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

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.

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.

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.

Colloidal transport within nematic liquid crystals with arrays of obstacles

We have investigated the gravity-driven transport of spherical colloids suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) within microfluidic arrays of cylindrical obstacles arranged in a square lattice. Homeotropic anchoring at the surfaces of the obstacles created periodic director-field patterns that strongly influenced the motion of the colloids, whose surfaces had planar anchoring. When the gravitational force was oriented parallel to a principal axis of the lattice, the particles moved along channels between columns of obstacles and displayed pronounced modulations in their velocity. Quantitative analysis indicates that this modulation resulted from a combination of a spatially varying effective drag viscosity and elastic interactions engendered by the periodic director field. The interactions differed qualitatively from a sum of pair-wise interactions between the colloids and isolated obstacles, reflecting the distinct nematic environment created by confinement within the array. As the angle α between the gravitational force and principal axis of the lattice was varied, the velocity did not follow the force but instead locked into a discrete set of directions commensurate with the lattice. The transitions between these directions occurred at values of α that were different from those observed when the spheres were in an isotropic liquid, indicating the ability of the liquid crystal forces to tune the lateral displacement behavior in such devices.

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.

Anisotropic colloidal transport and periodic stick-slip motion in cholesteric finger textures

We have investigated the mobility of discoidal colloidal particles sedimenting within cholesteric finger textures formed by mixtures of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) and the chiral dopant 4-(2-methylbutyl)-4'-cyanobiphenyl (CB15) with cholesteric pitch p between 24 and 114 μm. The nickel disks, with radius 17 μm and thickness 300 nm, displayed varied transport behavior that depended on the size of the pitch and the orientation of the gravitational force with respect to the cholesteric axis. In textures with small pitch (p < 40 μm), the disks moved perpendicular to the axis irrespective of the orientation of gravity as a result of an elastic retarding force that prevented motion along the axis. In textures with larger pitch, the disks similarly moved perpendicular to the axis when the angle between the force and axis was large. When the angle was small, the disks displayed stick-slip motion caused by periodic yielding of the finger texture. A model considering viscous drag on the particles and the elastic energy cost of deforming the finger texture describes the stick-slip motion accurately. The effective drag viscosities obtained from the disk motion are anomalously large compared with those of pure nematic 5CB indicating a large contribution to the dissipation from the motion of disclinations in the texture in the vicinity of the translating disks.

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.