Out-of-equilibrium interactions and collective locomotion of colloidal spheres with squirming of nematoelastic multipoles.

Many living and artificial systems show similar emergent behavior and collective motions on different scales, starting from swarms of bacteria to synthetic active particles, herds of mammals, and crowds of people. What all these systems often have in common is that new collective properties like flocking emerge from interactions between individual self-propelled or driven units. Such systems are naturally out-of-equilibrium and propel at the expense of consumed energy. Mimicking nature by making self-propelled or externally driven particles and studying their individual and collective motility may allow for deeper understanding of physical underpinnings behind collective motion of large groups of interacting objects or beings. Here, using a soft matter system of colloids immersed into a liquid crystal, we show that resulting so-called nematoelastic multipoles can be set into a bidirectional locomotion by external oscillating electric fields. Out-of-equilibrium elastic interactions between such colloidal objects lead to collective flock-like behaviors emerging from time-varying elasticity-mediated interactions between externally driven propelling particles. Repulsive elastic interactions in the equilibrium state can be turned into attractive interactions in the out-of-equilibrium state under applied external electric fields. We probe this behavior at different number densities of colloidal particles and show that particles in dense dispersions collectively select the same direction of a coherent motion due to elastic interactions between near neighbors. In our experimentally implemented design, their motion is highly ordered and without clustering or jamming often present in other colloidal transport systems, which is promising for technological and fundamental-science applications, like nano-cargo transport, out-of-equilibrium assembly, and microrobotics.

Design and Preparation of Nematic Colloidal Particles.

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

Electrically Powered Locomotion of Dual-Nature Colloid-Hedgehog and Colloid-Umbilic Topological and Elastic Dipoles in Liquid Crystals.

Colloidal particles in liquid crystals tend to induce topological defects and distortions of the molecular alignment within the surrounding anisotropic host medium, which results in elasticity-mediated interactions not accessible to their counterparts within isotropic fluid hosts. Such particle-induced coronae of perturbed nematic order are highly responsive to external electric fields, even when the uniformly aligned host medium away from particles exhibits no response to fields below the realignment threshold. Here we harness the nonreciprocal nature of these facile electric responses to demonstrate colloidal locomotion. Oscillations of the electric field prompt repetitive deformations of the corona of dipolar elastic distortions around the colloidal inclusions, which upon appropriately designed electric driving synchronize the displacement directions. We observe the colloid-hedgehog dipole accompanied by an umbilical defect in the tilt directionality field (c-field), along with the texture of elastic distortions that evolves with a change in the applied voltage. The temporal out-of-equilibrium evolution of the director and c-field distortions around particles when the voltage is turned on and off is not invariant upon reversal of time, prompting lateral translations and interactions that markedly differ from those accessible to these colloids under equilibrium conditions. Our findings may lead to both technological and fundamental science applications of nematic colloids as both model reconfigurable colloidal systems and as mesostructured materials with predesigned temporal evolution of structure and composition.

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

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

Transformation between elastic dipoles, quadrupoles, octupoles, and hexadecapoles driven by surfactant self-assembly in nematic emulsion.

Emulsions comprising isotropic fluid drops within a nematic host are of interest for applications ranging from biodetection to smart windows, which rely on changes of molecular alignment structures around the drops in response to chemical, thermal, electric, and other stimuli. We show that absorption or desorption of trace amounts of common surfactants can drive continuous transformations of elastic multipoles induced by the droplets within the uniformly aligned nematic host. Out-of-equilibrium dynamics of director structures emerge from a controlled self-assembly or desorption of different surfactants at the drop-nematic interfaces, with ensuing forward and reverse transformations between elastic dipoles, quadrupoles, octupoles, and hexadecapoles. We characterize intertransformations of droplet-induced surface and bulk defects, probe elastic pair interactions, and discuss emergent prospects for fundamental science and applications of the reconfigurable nematic emulsions.

Anisotropic electrostatic screening of charged colloids in nematic solvents.

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

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.

Aerogel from Sustainably Grown Bacterial Cellulose Pellicles as a Thermally Insulative Film for Building Envelopes.

Improving building energy performance requires the development of new highly insulative materials. An affordable retrofitting solution comprising a thin film could improve the resistance to heat flow in both residential and commercial buildings and reduce overall energy consumption. Here, we propose cellulose aerogel films formed from pellicles produced by the bacteria Gluconacetobacter hansenii as insulation materials. We studied the impact of the density and nanostructure on the aerogels' thermal properties. A thermal conductivity as low as 13 mW/(K·m) was measured for native pellicle-based aerogels that were dried as-is with minimal post-treatment. The use of waste from the beer brewing industry as a solution to grow the pellicle maintained the cellulose yield obtained with standard Hestrin-Schramm media, making our product more affordable and sustainable. In the future, our work can be extended through further diversification of food wastes as the substrate sources, facilitating higher potential production and larger applications.

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.

Elastic colloidal monopoles and reconfigurable self-assembly in liquid crystals.

Monopole-like electrostatic interactions are ubiquitous in biology1 and condensed matter2-4, but they are often screened by counter-ions and cannot be switched from attractive to repulsive. In colloidal science, where the main goal is to develop colloidal particles2,3 that mimic and exceed the diversity and length scales of atomic and molecular assembly, electrostatically charged particles cannot change the sign of their surface charge or transform from monopoles to higher-order multipoles4. In liquid-crystal colloids5-7, elastic interactions between particles arise to minimize the free energy associated with elastic distortions in the long-range alignment of rod-like molecules around the particles5. In dipolar6,8, quadrupolar8-12 and hexadecapolar13 nematic colloids, the symmetries of such elastic distortions mimic both electrostatic multipoles14 and the outermost occupied electron shells of atoms7,15,16. Electric and magnetic switching17,18, spontaneous transformations19 and optical control20 of elastic multipoles, as well as their interactions with topological defects and surface boundary conditions, have been demonstrated in such colloids21-23. However, it has long been understood5,24 that elastic monopoles should relax to uniform or higher-order multipole states because of the elastic torques that they induce5,7. Here we develop nematic colloids with strong elastic monopole moments and with elastic torques balanced by the optical torques induced by ambient light. We demonstrate the monopole-to-quadrupole reconfiguration of these colloidal particles by unstructured light, which resembles the driving of atoms between the ground state and various excited states. We show that the sign of the elastic monopoles can be switched, and that like-charged monopoles attract whereas oppositely charged ones repel, unlike in electrostatics14. We also demonstrate the out-of-equilibrium dynamic assembly of these colloidal particles. This diverse and surprising behaviour is explained using a model that considers the balance of the optical and elastic torques that are responsible for the excited-state elastic monopoles and may lead to light-powered active-matter systems and self-assembled nanomachines.

High-order elastic multipoles as colloidal atoms.

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

Degenerate conic anchoring and colloidal elastic dipole-hexadecapole transformations.

The defect structure associated with a colloid in a nematic liquid crystal is dictated by molecular orientation at the colloid surface. Perpendicular or parallel orientations to the surface lead to dipole-like or quadrupole-like defect structures. However, the so-called elastic hexadecapole discovered recently, has been assumed to result from a conic anchoring condition. In order to understand it at a fundamental level, a model for this anchoring is introduced here in the context of a Landau-de Gennes free energy functional. We investigate the evolution of defect configurations, as well as colloidal interactions, by tuning the preferred tilt angle (θe). The model predicts an elastic dipole whose stability decreases as θe increases, along with a dipole-hexadecapole transformation, which are confirmed by our experimental observations. Taken together, our results suggest that previously unanticipated avenues may exist for design of self-assembled structures via control of tilt angle.

Electric switching of visible and infrared transmission using liquid crystals co-doped with plasmonic gold nanorods and dichroic dyes.

Smart windows and many other applications require synchronous or alternating facile electric switching of transmitted light intensity in visible and near infrared spectral ranges, but most electrochromic devices suffer from slow, nonuniform switching, high power consumption and limited options for designing spectral characteristics. Here we develop a guest-host mesostructured composite with rod-like dye molecules and plasmonic nanorods spontaneously aligned either parallel or orthogonally to the director of the liquid crystal host. This composite material enables fast, low-voltage electric switching of electromagnetic radiation in visible and infrared ranges, which can be customized depending on the needs of applications, like climate-dependent optimal solar gain control in smart windows.

Hybrid molecular-colloidal liquid crystals.

Order and fluidity often coexist, with examples ranging from biological membranes to liquid crystals, but the symmetry of these soft-matter systems is typically higher than that of the constituent building blocks. We dispersed micrometer-long inorganic colloidal rods in a nematic liquid crystalline fluid of molecular rods. Both types of uniaxial building blocks, while freely diffusing, interact to form an orthorhombic nematic fluid, in which like-sized rods are roughly parallel to each other and the molecular ordering direction is orthogonal to that of colloidal rods. A coarse-grained model explains the experimental temperature-concentration phase diagram with one biaxial and two uniaxial nematic phases, as well as the orientational distributions of rods. Displaying properties of biaxial optical crystals, these hybrid molecular-colloidal fluids can be switched by electric and magnetic fields.

Chiral liquid crystal colloids.

Colloidal particles disturb the alignment of rod-like molecules of liquid crystals, giving rise to long-range interactions that minimize the free energy of distorted regions. Particle shape and topology are known to guide this self-assembly process. However, how chirality of colloidal inclusions affects these long-range interactions is unclear. Here we study the effects of distortions caused by chiral springs and helices on the colloidal self-organization in a nematic liquid crystal using laser tweezers, particle tracking and optical imaging. We show that chirality of colloidal particles interacts with the nematic elasticity to predefine chiral or racemic colloidal superstructures in nematic colloids. These findings are consistent with numerical modelling based on the minimization of Landau-de Gennes free energy. Our study uncovers the role of chirality in defining the mesoscopic order of liquid crystal colloids, suggesting that this feature may be a potential tool to modulate the global orientated self-organization of these systems.

Self-assembly of colloidal particles in deformation landscapes of electrically driven layer undulations in cholesteric liquid crystals.

We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is influenced by the presence of colloidal inclusions and, in turn, layers' undulations mediate the spatial patterning of particle locations. We find that the bending of cholesteric layers around a colloidal particle surface prompts the local nucleation of an undulations lattice at electric fields below the well-defined threshold known for liquid crystals without inclusions, and that the onset of the resulting lattice is locally influenced, both dimensionally and orientationally, by the initial arrangements of colloids defined using laser tweezers. Spherical particles tend to spatially localize in the regions of strong distortions of the cholesteric layers, while colloidal nanowires exhibit an additional preference for multistable alignment offset along various vectors of the undulations lattice. Magnetic rotation of superparamagnetic colloidal particles couples with the locally distorted helical axis and undulating cholesteric layers in a manner that allows for a controlled three-dimensional translation of these particles. These interaction modes lend insight into the physics of liquid crystal structure-colloid elastic interactions, as well as point the way towards guided self-assembly of reconfigurable colloidal composites with potential applications in diffraction optics and photonics.

Edge pinning and transformation of defect lines induced by faceted colloidal rings in nematic liquid crystals.

Nematic colloids exhibit a large diversity of topological defects and structures induced by colloidal particles in the orientationally ordered liquid crystal host fluids. These defects and field configurations define elastic interactions and medium-mediated self-assembly, as well as serve as model systems in exploiting the richness of interactions between topologies and geometries of colloidal surfaces, nematic fields, and topological singularities induced by particles in the nematic bulk and at nematic-colloidal interfaces. Here we demonstrate formation of quarter-strength surface-pinned disclinations, as well as a large variety of director field configurations with splitting and reconnections of singular defect lines, prompted by colloidal particles with sharp edges and size large enough to define strong boundary conditions. Using examples of faceted ring-shaped particles of genus g=1, we explore transformation of defect lines as they migrate between locations in the bulk of the nematic host to edge-pinned locations at the surfaces of particles and vice versa, showing that this behavior is compliant with topological constraints defined by mathematical theorems. We discuss how transformation of bulk and surface defect lines induced by faceted colloids can enrich the diversity of elasticity-mediated colloidal interactions and how these findings may impinge on prospects of their controlled reconfigurable self-assembly in nematic hosts.

Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions.

The self-assembly of nanoparticles can enable the generation of composites with predesigned properties, but reproducing the structural diversity of atomic and molecular crystals remains a challenge. We combined anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. The orientations of the nanocrystals, as well as the crystallographic axes of the ensuing triclinic colloidal crystals, are coupled to the uniform alignment direction of the nematic host, which can be readily controlled on large scales. We examine colloidal pair and many-body interactions and show how triclinic crystals with orientational ordering of the semiconductor nanorods emerge from competing long-range elastic and electrostatic forces.

Hexadecapolar colloids.

Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and f-orbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of 'colloidal atoms' displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. Here we describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Because of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and describe the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.

Colloidal spirals in nematic liquid crystals.

One of the central experimental efforts in nematic colloids research aims to explore how the interplay between the geometry of particles along with the accompanying nematic director deformations and defects around them can provide a means of guiding particle self-assembly and controlling the structure of particle-induced defects. In this work, we design, fabricate, and disperse low-symmetry colloidal particles with shapes of spirals, double spirals, and triple spirals in a nematic fluid. These spiral-shaped particles, which are controlled by varying their surface functionalization to provide tangential or perpendicular boundary conditions of the nematic molecular alignment, are found inducing director distortions and defect configurations with non-chiral or chiral symmetry. Colloidal particles also exhibit both stable and metastable multiple orientational states in the nematic host, with a large number of director configurations featuring both singular and solitonic nonsingular topological defects accompanying them, which can result in unusual forms of colloidal self-assembly. Our findings directly demonstrate how the symmetry of particle-generated director configurations can be further lowered, or not, as compared to the low point group symmetry of solid micro-inclusions, depending on the nature of induced defects while satisfying topological constraints. We show that achiral colloidal particles can cause chiral symmetry breaking of elastic distortions, which is driven by complex three-dimensional winding of induced topological line defects and solitons.