Entangled nematic disclinations using multi-particle collision dynamics

Colloids dispersed in nematic liquid crystals form topological composites in which colloid-associated defects mediate interactions while adhering to fundamental topological constraints. Better realising the promise of such materials requires numerical methods that model nematic inclusions in dynamic and complex scenarios. We employ a mesoscale approach for simulating colloids as mobile surfaces embedded in a fluctuating nematohydrodynamic medium to study the kinetics of colloidal entanglement. In addition to reproducing far-field interactions, topological properties of disclination loops are resolved to reveal their metastable states and topological transitions during relaxation towards ground state. The intrinsic hydrodynamic fluctuations distinguish formerly unexplored far-from-equilibrium disclination states, including configurations with localised positive winding profiles. The adaptability and precision of this numerical approach offers promising avenues for studying the dynamics of colloids and topological defects in designed and out-of-equilibrium situations.

Topology-driven collective dynamics of nematic colloidal entanglement

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

Moiré effect enables versatile design of topological defects in nematic liquid crystals

Recent advances in surface-patterning techniques of liquid crystals have enabled the precise creation of topological defects, which promise a variety of emergent applications. However, the manipulation and application of these defects remain limited. Here, we harness the moiré effect to engineer topological defects in patterned nematic liquid crystal cells. Specifically, we combine simulation and experiment to examine a nematic cell confined between two substrates of periodic surface anchoring patterns; by rotating one surface against the other, we observe a rich variety of highly tunable, novel topological defects. These defects are shown to guide the three-dimensional self-assembly of colloids, which can conversely impact defects by preventing the self-annihilation of loop-defects through jamming. Finally, we demonstrate that certain nematic moiré cells can engender arbitrary shapes represented by defect regions. As such, the proposed simple twist method enables the design and tuning of mesoscopic structures in liquid crystals, facilitating applications including defect-directed self-assembly, material transport, micro-reactors, photonic devices, and anti-counterfeiting materials.

Collective transport and reconfigurable assembly of nematic colloids by light-driven cooperative molecular reorientations

Nanomotors in nature have inspired scientists to design synthetic molecular motors to drive the motion of microscale objects by cooperative action. Light-driven molecular motors have been synthesized, but using their cooperative reorganization to control the collective transport of colloids and to realize the reconfiguration of colloidal assembly remains a challenge. In this work, topological vortices are imprinted in the monolayers of azobenzene molecules which further interface with nematic liquid crystals (LCs). The light-driven cooperative reorientations of the azobenzene molecules induce the collective motion of LC molecules and thus the spatiotemporal evolutions of the nematic disclination networks which are defined by the controlled patterns of vortices. Continuum simulations provide physical insight into the morphology change of the disclination networks. When microcolloids are dispersed in the LC medium, the colloidal assembly is not only transported and reconfigured by the collective change of the disclination lines but also controlled by the elastic energy landscape defined by the predesigned orientational patterns. The collective transport and reconfiguration of colloidal assemblies can also be programmed by manipulating the irradiated polarization. This work opens opportunities to design programmable colloidal machines and smart composite materials.

Active boundary layers in confined active nematics

The role of boundary layers in conventional liquid crystals is commonly related to the mesogen anchoring on confining walls. In the classical view, anchoring enslaves the orientational field of the passive material under equilibrium conditions. In this work, we show that an active nematic can develop active boundary layers that topologically polarize the confining walls. We find that negatively-charged defects accumulate in the boundary layer, regardless of the wall curvature, and they influence the overall dynamics of the system to the point of fully controlling the behavior of the active nematic in situations of strong confinement. Further, we show that wall defects exhibit behaviors that are essentially different from those of their bulk counterparts, such as high motility or the ability to recombine with another defect of like-sign topological charge. These exotic behaviors result from a change of symmetry induced by the wall in the director field around the defect. Finally, we suggest that the collective dynamics of wall defects might be described in terms of a model equation for one-dimensional spatio-temporal chaos.

Modularizable Liquid-Crystal-Based Open Surfaces Enable Programmable Chemical Transport and Feeding using Liquid Droplets

Droplet-based miniature reactors have attracted interest in both fundamental studies, for the unique reaction kinetics they enable, and applications in bio-diagnosis and material synthesis. However, the precise and automatic feeding of chemicals, important for the delicate reactions in these miniaturized chemical reactors, either requires complex, high-cost microfluidic devices or lacks the capability to maintain a pinning-free droplet movement. Here, the design and synthesis of a new class of liquid crystal (LC)-based open surfaces, which enable a controlled chemical release via a programmable LC phase transition without sacrificing the free transport of the droplets, are reported. It is demonstrated that their intrinsic slipperiness and self-healing properties enable a modularizable assembly of LC surfaces that can be loaded with different chemicals to achieve a wide range of chemical reactions carried out within the droplets, including sequential and parallel chemical reactions, crystal growth, and polymer synthesis. Finally, an LC-based chemical feeding device is developed that can automatically control the release of chemicals to direct the simultaneous differentiation of human induced pluripotent stem cells into endothelial progenitor cells and cardiomyocytes. Overall, these LC surfaces exhibit desirable levels of automation, responsiveness, and controllability for use in miniature droplet carriers and reactors.

Photocontrollable Crystallization at the Topological Defect of a Liquid Crystalline Droplet

Photocontrollable crystallization at topological defects in a liquid crystal (LC) droplet was demonstrated. The molecules dissolved in a surfactant solution outside the LC droplet were moved into the droplet via light absorption. Nuclei emerged tens of seconds after light irradiation and moved toward the topological defect located at the droplet center, thus forming a branch-shaped crystal. This phenomenon was reproduced for multiple different molecules; photoinduced migration, nucleation, and crystal formation were discussed as a plausible mechanism.

Topological barriers to defect nucleation generate large mechanical forces in an ordered fluid

Common fluids cannot sustain static mechanical stresses at the macroscopic scale because they lack molecular order. Conversely, crystalline solids exhibit long-range order and mechanical strength at the macroscopic scale. Combining the properties of fluids and solids, liquid crystal films respond to mechanical confinement by both flowing and generating static forces. The elastic response, however, is very weak for film thicknesses exceeding 10 nm. In this study, the mechanical strength of a fluid film was enhanced by introducing topological defects in a cholesteric liquid crystal, producing unique viscoelastic and optomechanical properties. The cholesteric was confined under strong planar anchoring conditions between two curved surfaces with sphere-sphere contact geometry similar to that of large colloidal particles, creating concentric dislocation loops. During surface retraction, the loops shrank and periodically disappeared at the surface contact point, where the cholesteric helix underwent discontinuous twist transitions, producing weak oscillatory surface forces. On the other hand, new loop nucleation was frustrated by a topological barrier during fluid compression, creating a metastable state. This generated exceptionally large forces with a range exceeding 100 nm as well as extended blueshifts of the photonic bandgap. The metastable cholesteric helix eventually collapsed under a high compressive load, triggering a stick-slip-like cascade of defect nucleation and twist reconstruction events. These findings were explained using a simple theoretical model and suggest a general approach to enhance the mechanical strength of one-dimensional periodic materials, particularly cholesteric colloid mixtures.

Liquid crystal-based open surface microfluidics manipulate liquid mobility and chemical composition on demand

The ability to control both the mobility and chemical compositions of microliter-scale aqueous droplets is an essential prerequisite for next-generation open surface microfluidics. Independently manipulating the chemical compositions of aqueous droplets without altering their mobility, however, remains challenging. In this work, we address this challenge by designing a class of open surface microfluidic platforms based on thermotropic liquid crystals (LCs). We demonstrate, both experimentally and theoretically, that the unique positional and orientational order of LC molecules intrinsically decouple cargo release functionality from droplet mobility via selective phase transitions. Furthermore, we build sodium sulfide–loaded LC surfaces that can efficiently precipitate heavy metal ions in sliding water droplets to final concentration less than 1 part per million for more than 500 cycles without causing droplets to become pinned. Overall, our results reveal that LC surfaces offer unique possibilities for the design of novel open surface fluidic systems with orthogonal functionalities.

Colloidal aggregation in anisotropic liquid crystal solvent

The mutual attraction between colloidal particles in an anisotropic fluid, such as the nematic liquid crystal phase, leads to the formation of hierarchical aggregate morphologies distinct from those that tend to form in isotropic fluids. Previously it was difficult to study this aggregation process for a large number of colloids due to the difficulty of achieving a well dispersed initial colloid distribution under good imaging conditions. In this paper, we report the use of a recently developed self-assembling colloidal system to investigate this process. Hollow, micron-scale colloids are formed in situ in the nematic phase and subsequently aggregate to produce fractal structures and colloidal gels, the structures of which are determined by colloid concentration and temperature quench depth through the isotropic to nematic phase transition point. This self-assembling colloidal system provides a unique method to study particle aggregation in liquid crystal over large length scales. We use fluorescence microscopy over a range of length scales to measure aggregate structure as a function of temperature quench depth, observe ageing mechanisms and explore the driving mechanisms in this unique system. Our analyses suggest that aggregate dynamics depend on a combination of Frank elasticity relaxation, spontaneous defect line annihilation and internal aggregate fracturing.

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.

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. 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.

Magnified charge carrier conduction, permittivity, and mesomorphic properties of columnar structure of a room temperature discotic liquid crystalline material due to the dispersion of low concentration ferroelectric nanoparticles

Liquid crystal nanocomposites have been a hot topic of research due to optimization of physical properties with such blending. There are several reports on enhancement of physical properties of nematic liquid crystals due to the blending of the nanomaterials. L. M. Lopatina and J. V. Selinger [Phys. Rev. Lett. 102, 197802 (2009)]10.1103/PhysRevLett.102.197802 have even proposed a theory based on experimental results for the enhancement of the properties of the nematic mesophase in the presence of ferroelectric nanoparticles. However, discotic liquid crystal nanocomposites are less studied. In the present experimental work, we have studied the effect of ferroelectric (BaTiO_{3}) nanoparticles on a room temperature discotic liquid crystalline material, namely 1,5-dihydroxy-2,3,6,7-tetrakis(3,7-dimethyloctyloxy)-9,10-anthraquinone. We investigated the physical properties of low concentration ferroelectric nanoparticle dispersed discotic columnar structure, using calorimetric, optical, x-ray diffraction, and dielectric spectroscopy tools. Results show that inclusion of ferroelectric nanoparticles in the discotic matrix consolidates the stability of the columnar matrix of the Col_{h} phase by virtue of their ferroic nature. An enhancement in charge carrier conductivity by several orders of magnitude at ambient conditions has been observed which makes such systems highly appropriate for one-dimensional conductors. Low concentration of BaTiO_{3} nanoparticles substantially enhanced permittivity of the system also. A molecular relaxation mode has been observed in the middle frequency range of the dielectric spectra. Enhancement of these important parameters could be possible due to the ferroelectric nature of the dispersed nanoparticles.

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.

Intrinsically Visible Light-Responsive Liquid Crystalline Physical Gels Driven by a Halogen Bond

Photoresponsive physical gels using liquid crystals (LCs) as solvents have attracted great interest owing to their potential applications. But, current investigations mainly focus on UV light, which is not environment-friendly enough. On the other hand, the halogen bond is a novel tool for constructing supramolecular gels because of good hydrophobicity, high directionality, tunable strength, and large size of halogen atoms. Herein, to construct an LC physical gel with both the advantages of a halogen bond and visible light response, azopyridine-containing Azopy-C₁₀ is chosen as a halogen bond acceptor, while 1,2-bis(2,3,5,6-tetrafluoro-4-iodophenyl)diazene is selected both as the halogen bond donor and for the intrinsically visible light response. Such a binary gelator can self-assemble in the anisotropic solvent of nematic LC 5CB to form an LC physical gel. It experiences the gel-to-sol transition by green light irradiation. As the gelator concentration increases, the saturation voltage increases, but the switch-off time decreases. The combination of the halogen bond and controllable visible light-responsive LC physical gel provides the feasibilities of manipulating these smart soft materials.

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.

Self-assembled toron-like structures in inverse nematic gels

A novel form of nematic gel (N-gel) wherein bright flower-like domains (BFDs) rich in gelator fibres are embedded in a matrix of liquid crystal (LC) molecules has been reported. These gels which we denote as inverse N-gels are unlike typical N-gels in which the LC is encapsulated within an aggregated network of gelator molecules. The self-organization of the helical gelator fibres within the BFDs leads to the creation of localized toron-like structures that are topologically protected due to their skyrmion director profile. Optical and confocal microscopy have been used to deduce the LC director configuration, in order to understand possible intermolecular interactions that can lead to the formation of the twisted structures and the inverse N-gels.

Electrically powered motions of toron crystallites in chiral liquid crystals

Malleability of metals is an example of how the dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these defects move merely to comply with the mechanical forces applied on macroscopic scales, whereas the molecular and atomic building blocks behave like rigid particles. Here, we demonstrate how motions of crystallites and the defects between them can arise within the soft matter medium in an oscillating electric field applied to a chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of self-assembled topological solitons called "torons." Periodic oscillations of electric field applied perpendicular to the plane of hexagonal lattices prompt repetitive shear-like deformations of the solitons, which synchronize the electrically powered self-shearing directions. The temporal evolution of deformations upon turning voltage on and off is not invariant upon reversal of time, prompting lateral translations of the crystallites of torons within quasi-hexagonal periodically deformed lattices. We probe how these motions depend on voltage and frequency of oscillating field applied in an experimental geometry resembling that of liquid crystal displays. We study the interrelations between synchronized deformations of the soft solitonic particles and their arrays, and the ensuing dynamics and giant number fluctuations mediated by motions of crystallites, five-seven defects pairs, and grain boundaries in the orderly organizations of solitons. We discuss how our findings may lead to technological and fundamental science applications of dynamic self-assemblies of topologically protected but highly deformable particle-like solitons.

Defect-mediated colloidal interactions in a nematic-phase discotic solvent

Interactions between colloidal inclusions dispersed in a nematic discotic liquid-crystalline solvent were investigated for different solute-solvent coupling conditions. The solvent was treated at the level of Gay-Berne discogens. Colloidal inclusions were coupled to the solvent with a generalized sphere-ellipsoid interaction potential. Energy strengths were varied to promote either homeotropic or planar mesogenic anchoring. Colloid-colloid interactions were modeled using a soft, excluded-volume contribution. Single-colloid and colloid-pair samples were evolved with Molecular Dynamics simulations. Equilibrium trajectories were used to characterize structural and dynamical properties of topological defects arising in the mesomorphic phase due to colloidal inclusions. Boojums were observed with planar anchoring, whereas Saturn rings were obtained with homeotropic anchoring. The manner in which these topological defects drive colloidal interactions was assessed through a free energy analysis, taking into account the relative orientation between a colloidal dyad and the nematic-field director. The dynamical behavior of defects was qualitatively surveyed from equilibrium trajectories borne from computer simulations.

Soft matter from liquid crystals

Liquid crystals (LCs) are fluids within which molecules exhibit long-range orientational order, leading to anisotropic properties such as optical birefringence and curvature elasticity. Because the ordering of molecules within LCs can be altered by weak external stimuli, LCs have been widely used to create soft matter systems that respond optically to electric fields (LC display), temperature (LC thermometer) or molecular adsorbates (LC chemical sensor). More recent studies, however, have moved beyond investigations of optical responses of LCs to explore the design of complex LC-based soft matter systems that offer the potential to realize more sophisticated functions (e.g., autonomous, self-regulating chemical responses to mechanical stimuli) by directing the interactions of small molecules, synthetic colloids and living cells dispersed within the bulk of LCs or at their interfaces. These studies are also increasingly focusing on LC systems driven beyond equilibrium states. This review presents one perspective on these advances, with an emphasis on the discovery of fundamental phenomena that may enable new technologies. Three areas of progress are highlighted; (i) directed assembly of amphiphilic molecules either within topological defects of LCs or at aqueous interfaces of LCs, (ii) templated polymerization in LCs via chemical vapor deposition, an approach that overcomes fundamental challenges related to control of LC phase behavior during polymerization, and (iii) studies of colloids in LCs, including chiral colloids, soft colloids that are strained by LCs, and active colloids that are driven into organized states by dissipation of energy (e.g. bacteria). These examples, and key unresolved issues discussed at the end of this perspective, serve to convey the message that soft matter systems that integrate ideas from LC, surfactant, polymer and colloid sciences define fertile territory for fundamental studies and creation of future transformative technologies.

Dynamic clustering and re-dispersion in concentrated colloid-active gel composites

We study the dynamics of quasi-two-dimensional concentrated suspensions of colloidal particles in active gels by computer simulations. Remarkably, we find that activity induces a dynamic clustering of colloids even in the absence of any preferential anchoring of the active nematic director at the particle surface. When such an anchoring is present, active stresses instead compete with elastic forces and re-disperse the aggregates observed in passive colloid-liquid crystal composites. Our quasi-two-dimensional "inverse" dispersions of passive particles in active fluids (as opposed to the more common "direct" suspensions of active particles in passive fluids) provide a promising route towards the self-assembly of new soft materials.

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.

Isotropic-isotropic phase separation and spinodal decomposition in liquid crystal-solvent mixtures

Phase separation in mixtures forming liquid crystal (LC) phases is an important yet under-appreciated phenomenon that can drastically influence the behaviour of a multi-component LC. Here we demonstrate, using polarising microscopy with active cooling as well as differential scanning calorimetry, that the phase diagram for mixtures of the LC-forming compound 4'-n-pentylbiphenyl-4-carbonitrile (5CB) with ethanol is surprisingly complex. Binary mixtures reveal a broad miscibility gap that leads to phase separation between two distinct isotropic phases via spinodal decomposition or nucleation and growth. On further cooling the nematic phase enters on the 5CB-rich side, adding to the complexity. Significantly, water contamination dramatically raises the temperature range of the miscibility gap, bringing up the critical temperature for spinodal decomposition from ∼ 2 °C for the anhydrous case to >50 °C if just 3 vol% water is added to the ethanol. We support the experiments with a theoretical treatment that qualitatively reproduces the phase diagrams as well as the transition dynamics, with and without water. Our study highlights the impact of phase separation in LC-forming mixtures, spanning from equilibrium coexistence of multiple liquid phases to non-equilibrium effects due to persistent spatial concentration gradients.

Liquid crystal hydroglass formed via phase separation of nanocellulose colloidal rods

A new anisotropic soft material - a liquid crystal 'hydroglass' (LCH) - is created from aqueous suspensions of nanocrystalline cellulose (NCC) colloidal rods. Under specific conditions, the NCC suspension separates into a colloid-rich attractive glass matrix phase and a coexisting liquid crystal phase. LCH provides similar viscoelastic properties to polymer and colloidal gels, but permits reversibly-orientating the colloidal rods through shear forces.

Orientation, elastic interaction and magnetic response of asymmetric colloids in a nematic liquid crystal

Colloidal particles in nematic liquid crystals create elastic distortion and experience long-range forces. The symmetry of elastic distortion and consequently the complexity of interaction strongly depends largely on the liquid crystal anchoring, topology and shape of the particles. Here, we introduce a new nematic colloidal system made of peanut-shaped hematite particles. We report experimental studies on spontaneous orientation, mutual interaction, laser assisted self-assembly and the effect of external magnetic fields on the colloids. Majority of the colloids spontaneously orient either parallel or perpendicular to the nematic director. The colloids that are oriented perpendicularly exhibit two types of textures due to the out of plane tilting, which is corroborated by the Landau-de Gennes Q-tensor modelling. The transverse magnetic moment of the peanut-shaped colloids is estimated by using a simple analysis based on the competing effects of magnetic and elastic torques.

Chirality-Enabled Liquid Crystalline Physical Gels with High Modulus but Low Driving Voltage

Self-supporting liquid crystalline physical gels with facile electro-optic response are highly desirable, but their development is challenging because both the storage modulus and driving voltage increase simultaneously with gelator loading. Herein, we report liquid crystalline physical gels with high modulus but low driving voltage. This behavior is enabled by chirality transfer from the molecular level to three-dimensional fibrous networks during the self-assembly of 1,4-benzenedicarboxamide phenylalanine derivatives. Interestingly, the critical gel concentration is as low as 0.1 wt %. Our findings open doors to understanding and exploiting the role of chirality in organic gels.

Amphiphile-Induced Phase Transition of Liquid Crystals at Aqueous Interfaces

Monolayer assemblies of amphiphiles at planar interfaces between thermotropic liquid crystals (LCs) and an aqueous phase can give rise to configurational transitions of the underlying LCs. A common assumption has been that a reconfiguration of the LC phase is caused by an interdigitation of the hydrophobic tails of amphiphiles with the molecules of the LC at the interface. A different mechanism is discovered here, whereby reorientation of the LC systems is shown to occur through lowering of the orientation-dependent surface energy of the LC due to formation of a thin isotropic layer at the aqueous interface. Using a combination of atomistic molecular dynamics simulations and experiments, we demonstrate that a monolayer of specific amphiphiles at an aqueous interface can cause a local nematic-to-isotropic phase transition of the LC by disturbing the antiparallel configuration of the LC molecules. These results provide new insights into the interfacial, molecular-level organization of LCs that can be exploited for rational design of biological sensors and responsive systems.

Tools and Functions of Reconfigurable Colloidal Assembly

We review work in reconfigurable colloidal assembly, a field in which rapid, back-and-forth transitions between the equilibrium states of colloidal self-assembly are accomplished by dynamic manipulation of the size, shape, and interaction potential of colloids, as well as the magnitude and direction of the fields applied to them. It is distinguished from the study of colloidal phase transitions by the centrality of thermodynamic variables and colloidal properties that are time switchable; by the applicability of these changes to generate transitions in assembled colloids that may be spatially localized; and by its incorporation of the effects of generalized potentials due to, for example, applied electric and magnetic fields. By drawing upon current progress in the field, we propose a matrix classification of reconfigurable colloidal systems based on the tool used and function performed by reconfiguration. The classification distinguishes between the multiple means by which reconfigurable assembly can be accomplished (i.e., the tools of reconfiguration) and the different kinds of structural transitions that can be achieved by it (i.e., the functions of reconfiguration). In the first case, the tools of reconfiguration can be broadly classed as (i) those that control the colloidal contribution to the system entropy-as through volumetric and/or shape changes of the particles; (ii) those that control the internal energy of the colloids-as through manipulation of colloidal interaction potentials; and (iii) those that control the spatially resolved potential energy that is imposed on the colloids-as through the introduction of field-induced phoretic mechanisms that yield colloidal displacement and accumulation. In the second case, the functions of reconfiguration include reversible: (i) transformation between different phases-including fluid, cluster, gel, and crystal structures; (ii) manipulation of the spacing between colloids in crystals and clusters; and (iii) translation, rotation, or shape-change of finite-size objects self-assembled from colloids. With this classification in hand, we correlate the current limits on the spatiotemporal scales for reconfigurable colloidal assembly and identify a set of future research challenges.

Oligomers as Triggers for Responsive Liquid Crystals

We report an investigation of the influence of aqueous solutions of amphiphilic oligomers on the ordering of micrometer-thick films of thermotropic liquid crystals (LCs), thus addressing the gap in knowledge arising from previous studies of the interactions of monomeric and polymeric amphiphiles with LCs. Specifically, we synthesized amphiphilic oligomers (with decyl hydrophobic and pentaethylene glycol hydrophilic domains) in monomer, dimer, and trimer forms, and incubated aqueous solutions of the oligomers against nematic films of 4'-pentyl-4-biphenylcarbonitrile (5CB). All amphiphilic oligomers caused sequential surface-driven orientational (planar to homeotropic) and then bulk phase transitions (nematic to isotropic) with dynamics depending strongly on the degree of oligomerization. The dynamics of the orientational transitions accelerated from monomer to trimer, consistent with the effects of an increase in adsorption free energy. The mechanism underlying the orientational transition, however, involved a decrease in anchoring energy and not change in the easy axis of the LC. In contrast, the rate of the phase transition induced by absorption of oligomers into the LC decreased from monomer to trimer, suggesting that constraints on configurational degrees of freedom influence the absorption free energies of the oligomers. Interestingly, the oligomer-induced transition from the nematic to isotropic phase of 5CB was observed to nucleate at the aqueous-5CB interface, consistent with surface-induced disorder underlying the above-reported decrease in anchoring energy caused by the oligomers. Finally, we provided proof-of-concept experiments of the triggering of LCs using a trimeric amphiphile that is photocleaved by UV illumination into monomeric fragments. Overall, our results provide insight into the rational design of oligomers that can be used as triggers to create responsive LCs.

Mixtures of Blue Phase Liquid Crystal with Simple Liquids: Elastic Emulsions and Cubic Fluid Cylinders

We numerically investigate the behavior of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, χ, setting the balance between interfacial and elastic forces. When χ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger χ, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous elastic network. Our blue phase-simple fluid composites can be externally manipulated: an electric field can trigger a morphological transition between cubic fluid cylinder phases with different topologies.

Robust multi-responsive supramolecular hydrogel based on a mono-component host-guest gelator

Supramolecular hydrogels have been widely investigated, but the construction of stimuli-responsive mono-component host-guest hydrogels remains a challenge in that it is still hard to balance the solubility and gelation ability of the gelator. In this work, three azobenzene-modified β-cyclodextrin derivatives with different alkyl lengths (β-CD-Azo-Cn) have been synthesized. The length of the alkyl chain dramatically influences the solubility and gelation ability of β-CD derivatives in water. Among these derivatives, β-CD-Azo-C8 possesses the lowest minimum gelation concentration (MGC). Based on the host-guest interaction between β-CD and azobenzene units in aqueous solution, which is confirmed by UV-visible and ROESY NMR spectra, the gelators self-assemble and further interwine into networks through the hydrogen bonds on the surface of β-CD cavities. Hydrogels formed by mono-component gelators can collapse under external stimuli such as heating, competition guests and hosts, and UV irradiation. When the concentration of the gelator is more than 8 wt%, the hydrogel exhibits good self-supporting ability with a storage modulus higher than 104 Pa. The gel-sol transition temperature of the hydrogel is near body temperature, indicating its potential applications in biological materials.

Photomodulated Electro-optical Response in Self-Supporting Liquid Crystalline Physical Gels

Photoresponsive liquid crystal (LC) physical gels have attracted more and more attention because of the nature of strong response via light stimulus. Although many efforts on the breaking and recovering of physical gels through photoisomerization have been focused, fast electro-optical response and high mechanical properties even upon light irradiations are difficult to achieve at the same time. In this work, two kinds of azobenzene-containing gelators (AG1 and AG2) with different terminal groups were designed and synthesized. Both gelators could induce the nematic LC P0616A self-assemble into anisotropic phase-separated LC physical gels at low contents. Their phase-transition behavior, thermal stability, microstructure, and mechanical strength were systematically studied. Compared with AG2 in P0616A, the P0616A/AG1 gels showed better mechanical property. When the gelator content was above 3 wt %, the P0616A/AG1 gels possessed good self-supporting ability with a storage modulus more than 10⁴ Pa. Thus, the photoresponsive electro-optical properties and structures of P0616A/AG1 gels were focused in detail. It was surprising that the electro-optical response speed of the P0616A/AG1 gels could be promoted upon UV irradiation. In particular, the decay time (τ_off) was only about half when compared with the initial state, whereas the gels still exhibited good self-supporting ability; also the network of the LC physical gels had no change at macro- and microstructural levels. These exciting results would open a door for the application of this material in electro-optical devices.

Defect transitions in nematic liquid-crystal capillary bridges

We use experiment and computational modeling to understand the defect structure and director configuration in a nematic liquid crystal capillary bridge confined between two parallel plates. We find that tuning of the aspect ratio of the bridge drives a transition between a ring defect and a point defect. This transition exhibits hysteresis, due to the metastability of the point-defect structure. In addition, we see that the shape of the capillary-bridge surface determines whether the defect is hyperbolic or radial, with waistlike bridges containing hyperbolic defects and barrel-like bridges containing radial defects.

Active nematic emulsions

The formation of emulsions from multiple immiscible fluids is governed by classical concepts such as surface tension, differential chemical affinity and viscosity, and the action of surface-active agents. Much less is known about emulsification when one of the components is active and thus inherently not constrained by the laws of thermodynamic equilibrium. We demonstrate one such realization consisting in the encapsulation of an active liquid crystal (LC)-like gel, based on microtubules and kinesin molecular motors, into a thermotropic LC. These active nematic emulsions exhibit a variety of dynamic behaviors that arise from the cross-talk between topological defects separately residing in the active and passive components. Using numerical simulations, we show a feedback mechanism by which active flows continuously drive the passive defects that, in response, resolve the otherwise degenerated trajectories of the active defects. Our experiments show that the choice of surfactant, which stabilizes the active/passive interface, allows tuning the regularity of the self-sustained dynamic events. The hybrid active-passive system demonstrated here provides new perspectives for dynamic self-assembly driven by an active material but regulated by the equilibrium properties of the passive component.

Photonic band structure of diamond colloidal crystals in a cholesteric liquid crystal

In this paper, we demonstrate the presence of a photonic band gap for a diamond lattice structure made of particles with normal anchoring inside a cholesteric liquid crystal. As is typical for liquid crystals (LCs), there is considerable contrast between the dielectric constant parallel ε_{∥} and perpendicular ε_{⊥} to the director, with ε_{∥}/ε_{⊥}∼4 here. It is shown that the size of the photonic band gap is directly related to the size of colloidal particles and the contrast between the dielectric constant in the particles and the extreme values of ε in the LC medium (one needs either ε in the particle much smaller than ε_{⊥} or much bigger than ε_{∥}). No opening is seen in the band diagrams for small particles. For larger particles a partial gap opens when the particles are composed of very low dielectric material but never a complete gap. On the other hand, a complete gap starts to be revealed when the size of the colloidal particles is increased and when a high dielectric constant is used for filling inside the particles. The maximum size of the gap is observed when the particles are large enough so that their surfaces overlap.

Coupling free energy and surface anchoring mechanism in gold nanorod–nematic liquid crystal dispersions

Dependence of both the induced optical birefringence signals and simulated free energy f_total with the pump H.

Heterogeneous colloidal particles immersed in a liquid crystal

In this paper, we explore anisotropic interactions between particles with heterogeneous boundary conditions inside both nematic and cholesteric liquid crystals. The results show that when particles are put at different distances and angles with respect to each other, new types of defect structures are produced, depending on the relative distances and directions. In a cholesteric liquid crystal, the value of the pitch affects the defect structures and induced forces. Moreover, it was observed that it is energetically favorable for the particles to remain in a plane parallel to the far-field director in a nematic liquid crystal, while for particles immersed in a cholesteric there are multiple energy minima not all located in the same plane.

Body Temperature Controlled Optical and Thermal Information Storage Light Scattering Display with Fluorescence Effect and High Mechanical Strength

A kind of body temperature controlled optical and thermal information storage light scattering display based on super strong liquid crystalline physical gel with special "loofah-like gel network" was successfully prepared. Such liquid crystal (LC) gel was obtained by mixing a dendritic gelator (POSS-G1-BOC), an azobenzene compound (2Azo2), and a phosphor tethered liquid crystalline host (5CB), which could show its best contrast ratio at around human body temperature under UV light because of the phosphor's fluorescence effect. The gel also has quite strong mechanical strength, which could be used in wearable device field especially under sunlight, even under the forcing conditions as harsh as being centrifuged for 10 min at the speed of 2000 r/min. The whole production process of such a display is quite simple and could lead to displays at any size through noncontact writing. We believe it will have wide applications in the future.

Periodic assembly of nanoparticle arrays in disclinations of cholesteric liquid crystals

An important goal of the modern soft matter science is to discover new self-assembly modalities to precisely control the placement of small particles in space. Spatial inhomogeneity of liquid crystals offers the capability to organize colloids in certain regions such as the cores of the topological defects. Here we report two self-assembly modes of nanoparticles in linear defects-disclinations in a lyotropic colloidal cholesteric liquid crystal: a continuous helicoidal thread and a periodic array of discrete beads. The beads form one-dimensional arrays with a periodicity that matches half a pitch of the cholesteric phase. The periodic assembly is governed by the anisotropic surface tension and elasticity at the interface of beads with the liquid crystal. This mode of self-assembly of nanoparticles in disclinations expands our ability to use topological defects in liquid crystals as templates for the organization of nanocolloids.

Controlling placement of nonspherical (boomerang) colloids in nematic cells with photopatterned director

Placing colloidal particles in predesigned sites represents a major challenge of the current state-of-the-art colloidal science. Nematic liquid crystals with spatially varying director patterns represent a promising approach to achieve a well-controlled placement of colloidal particles thanks to the elastic forces between the particles and the surrounding landscape of molecular orientation. Here we demonstrate how the spatially varying director field can be used to control placement of non-spherical particles of boomerang shape. The boomerang colloids create director distortions of a dipolar symmetry. When a boomerang particle is placed in a periodic splay-bend director pattern, it migrates towards the region of a maximum bend. The behavior is contrasted to that one of spherical particles with normal surface anchoring, which also produce dipolar director distortions, but prefer to compartmentalize into the regions with a maximum splay. The splay-bend periodic landscape thus allows one to spatially separate these two types of particles. By exploring overdamped dynamics of the colloids, we determine elastic driving forces responsible for the preferential placement. Control of colloidal locations through patterned molecular orientation can be explored for future applications in microfluidic, lab on a chip, sensing and sorting devices.

Nonsingular defects and self-assembly of colloidal particles in cholesteric liquid crystals

Cholesteric liquid crystals can potentially provide a means for tunable self-organization of colloidal particles. However, the structures of particle-induced defects and the ensuing elasticity-mediated colloidal interactions in these media remain much less explored and understood as compared to their nematic liquid crystal counterparts. Here we demonstrate how colloidal microspheres of varying diameter relative to the helicoidal pitch can induce dipolelike director field configurations in cholesteric liquid crystals, where these particles are accompanied by point defects and a diverse variety of nonsingular line defects forming closed loops. Using laser tweezers and nonlinear optical microscopy, we characterize the ensuing medium-mediated elastic interactions and three-dimensional colloidal assemblies. Experimental findings show a good agreement with numerical modeling based on minimization of the Landau-de Gennes free energy and promise both practical applications in the realization of colloidal composite materials and a means of controlling nonsingular topological defects that attract a great deal of fundamental interest.

Three Gel States of Colloidal Composites Consisting of Polymer-Brush-Afforded Silica Particles and a Nematic Liquid Crystal with Distinct Viscoelastic and Optical Properties

Colloidal composites consisting of polymer-brush-afforded silica particles (P-SiPs) and a nematic liquid crystal (LC) exhibited three gel states with distinct viscoelastic and/or optical properties depending on temperature: (1) opaque hard gel, (2) translucent hard gel, and (3) translucent soft gel. We demonstrated that the transitions of the optical property and the hardness of the gels were due to the phase transition of the LC matrix and the glass transition of the grafted polymers of P-SiPs, respectively. We then revealed that the gelation (the formation of the translucent soft gel) was caused by the phase separation of P-SiPs and LC matrix in an isotropic phase based on spinodal decomposition. In addition, the particle concentration and molecular weight of the grafted polymer of P-SiPs were observed to significantly affect the elastic moduli and thermal stability of the composite gels. By the addition of an azobenzene derivative into an LC matrix, we achieved photochemical switching of the transparency of the composites based on the photoinduced phase transition of LCs, while keeping self-supporting ability of the composite gel.

Control of colloidal placement by modulated molecular orientation in nematic cells

Colloids self-assemble into various organized superstructures determined by particle interactions. There is tremendous progress in both the scientific understanding and the applications of self-assemblies of single-type identical particles. Forming superstructures in which the colloidal particles occupy predesigned sites and remain in these sites despite thermal fluctuations represents a major challenge of the current state of the art. We propose a versatile approach to directing placement of colloids using nematic liquid crystals with spatially varying molecular orientation preimposed by substrate photoalignment. Colloidal particles in a nematic environment are subject to the long-range elastic forces originating in the orientational order of the nematic. Gradients of the orientational order create an elastic energy landscape that drives the colloids into locations with preferred type of deformations. As an example, we demonstrate that colloidal spheres with perpendicular surface anchoring are driven into the regions of maximum splay, whereas spheres with tangential surface anchoring settle into the regions of bend. Elastic forces responsible for preferential placement are measured by exploring overdamped dynamics of the colloids. Control of colloidal self-assembly through patterned molecular orientation opens new opportunities for designing materials and devices in which particles should be placed in predesigned locations.