Geometrically unrestricted, topologically constrained control of liquid crystal defects using simultaneous holonomic magnetic and holographic optical manipulation

Topological Metadefects: Tangles of Dislocations

The concept of topological defects is universal. In condensed matter, it applies to disclinations, dislocations, or vortices that are fingerprints of symmetry breaking during phase transitions. Using as a generic example the tangles of dislocations, we introduce the concept of topological metadefects, i.e., defects made of defects. We show that in cholesterics, dextrogyre and levogyre primary tangles are generated through the D_{2}→C_{2} symmetry breaking from the coplanar dislocation pair called Lehmann cluster submitted to a high enough tensile strain. The primary tangles can be wound up individually into double helices. They can also annihilate in pairs or associate into tangles of higher orders following simple algebraic rules.

Topological steering of light by nematic vortices and analogy to cosmic strings

Liquid crystals are widely known for their technological uses in displays, electro-optics, photonics and nonlinear optics, but these applications typically rely on defining and switching non-topological spatial patterns of the optical axis. Here, we demonstrate how a liquid crystal's optical axis patterns with singular vortex lines can robustly steer beams of light. External stimuli, including an electric field and light itself, allow us to reconfigure these unusual light-matter interactions. Periodic arrays of vortices obtained by photo-patterning enable the vortex-mediated fission of optical solitons, yielding their lightning-like propagation patterns. Predesigned patterns and spatial trajectories of vortex lines in high-birefringence liquid crystals can steer light into closed loops or even knots. Our vortex lattices might find technological uses in beam steering, telecommunications, virtual reality implementations and anticounterfeiting, as well as possibly offering a model system for probing the interaction of light with defects, including the theoretically predicted, imagination-capturing light-steering action of cosmic strings, elusive defects in cosmology.

Nonequilibrium Dynamics of a Magnetic Nanocapsule in a Nematic Liquid Crystal

Colloidal particles in nematic liquid crystals show a beautiful variety of complex phenomena with promising applications. Their dynamical behaviour is determined by topology and interactions with the liquid crystal and external fields. Here, a nematic magnetic nanocapsule reoriented periodically by time-varying magnetic fields is studied using numerical simulations. The approach combines Molecular Dynamics to resolve solute–solvent interactions and Nematic Multiparticle Collision Dynamics to incorporate nematohydrodynamic fields and fluctuations. A Saturn ring defect resulting from homeotropic anchoring conditions surrounds the capsule and rotates together with it. Magnetically induced rotations of the capsule can produce transformations of this topological defect, which changes from a disclination curve to a defect structure extending over the surface of the capsule. Transformations occur for large magnetic fields. At moderate fields, elastic torques prevent changes of the topological defect by tilting the capsule out from the rotation plane of the magnetic field.

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.

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.

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.

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.

Optical trapping performance of dielectric-metallic patchy particles

We demonstrate a series of simulation experiments examining the optical trapping behavior of composite micro-particles consisting of a small metallic patch on a spherical dielectric bead. A full parameter space of patch shapes, based on current state of the art manufacturing techniques, and optical properties of the metallic film stack is examined. Stable trapping locations and optical trap stiffness of these particles are determined based on the particle design and potential particle design optimizations are discussed. A final test is performed examining the ability to incorporate these composite particles with standard optical trap metrology technologies.

Optomagnetically Controlled Microparticles Manufactured with Glancing Angle Deposition

Optical trapping and magnetic trapping are common micro-manipulation techniques for controlling colloids including micro- and nano-particles. Combining these two manipulation strategies allows for a larger range of applied forces and decoupled control of rotation and translation; each of which are beneficial properties for many applications including force spectroscopy and advanced manufacturing. However, optical trapping and magnetic trapping have conflicting material requirements inhibiting the combination of these methodologies. In this paper, anisotropic micron scaled particles capable of being simultaneously controlled by optical and magnetic trapping are synthesized using a glancing angle deposition (GLAD) technique. The anisotropic alignment of dielectric and ferromagnetic materials limits the optical scattering from the metallic components which typically prevents stable optical trapping in three dimensions. Compared to the current state of the art, the benefits of this approach are two-fold. First, the composite structure allows for larger volumes of ferromagnetic material so that larger magnetic moments may be applied without inhibiting the stability of optical trapping. Secondly, the robustness of the synthesis process is greatly improved. The dual optical and magnetic functionality of the synthesized colloids is demonstrated by simultaneously optically translating and magnetically rotating a magnetic GLAD particle using a custom designed opto-magnetic trapping system.

Stick-slip motion of surface point defects prompted by magnetically controlled colloidal-particle dynamics in nematic liquid crystals

We explore the dynamics of topological point defects on surfaces of magnetically responsive colloidal microspheres in a uniformly aligned nematic liquid crystal host. We show that pinning of the liquid crystal director to a particle surface with random nanostructured morphology results in unexpected translational dynamics of both particles and topological point defects on their surfaces when subjected to rotating magnetic fields. We characterize and quantify the "stick-slip" motion of defects as a function of field rotation rates as well as temperature, demonstrating the roles played by the competition of elastic forces, surface anchoring, and magnetic torques on the sphere as well as random-surface-mediated pinning of the easy axis of the nematic director on colloidal microspheres. We analyze our findings through their comparison to similar dynamic processes in other branches of science.

Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Periodic dynamics, localization metastability, and elastic interaction of colloidal particles with confining surfaces and helicoidal structure of cholesteric liquid crystals

Nematic and cholesteric liquid crystals are three-dimensional fluids that possess long-range orientational ordering and can support both topological defects and chiral superstructures. Implications of this ordering remain unexplored even for simple dynamic processes such as the ones found in so-called "fall experiments," or motion of a spherical inclusion under the effects of gravity. Here we show that elastic and surface anchoring interactions prompt periodic dynamics of colloidal microparticles in confined cholesterics when gravity acts along the helical axis. We explore elastic interactions between colloidal microparticles and confining surfaces as well as with an aligned ground-state helical structure of cholesterics for different sizes of spheres relative to the cholesteric pitch, demonstrating unexpected departures from Stokes-like behavior at very low Reynolds numbers. We characterize metastable localization of microspheres under the effects of elastic and surface anchoring periodic potential landscapes seen by moving spheres, demonstrating the important roles played by anchoring memory, confinement, and topological defect transformation. These experimental findings are consistent with the results of numerical modeling performed through minimizing the total free energy due to colloidal inclusions at different locations along the helical axis and with respect to the confining substrates. A potential application emerging from this work is colloidal sorting based on particle shapes and sizes.

Magnetically responsive gourd-shaped colloidal particles in cholesteric liquid crystals

Particle shape and medium chirality are two key features recently used to control anisotropic colloidal self-assembly and dynamics in liquid crystals. Here, we study magnetically responsive gourd-shaped colloidal particles dispersed in cholesteric liquid crystals with periodicity comparable or smaller than the particle's dimensions. Using magnetic manipulation and optical tweezers, which allow one to position colloids near the confining walls, we measured the elastic repulsive interactions of these particles with confining surfaces and found that separation-dependent particle-wall interaction force is a non-monotonic function of separation and shows oscillatory behavior. We show that gourd-shaped particles in cholesterics reside not on a single sedimentation level, but on multiple long-lived metastable levels separated by a distance comparable to cholesteric periodicity. Finally, we demonstrate three-dimensional laser tweezers assisted assembly of gourd-shaped particles taking advantage of both orientational order and twist periodicity of cholesterics, potentially allowing new forms of orientationally and positionally ordered colloidal organization in these media.