Monopole-like electrostatic interactions are ubiquitous in biology and condensed matter, but they are often screened by counter-ions and cannot be switched from attractive to repulsive. In colloidal science, where the prime goal is to develop colloidal particles 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 multipoles. In liquid-crystal colloids, 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 particles. In dipolar, quadrupolar and hexadecapolar nematic colloids, the symmetries of such elastic distortions mimic both electrostatic multipoles and the outmost occupied electron shells of atoms. Electric and magnetic switching, spontaneous transformations and optical control of elastic multipoles, as well as their interactions with topological defects and surface boundary conditions, have been demonstrated in such colloids. However, it has long been understood that elastic monopoles should relax to uniform or higher-order multipole states because of the elastic torques that they induce. Here we develop nematic colloids with strong elastic monopole moments and with elastic torques balanced by optical torques exerted 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 electrostatics. We also demonstrate the out-of-equilibrium dynamic assembly of these colloidal particles.
We present experiments where anisometric colloidal microparticles dispersed in a nematic liquid crystal cell with homeotropic anchoring conditions are dynamically assembled by means of liquid-crystal-enabled electrophoresis (LCEEP) using an AC electric field perpendicular to the confining plates. A nematic host with negative dielectric anisotropy leads to a driving force parallel to the cell plates. We take advantage of the resulting gliding anchoring conditions and the degeneracy in the direction of particle motion to design reconfigurable trajectories using a photosensitive anchoring layer (…
Colloidal molecules are designed to mimic their molecular analogues through their anisotropic shape and interactions. However, current experimental realizations are missing the structural flexibility present in real molecules thereby restricting their use as model systems. We overcome this limitation by assembling reconfigurable colloidal molecules from silica particles functionalized with mobile DNA linkers in high yields. We achieve this by steering the self-assembly pathway towards the formation of finite-sized clusters by employing high number ratios of particles functionalized with comple…
Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications - such as nanoantennas, plasmonic sensors, and nanocircuits - pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find…
Colloidal interactions in nematic liquid crystals can be described as interactions between elastic multipoles that depend on particle shape, topology, chirality, boundary conditions and induced topological defects. Here, we describe a nematic colloidal system consisting of mesostructures of gold capable of inducing elastic multipoles of different order. Elastic monopoles are formed by relatively large asymmetric mesoflower particles, for which gravity and elastic torque balancing yields monopole-type interactions. High-order multipoles are instead formed by smaller mesoflowers with a myriad of…
Biological cells self-organize into living materials that uniquely blend structure with functionality and responsiveness to the environment. The integration of similar life-like features in man-made materials remains challenging, yet desirable to manufacture active, adaptive and autonomous systems. Here we show the self-organization of programmable random lasers from the reversible out-of-equilibrium self-assembly of colloids. Random lasing originates from the optical amplification of light undergoing multiple scattering within the dissipative colloidal assemblies and therefore is crucially de…
We study the defect dynamics in a colloidal spin ice system realized by filling a square lattice of topographic double well islands with repulsively interacting magnetic colloids. We focus on the contraction of defects in the ground state, and contraction/expansion in a metastable biased state. Combining real-time experiments with simulations, we prove that these defects behave like emergent topological monopoles obeying a Coulomb law with an additional line tension. We further show how to realize a completely resettable "NOR" gate, which provides guidelines for fabrication of nanoscale logic …
Up to now it is commonly believed that a colloidal particle suspended in a nematic liquid crystal never produces elastic monopoles because this violates the mechanical equilibrium condition. And the only way to obtain deformations of director field falling off with distance as r^{-1} is to exert an external torque Γ_{ext} on the colloid \cite{de_Gennes}. In this paper we demonstrate that this statement is not quite correct and elastic monopoles, as well as dipoles and quadrupoles, can be induced without any external influence just by the particle itself. A behavior of a spherical colloidal par…
Filamentous bacteriophages such as fd-like viruses are monodisperse rod-like colloids that have well defined properties: diameter, length, rigidity, charge and chirality. Engineering those viruses leads to a library of colloidal rods which can be used as building blocks for reconfigurable and hierarchical self-assembly. Their condensation in aqueous solution þ{with additive polymers which act as depletants to induce} attraction between the rods leads to a myriad of fluid-like micronic structures ranging from isotropic/nematic droplets, colloid membranes, achiral membrane seeds, twisted ribbons…
We report a technique to realize reconfigurable colloidal crystals by using the controlled motion of particle defects above an externally modulated magnetic substrate. The transport of particles is induced by applying a uniform rotating magnetic field to a ferrite garnet film characterized by a periodic lattice of magnetic bubbles. For filling factor larger than one colloid per bubble domain, the particle current arises from propagating defects where particles synchronously exchange their position when passing from one occupied domain to the next. The amplitude of an applied alternating magnet…
Materials adopting the diamond structure possess useful properties in atomic and colloidal systems, and are a popular target for synthesis in colloids where a photonic band gap is possible. The desirable photonic properties of the diamond structure pose an interesting opportunity for reconfigurable matter: can we create a colloidal crystal able to switch reversibly to and from the diamond structure? Drawing inspiration from high-pressure transitions of diamond-forming atomic systems, we design a system of polyhedrally-shaped particles that transitions from diamond to a tetragonal diamond deriv…
Micron-size self-propelling particles are often proposed as synthetic models for biological microswimmers, yet they lack internally regulated adaptation, which is central to the autonomy of their biological counterparts. Conversely, adaptation and autonomy can be encoded in larger-scale soft-robotic devices, but transferring these capabilities to the colloidal scale remains elusive. Here, we create a new class of responsive microswimmers, powered by induced-charge electrophoresis, which can adapt their motility to external stimuli via an internal feedback. Using sequential capillary assembly, …
We demonstrate several examples of driving and steering of colloids when dispersed in nematic liquid crystals. The driving mechanism is based on the principle of nonlinear electrophoresis which is mediated by the asymmetry in the structure of the defects that the inclusions generate in the host elastic matrix. The steering mechanism originates in the photoactivation of the anchoring conditions of the nematic liquid crystal on one of the enclosing plates. As experimental realizations we first review a scenario of water microdroplets being phoretically transported for cargo release and chemical …
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 incl…
Artificial spin ice systems, namely lattices of interacting single domain ferromagnetic islands, have been used to date as microscopic models of frustration induced by lattice topology, allowing for the direct visualization of spin arrangements and textures. However, the engineering of frustrated ice states in which individual spins can be manipulated in situ and the real-time observation of their collective dynamics remain both challenging tasks. Inspired by recent theoretical advances, here we realize a colloidal version of an artificial spin ice system using interacting polarizable particle…
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 disc…
Topological defects that form on surfaces of ordered media, dubbed boojums, are ubiquitous in superfluids, liquid crystals (LCs), Langmuir monolayers, and Bose-Einstein condensates. They determine supercurrents in superfluids, impinge on electrooptical switching in polymer-dispersed LCs, and mediate chemical response at nematic-isotropic fluid interfaces, but the role of surface topology in the appearance, stability, and core structure of these defects remains poorly understood. Here, we demonstrate robust generation of boojums by controlling surface topology of colloidal particles that impose…
Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly understood. We introduce a class of {simple} model systems in which the direct control of local order, via colloid shape change, induces solid--solid phase transitions, and characterize how the transitions happen thermodynamically. We find that within a single shape family there are solid--solid transitions that can occur with or without a thermal activation barrier.…
Artificial particle ices are model systems of constrained, interacting particles. They have been introduced theoretically to study ice-manifolds emergent from frustration, along with domain wall and grain boundary dynamics, doping, pinning-depinning, controlled transport of topological defects, avalanches, and memory effects. Recently such particle-based ices have been experimentally realized with vortices in nano-patterned superconductors or gravitationally trapped colloids. Here we demonstrate that, although these ices are generally considered equivalent to magnetic spin ices, they can acces…
We demonstrate facile optical manipulation of shape of birefringent colloidal microparticles made from liquid crystal elastomers. Using soft lithography and polymerization, we fabricate elastomeric microcylinders with weakly undulating director oriented on average along their long axes. These particles are infiltrated with gold nanospheres acting as heat transducers that allow for an efficient localized transfer of heat from a focused infrared laser beam to a submicrometer region within a microparticle. Photothermal control of ordering in the liquid crystal elastomer using scanned beams allows…
We show that the interaction potential between sterically stabilized, nearly hard-sphere [poly(methylmethacrylate)-poly(lauryl methacrylate) (PMMA-PLMA)] colloids at a water-oil interface has a negligible unscreened-dipole contribution, suggesting that models previously developed for charged particles at liquid interfaces are not necessarily applicable to sterically stabilized particles. Interparticle potentials, $U(r)$, are extracted from radial distribution functions [$g(r)$, measured by fluorescence microscopy] via Ornstein-Zernike inversion and via a reverse Monte Carlo scheme. The results…
Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David and the Borromean rings are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are clas…
The Kibble-Zurek mechanism describes the evolution of topological defect structures like domain walls, strings, and monopoles when a system is driven through a second order phase transition. The model is used on very different scales like the Higgs field in the early universe or quantum fluids in condensed matter systems. A defect structure naturally arises during cooling if separated regions are too far apart to `communicate' (e.g. about their orientation or phase) due to finite signal velocity. This results in separated domains with different (degenerated) locally broken symmetry. Within thi…
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 forbitals. 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 …
We study the free energy landscapes of a pair of submicron spherical particles floating at the surface of a sessile droplet. The particles are subjected to radial external forces resulting in a deformation of the droplet shape relative to the reference shape of a spherical cap. This deformation leads to tangential forces on the particles. For small deformations and for the contact angle $θ_0$ at the substrate being equal to $π/2$, the corresponding linearized Young-Laplace equation is solved analytically. The solution is constructed by employing the method of images from electrostatics, where …
Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetti…
The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $π/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the par…
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 non-reciprocal nature of these facile electric responses to de…
The ability to dictate colloid motion is an important challenge in fields ranging from materials science to living systems. Here, by embedding energy landscapes in confined nematic liquid crystals, we design a versatile platform to define colloidal migration. This is achieved by placing a wavy wall, with alternating hills and wells, in nematic liquid crystals, to impose a smooth elastic energy field with alternating splay and bend distortions. This domain generates (meta) stable loci that act as attractors and unstable loci that repel colloids over distances large compared to the colloid radiu…
We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic liquid crystal 5CB create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here we report on complex, open structures organized via interactions with defects in the bulk. Specifi…
