Exploiting imperfections in the bulk to direct assembly of surface colloids

Abstract

We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals (LCs) to assemble colloidal particles trapped at the LC interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic LC 4-cyano-4′-pentylbiphenyl 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. Specifically, by confining the nematic LC in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. These defects source elastic deformations that direct the assembly of the interfacially trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. When the surface density of the colloids is high, they form a ring near the defect and a hexagonal lattice far from it. Because topographically complex substrates are easily fabricated and LC defects are readily reconfigured, this work lays the foundation for a versatile, robust mechanism to direct assembly dynamically over large areas by controlling surface anchoring and associated bulk defect structure.lassically, the bulk of a material system is where the action is, and the interface is often relegated to a set of "boundary conditions." However, crystal faceting (1), the quantum hall effect (2), and even the anti-de Sitter space-conformal field theory (AdS-CFT) correspondence (3) fundamentally reverse this relationship: The bulk properties can be read off from their effects on the boundaries. In this contribution, we demonstrate migration and organization of colloids constrained to a liquid crystal (LC)-air interface, driven remotely by the elastic distortion created by the presence of topological defects in the liquid crystalline bulk. Just as phantoms are used in MRI (4), it is necessary for us to prepare bulk defects in known configurations to verify our bulk/ boundary connection. To do this, we prepare a substrate patterned with microposts that, with appropriate surface treatment, seed a reproducible defect complexion. Colloidal spheres on the interface experience an attraction to the regions above the submerged defects, as well as an elastic repulsion from each other, leading to complex new assemblies. The long range of these elastic interactions allows defects in the bulk nematic phase far below the interface to direct assembly at the interface. Other recent work on producing ordered arrangements of particles at LC interfaces beyond simple triangular lattices, such as chains (5), stripes (6), and dense quasihexagonal lattices (7), has focused on confining the nematic in thin film or droplet geometries and on varying the surface coverage fraction. Our sensitive control over substrate topography provid...

Light-controlled topological charge in a nematic liquid crystal

“…Whereas the structure of the Saturn ring (with winding number −1/2 and topological charge −1 is well known 17,24 , the Saturn anti-ring with the opposite winding and topological charge is not stable around a sphere. A single Saturn anti-ring is stable inside a nematic droplet 22,23 , or in a carefully designed confinement geometry 26 . The sign of the topological charge of the two rings can be determined by probing the elastic deformation field around the fibre, as opposite topological charges generally attract.…”

Lassoing saddle splay and the geometrical control of topological defects

“…We use a phenomenological LdG free energy of a nematic Q-tensor field, based on the approach reviewed by Ravnik and Žumer (28,32,33). The free energy is minimized in a finite difference scheme on a cubic mesh, on which a traceless, symmetric rank-2 tensor Q is defined.…”

“…A 10 × 10 array of holes with radius of 50 μm is prepared by drilling a Mylar sheet using IPG Microsystem's IX-255 UV excimer laser in the low fluence setting, provided by the University of Pennsylvania's Quattrone Nanofabrication Facility (QNF). The Mylar is coated with silicon tetrachloride (SiCl 4 ) through vapor deposition for the surface to be treated with DMOAP (Sigma-Aldrich) to obtain strong homeotropic anchoring (3,32,35). Coverslips coated with indium tin oxide (ITO; SPI Supplies), for the application of an electric field across the sample, are treated to have oriented planar anchoring by spin coating a thin layer of PVA (SigmaAldrich), which is subsequently baked at 80°C for 1 h, then rubbed with a velvet cloth in the desired direction (35).…”

“…PM micrographs are taken using an upright microscope in transmission mode furnished with crossed polarizers (Zeiss Axiolmager M1m) and a high-resolution color camera (Zeiss AxioCam HRc). FCPM images are obtained using an inverted IX81 Olympus microscope with an FV300 Olympus confocal scan box and a half-wave plate between the objective and filter cubes to rotate the scanning laser polarization (20,32). To allow LC director determination via FCPM (20,36), 0.01% weight of the dye N,NBis(2,5-di-tert-butylphenyl)-3,4,9,10-preylenedicarboximide (Sigma-Aldrich) was incorporated into the CCN mixture.…”

Curvature capillary repulsion

“…More complex arrangements can be achieved by a number of routes. For example, if complex fluids like nematic liquid crystals are used as subphases, repulsion between the colloids owing to their topological defects can also form crystalline packings [2], and elastic energies in the nematic subphase can guide complex open structures to form [3]. Particle shape can also dictate the symmetries of structures at fluid interfaces; the capillary energy, given by the product of surface tension and area, near a particle depends on features like particle aspect ratio and the presence of sharp edges.…”