Novel defect structures in nematic liquid crystal shells

Edge-on anchored discotic liquid crystals in spherical shells: A computational study of the phases and defects

The self-assembly of liquid crystal droplets and shells represents a captivating frontier in soft matter physics, promising precision engineering of functional materials. In this study, we delve into the phase behavior and investigate defect formation patterns in spherical shell-confined discotic liquid crystals (DLCs) through NpT Monte Carlo simulations. These shells are created by confining DLCs between two spherical surfaces, promoting the same anchoring. In this study, we focus on the case when both surfaces promote edge-on (planar) anchoring. Our study confirms a general result which states that, when a liquid crystal is under strong confinement, the nature of the isotropic-nematic transition changes from first order into continuous. Furthermore, as expected, topological defects at the spherical surface arise due to the topological constraints on the director field. Notably, our investigation reveals a unique topological defect configuration, characterized by the formation of four disclination lines that bridge the inner and external surfaces. Additionally, we observe a mixed ±1/2 wedge-twist disclination line that forms an arch that terminates at the outer surface. This arch decreases its length with decreasing temperature to eventually disappear.

Topological defects as nucleation points of the nematic-isotropic phase transition in liquid crystal shells

The transition from a nematic to an isotropic state in a self-closing spherical liquid crystal shell with tangential alignment is a stimulating phenomenon to investigate, as the topology dictates that the shell exhibits local isotropic points at all temperatures in the nematic phase range, in the form of topological defects. The defects may thus be expected to act as nucleation points for the phase transition upon heating beyond the bulk nematic stability range. Here we study this peculiar transition, theoretically and experimentally, for shells with two different configurations of four +1/2 defects, finding that the defects act as the primary nucleation points if they are co-localized in each other's vicinity. If the defects are instead spread out across the shell, they again act as nucleation points, albeit not necessarily the primary ones. Beyond adding to our understanding of how the orientational order-disorder transition can take place in the shell geometry, our results have practical relevance for, e.g., the use of curved liquid crystals in sensing applications or for liquid crystal elastomer actuators in shell shape, undergoing a shape change as a result of the nematic-isotropic transition.

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

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

Statics and dynamics of point boojums, line and modified Saturn ring topological defects in nematic confined geometry

In this paper we study the static structure and the dynamics of topological defects associated with isotropic droplets in nematic environment. Investigations were made in confined geometry of optical cells when the droplet size was of the order of or larger than the gap of the cell. We observed the coexistence of point boojums and Saturn ring or modified Saturn ring defects. We found transformation of the Saturn ring defect to two localized broad defects at increasing the droplet size. At droplet coalescence antipodes of point and localized broad defects were born and the dynamics of their annihilation with existing defects was investigated. We found strong difference in the process of annihilation of point and localized broad defects. Microscope images of isotropic droplets in nematic environment in a planar cell. The director orientation far from the droplets is in horizontal direction. The photographs were taken with crossed vertical and horizontal polarizers (a) and with a single horizontal polarizer (b). The cell thickness is 100 μm. Droplet diameter is less than the cell thickness. 1 and 2 are point boojums, L is the Saturn ring defect.

Effect of confinement and topology: 2-TIPS vs. MIPS

2-TIPS (two temperature induced phase separation) refers to the phase separation phenomenon observed in mixtures of active and passive particles which are modelled using scalar activity. The active particles are connected to a thermostat at high temperature while the passive particles are connected to the thermostat at low temperature and the relative temperature difference between "hot" and "cold" particles is taken as the measure of the activity χ of the non-equilibrium system. The study of such binary mixtures of hot and cold particles under various kinds of confinement is an important problem in many physical and biological processes. The nature and extent of phase separation are heavily influenced by the geometry of confinement, activity, and density of the non-equilibrium binary mixture. Investigating such 3D binary mixtures confined by parallel walls, we observe that the active and passive particles phase separate, but the extent of phase separation is reduced compared to bulk phase separation at high densities and enhanced at low densities. However, when the binary mixture of active and passive particles is confined inside a spherical cavity, the phase separation is radial for small radii of the confining sphere and the extent of phase separation is higher compared to their bulk counterparts. Confinement leads to interesting properties in the passive (cold) region like enhanced layering and high compression in the direction parallel to the confining wall. In 2D, both the bulk and confined systems of the binary mixture show a significant decrement in the extent of phase separation at higher densities. This observation is attributed to the trapping of active particles inside the passive cluster, which increases with density. Thus the 2D systems show structures more akin to dense-dilute phase co-existence, which is observed in motility induced phase separation in 2D active systems. The binary mixture constrained on the spherical surface also shows similar phase co-existence. Our analyses reveal that the coexistent densities observed in 2-TIPS on the spherical surface agree with the findings of previous studies on MIPS in active systems on a sphere.

Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

The impact of the intrinsic curvature of in-plane orientationally ordered curved flexible nematic molecules attached to closed 3D flexible shells was studied numerically. A Helfrich-Landau-de Gennes-type mesoscopic approach was adopted where the flexible shell's curvature field and in-plane nematic field are coupled and concomitantly determined in the process of free energy minimisation. We demonstrate that this coupling has the potential to generate a rich diversity of qualitatively new shapes of closed 3D nematic shells and the corresponding specific in-plane orientational ordering textures, which strongly depend on the shell's volume-to-surface area ratio, so far not predicted in mesoscopic-type numerical studies of 3D shapes of closed flexible nematic shells.

Impact of mesogenic aromaticity and cyano termination on the alignment and stability of liquid crystal shells

We carry out a strategic and systematic variation of the molecular structure of liquid crystals (LCs) molded into spherical shells, surrounded by aqueous isotropic phases internally and externally. Contrary to common expectation, based on previous studies that have almost exclusively been carried out with cyanobiphenyl-based LCs, we find that the director field aligns normal to the LC-water interface when we use an LC molecule that is entirely non-aromatic. We propose to explain this by the inability of such an LC to participate in hydrogen bonding, rendering the normal configuration favorable as it minimizes the molecular cross section in contact with the water. We also find that cyano-terminated LC molecules contribute greatly to stabilizing the LC-water interface. This explains why shells made of cyanobiphenyl LCs are much more stable than shells of LCs with non-cyano-terminated molecules, even if the latter exhibit aromatic cores. Unstable LC shells can be stabilized very efficiently, however, through the addition of a low concentration of molecules that are cyano-terminated, preferably below the threshold for dimerization. Our study provides a much clarified understanding of how the molecular structure dictates the stability and alignment of LC shells, and it will enable a diversification of LC shell research and applications to systems where the use of non-cyanobiphenyl LCs is required.

Packing and emergence of the ordering of rods in a spherical monolayer

Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational and translational order. The study of these structures is important for investigating the interplay between the geometry, topology, and elasticity, and for their potential applications in materials science, such as engineering directionally binding particles. In this work, we numerically simulate a spherical monolayer of soft repulsive spherocylinders (SRSs) and study the packing of rods and their ordering transition as a function of the packing fraction. In the model that we study, the centers of mass of the spherocylinders (situated at their geometric centers) are constrained to move on a spherical surface. The spherocylinders are free to rotate about any axis that passes through their respective centers of mass. We show that, up to moderate packing fractions, a two dimensional liquid crystalline phase is formed whose orientational ordering increases continuously with increasing density. This monolayer of orientationally ordered SRS particles at medium densities resembles a hedgehog-long axes of the SRS particles are aligned along the local normal to the sphere. At higher packing fractions, the system undergoes a transition to the solid phase, which is riddled with topological point defects (disclinations) and grain boundaries that divide the whole surface into several domains.

Geometry and physics in the deformations of crystalline caps

Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic regimes. Based on the revealed quasi-conformal ordering, we discover the partial but uniform screening of the substrate curvature by the induced curvature underlying the inhomogeneous lattice. This scenario is fundamentally different from the conventional screening mechanism based on topological defects. In the plastic regime, the yield of highly stressed caps leads to fractures with featured morphologies not found in planar systems. We also demonstrate the strategy of engineering stress and fractures by vacancies. These results advance our general understanding of the organization and adaptivity of the geometrically frustrated crystalline order.

Hollow nanoparticles synthesized via Ostwald ripening and their upconversion luminescence-mediated Boltzmann thermometry over a wide temperature range

Upconversion nanoparticles (UCNPs) with hollow structures exhibit many fascinating optical properties due to their special morphology. However, there are few reports on the exploration of hollow UCNPs and their optical applications, mainly because of the difficulty in constructing hollow structures by conventional methods. Here, we report a one-step template-free method to synthesize NaBiF₄:Yb,Er (NBFYE) hollow UCNPs via Ostwald ripening under solvothermal conditions. Moreover, we also elucidate the possible formation mechanism of hollow nanoparticles (HNPs) by studying the growth process of nanoparticles in detail. By changing the contents of polyacrylic acid and H₂O in the reaction system, the central cavity size of NBFYE nanoparticles can be adjusted. Benefiting from the structural characteristics of large internal surface area and high surface permeability, NBFYE HNPs exhibit excellent luminescence properties under 980 nm near-infrared irradiation. Importantly, NBFYE hollow UCNPs can act as self-referenced ratiometric luminescent thermometers under 980 nm laser irradiation, which are effective over a wide temperature range from 223 K to 548 K and have a maximum sensitivity value of 0.0065 K^-1 at 514 K. Our work clearly demonstrates a novel method for synthesizing HNPs and develops their applications, which provides a new idea for constructing hollow structure UCNPs and will also encourage researchers to further explore the optical applications of hollow UCNPs.

Formation of topological defects in nematic shells with a dumbbell-like shape

The present study investigates dumbbell-shaped nematic liquid crystal shells. Using molecular dynamics (MD) simulations, we consider the effects of an external electric field on nematic ordering by computing the average molecular alignment's time evolution and equilibrium configuration. We show that the number and location of topological defects are strongly affected by the external field, with the orientational ordering's equilibrium configuration depending on field direction about the shell's long axis. For a transverse external field, it is verified that the defect rearrangement presents a non-linear dynamics, with a field independent characteristic time scale delimiting the short and long time regimes. Effects associated with varying the shell's Gaussian curvature are also analyzed.

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

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

Defect patterns of two-dimensional nematic liquid crystals in confinement

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

From nematic shells to nematic droplets: energetics and defect transitions

In this work, we investigate the possibility of inducing valence transitions, i.e. transitions between different defect configurations, by transforming a nematic shell into a nematic droplet. Our shells are liquid crystal droplets containing a smaller aqueous droplet inside, which are suspended in an aqueous phase. When osmotically de-swelling the inner droplet, the shell progressively increases its thickness until it eventually becomes a single droplet. During the process, the shell energy landscape evolves, triggering a response in the system. We observe two different scenarios. Either the inner droplet progressively shrinks and disappears, inducing a defect reorganization, or it is expelled from the shell at a critical radius of the inner droplet, abruptly changing the geometry of the system. We use numerical simulations and modeling to investigate the origin of these behaviors. We find that the selected route depends on the defect structure and the energetics of the system as it evolves. The critical inner radius and time for expulsion depend on the osmotic pressure of the outer phase, suggesting that the flow through the shell plays a role in the process.

Nematic shells: new insights in topology- and curvature-induced effects

Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, yields different textures on surfaces with the same topology as the sphere. In particular, we show that the extrinsic curvature governs the ground state configuration on a nematic spherical shell, favouring two antipodal disclinations of charge +1 on small particles and four +1/2 disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.

Cooling a spherical nematic shell

Within the framework of Landau-de Gennes theory for nematic liquid crystals, we study the temperature-induced isotropic-nematic phase transition on a spherical shell under the assumption of degenerate tangential anchoring. Below a critical temperature, a thin layer of nematic coating a microscopic spherical particle exhibits nonuniform textures due to the geometrical frustration. We find the exact value of the critical threshold for the temperature and determine exactly the nematic textures at the transition by means of a weakly nonlinear analysis. The critical temperature is affected by the extrinsic curvature of the sphere, and the nematic alignment is consistent with the Poincaré-Hopf index theorem and experimental observations. The stability analysis of the bifurcate textures at the isotropic-nematic transition highlights that only the tetrahedral configuration is stable.

Conically degenerate anchoring effect in planar nematic-liquid-crystal shells

We study the defect texture in symmetric and asymmetric states of a nematic-liquid-crystal shell with conic and planar degenerate surface anchorings on the inner and outer spherical boundaries, respectively. To achieve the equilibrium nematic orientation, we numerically minimize the Landau-de Gennes free energy by employing surface potentials on the shell walls. The symmetric nematic shells energetically have stable configurations independent of thickness. In thick shells, the director field satisfies bipolar and hexadecapolar configurations between boundaries. In thin shells, the boojums transform into two stable disclination curves.

Structural transformations in tetravalent nematic shells induced by a magnetic field

The role of applied fields on the structure of liquid crystals confined to shell geometries has been studied in past theoretical work, providing strategies to produce liquid crystal shells with controlled defect structure or valence. However, the predictions of such studies have not been experimentally explored yet. In this work, we study the structural transformations undergone by tetravalent nematic liquid crystal shells under a strong uniform magnetic field, using both experiments and simulations. We consider two different cases in terms of shell geometry and initial defect symmetry: (i) homogeneous shells with four s = +1/2 defects in a tetrahedral arrangement, and (ii) inhomogeneous shells with four s = +1/2 defects localized in their thinner parts. Consistently with previous theoretical results, we observe that the initial defect structure evolves into a bipolar one, in a process where the defects migrate towards the poles. Interestingly, we find that the defect trajectories and dynamics are controlled by curvature walls that connect the defects by pairs. Based on the angle between Bs, the local projection of the magnetic field on the shell surface, and n+½, a vector describing the defect orientations, we are able to predict the nature and shape of those inversion walls, and therefore, the trajectory and dynamics of the defects. This rule, based on symmetry arguments, is consistent with both experiments and simulations and applies for shells that are either homogeneous or inhomogeneous in thickness. By modifying the angle between Bs and n+½, we are able to induce, in controlled way, complex routes towards the final bipolar state. In the case of inhomogeneous shells, the specific symmetry of the shell allowed us to observe a hybrid splay-bend Helfrich wall for the first time.

Temperature-Driven Anchoring Transitions at Liquid Crystal/Water Interfaces

Controlling the anchoring of liquid crystal molecules at an interface with a water solution influences the entire organization of the underlying liquid crystal phase, which is crucial for many applications. The simplest way to stabilize such interfaces is by fabricating liquid crystal droplets in water; however, a greater sensitivity to interfacial effects can be achieved using liquid crystal shells, that is, spherical films of liquid crystal suspended in water. Anchoring transitions on those systems are traditionally triggered by the adsorption of surfactant molecules onto the interface, which is neither an instantaneous nor a reversible process. In this study, we report the ability to change the anchoring of 4-cyano-4'-pentylbiphenyl (5CB), one of the most widely used liquid crystals, at the interface with dilute water solutions of polyvinyl alcohol (PVA), a polymer commonly used for stabilizing liquid crystal shells, simply by controlling the temperature in the close vicinity of the liquid crystal clearing point. A quasi-static increase in temperature triggers an instantaneous reorientation of the molecules from parallel to perpendicular to the interfaces, owing to the local disordering effect of PVA on 5CB, prior to the phase transition of the bulk 5CB. We study this anchoring transition on both flat suspended films and spherical shells of liquid crystals. Switching anchoring entails a series of structural transformations involving the formation of transient structures in which topological defects are stabilized. The type of defect structure depends on the topology of the film. This method has the ability to influence both interfaces of the film nearly at the same time and can be applied to transform an initially polydisperse group of nematic shells into a monodisperse population of bivalent shells.

Rodlike molecules in extreme confinement

A unique feature of colloid particles and biopolymers is the molecule's intrinsic rigidity characterized by a molecular-level length scale. Under extreme confinement conditions at cellular scales or in nanodevices, these molecules can display orientational ordering accompanied by severe density depletion. Conventional liquid-crystal theories, such as the Oseen-Frank or Landau-de Gennes theories, cannot capture the essential molecular-level properties: the boundary effects, which extend to a distance of the rigidity length scale, and the drastic variations of the inhomogeneous molecular density. Here we show, based on a simple interpretation of the Onsager model, that rodlike molecules in extreme annular confinement produce unusual liquid-crystal defect structures that are independent phases from the patterns usually seen in a weaker confinement environment.

Photonic Multishells Composed of Cholesteric Liquid Crystals Designed by Controlled Phase Separation in Emulsion Drops

Cholesteric liquid crystals (CLCs), also known as chiral nematic LCs, show a photonic stopband, which is promising for various optical applications. In particular, CLCs confined in microcompartments are useful for sensing, lasing, and optical barcoding at the microscale. The integration of distinct CLCs into single microstructures can provide advanced functionality. In this work, CLC multishells with multiple stopbands are created by liquid-liquid phase separation (LLPS) in a simple yet highly controlled manner. A homogeneous ternary mixture of LC, hydrophilic liquid, and co-solvent is microfluidically emulsified to form uniform oil-in-water drops, which undergo LLPS to form onion-like drops composed of alternating CLC-rich and CLC-depleted layers. The multiplicity is controlled from one to five by adjusting the initial composition of the ternary mixture, which dictates the number of consecutive steps of LLPS. Interestingly, the concentration of the chiral dopant becomes reduced from the outermost to the innermost CLC drop due to uneven partitioning during LLPS, which results in multiple stopbands. Therefore, the photonic multishells show multiple structural colors. In addition, dye-doped multishells provide band-edge lasing at two different wavelengths. This new class of photonic multishells will provide new opportunities for advanced optical applications.

Swelling Cholesteric Liquid Crystal Shells to Direct the Assembly of Particles at the Interface

Cholesteric liquid crystals can exhibit spatial patterns in molecular alignment at interfaces that can be exploited for particle assembly. These patterns emerge from the competition between bulk and surface energies, tunable with the system geometry. In this work, we use the osmotic swelling of cholesteric double emulsions to assemble colloidal particles through a pathway-dependent process. Particles can be repositioned from a surface-mediated to an elasticity-mediated state through dynamically thinning the cholesteric shell at a rate comparable to that of colloidal adsorption. By tuning the balance between surface and bulk energies with the system geometry, colloidal assemblies on the cholesteric interface can be molded by the underlying elastic field to form linear aggregates. The transition of adsorbed particles from surface regions with homeotropic anchoring to defect regions is accompanied by a reduction in particle mobility. The arrested assemblies subsequently map out and stabilize topological defects. These results demonstrate the kinetic arrest of interfacial particles within definable patterns by regulating the energetic frustration within cholesterics. This work highlights the importance of kinetic pathways for particle assembly in liquid crystals, of relevance to optical and energy applications.

Properties of surface Landau-de Gennes Q-tensor models

Uniaxial nematic liquid crystals whose molecular orientation is subjected to tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of freedom. We consider a general thin film limit of a Landau-de Gennes Q-tensor model which retains the characteristics of the 3D model. From this, previously proposed surface models follow as special cases. We compare fundamental properties, such as the alignment of the orientational degrees of freedom with principle curvature lines, order parameter symmetry and phase transition type for these models, and suggest experiments to identify suitable model assumptions.

Chiral nematic liquid crystals in torus-shaped and cylindrical cavities

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

Reconfigurable Multicompartment Emulsion Drops Formed by Nematic Liquid Crystals and Immiscible Perfluorocarbon Oils

Liquid crystalline (LC) oils offer the basis of stimuli-responsive LC-in-water emulsions. Although past studies have explored the properties of single-phase LC emulsions, few studies have focused on complex multicompartment emulsions containing co-existing isotropic and LC domains. In this paper, we report a study of multiphase emulsions using LCs and immiscible perfluoroalkanes dispersed in water or glycerol (the latter continuous phase is used to enable characterization). We found that the nematogen 4'-pentyl-4-biphenylcarbonitrile (5CB) anchors homeotropically (perpendicularly) and weakly at liquid perfluorononane (F9) interfaces, consistent with the smectic layering of 5CB molecules. The proposed role of smectic layering is supported by experiments performed with 4-(trans-4-pentylcyclohexyl)benzonitrile, a nematogen that possesses a cyclohexyl group that frustrates the smectic packing and leads to tilted orientations at the F9 interface. By employing perfluorocarbon and hydrocarbon surfactants in combination with multiphase 5CB and F9 emulsion droplets dispersed in a continuous water or glycerol phase, we observe a range of emulsion droplet morphologies to form, including core-shell and Janus structures, with internal organizations that reflect an interplay of interfacial (anchoring energies; F9 and glycerol) and elastic energies within the confines of the geometry of the emulsion droplet. By comparing experimental observations to simulations of the LC-perfluorocarbon droplets based on a Landau-de Gennes model of the free energy, we place bounds on the orientation-dependent interfacial energies that underlie the internal ordering of these complex emulsions. Additionally, by forming core-shells emulsion droplets from 5CB (shell) and perfluoroheptane (cores), we demonstrate how a liquid-to-vapor phase transition in the perfluorocarbon core can be used to actuate the droplet and rapidly thin the nematic shell. Overall, the results reported in this paper demonstrate that multiphase LC emulsions formed from mixtures of perfluoroalkanes and LCs provide new opportunities to engineer hierarchical and stimuli-responsive emulsion systems.

Precise Self-Positioning of Colloidal Particles on Liquid Emulsion Droplets

Decorating emulsion droplets by particles stabilizes foodstuff and pharmaceuticals. Interfacial particles also influence aerosol formation, thus impacting atmospheric CO₂ exchange. While studies of particles at disordered droplet interfaces abound in the literature, such studies for ubiquitous ordered interfaces are not available. Here, we report such an experimental study, showing that particles residing at crystalline interfaces of liquid droplets spontaneously self-position to specific surface locations, identified as structural topological defects in the crystalline surface monolayer. This monolayer forms at temperature T = T_s, leaving the droplet liquid and driving at T_d < T_s a spontaneous shape-change transition of the droplet from spherical to icosahedral. The particle's surface position remains unchanged in the transition, demonstrating these positions to coincide with the vertices of the sphere-inscribed icosahedron. Upon further cooling, droplet shape-changes to other polyhedra occur, with the particles remaining invariably at the polyhedra's vertices. At still lower temperatures, the particles are spontaneously expelled from the droplets. Our results probe the molecular-scale elasticity of quasi-two-dimensional curved crystals, impacting also other fields, such as protein positioning on cell membranes, controlling essential biological functions. Using ligand-decorated particles, and the precise temperature-tunable surface position control found here, may also allow using these droplets for directed supra-droplet self-assembly into larger structures, with a possible post-assembly structure fixation by UV polymerization of the droplet's liquid.

Optical motion control of liquid crystalline droplets by host-guest molecular interaction

Photo-induced motion is demonstrated for a photo-responsive dye-doped liquid crystal (LC) droplet in a surfactant solution. The LC droplets started rolling on a substrate during UV irradiation and moved either toward or away from the UV light, depending on the functional groups of the guest dyes. The mechanism is explained by the Marangoni flow caused by the photo-isomerization-induced adsorption and desorption of the dye molecules to and from the LC/solution interfaces.

Realignment of Liquid Crystal Shells Driven by Temperature-Dependent Surfactant Solubility

We investigate dynamic director field variations in shells of the nematic liquid crystal (LC) compound, 4-cyano-4'-pentylbiphenyl, suspended in and containing immiscible aqueous phases. The outer and inner shell interfaces are stabilized by the cationic surfactant, cetyl trimethyl ammonium bromide (CTAB), and by the water soluble polymer, poly(vinyl alcohol) (PVA), respectively. PVA and surfactant solutions normally promote tangential and orthogonal alignments, respectively, of the LC director. The rather high Krafft temperature of CTAB, T_K ≈ 25 °C, means that its solubility in water is below the critical micelle concentration at room temperature in most labs. Here, we study the effect of cooling/heating past T_K on the LC shell director configuration. Within a certain concentration range, CTAB in the outer aqueous phase (and PVA in the inner) switches the LC director field from hybrid to uniformly orthogonal upon cooling below T_K. We argue that the effect is related to the migration of the surfactant through the fluid LC membrane into the initially surfactant-free aqueous PVA solution, triggered by the drastically reduced water solubility of CTAB at T < T_K. The results suggest that LC shells can detect solutes in the continuous phase, provided there is sufficient probability that the solute migrates through the LC into the inner aqueous phase.

Liquid crystal elastomer shell actuators with negative order parameter

Liquid crystals (LCs) are nonsolids with long-range orientational order, described by a scalar order parameter 〈 P 2 〉 = 1 2 〈 3 cos 2 β - 1 〉 . Despite the vast set of existing LC materials, one-third of the order parameter value range, ^-1/₂ < 〈P ₂〉 < 0, has until now been inaccessible. Here, we present the first material with negative LC order parameter in its ground state, in the form of elastomeric shells. The optical and actuation characteristics are opposite to those of conventional LC elastomers (LCEs). This novel class of anti-ordered elastomers gives access to the previously secluded range of liquid crystallinity with 〈P ₂〉 < 0, providing new challenges for soft matter physics and adding a complementary type of LCE actuator that is attractive for applications in, e.g., soft robotics.

Nanoparticle-based hollow microstructures formed by two-stage nematic nucleation and phase separation

Rapid bulk assembly of nanoparticles into microstructures is challenging, but highly desirable for applications in controlled release, catalysis, and sensing. We report a method to form hollow microstructures via a two-stage nematic nucleation process, generating size-tunable closed-cell foams, spherical shells, and tubular networks composed of closely packed nanoparticles. Mesogen-modified nanoparticles are dispersed in liquid crystal above the nematic-isotropic transition temperature (TNI). On cooling through TNI, nanoparticles first segregate into shrinking isotropic domains where they locally depress the transition temperature. On further cooling, nematic domains nucleate inside the nanoparticle-rich isotropic domains, driving formation of hollow nanoparticle assemblies. Structural differentiation is controlled by nanoparticle density and cooling rate. Cahn-Hilliard simulations of phase separation in liquid crystal demonstrate qualitatively that partitioning of nanoparticles into isolated domains is strongly affected by cooling rate, supporting experimental observations that cooling rate controls aggregate size. Microscopy suggests the number and size of internal voids is controlled by second-stage nucleation.

Spherical-cap droplets of a photo-responsive bent liquid crystal dimer

Using a photo-responsive dimer exhibiting the transition between nematic (N) and twist-bend nematic (NTB) phases, we prepared spherical cap-shaped droplets on solid substrates exposed to air. The internal director structures of these droplets vary depending on the phase and on the imposed boundary conditions. The structural switching between the N and NTB phases was successfully performed either by temperature control or by UV light-irradiation. The N phase is characterized by an extremely small bend elastic constant K3, and surprisingly, we found that the droplet-air interface induces a planar alignment, in contrast to that seen for typical calamitic liquid crystals. As a consequence, the director configuration was stabilized in a structure substantially different from that normally found in conventional nematic liquid crystalline droplets. In the twist-bend nematic droplets characteristic structures with macroscopic length scales were formed, and they were well controlled by the droplet size. These results indicated that a continuum theory is effective in describing the stabilization mechanism of the macroscopic structure even in the twist-bend nematic liquid crystal droplets exhibiting director modulations on a scale of several molecular lengths.

Topology and ground-state degeneracy of tetrahedral smectic vesicles

Chemical design of block copolymers makes it possible to create polymer vesicles with tunable microscopic structure. Here we focus on a model of a vesicle made of smectic liquid-crystalline block copolymers at zero temperature. The vesicle assumes a faceted tetrahedral shape and the smectic layers arrange in a stack of parallel straight lines with topological defects localized at the vertices. We counted the number of allowed states at [Formula: see text]. For any fixed shape, we found a two-dimensional countable degeneracy in the smectic pattern depending on the tilt angle between the smectic layers and the edge of the tetrahedral shell. For most values of the tilt angle, the smectic layers contain spiral topological defects. The system can spontaneously break chiral symmetry when the layers organize into spiral patterns, composed of a bound pair of +1/2 disclinations. Finally, we suggest possible applications of tetrahedral smectic vesicles in the context of functionalizing defects and the possible consequences of the spiral structures for the rigidity of the vesicle.

Cylindrical nematic liquid crystal shell: effect of saddle-splay elasticity

This study introduces cylindrical nematic liquid crystal (LC) shells. Shells as confinement can provide soft matter with intriguing topology and geometry. Indeed, in spherical shells of LCs, rich defect structures have been reported. Avoiding the inherent Plateau-Rayleigh instability of cylindrical liquid-liquid interfaces, we realize the cylindrical nematic LC shell by two different methods: the phase separation in the nematic-isotropic coexistence phase and a cylindrical cavity with a glass rod suspended in the middle. Specifically, the director configurations of lyotropic chromonic LCs (LCLCs) in the cylindrical shell and their energetics are investigated theoretically and experimentally. Unusual elastic properties of LCLCs, i.e., a large saddle-splay modulus, and a shell geometry with both concave and convex curvatures, result in a double-twist director configuration.

Length segregation in mixtures of spherocylinders induced by imposed topological defects

We explore length segregation in binary mixtures of spherocylinders of lengths L1 and L2 which are tangentially confined on a spherical surface of radius R. The orientation of the spherocylinders is constrained along an externally imposed direction field on the sphere which is either along the longitude or the latitude lines of the sphere. In both situations, integer orientational defects at the poles are imposed. Using computer simulations we show that these topological defects induce a complex segregation picture also depending on the length ratio factor γ = L2/L1 and the total packing fraction η of the spherocylinders. When the binary mixture is aligned along the longitude lines of the sphere, shorter rods tend to accumulate at the topological defects of the polar caps whereas longer rods occupy the central equatorial area of the spherical surface. In the reverse case of latitude ordering, a new state can emerge where longer rods are predominantly both in the cap and in the equatorial areas and shorter rods are localized in between. As a reference situation, we consider a defect-free situation in the flat plane and do not find any length segregation there at similar γ and η; hence, the segregation is purely induced by the imposed topological defects. We also develop an Onsager-like density functional theory which is capable of predicting length segregation in ordered mixtures. At low density, the results of this theory are in good agreement with the simulation data.

Optically induced motion of liquid crystalline droplets

The controlled motion of a liquid crystalline active droplet was demonstrated in a surfactant solution and by irradiation with UV light. The droplet could be induced to roll on a glass substrate toward the UV light source. This was explained by the Marangoni flow induced by the UV-induced desorption of surfactants.

Self-assembly of semiflexible polymers confined to thin spherical shells

Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.

Self-assembly of convex particles on spherocylindrical surfaces

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.

Modeling deformation and chaining of flexible shells in a nematic solvent with finite elements on an adaptive moving mesh

A micrometer-scale elastic shell immersed in a nematic liquid crystal may be deformed by the host if the cost of deformation is comparable to the cost of elastic deformation of the nematic. Moreover, such inclusions interact and form chains due to quadrupolar distortions induced in the host. A continuum theory model using finite elements is developed for this system, using mesh regularization and dynamic refinement to ensure quality of the numerical representation even for large deformations. From this model, we determine the influence of the shell elasticity, nematic elasticity, and anchoring condition on the shape of the shell and hence extract parameter values from an experimental realization. Extending the model to multibody interactions, we predict the alignment angle of the chain with respect to the host nematic as a function of aspect ratio, which is found to be in excellent agreement with experiments.

Liquid crystals of hard rectangles on flat and cylindrical manifolds

The self-assembly of rectangular particles on flat and curved substrates was investigated using density functional theory and simulations.

Smectic monolayer confined on a sphere: topology at the particle scale

The impact of topology on the structure of a smectic monolayer confined to a sphere is explored by particle-resolved computer simulations of hard rods. The orientations of the particles are tangential to the sphere and either free or restricted to a prescribed director field with a latitude or longitude orderings. Depending on the imprinted topology, a wealth of different states are found including equatorial smectic with isotropic poles, equatorial smectic with empty poles, a broken egg-shell like modulated smectic, a capped nematic with equatorial bald patches, equatorial nematic with empty poles, and a situation with 4 or 8 half-strength topological defects. Potentially these states could be verified in experiments with Pickering emulsions of droplets with colloidal rods. The unique nature of dipolar structures consisting of positive and negative half-strength disclinations is revealed. These structures, classified by their density and interaction with other defects in the system, relieve the strain of the poles by separating closely positioned half-strength defects. The proximity of these structures to the half-strength defects might enhance the structural diffusion of the defects across the system.

Optically Reconfigurable Chiral Microspheres of Self-Organized Helical Superstructures with Handedness Inversion

Optically reconfigurable monodisperse chiral microspheres of self-organized helical superstructures with dynamic chirality were fabricated via a capillary-based microfluidic technique. Light-driven handedness-invertible transformations between different configurations of microspheres were vividly observed and optically tunable RGB photonic cross-communications among the microspheres were demonstrated.

Bistable curvature potential at hyperbolic points of nematic shells

Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.

Fast Dynamic Visualizations in Microfluidics Enabled by Fluorescent Carbon Nanodots

Microfluidic systems have become a superior platform for explorations of fascinating fluidic physics at microscale as well as applications in biomedical devices, chemical reactions, drug delivery, etc. Exploitations of this platform are built upon the fundamental techniques of flow visualizations. However, the currently employed fluorescent materials for microfluidic visualization are far from satisfaction, which severely hinders their widespread applications. Here fluorescent carbon nanodots are documented as a game-changer, applicable in versatile fluidic environment for the visualization in microfluidics with unprecedented advantages. One of the fastest fluorescent imaging speeds up to 2500 frames per second under a normal contionous wave (CW) laser line is achieved by adopting carbon nanodots in microfluidics. Besides better visualizations of the fluid or interface, fluorescent carbon nanodots-based microparticles enable quantitative studies of high speed dynamics in fluids at microscale with a more than 90% lower cost, which is inaccessible by traditionally adopted fluorescent dye based seeding particles. The findings hold profound influences to microfluidic investigations and may even lead to revolutionary changes to the relevant industries.

Aging and rejuvenation of active matter under topological constraints

The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these non-equilibrium processes, and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. Our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.

Intradomain Textures in Block Copolymers: Multizone Alignment and Biaxiality

Block copolymer (BCP) melt assembly has been studied for decades, focusing largely on self-organized spatial patterns of periodically ordered segment density. Here, we demonstrate that underlying the well-known composition profiles (i.e., ordered lamella, cylinders, spheres, and networks) are generic and heterogeneous patterns of segment orientation that couple strongly to morphology, even in the absence of specific factors that promote intra or interchain segment alignment. We employ both self-consistent field theory and coarse-grained simulation methods to measure polar and nematic order parameters of segments in a freely jointed chain model of diblock melts. We show that BCP morphologies have a multizone texture, with segments predominantly aligned normal and parallel to interdomain interfaces in the respective brush and interfacial regions of the microdomain. Further, morphologies with anisotropically curved interfaces (i.e., cylinders and networks) exhibit biaxial order that is aligned to the principal curvature axes of the interface.

Curvature-driven stability of defects in nematic textures over spherical disks

Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature-driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defects are repelled to the boundary of the disk. Our calculations reveal that the movement of the equilibrium position of the +1 defect from the boundary to the center of the spherical disk occurs in a very narrow window of the disk area, exhibiting the first-order phase-transition-like behavior. For the pair of +1/2 defects by splitting a +1 defect, we find the curvature-driven alternating repulsive and attractive interactions between the two defects. With the growth of the spherical disk these two defects tend to approach and finally recombine towards a +1 defect texture. The sensitive response of defects to curvature and the curvature-driven stability mechanism demonstrated in this work in nematic disk systems may have implications towards versatile control and engineering of liquid-crystal textures in various applications.

Segregation of liquid crystal mixtures in topological defects

The structure and physical properties of liquid crystal (LC) mixtures are a function of composition, and small changes can have pronounced effects on observables, such as phase-transition temperatures. Traditionally, LC mixtures have been assumed to be compositionally homogenous. The results of chemically detailed simulations presented here show that this is not the case; pronounced deviations of the local order from that observed in the bulk at defects and interfaces lead to significant compositional segregation effects. More specifically, two disclination lines are stabilized in this work by introducing into a nematic liquid crystal mixture a cylindrical body that exhibits perpendicular anchoring. It is found that the local composition deviates considerably from that of the bulk at the interface with the cylinder and in the defects, thereby suggesting new assembly and synthetic strategies that may capitalize on the unusual molecular environment provided by liquid crystal mixtures.

Liquid crystal mixtures are used in commercial applications and their composition affects their properties. Here Rahimi et al. use atomistic simulations to show that defects influence the molecular arrangement of the mixture components leading to a deviation of the local order from that of the bulk.