Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels

Liquid crystalline media mediate interactions between suspended particles and confining geometries, which not only has potential to guide patterning and bottom-up colloidal assembly, but can also control colloidal migration in microfluidic devices. However, simulating such dynamics is challenging because nemato-elasticity, diffusivity and hydrodynamic interactions must all be accounted for within complex boundaries. We model the advection of colloids dispersed in flowing and fluctuating nematic fluids confined within 2D wavy channels. A lock-key mechanism between homeotropic colloids and troughs is found to be stronger for planar anchoring on the wavy walls compared to homeotropic anchoring on the wavy walls due to the relative location of the colloid-associated defects. Sufficiently large amplitudes result in stick-slip trajectories and even permanent locking of colloids in place. These results demonstrate that wavy walls not only have potential to direct colloids to specific docking sites but also to control site-specific resting duration and intermittent elution.

Exploiting Molecular Orders at the Interface of Microdroplets for Intelligent Materials

ConspectusThe intrinsic molecular order of liquid crystals (LCs) and liquid crystalline elastomers (LCEs) is the origin of their stimuli-responsive properties. The programmable responsiveness and functionality, such as shape morphing and color change under external stimuli, are the key features that attract interest in designing LC- and LCE-based intelligent material platforms. Methods such as mechanical stretching and shearing, surface alignment, and field-assisted alignment have been exploited to program the order of LC molecules for the desired responsiveness. However, the huge size mismatch between the nanometer-sized LC mesogens and the targeted macroscopic objects calls for questions about how to delicately control molecular order for desired performance. Microparticles that can be synthesized with intrinsic molecular order precisely controlled to micrometer size can be used as building blocks for bulk materials, thus offering opportunities to bridge the gap and transcend molecular orders across scales. By taking advantage of the interfacial anchoring effects, we can control and engineer the molecular orders inside the microdroplets, allowing for the realization of various responsive behaviors. Furthermore, designer LC microparticles with multiple responsiveness can be assembled and confined within a matrix, opening a new pathway to engineering LC-enabled intelligent materials.In this Account, we present our recent work on exploiting the molecular order inside microdroplets for the construction of intelligent materials. We briefly introduce the typical chemicals used in the synthesis and the methods developed to control LC molecular alignment within a microdroplets. We then present examples of microparticles synthesized from microdroplets that can transform into complex morphologies upon cooling from the isotropic to nematic phase or due to phase separation within the droplets coupled with the segregation of LC oligomers (LCOs) with polydisperse chain lengths. Furthermore, we show the synthesis of elliptical LCE microparticles and exploit their thermal and magnetic responsiveness to program shape-morphing behaviors and microarrays with switchable optical polarization. By mixing magnetic nanoparticles in cholesteric liquid crystals (CLCs) and silicone oils, we created Janus microparticles capable of color switching for camouflage and information encryption. Moreover, we can engineer complex molecular orders in LCE microparticles by mixing different surfactants, yielding microparticles of diverse anisotropic, temperature-responsive shapes after photopolymerization and extraction of the template LC molecules with different solvents. We conclude the Account with an outlook on the design of intelligent material systems via the design of unprecedented molecular ordering within the microparticles and their coupling with bulk materials.

Qualitatively and Quantitatively Different Configurations of Nematic-Nanoparticle Mixtures

We consider the influence of different nanoparticles or micrometre-scale colloidal objects, which we commonly refer to as particles, on liquid crystalline (LC) orientational order in essentially spatially homogeneous particle-LC mixtures. We first illustrate the effects of coupling a single particle with the surrounding nematic molecular field. A particle could either act as a "dilution", i.e., weakly distorting local effective orientational field, or as a source of strong distortions. In the strong anchoring limit, particles could effectively act as topological point defects, whose topological charge q depends on particle topology. The most common particles exhibit spherical topology and consequently act as q = 1 monopoles. Depending on the particle's geometry, these effective monopoles could locally induce either point-like or line-like defects in the surrounding LC host so that the total topological charge of the system equals zero. The resulting system's configuration is topologically equivalent to a crystal-like array of monopole defects with alternating topological charges. Such configurations could be trapped in metastable or stable configurations, where the history of the sample determines a configuration selection.

Criticality Controlling Mechanisms in Nematic Liquid Crystals

We theoretically study the generic mechanisms that could establish critical behavior in nematic liquid crystals (NLCs). The corresponding free energy density terms should exhibit linear coupling with the nematic order parameter and, via this coupling, enhance the nematic order. We consider both temperature- and pressure-driven, order-disorder phase transitions. We derive a scaled effective free energy expression that describes how qualitatively different mechanisms enforce critical behavior. Our main focus is on the impact of nanoparticles (NPs) in homogeneous NP-NLC mixtures. We illustrate that in the case of pressure-driven phase changes, lower concentrations are needed to impose critical point conditions in comparison with pure temperature variations.

Electrophoretic propulsion of matchstick-shaped magnetodielectric particles in the presence of external magnetic fields in a nematic liquid crystal

Synthesis of micro- and nanoparticles of pre-designed shape and surface properties is an integral part of soft and synthetic active matter. We report synthesis of matchstick-shaped (MS) magnetodielectric particles and demonstrate their potential as active agents with field-controllable trajectories in a nematic liquid crystal (NLC). The MS particles with homeotropic anchoring in NLCs align either parallel or perpendicular to the director depending on the dipolar or quadrupolar director distortions. When subjected to transverse electric and magnetic fields, the particles experience electric and magnetic torques trying to align them in the respective field directions. At equilibrium, the long axis is tilted at an angle with respect to the director. The change in orientation alters the surrounding elastic distortion, which results in unbalanced electroosmotic flows. These flows provide the necessary impetus for propelling the particles in various directions with different velocities depending on their orientations.

Nanoparticle localization within chiral liquid crystal defect lines and nanoparticle interactions

Self-assembly of colloidal particles into predefined structures is a promising way to design inexpensive manmade materials with advanced macroscopic properties. Doping of nematic liquid crystals (LCs) with nanoparticles has a series of advantages in addressing these grand scientific and engineering challenges. It also provides a very rich soft matter platform for the discovery of unique condensed matter phases. The LC host naturally allows the realization of diverse anisotropic interparticle interactions, enriched by the spontaneous alignment of anisotropic particles due to the boundary conditions of the LC director. Here we demonstrate theoretically and experimentally that the ability of LC media to host topological defect lines can be used as a tool to probe the behavior of individual nanoparticles as well as effective interactions between them. LC defect lines irreversibly trap nanoparticles enabling controlled particle movement along the defect line with the use of a laser tweezer. Minimization of Landau-de Gennes free energy reveals a sensitivity of the ensuing effective nanoparticle interaction to the shape of the particle, surface anchoring strength, and temperature, which determine not only the strength of the interaction but also its repulsive or attractive character. Theoretical results are supported qualitatively by experimental observations. This work may pave the way toward designing controlled linear assemblies as well as one-dimensional crystals of nanoparticles such as gold nanorods or quantum dots with tunable interparticle spacing.

Dispersion and Tunable Alignment of Colloidal Silver Nanowires in a Nematic Liquid Crystal for Applications in Electric-Optic Devices

The dispersion and tunable alignment of colloidal nanomaterials is desirable for practical applications in electric-optic (E-O) devices; however, it remains challenging for large one-dimensional nanomaterials with a large aspect ratio. Here, we demonstrate a large-scale, simple, multi-microdomain, and noncontact photoalignment technology to align colloidal silver nanowires (AgNWs, length ∼4.5 μm, diameter ∼70.6 nm) in a liquid crystal (LC) with a high two-dimensional order parameter (about 0.9). The AgNWs are precisely self-assembled via photomasks with twisted nematic and planar alignment models in microdomain regions. The AgNW orientation is tuned with an electric field, through the rotation of an LC director n, which allows three-dimensional (3D) tunable orientation combined with photoalignment. The colloidal dispersions of AgNWs in the LC cell influenced the ion transfer, elastic constant, dielectric anisotropy, and near LC alignment, changing the E-O properties of the LC devices. The 3D tunable orientation of an AgNW by photoalignment and an electric field could provide a new way to assemble large colloidal nanomaterials and fabricate functional E-O devices.

Nanotechnology for purifying nematic liquid crystals based on magnetic separation accompanied by phase transition

Free ions are generally unfavorable in liquid crystal (LC) displays, and LC purification technologies are critically important. The colloidal γ-Fe₂O₃ magnetic nanoparticles coated with oleic acid (γ-Fe₂O₃@OA MNPs) have a high ratio of surface to volume, which may adsorb more free ions and are uniform in the LC at room temperature. In this work, the precipitation and separation of the doped colloidal γ-Fe₂O₃@OA MNPs resulting from the magnetic field accompanied by an isotropic-nematic phase transition are more efficient than in the single case of the phase transition or the magnetic field. The residual ion concentrations have decreased distinctly using the low gradient magnetic field (∇ B ∼ 2 T/m) with the phase transition. In addition, when the doped colloidal γ-Fe₂O₃@OA MNPs are 0.4 % and 0.2 % by weight, the former concentrations of the residual ions and γ-Fe₂O₃@OA MNPs are lower than the latter. As a result, the commercial nematic LC can be purified by this approach based on nanotechnology in our study.

Biferroelectricity of a homochiral organic molecule in both solid crystal and liquid crystal phases

Ferroelectricity, existing in either solid crystals or liquid crystals, gained widespread attention from science and industry for over a century. However, ferroelectricity has never been observed in both solid and liquid crystal phases of a material simultaneously. Inorganic ferroelectrics that dominate the market do not have liquid crystal phases because of their completely rigid structure caused by intrinsic chemical bonds. We report a ferroelectric homochiral cholesterol derivative, β-sitosteryl 4-iodocinnamate, where both solid and liquid crystal phases can exhibit the behavior of polarization switching as determined by polarization–voltage hysteresis loops and piezoresponse force microscopy measurements. The unique long molecular chain, sterol structure, and homochirality of β-sitosteryl 4-iodocinnamate molecules enable the formation of polar crystal structures with point group 2 in solid crystal phases, and promote the layered and helical structure in the liquid crystal phase with vertical polarization. Our findings demonstrate a compound that can show the biferroelectricity in both solid and liquid crystal phases, which would inspire further exploration of the interplay between solid and liquid crystal ferroelectric phases.

Ferroelectricity normally exists in either solid crystals or liquid crystals. Here, the authors report a homochiral organic compound which shows ferroelectricity in both solid crystal and liquid crystal phases.

Unusual Mathematical Approaches Untangle Nervous Dynamics

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.

Design and Preparation of Nematic Colloidal Particles

Colloidal systems are abundant in technology, in biomedical settings, and in our daily life. The so-called "colloidal atoms" paradigm exploits interparticle interactions to self-assemble colloidal analogs of atomic and molecular crystals, liquid crystal glasses, and other types of condensed matter from nanometer- or micrometer-sized colloidal building blocks. Nematic colloids, which comprise colloidal particles dispersed within an anisotropic nematic fluid host medium, provide a particularly rich variety of physical behaviors at the mesoscale, not only matching but even exceeding the diversity of structural and phase behavior in conventional atomic and molecular systems. This feature article, using primarily examples of works from our own group, highlights recent developments in the design, fabrication, and self-assembly of nematic colloidal particles, including the capabilities of preprogramming their behavior by controlling the particle's surface boundary conditions for liquid crystal molecules at the colloidal surfaces as well as by defining the shape and topology of the colloidal particles. Recent progress in defining particle-induced defects, elastic multipoles, self-assembly, and dynamics is discussed along with open issues and challenges within this research field.

Ferroelectric nematic liquid-crystalline phases

Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these phases, guided by their fundamental and applicative interest. In this Perspective, we give an overview of this emerging field by linking history and theoretical predictions to a general outlook of the development and properties of the materials exhibiting ferroelectric nematic phases. We will highlight the most relevant observations to date, e.g., giant dielectric permittivity values, polarization values an order of magnitude larger than in classical ferroelectric liquid crystals, and nonlinear optical coefficients comparable with several ferroelectric solid materials. Key observations of anchoring and electro-optic behavior will also be examined. The collected contributions lead to a final discussion on open challenges in materials development, theoretical description, experimental explorations, and possible applications of the ferroelectric phases.

High-Strength Liquid Crystal Polymer-Graphene Oxide Nanocomposites from Water

We report on the morphology and mechanical properties of nanocomposite films derived from aqueous, hybrid liquid crystalline mixtures of rodlike aggregates of a sulfonated, all-aromatic polyamide, poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) (PBDT), and graphene oxide (GO) platelets. An isothermal step at 200 °C facilitates in situ partial thermal reduction of GO to reduced GO (rGO) in nanocomposite films. X-ray scattering studies reveal that PBDT-rGO nanocomposites exhibit both higher in-plane alignment of PBDT (the order parameter increases from 0.79 to 0.9 at 1.8 vol % rGO) and alignment along the casting direction (from 0.1 to 0.6 at 1.8 vol % rGO). From dynamic mechanical thermal analysis, the interaction between PBDT and rGO causes the β-relaxation activation energy for PBDT to increase with rGO concentration. Modulus mapping of nanocomposites using atomic force microscopy demonstrates enhanced local stiffness, indicating reinforcement. From stress-strain analysis, the average Young's modulus increases from 16 to 37 GPa at 1.8 vol % rGO and the average tensile strength increases from 210 to 640 MPa. Despite polymer alignment along the casting direction, an average transverse tensile strength of 230 MPa is obtained.

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

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

Second-virial theory for shape-persistent living polymers templated by disks

Living polymers composed of noncovalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (nonadsorbing) rigid colloidal disks which act as an entropic reorienting "template" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and disks, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disk concentrations, however, the phase is disrupted by collective disk alignment in favor of a discotic nematic fluid in which the polymers are dispersed antinematically. We show that the antinematic arrangement of the polymers generates a nonexponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the disks facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

Liquid Crystals: Versatile Self-Organized Smart Soft Materials

Smart soft materials are envisioned to be the building blocks of the next generation of advanced devices and digitally augmented technologies. In this context, liquid crystals (LCs) owing to their responsive and adaptive attributes could serve as promising smart soft materials. LCs played a critical role in revolutionizing the information display industry in the 20th century. However, in the turn of the 21st century, numerous beyond-display applications of LCs have been demonstrated, which elegantly exploit their controllable stimuli-responsive and adaptive characteristics. For these applications, new LC materials have been rationally designed and developed. In this Review, we present the recent developments in light driven chiral LCs, i.e., cholesteric and blue phases, LC based smart windows that control the entrance of heat and light from outdoor to the interior of buildings and built environments depending on the weather conditions, LC elastomers for bioinspired, biological, and actuator applications, LC based biosensors for detection of proteins, nucleic acids, and viruses, LC based porous membranes for the separation of ions, molecules, and microbes, living LCs, and LCs under macro- and nanoscopic confinement. The Review concludes with a summary and perspectives on the challenges and opportunities for LCs as smart soft materials. This Review is anticipated to stimulate eclectic ideas toward the implementation of the nature's delicate phase of matter in future generations of smart and augmented devices and beyond.

Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Colloidal self-assembly refers to a solution-processed assembly of nanometer-/micrometer-sized, well-dispersed particles into secondary structures, whose collective properties are controlled by not only nanoparticle property but also the superstructure symmetry, orientation, phase, and dimension. This combination of characteristics makes colloidal superstructures highly susceptible to remote stimuli or local environmental changes, representing a prominent platform for developing stimuli-responsive materials and smart devices. Chemists are achieving even more delicate control over their active responses to various practical stimuli, setting the stage ready for fully exploiting the potential of this unique set of materials. This review addresses the assembly of colloids into stimuli-responsive or smart nanostructured materials. We first delineate the colloidal self-assembly driven by forces of different length scales. A set of concepts and equations are outlined for controlling the colloidal crystal growth, appreciating the importance of particle connectivity in creating responsive superstructures. We then present working mechanisms and practical strategies for engineering smart colloidal assemblies. The concepts underpinning separation and connectivity control are systematically introduced, allowing active tuning and precise prediction of the colloidal crystal properties in response to external stimuli. Various exciting applications of these unique materials are summarized with a specific focus on the structure-property correlation in smart materials and functional devices. We conclude this review with a summary of existing challenges in colloidal self-assembly of smart materials and provide a perspective on their further advances to the next generation.

Nematic Order, Plasmonic Switching and Self-Patterning of Colloidal Gold Bipyramids

Dispersing inorganic colloidal nanoparticles within nematic liquid crystals provides a versatile platform both for forming new soft matter phases and for predefining physical behavior through mesoscale molecular-colloidal self-organization. However, owing to formation of particle-induced singular defects and complex elasticity-mediated interactions, this approach has been implemented mainly just for colloidal nanorods and nanoplatelets, limiting its potential technological utility. Here, orientationally ordered nematic colloidal dispersions are reported of pentagonal gold bipyramids that exhibit narrow but controlled polarization-dependent surface plasmon resonance spectra and facile electric switching. Bipyramids tend to orient with their C₅ rotation symmetry axes along the nematic director, exhibiting spatially homogeneous density within aligned samples. Topological solitons, like heliknotons, allow for spatial reorganization of these nanoparticles according to elastic free energy density within their micrometer-scale structures. With the nanoparticle orientations slaved to the nematic director and being switched by low voltages ≈1 V within a fraction of a second, these plasmonic composite materials are of interest for technological uses like color filters and plasmonic polarizers, as well as may lead to the development of unusual nematic phases, like pentatic liquid crystals.

Nematoelasticity of hybrid molecular-colloidal liquid crystals

Colloidal rods immersed in a thermotropic liquid-crystalline solvent are at the basis of so-called hybrid liquid crystals, which are characterized by tunable nematic fluidity with symmetries ranging from conventional uniaxial nematic or antinematic to orthorhombic [Mundoor et al., Science 360, 768 (2018)SCIEAS0036-807510.1126/science.aap9359]. We provide a theoretical analysis of the elastic moduli of such systems by considering interactions between the individual rods with the embedding solvent through surface-anchoring forces, as well as steric and electrostatic interactions between the rods themselves. For uniaxial systems, the presence of colloidal rods generates a marked increase of the splay elasticity, which we found to be in quantitative agreement with experimental measurements. For orthorhombic hybrid liquid crystals, we provide estimates of all 12 elastic moduli and show that only a small subset of those elastic constants play a relevant role in describing the nematoelastic properties. The complexity and possibilities related to identifying the elastic moduli in experiments are briefly discussed.

Interactions of charged microrods in chiral nematic liquid crystals

We study the pair interaction of charged silica microrods in chiral nematic liquid crystals and show that the microrods with homeotropic surface anchoring form a bound state due to the competing effect of electrostatic (Coulomb) and elastic interactions. The robustness of the bound state is demonstrated by applying external electrical and mechanical forces that perturbs their equilibrium position as well as orientation. In the bound state we have measured the correlated thermal fluctuations of the position, using two-particle cross-correlation spectroscopy that uncovers their hydrodynamic interaction. These findings reveal unexplored aspects of liquid-crystal dispersions which are important for understanding the assembly and dynamics of nano- and microparticles in chiral nematic liquid crystals.

Liquid Crystal-Mediated 3D Printing Process to Fabricate Nano-Ordered Layered Structures

The emergence of three-dimensional (3D) printing promises a disruption in the design and on-demand fabrication of smart structures in applications ranging from functional devices to human organs. However, the scale at which 3D printing excels is within macro- and microlevels and principally lacks the spatial ordering of building blocks at nanolevels, which is vital for most multifunctional devices. Herein, we employ liquid crystal (LC) inks to bridge the gap between the nano- and microscales in a single-step 3D printing. The LC ink is prepared from mixtures of LCs of nanocellulose whiskers and large sheets of graphene oxide, which offers a highly ordered laminar organization not inherently present in the source materials. LC-mediated 3D printing imparts the fine-tuning required for the design freedom of architecturally layered systems at the nanoscale with intricate patterns within the 3D-printed constructs. This approach empowered the development of a high-performance humidity sensor composed of self-assembled lamellar organization of NC whiskers. We observed that the NC whiskers that are flat and parallel to each other in the laminar organization allow facile mass transport through the structure, demonstrating a significant improvement in the sensor performance. This work exemplifies how LC ink, implemented in a 3D printing process, can unlock the potential of individual constituents to allow macroscopic printing architectures with nanoscopic arrangements.

Largely Tunable Magneto-Coloration of Monolayer 2D Materials via Size Tailoring

Magnetically influenced light-matter interaction provides a contactless, noninvasive and power-free way for material characterization and light modulation. Shape anisotropy of active materials mainly determines the sensitivity of magneto-optic response, thereby making magnetic two-dimensional (2D) materials suitable in achieving the giant magneto-birefringence effect as discovered recently. Consequently, relationship between magneto-birefringence response and shape anisotropy of 2D materials is critical but has remained elusive, restricting its widespread applications. Here, we report the highly sensitive and largely tunable magneto-coloration via manipulating the shape-anisotropy of magnetic 2D materials. We reveal a quadratic increasing relationship between the magneto-optic Cotton-Mouton coefficient and the lateral size of 2D materials and achieve a more than one order of magnitude tunable response. This feature enables the engineerable transmissive magneto-coloration of 2D materials by tailoring their shape anisotropy. Our work deepens the understanding of the tunability of magneto-optic response by size effect of active materials, offering various opportunities for their applications in vast areas where color is concerned.

From n-layer planar ordering to the monolayer homeotropic structure of confined hard rods: The effect of shape anisotropy and wall-to-wall separation

Using the Parsons-Lee theory, we examined the effect of shape anisotropy and the wall-to-wall separation (H) on the phase behavior of the hard parallelepiped rods with dimensions L, D, and D (L>D) in such narrow slitlike pores which only one homeotropic layer can form. The phase structures, including biaxiality, planar nematic layering transition as well as planar to homeotropic, were studied for some separations in the range 2.5D≤H≤10.0D for H-D≤L<H.

Thermally reconfigurable monoclinic nematic colloidal fluids

Fundamental relationships are believed to exist between the symmetries of building blocks and the condensed matter phases that they form¹. For example, constituent molecular and colloidal rods and disks impart their uniaxial symmetry onto nematic liquid crystals, such as those used in displays^1,2. Low-symmetry organizations could form in mixtures of rods and disks^3-5, but entropy tends to phase-separate them at the molecular and colloidal scales, whereas strong elasticity-mediated interactions drive the formation of chains and crystals in nematic colloids^6-11. To have a structure with few or no symmetry operations apart from trivial ones has so far been demonstrated to be a property of solids alone¹, but not of their fully fluid condensed matter counterparts, even though such symmetries have been considered theoretically^12-15 and observed in magnetic colloids¹⁶. Here we show that dispersing highly anisotropic charged colloidal disks in a nematic host composed of molecular rods provides a platform for observing many low-symmetry phases. Depending on the temperature, concentration and surface charge of the disks, we find nematic, smectic and columnar organizations with symmetries ranging from uniaxial^1,2 to orthorhombic^17-21 and monoclinic^12-15. With increasing temperature, we observe unusual transitions from less- to more-ordered states and re-entrant²² phases. Most importantly, we demonstrate the presence of reconfigurable monoclinic colloidal nematic order, as well as the possibility of thermal and magnetic control of low-symmetry self-assembly^2,23,24. Our experimental findings are supported by theoretical modelling of the colloidal interactions between disks in the nematic host and may provide a route towards realizing many low-symmetry condensed matter phases in systems with building blocks of dissimilar shapes and sizes, as well as their technological applications.

Anisotropic electrostatic screening of charged colloids in nematic solvents

The physical behavior of anisotropic charged colloids is determined by their material dielectric anisotropy, affecting colloidal self-assembly, biological function, and even out-of-equilibrium behavior. However, little is known about anisotropic electrostatic screening, which underlies all electrostatic effective interactions in such soft or biological materials. In this work, we demonstrate anisotropic electrostatic screening for charged colloidal particles in a nematic electrolyte. We show that material anisotropy behaves markedly different from particle anisotropy. The electrostatic potential and pair interactions decay with an anisotropic Debye screening length, contrasting the constant screening length for isotropic electrolytes. Charged dumpling-shaped near-spherical colloidal particles in a nematic medium are used as an experimental model system to explore the effects of anisotropic screening, demonstrating competing anisotropic elastic and electrostatic effective pair interactions for colloidal surface charges tunable from neutral to high, yielding particle-separated metastable states. Generally, our work contributes to the understanding of electrostatic screening in nematic anisotropic media.

Quantification of nematic cell polarity in three-dimensional tissues

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids.

Interplay of Electrostatic Dipoles and Monopoles with Elastic Interactions in Nematic Liquid Crystal Nanocolloids

Doping of nematic liquid crystals with colloidal nanoparticles presents a rich soft matter platform for controlling material properties and discovering diverse condensed matter phases. We describe nematic nanocolloids that simultaneously exhibit strong electrostatic monopole and dipole moments and yield competing long-range anisotropic interactions. Combined with interactions due to orientational elasticity and order parameter gradients of the nematic host medium, they lead to diverse forms of self-assembly both in the bulk of an aligned liquid crystal and when one-dimensionally confined by singular topological defect lines. Such nanocolloids exhibit facile responses to electric fields. We demonstrate electric reconfigurations of nanocolloidal pair-interactions and discuss how our findings may lead to realizing ferroelectric and dielectric molecular-colloidal fluids with different point group symmetries.

Review: knots and other new topological effects in liquid crystals and colloids

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Optical Forces: From Fundamental to Biological Applications

Optical forces, generally arising from changes of field gradients or linear momentum carried by photons, form the basis for optical trapping and manipulation. Advances in optical forces help to reveal the nature of light-matter interactions, giving answers to a wide range of questions and solving problems across various disciplines, and are still yielding new insights in many exciting sciences, particularly in the fields of biological technology, material applications, and quantum sciences. This review focuses on recent advances in optical forces, ranging from fundamentals to applications for biological exploration. First, the basics of different types of optical forces with new light-matter interaction mechanisms and near-field techniques for optical force generation beyond the diffraction limit with nanometer accuracy are described. Optical forces for biological applications from in vitro to in vivo are then reviewed. Applications from individual manipulation to multiple assembly into functional biophotonic probes and soft-matter superstructures are discussed. At the end future directions for application of optical forces for biological exploration are provided.

Dynamics of hard colloidal cuboids in nematic liquid crystals

We perform dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard board-like colloidal particles in oblate and prolate nematic liquid crystals. In particular, we characterize the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depends on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular to the nematic director. Our simulation results highlight the occurrence of Fickian and Gaussian dynamics at short and long times, locate the minimum diffusivity at the self-dual shape, the particle geometry that would preferentially stabilise biaxial nematics, and exclude the existence of dynamically correlated particles.

Strong graphene oxide nanocomposites from aqueous hybrid liquid crystals

Combining polymers with small amounts of stiff carbon-based nanofillers such as graphene or graphene oxide is expected to yield low-density nanocomposites with exceptional mechanical properties. However, such nanocomposites have remained elusive because of incompatibilities between fillers and polymers that are further compounded by processing difficulties. Here we report a water-based process to obtain highly reinforced nanocomposite films by simple mixing of two liquid crystalline solutions: a colloidal nematic phase comprised of graphene oxide platelets and a nematic phase formed by a rod-like high-performance aramid. Upon drying the resulting hybrid biaxial nematic phase, we obtain robust, structural nanocomposites reinforced with graphene oxide.

Colloidal interactions and unusual crystallization versus de-mixing of elastic multipoles formed by gold mesoflowers

Colloidal interactions in nematic liquid crystals can be described as interactions between elastic multipoles that depend on particle shape, topology, chirality, boundary conditions and induced topological defects. Here, we describe a nematic colloidal system consisting of mesostructures of gold capable of inducing elastic multipoles of different order. Elastic monopoles are formed by relatively large asymmetric mesoflower particles, for which gravity and elastic torque balancing yields monopole-type interactions. High-order multipoles are instead formed by smaller mesoflowers with a myriad of shapes corresponding to multipoles of different orders, consistent with our computer simulations based on free energy minimization. We reveal unexpected many-body interactions in this colloidal system, ranging from de-mixing of elastic monopoles to a zoo of unusual colloidal crystals formed by high-order multipoles like hexadecapoles. Our findings show that gold mesoflowers may serve as a designer toolkit for engineering colloidal interaction and self-assembly, potentially exceeding that in atomic and molecular systems.

Elasticity-mediated particle interaction in a hosting medium holds promise for material engineering of unusual structures. Yuan et al. show that the gold microparticles can induce elastic multipoles of different symmetries when dispersed in a nematic liquid crystal as building blocks for various crystals.

Incident angle dependence-reduced polarization grating performance by using optically biaxial polymer liquid crystal

We have succeeded in forming a polarization grating whose polarization diffraction properties are extremely independent of the incident angle by using polymer liquid crystal exhibiting biaxial optical anisotropy. It is considered that the extension of the optical path length and the decrease in the effective amplitude of optical anisotropy due to oblique incidences are offset by the biaxial optical anisotropy and, as a result, the retardation is compensated. The properties of this developed device have been experimentally demonstrated and theoretically explained.

Electrostatically controlled surface boundary conditions in nematic liquid crystals and colloids

Differing from isotropic fluids, liquid crystals exhibit highly anisotropic interactions with surfaces, which define boundary conditions for the alignment of constituent rod-like molecules at interfaces with colloidal inclusions and confining substrates. We show that surface alignment of the nematic molecules can be controlled by harnessing the competing aligning effects of surface functionalization and electric field arising from surface charging and bulk counterions. The control of ionic content in the bulk and at surfaces allows for tuning orientations of shape-anisotropic particles like platelets within an aligned nematic host and for changing the orientation of director relative to confining substrates. The ensuing anisotropic elastic and electrostatic interactions enable colloidal crystals with reconfigurable symmetries and orientations of inclusions.

Gold Nanoparticles Thin Films with Thermo- and Photoresponsive Plasmonic Properties Realized with Liquid-Crystalline Ligands

Robust synthesis of large-scale self-assembled nanostructures with long-range organization and a prominent response to external stimuli is critical to their application in functional plasmonics. Here, the first example of a material made of liquid crystalline nanoparticles which exhibits UV-light responsive surface plasmon resonance in a condensed state is presented. To obtain the material, metal cores are grafted with two types of organic ligands. A promesogenic derivative softens the system and induces rich liquid crystal phase polymorphism. Second, an azobenzene derivative endows nanoparticles with photoresponsive properties. It is shown that nanoparticles covered with a mixture of these ligands assemble into long-range ordered structures which exhibit a novel dual-responsivity. The structure and plasmonic properties of the assemblies can be controlled by a change in temperature as well as by UV-light irradiation. These results present an efficient way to obtain bulk quantities of self-assembled nanostructured materials with stability that is unattainable by alternative methods such as matrix-assisted or DNA-mediated organization.

Evolution of nematic and ferromagnetic ordering in suspensions of magnetic nanoplatelets

Suspensions of magnetic nanoplatelets in isotropic solvents are very interesting examples of ferrofluids. It has been shown that above a certain concentration ΦNI such suspensions form a ferromagnetic nematic phase, which makes this system a unique example of a dipolar fluid. The formation of a nematic phase is driven by anisotropic electrostatic and long-range dipolar magnetic interactions. Here, we present studies of the evolution of short range positional and orientational magnetic order in suspensions with volume fractions below and above ΦNI, using small angle neutron scattering (SANS). The results show that in the absence of an external magnetic field, short range positional and orientational order already exist at relatively low volume fractions. Polarized SANS revealed that the contribution of ferromagnetic ordering to the formation of the nematic phase is significant. The ferromagnetic correlations can be qualitatively explained by a simple model, which takes into account anisotropic screened electrostatic and dipolar magnetic interactions.

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.

High-order elastic multipoles as colloidal atoms

Achieving and exceeding diversity of colloidal analogs of chemical elements and molecules as building blocks of matter has been the central goal and challenge of colloidal science ever since Einstein introduced the colloidal atom paradigm. Recent advances in colloids assembly have been achieved by exploiting the machinery of DNA hybridization but robust physical means of defining colloidal elements remain limited. Here we introduce physical design principles allowing us to define high-order elastic multipoles emerging when colloids with controlled shapes and surface alignment are introduced into a nematic host fluid. Combination of experiments and numerical modeling of equilibrium field configurations using a spherical harmonic expansion allow us to probe elastic multipole moments, bringing analogies with electromagnetism and a structure of atomic orbitals. We show that, at least in view of the symmetry of the "director wiggle wave functions," diversity of elastic colloidal atoms can far exceed that of known chemical elements.

Colloidal analogues of polymer chains, ribbons and 2D crystals employing orientations and interactions of nano-rods dispersed in a nematic liquid crystal

Robust control over the position, orientation and self-assembly of nonspherical colloids facilitate the creation of new materials with complex architecture that are important from technological and fundamental perspectives. We study orientation, elastic interaction and co-assembly of surface functionalized silica nano-rods in thin films of nematic liquid crystal. With homeotropic boundary condition, the nano-rods are predominantly oriented perpendicular to the nematic director which is different than the mostly parallel orientation of the micro-rods. The percentage of perpendicular nano-rods are significantly larger than the parallel nano-rods. The perpendicular nano-rods create very weak elastic deformation and exhibit unusual, out-of-plane, attractive interaction. On the other hand, the nano-rods oriented parallel to the director create strong elastic deformation and shows anisotropic, in-plane, dipolar interaction. In both orientations, the induced defects reside in the nano-rods. With the help of a dynamic laser tweezers and using nano-rods as building blocks we demonstrate colloidal analogues of linear polymer chains, ribbons and two-dimensional binary crystals.

Frank elasticity of composite colloidal nematics with anti-nematic order

Mixing colloid shapes with distinctly different anisotropy generates composite nematics in which the order of the individual components can be fundamentally different. In colloidal rod-disk mixtures or hybrid nematics composed of anisotropic colloids immersed in a thermotropic liquid crystal, one of the components may adopt so-called anti-nematic order while the other exhibits conventional nematic alignment. Focussing on simple models for hard rods and disks, we employ Onsager-Straley's second-virial theory to derive scaling expressions for the elastic moduli of rods and disks in both nematic and anti-nematic configurations and identify their explicit dependence on particle concentration and shape. We demonstrate that the splay, bend and twist elasticity of anti-nematically ordered particles scale logarithmically with the degree of anti-nematic order, with the bend-splay ratio for anti-nematic discotic nematics being far greater than for conventional nematic systems. The impact of surface anchoring on the elastic properties of hybrid nematics will also be discussed in detail. We further demonstrate that the elasticity of mixed uniaxial rod-disk nematics depends exquisitely on the shape of the components and we provide simple scaling expressions that could help engineer the elastic properties of composite nematic liquid crystals.

How to achieve a successful biaxial marriage

Coupling between organic and inorganic components results in a biaxial liquid crystal