Daniel A. Beller

Exploiting imperfections in the bulk to direct assembly of surface colloids

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. Specifically, by confining the nematic liquid crystal 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. Since topographically complex substrates are easily fabricated and liquid crystal defects are readily reconfigured, this work lays the foundation for a new, robust mechanism to dynamically direct assembly over large areas by controlling surface anchoring and associated bulk defect structure.Significance In this research, we develop new means of directing colloids at an interface to assemble into complex configurations by exploiting defects in a liquid crystal (LC). Through confinement of a nematic LC over a topographically patterned surface, we demonstrate the formation of defects at precise locations in the LC bulk. These defects source elastic distortion fields that guide the assembly of colloids constrained to the LC–air interface. This work significantly extends prior work in which LCs confined in film or droplet geometries guide colloidal assembly beyond simple triangular lattices and chains. Here, we demonstrate colloidal assembly at precise locations, with particle-rich and -poor regions, determined remotely by defects deliberately seeded in the LC bulk. Experimental results are supported by numerical and analytical investigation. 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.

Pillar-Assisted Epitaxial Assembly of Toric Focal Conic Domains of Smectic-A Liquid Crystals

SU-8 pillar-assisted epitaxial assembly of toric focal conic domains (TFCDs) arrays of smectic-A liquid crystals is studied. The 3D nature of the pillar array is crucial to confine and direct the formation of TFCDs on the top of each pillar and between neighboring pillars, leading to highly ordered square and hexagonal array TFCDs. Excellent agreement between the experimentally obtained critical pillar diameter and elasticity calculation is found.

Topographically induced hierarchical assembly and geometrical transformation of focal conic domain arrays in smectic liquid crystals.

Controlling topological defects in 3D liquid crystal phases is a crucial element in the development of novel devices, from blue-phase displays to passive biochemical sensors. However, it remains challenging to realize the 3D topological conditions necessary to robustly and arbitrarily direct the formation of defects. Here, using a series of short pillar arrays as topological templates, we demonstrate the hierarchical assembly of focal conic domains (FCDs) in smectic-A liquid crystals that break the underlying symmetry of the pillar lattice, exhibit tunable eccentricity, and together develop a nontrivial yet organized array of defects. The key to our approach lies in the selection of the appropriate ratio of the size of focal domain to the dimension of pillars such that the system favors the “pinning” of FCD centers near pillar edges while avoiding the opposing effect of confinement. Our study unequivocally shows that the arrangement of FCDs is strongly influenced by the height and shape of the pillars, a feature that promotes both a variety of nontrivial self-assembled lattice types and the attraction of FCD centers to pillar edges, especially at regions of high curvature. Finally, we propose a geometric model to reconstruct the smectic layer structure in the gaps between neighboring FCDs to estimate the energetic effects of nonzero eccentricity and assess their thermodynamic stability.

Ring around the colloid

In this work, we show that Janus washers, genus-one colloids with hybrid anchoring conditions, form topologically required defects in nematic liquid crystals. Experiments under crossed polarizers reveal the defect structure to be a rigid disclination loop confined within the colloid, with an accompanying defect in the liquid crystal. When confined to a homeotropic cell, the resulting colloid-defect ring pair tilts relative to the far field director, in contrast to the behavior of toroidal colloids with purely homeotropic anchoring. We show that this tilting behavior can be reversibly suppressed by the introduction of a spherical colloid into the center of the toroid, creating a new kind of multi-shape colloidal assemblage.

Microbullet assembly: interactions of oriented dipoles in confined nematic liquid crystal

Microbullet particles, cylinders with one blunt end and one hemispherical end, offer a novel platform to study the effects of anisotropy and curvature on colloidal assembly in complex fluids. Here, we disperse microbullets in 4-cyano-4′-pentylbiphenyl nematic liquid crystal (NLC) cells and form oriented elastic dipoles with a nematic point defect located near the curved end. This feature allows us to study particle interactions as a function of dipole alignment. By careful control of the surface anchoring at the particle surface and the confining boundaries, we study the interactions and assembly of microbullets under various conditions. When microbullets with homeotropic surface anchoring are dispersed in a planar cell, parallel dipoles form linear chains parallel to the director, similar to those observed with spherical particles in a planar cell, while antiparallel dipoles orient side-to-side. In a homeotropic cell, however, particles rotate to orient their long axis parallel to the director. When so aligned, parallel dipoles repel and form 2D ordered assemblies with hexagonal symmetry that ripen over time owing to attraction between antiparallel neighbours. Further, we show that the director orientation inside the cell can be altered by application of an electrical field, allowing us to flip microbullets to orient parallel to the director, an effect driven by an elastic torque. Finally, we detail the mechanisms that control the formation of 1D chains and hexagonal lattices with respect to the elasticity of the NLC.

Lassoing saddle splay and the geometrical control of topological defects

Significance The liquid crystalline state of matter exhibits amazing, diverse defect structures. Whereas often these structures are found in exotic, specially designed materials, we find exotic defect structures in even the simplest liquid crystals by placing them in templates with special boundary cues. We find that a sheet filled with an array of holes placed in a liquid crystal cell induces arrays of defect lines. We also find that the anchoring conditions at the cell surfaces strongly modify the observed liquid-crystal states. We characterize and explain our experimental observations using simulations and theoretical considerations. Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4′-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system’s overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.

Focal Conic Flower Textures at Curved Interfaces

Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA(Received 23 October 2013; published 10 December 2013)Focal conic domains (FCDs) in smectic-A liquid crystals have drawn much attention, both for theirexquisitely structured internal form and for their ability to direct the assembly of micromaterials andnanomaterials in a variety of patterns. A key to directing FCD assembly is control over the eccentricity ofthe domain. Here, we demonstrate a new paradigm for creating spatially varying FCD eccentricity byconfining a hybrid-aligned smectic with curved interfaces. In particular, we manipulate interface behaviorwith colloidal particles in order to experimentally produce two examples of what has recently beendubbed the flower texture [C. Meyer et al., Focal Conic Stacking in Smectic A Liquid Crystals: SmecticFlower and Apollonius Tiling, Materials 2, 499, 2009], where the focal hyperbolae diverge radiallyoutward from the center of the texture, rather than inward as in the canonical e´ventail or fan texture. Weexplain how this unconventional assembly can arise from appropriately curved interfaces. Finally, wepresent a model for this system that applies the law of corresponding cones, showing how FCDs may beembedded smoothly within a ‘‘background texture’’ of large FCDs and concentric spherical layers, in amannerconsistentwiththequalitativefeaturesofthesmecticflower.Suchunderstandingcouldpotentiallylead to disruptive liquid-crystal technologies beyond displays, including patterning, smart surfaces,microlens arrays, sensors, and nanomanufacturing.

Better Actuation Through Chemistry: Using Surface Coatings to Create Uniform Director Fields in Nematic Liquid Crystal Elastomers.

Controlling the molecular alignment of liquid crystal monomers (LCMs) within nano- and microstructures is essential in manipulating the actuation behavior of nematic liquid crystal elastomers (NLCEs). Here, we study how to induce uniformly vertical alignment of nematic LCMs within a micropillar array to maximize the macroscopic shape change using surface chemistry. Landau-de Gennes numerical modeling suggests that it is difficult to perfectly align LCMs vertically in every pore within a poly(dimethylsiloxane) (PDMS) mold with porous channels during soft lithography. In an untreated PDMS mold that provides homeotropic anchoring of LCMs, a radially escaped configuration of LCMs is observed. Vertically aligned LCMs, a preferred configuration for actuation, are only observed when using a PDMS mold with planar anchoring. Guided by the numerical modeling, we coat the PDMS mold with a thin layer of poly(2-hydroxyethyl methacrylate) (PHEMA), leading to planar anchoring of LCM. Confirmed by polarized optical microscopy, we observe monodomains of vertically aligned LCMs within the mold, in agreement with modeling. After curing and peeling off the mold, the resulting NLCE micropillars showed a relatively large and reversible radial strain (∼30%) when heated above the nematic to isotropic transition temperature.

Geometry of the cholesteric phase

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool, we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot, in general, be translated from one phase to the other.

Plastic deformation of tubular crystals by dislocation glide.

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tubes radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii.