Simon Čopar

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.

Visualisation methods for complex nematic fields

In analysis of numerically simulated or experimentally obtained nematic textures, data visualisation plays an important role in interpretation and comparison of results. We review both commonly used, and more recently developed visual presentation methods that expose different aspects of the textures, from director field patterns and topological content of nematic defects, to deformation modes and simulated optical effects. We outline the theoretical background and potential uses, with examples that highlight the features of each of the described techniques.

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.

Quaternions and hybrid nematic disclinations

Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterized by their director profile. In certain confined colloidal suspensions and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile in closed disclination loops and use it to apply topological classification to linked loops with arbitrary variation of the profile, generalizing the self-linking number description of disclination loops with the winding number . The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations, allowing application of said theory to structures that occur in practice.Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in closed disclination loops based on a quaternion description and use it to apply topological classification to linked loops with arbitrary variation of the profile. The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations. We compare the resulting decomposition of disclination loop features to a similar decomposition of nematic textures on closed surfaces. 1 ar X iv :1 21 1. 21 43 v1 [ co nd -m at .s of t] 9 N ov 2 01 2

Elementary building blocks of nematic disclination networks in densely packed 3D colloidal lattices

Nematic liquid crystals in frustrated environments are known to form a variety of topological defect conformations – possibly networks – with multiple meta-stable states of the nematic order. Here, we study the defect networks and their reconfigurability in a periodically spatially frustrated nematic, focusing specifically on the network formed in the nematic-filled voids of opal-like closely packed face centred cubic colloidal crystals. Using spherical colloidal particles with homeotropic anchoring, the liquid crystal fills a network of interconnected cavities with complicated surface-imposed conditions, generating a complex defect network of −1/2-winding number disclinations. We show that this network can be decomposed into a network of cubic and tetrahedral nematic elements, allowing us to enumerate the possible network conformations and use topological methods for their characterisation. We use combinatorics and geometry to predict all the possible conformations, their topology, and their free energy. The predictions are completely confirmed with numerical simulations. More generally, the presented results demonstrate an analytic approach towards achieving exactly addressable memory states in soft matter composite materials.

Singular values, nematic disclinations, and emergent biaxiality

Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.

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.