compound 4-[(4-nitrophenoxy)carbonyl]phenyl 2-isopropoxy-4-methoxybenzoate (RT11165). The molecular structure of RT11165 with a 2-isopropoxy group differs only by a substitution of the 2-methoxy group found in the prototype ferroelectric nematic material 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). This small structure change produces a rather dramatic change in phase behaviour leading to an NF phase from 63°C down to room temperature. Below about 45°C the rotational viscosity of RT11165 increases critically and the temperature dependence indicates a glass transition at ~19°C. The transparent and polar glassy state of RT11165, which should be also piezoelectric, is a good candidate for energy storage, piezoecatalysis, data storage and other applications. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem of the new model of the three dimensional inertial nematic electrolyte, which models the N-species charged particles diffuse and advect in the nematic liquid crystalline matrix. This new model was proposed by [Calderer MC, Golovaty D, Lavrentovich O, et al. Modeling of nematic electrolytes and nonlinear electroosmosis. SIAM J Appl Math. 2016;76:2260–2285. doi: 10.1137/16M1056225]. The inertial effect is such that the system involves a hyperbolic feature. We first derive the local existence in large initial data when the flow is isotropy, i.e. $ \lambda =1 $ λ = 1. For the anisotropy case ( $ \lambda \gt 0 $ λ > 0 , $ \lambda \neq ~1 $ λ ≠ 1), we obtain small data local solutions. Then, by seeking some further dissipative mechanisms from the elliptic structures, the local solution can be extended globally near the constant states with electro-neutrality condition. [ABSTRACT FROM AUTHOR]