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At least 145 records · Page 8

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

Abstract 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.

Physics↗

Intrinsically Chiral Twist‐Bend Nematogens: Interplay of Molecular and Structural Chirality in the N TB Phase

Abstract Non‐symmetric lactate‐based chiral liquid crystal dimers containing an odd‐membered spacer are shown to exhibit a chiral twist‐bend nematic phase which is stable on cooling to room temperature. A comparison of racemic and optically pure materials reveals that the pitch length in the N* TB phase is not influenced by molecular chirality, whereas the nematic‐twist‐bend nematic transition temperature is increased.

Chemistry↗

Probing the Self-Assembly dynamics of cellulose nanocrystals by X-ray photon correlation spectroscopy

Charge-stabilized colloidal cellulose nanocrystals (CNCs) can self-assemble into higher-ordered chiral nematic structures by varying the volume fraction. The assembly process exhibits distinct dynamics during the isotropic to liquid crystal phase transition, which can be elucidated using X-ray photon correlation spectroscopy (XPCS). Anionic CNCs were dispersed in propylene glycol (PG) and water spanning a range of volume fractions, encompassing several phase transitions. Coupled with traditional characterization techniques, XPCS was conducted to monitor the dynamic evolution of the different phases. Additionally, simulated XPCS results were obtained using colloidal rods and compared with the experimental data, offering additional insights into the dynamic behavior of the system. The results indicate that the particle dynamics of CNCs undergo a stepped decay in three stages during the self-assembly process in PG, coinciding with the observed phases. The phase transitions are associated with a total drop of Brownian diffusion rates by four orders of magnitude, a decrease of more than a thousand times slower than expected in an ideal system of repulsive Brownian rods. Given the similarity in the phase behaviors in CNCs dispersed in PG and in water, we hypothesize that these dynamic behaviors can be extrapolated to other polar solvent environments. Importantly, these findings represent the direct measurement of CNC dynamics using XPCS, underscoring the feasibility of directly assessing the dynamic behavior of other rod-like colloidal suspensions.

36 MATERIALS SCIENCE↗

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Pre-formed Cooper pairs in copper oxides and LaAlO 3 —SrTiO 3 heterostructures

The Bardeen–Cooper–Schrieffer theory of superconductivity and the Landau–Fermi liquid theory form the basis of our current understanding of conventional superconductors and their parent non-superconducting phases. However, some exotic superconductors do not conform to this physical picture but instead feature an unusual ‘normal’ state that is not a Fermi liquid. One explanation of this unusual behaviour is that pre-formed pairs of electrons are established above the superconducting temperature T c . Here, we highlight recent experiments that show the likely existence of these pre-formed pairs in two rather different materials—a high-temperature cuprate superconductor and strontium titanate. Moreover, in both materials the normal state from which superconductivity emerges has other shared properties, including a pseudogap and electronic nematicity—rotational symmetry breaking in the electron fluid that is not expected in Fermi liquid theory nor more generally from the crystal lattice symmetry. These experimental findings should provoke more interaction between the communities working on these materials and new insights into the underlying mechanism of the creation of pre-formed pairs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Elastomeric nematic colloids, colloidal crystals and microstructures with complex topology

Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and actuation when heated. With the thermal control, elastomeric microstructures are capable of changing from genus-one to genus-zero surface topology. Using these particles as building blocks, we investigated elastomeric colloidal crystals immersed within a liquid crystal fluid, which exhibit crystallographic symmetry transformations. Furthermore, our findings may lead to colloidal crystals responsive to a large variety of external stimuli, including electric fields and light. Pre-designed response of elastomeric nematic colloids, including changes of colloidal surface topology and lattice symmetry, are of interest for both fundamental research and applications.

36 MATERIALS SCIENCE↗

Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers

One of the major challenges for NASA's next-generation reusable-launch-vehicle (RLV) program is the design of a cryogenic lightweight composite fuel tank. Potential matrix resin systems need to exhibit a low coefficient of thermal expansion (CTE), good mechanical strength, and excellent barrier properties at cryogenic temperatures under load. In addition, the resin system needs to be processable by a variety of non-autoclavable techniques, such as vacuum-bag curing, resin-transfer molding (RTM), vacuum-assisted resin-transfer molding (VaRTM), resin-film infusion (RFI), pultrusion, and advanced tow placement (ATP). To meet these requirements, the Advanced Materials and Processing Branch (AMPB) at NASA Langley Research Center developed a new family of wholly aromatic liquid-crystal oligomers that can be processed and thermally cross-linked while maintaining their liquid-crystal order. All the monomers were polymerized in the presence of a cross-linkable unit by use of an environmentally benign melt-condensation technique. This method does not require hazardous solvents, and the only side product is acetic acid. The final product can be obtained as a powder or granulate and has an infinite shelf life. The obtained oligomers melt into a nematic phase and do not exhibit isotropization temperatures greater than the temperatures of decomposition (Ti > T(sub dec)). Three aromatic formulations were designed and tested and included esters, ester-amides, and ester-imides. One of the major advantages of this invention, named LaRC-LCR or Langley Research Center-Liquid Crystal Resin, is the ability to control a variety of resin characteristics, such as melting temperature, viscosity, and the cross-link density of the final part. Depending on the formulation, oligomers can be prepared with melt viscosities in the range of 10-10,000 poise (100 rad/s), which can easily be melt-processed using a variety of composite-processing techniques. This capability provides NASA with custom-made matrix resins that meet the required processing conditions for the fabrication of textile composites. Once the resin is in place, the temperature is raised to 375 C and the oligomers are cross-linked into a high-glass-transition-temperature (Tg) nematic network without releasing volatiles. The mechanical properties of the fully crosslinked, composite articles are comparable to typical composites based on commercially available epoxy resins.

Dingemans, Theo↗

Reversible Physical Gelation of Thermotropic Liquid Crystals Driven by Nanoplate Self-Assembly

Physically gelled soft materials, driven by the self-assembly of low-molecular-mass gelators (LMGs), have emerged as a platform for designing advanced gels that exhibit reversible gelation and property tunability. Liquid crystal (LC) gels are of great interest due to their supramolecular orderings as gel hosts and their enhanced electro-optical properties. In this study, we demonstrate the physical gelation of a nematic LC driven by nanoplate self-assembly, expanding the concept of gelators from small molecules to nanoparticles. These nanoplates are functionalized with promesogenic ligands and form a fibrillar network in LCs with face-to-face interplate stacking, resembling LMGs. The critical gelation volume fraction in the tilt test is only 0.14 v %, comparable to values reported for LMGs. Rheological analyses confirm viscoelastic properties characteristic of gelation. In situ small-angle X-ray scattering (SAXS) characterizes the formation of nanoplate networks in the LC with decreasing temperature, wherein LC mesogens become trapped in pores. Molecular dynamics (MD) simulations reveal that the interaction between ligand-coated nanoplates and LC-forming mesogens induces a multidomain LC structure, increasing friction between LC domains and stabilizing the gel. This study establishes direct relationships among molecular interactions, nanostructures, and mechanical properties in physically gelled LCs. In conclusion, the findings inspire the future gelator design of both LMGs and nanoplates, with potential applicability in bioscaffold engineering and liquid crystalline nanocomposites.

36 MATERIALS SCIENCE↗

Command of active and responsive elastomers by topological defects and patterns

The project resulted in the development of stimuli-responsive elastomer coatings formed by photopolymerized liquid crystal molecules. The molecular orientation of the liquid crystal elastomers is coupled to rubber-like elasticity. The project developed an approach to produce complex patterns of molecular orientation in elastomers by employing photopatterning technique based on plasmonic metamasks that convert unpolarized incoming light into a transmitted light beam with spatially-varying linear polarization. The polarization-modulated light beam aligns the film of azodye molecules, which serves as the substrate for liquid crystal elastomer coating. The alignment of the azodye molecules follows the polarization pattern with a phase shift of the alignment direction by 90 degrees. The azodye substrate imposes orientation of molecules in the adjacent liquid crystal layer which is preserved after the monomers are polymerized into a liquid crystal elastomer. By using differently aligned substrates one could produce various patterns of molecular orientation in the elastomer, which dictate the mechanical properties of the elastomers and their response to external stimuli such as temperature, humidity, and ultraviolet irradiation. In particular, the predesigned molecular orientation produces deterministically defined topography response of the liquid crystal coatings, in which their free surface changes from flat to either locally elevated or locally compressed, depending on whether the pre-inscribed molecular orientation is predesigned with a splay or bend deformation. The research established that the mechanism of this deterministic relation between the dynamic topography and pre-inscribed molecular orientation is rooted in the change of the tensorial order parameter that characterizes the degree of orientational order, and in the contraction/expansion of polymer molecules in response to the order parameter changes. In particular, lowering the order causes contraction of polymer globules. The work demonstrated that the dynamic topography of elastomer coatings with three-dimensional pattern of orientational order includes up and down motion of the material (along the normal to the coating) and also shifts in lateral directions. We demonstrate that the deterministic relationship between the orientational patterns and variations of coatings’ profile is caused by forces that are mathematically equivalent to active forces in the system of “pullers” or “pushers” in active matter, demonstrating universality of the out-of-equilibrium behavior. The project resulted in theoretical models that predictively describe the dynamic response of coatings. The topography of liquid crystal elastomers is sensitive to stimuli such as temperature, ultraviolet irradiation, and humidity. The applicability of the patterned approach to produce dynamic coatings was expanded from nematic elastomers to their smectic counterparts. The project combined a battery of imaging techniques to unveil the dynamic properties of the coatings, ranging from the state-of-the-art dynamic holographic microscopy to fluorescent confocal polarizing microscopy and polscope microscopy. The research uncovered potential applications of dynamic elastomer coatings, such as control placement of colloidal particles, engineering of living tissues with alignment patterns of cells that follow the orientational order of elastomer coatings. The approach developed in the project can be used to design programmable dynamic coatings with functionalities that mimic biological tissues such as skin.

36 MATERIALS SCIENCE↗

Rheological Properties of Quasi-2D Fluids in Microgravity

In recent years, research on complex fluids and fluids in restricted geometries has attracted much attention in the scientific community. This can be attributed not only to the development of novel materials based on complex fluids but also to a variety of important physical phenomena which have barely been explored. One example is the behavior of membranes and thin fluid films, which can be described by two-dimensional (2D) rheology behavior that is quite different from 3D fluids. In this study, we have investigated the rheological properties of freely suspended films of a thermotropic liquid crystal in microgravity experiments. This model system mimics isotropic and anisotropic quasi 2D fluids [46]. We use inkjet printing technology to dispense small droplets (inclusions) onto the film surface. The motion of these inclusions provides information on the rheological properties of the films and allows the study of a variety of flow instabilities. Flat films have been investigated on a sub-orbital rocket flight and curved films (bubbles) have been studied in the ISS project OASIS. Microgravity is essential when the films are curved in order to avoid sedimentation. The experiments yield the mobility of the droplets in the films as well as the mutual mobility of pairs of particles. Experimental results will be presented for 2D-isotropic (smectic-A) and 2D-nematic (smectic-C) phases.

microgravity↗

Active liquid crystals powered by force-sensing DNA-motor clusters

Significance Single-molecule techniques have elucidated how isolated molecular motors generate piconewton forces with unprecedented detail. However, in diverse biological and synthetic settings, force-generating proteins collectively power nonequilibrium dynamics, including continuous large-scale rearrangements and persistent fluid flows. Characterizing motor-generated forces in these dense and dynamical environments remains a challenge. We assembled a reversible DNA-based force-sensing probe that, by an optical readout, reveals the molecular arrangements and the force loads experienced by kinesin motors. These probes provide insight into motor-generated forces that collectively power the unique dynamics of microtubule-based active nematics, a noteworthy example of an internally driven active matter system. DNA-based force probes can be extended to study forces and stresses in various synthetic systems as well as diverse cellular environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Chiral, Topological, and Knotted Colloids in Liquid Crystals

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low symmetry and nontrivial topology of surface confinement are of particular interest, including surfaces shaped as handlebodies, spirals, knots, multi-component links, and so on. These types of colloidal surfaces induce topologically nontrivial three-dimensional director field configurations and topological defects. Director switching by electric fields, laser tweezing of defects, and local photo-thermal melting of the liquid crystal host medium promote transformations among many stable and metastable particle-induced director configurations that can be revealed by means of direct label-free three-dimensional nonlinear optical imaging. The interplay between topologies of colloidal surfaces, director fields, and defects is found to show a number of unexpected features, such as knotting and linking of line defects, often uniquely arising from the nonpolar nature of the nematic director field. This review article highlights fascinating examples of new physical behavior arising from the interplay of nematic molecular order and both chiral symmetry and topology of colloidal inclusions within the nematic host. Furthermore, the article concludes with a brief discussion of how these findings may lay the groundwork for new types of topology-dictated self-assembly in soft condensed matter leading to novel mesostructured composite materials, as well as for experimental insights into the pure-math aspects of low-dimensional topology.

chirality↗

Lyotropic Liquid Crystal Mediated Assembly of Donor Polymers Enhances Efficiency and Stability of Blade-Coated Organic Solar Cells

Conjugated polymers can undergo complex, concentration-dependent self-assembly during solution processing, yet little is known about its impact on film morphology and device performance of organic solar cells. Herein, lyotropic liquid crystal (LLC) mediated assembly across multiple conjugated polymers is reported, which generally gives rise to improved device performance of blade-coated non-fullerene bulk heterojunction solar cells. Using D18 as a model system, the formation mechanism of LLC is unveiled employing solution X-ray scattering and microscopic imaging tools: D18 first aggregates into semicrystalline nanofibers, then assemble into achiral nematic LLC which goes through symmetry breaking to yield a chiral twist-bent LLC. The assembly pathway is driven by increasing solution concentration – a common driving force during evaporative assembly relevant to scalable manufacturing. This assembly pathway can be largely modulated by coating regimes to give 1) lyotropic liquid crystalline assembly in the evaporation regime and 2) random fiber aggregation pathway in the Landau–Levich regime. The chiral liquid crystalline assembly pathway resulted in films with crystallinity 2.63 times that of films from the random fiber aggregation pathway, significantly enhancing the T80 lifetime by 50-fold. The generality of LLC-mediated assembly and enhanced device performance is further validated using polythiophene and quinoxaline-based donor polymers.

14 SOLAR ENERGY↗

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

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

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-symmetric pinning of topological defects in living liquid crystals

Topological defects, such as vortices and disclinations, play a crucial role in spatiotemporal organization of equilibrium and non-equilibrium systems. The defect immobilization or pinning is a formidable challenge in the context of the out-of-equilibrium system, like a living liquid crystal, a suspension of swimming bacteria in lyotropic liquid crystal. Here we control the emerged topological defects in a living liquid crystal by arrays of 3D-printed microscopic obstacles (pillars). Our studies show that while –1/2 defects may be easily immobilized by the pillars, +1/2 defects remain motile. Due to attraction between oppositely charged defects, positive defects remain in the vicinity of pinned negative defects, and the diffusivity of positive defects is significantly reduced. Experimental findings are rationalized by computational modeling of living liquid crystals. Our results provide insight into the engineering of active systems via targeted immobilization of topological defects.

42 ENGINEERING↗

Structural and Optical Response of Polymer-Stabilized Blue Phase Liquid Crystal Films to Volatile Organic Compounds

Engineering useful mechanical properties into stimuli-responsive soft materials without compromising their responsiveness is, in many cases, an unresolved challenge. For example, polymer networks formed within blue-phase liquid crystals (BPs) have been shown to form mechanically robust films, but the impact of polymer networks on the response of these soft materials to chemical stimuli has not been explored. In this work, we report on the response of polymer-stabilized BPs (PSBPs) to volatile organic compounds (VOCs, using toluene as a model compound) and compare the response to BPs without polymer stabilization and to polymerized nematic and cholesteric phases. We find that PSBPs generate an optical response to toluene vapor (change in reflection intensity under crossed polars) that is sixfold greater in sensitivity than the polymerized nematic or cholesteric phases and with a limit of detection (140 ± 10 ppm at 25 °C) that is relevant to the measurement of permissible exposure limits for humans. Additionally, when compared to BPs that have not been polymerized, PSBPs respond to a broader range of toluene vapor concentrations (5000 vs <1000 ppm) over a wider temperature interval (25–45 vs 45–53 °C). We place these experimental observations into the context of a simple thermodynamic model to explore how the PSBP response reflects the effect of toluene on competing contributions of double-twisted LC cylinders, disclinations, and polymer network to the free energy that controls the PSBP lattice spacing. Overall, we conclude that the mechanical and thermal stability of PSBPs, when combined with their optical responsiveness to toluene, make this class of self-supporting LCs a promising one as the basis of passive and compact (e.g., wearable) sensors for VOCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hybrid microstructure of smectite clay gels revealed using neutron and synchrotron X-ray scattering

Aqueous suspensions of swelling clays display a nematic sol-gel transition at very low solid concentrations. The underlying microstructure of the gel has remained a point of contention since the time of Irving Langmuir and has been a major obstacle to fully realizing the potential of clays for practical applications. Here, we comprehensively probe the microstructure of a smectite clay suspension using ultra-small angle neutron/X-ray scattering and find that the nematic gel is structurally ordered and contains entities that are at least an order of magnitude larger than the individual particles. Complementary cryo-electron microscopy shows the presence of domains having particle-particle ordering responsible for nematic texture and regions of particle-particle aggregation responsible for gel-like behavior. We find that the smectic clay gels have a hybrid microstructure with co-existing repulsive nematic domains and attractive disordered domains.

36 MATERIALS SCIENCE↗

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.

36 MATERIALS SCIENCE↗