Session H44: Focus Session: Nano to Mesoscale Structure in Ordered Systems: Liquid Crystal Topology and Defects

Chiral Self-Assembly

Chirality, the lack of reflection symmetry, at the molecular level has a profound influence on the ordering of molecular assemblages at the macroscopic scale. The example discussed here is the self-assembly of monolayers of rod-like fd virus particles, with the virus particles oriented on the average perpendicular to the plane of the layer, like a single layer of a smectic-A liquid crystal. Because these virus particles are chiral, they would prefer a twisted packing, which is incompatible with the layer structure. The twisted packing can only appear locally, at layer edges or in isolated defects in the interior of the layer. As chirality increases, the twisted regions achieve lower energy, until they can drive remarkable transformations to structures with longer edges and/or a greater number of defects.   

Pillar-Assisted Epitaxial Assembly of Focal Conic Domain Arrays in Smectic-A Liquid Crystals

We demonstrate a versatile approach to tailor the spacing and symmetry of periodic arrays of toric focal conic domains (TFCDs) over a large area via confinement of smectic-A liquid crystals (SmA LCs) in patterned substrates. Arrays of pillars with variable dimensions are employed to direct the assembly of TFCDs, determining both the domain positions and the size of the defects. Highly ordered square and hexagonal arrays of TFCDs result from topographical confinement of the LC in square and hexagonal arrays of pillars. Focal conic domains are shown to form only when the confined geometry provides sufficient area so that substrate-induced planar alignment of LC molecules is energetically favorable. Since the spacing and symmetry of the TFCD array can be readily pre-determined by the arrangement of the directing pillars, this pillar-assisted assembly technique serves as a model study for directed assembly of liquid crystals in three dimensions and offers improvements to the capability of LC-based templates for device fabrication and lithography.   

Shape and chirality transitions in twisted nematic elastomer ribbons: Finite element simulation studies

We use finite element simulation studies to explore transitions of shape and chirality in nematic elastomer ribbons with a twisted director configuration. Recent experimental and theoretical studies demonstrated that these fascinating materials show reversal of macroscopic chiral sense under a change of temperature, and explored shape selection as a function of the sample's aspect ratio. We explore these phenomena via three dimensional finite element simulation studies. For ribbons with width/thickness ratio above a threshold value, we find that on heating the sample undergoes a sequence of shape transitions from right handed helix -- right handed twisted ribbon -- flat ribbon -- left handed twisted ribbon -- left handed helix. Ribbons with width/thickness ratio below the threshold show fewer shape transitions, from right handed twisted ribbon -- flat ribbon -- left handed twisted ribbon. These results are in qualitative agreement with theoretical predictions, provide insight into experimental observations, and demonstrate the value of finite element methods for future engineering design of nematic elastomer devices.   

Frustrated orientational order on extrinsic geometries

The ground state of an anisotropic liquid on a curved surface has topological defects due to the surface's Gaussian curvature. The extrinsic geometry of the surface, however, frustrates the ground state arising from Gaussian curvature alone, changing the defect configurations in the ground state or expelling them from the surface altogether. We study nematic order on unduloids - a family of undulated cylinders with constant mean curvature spanning from the cylinder to a chain of spherical droplets - arising in systems ranging from liquid bridges to fluid membranes. We identify structural transitions in which pairs of disclinations of opposite signs are nucleated as the unduloid progresses from cylinder to spheres, explicitly separating the role of intrinsic geometry, which nucleates disclinations to screen Gaussian curvature, and extrinsic geometry, which expels defects from the neck. We describe some implications for the pinching off of a cylinder.   

Topology of knots and links in chiral nematic colloids

Nematic braids formed by disclinations entangling colloidal particles in chiral and achiral nematic liquid crystals are geometrically stabilized and restricted by topology. We report how self-linking number enables a classification of entangled defect lines [1, 2] and how a simple rewiring scheme for the orthogonal crossing of two half integer disclinations, based on a tetrahedral rotation of two relevant disclination segments allows us to predict nematic braids and their self-linking numbers. We further describe how using of laser micromanipulation enable the knotting of defect lines in chiral nematic colloids into knots and links of arbitrary complexity [3]. Colloids stabilized by nematic braids based on all knots and links with up to six crossings, including Hopf link, Star of David, Borromean rings are realized. We demonstrate how topology leads to the engineering of complex soft materials.\\[4pt] [1] S. Copar and S.Zumer, Nematic Braids: Topological Invariants and Rewiring of Disclinations, Phys. Rev. Lett. 106, 177801 (2011).\\[0pt] [2] S. Copar, T. Porenta and S. Zumer, Nematic Disclinations as Twisted Ribbons, Phys. Rev. E 84, 051702 (2011).\\[0pt] [3] U. Tkalec, M. Ravnik, S. Copar, S. Zumer and I. Musevic, Reconfigurable Knots and Links in Chiral Nematic Colloids, Science 333, 62 (2011).   

Modeling texture transitions in cholesteric liquid crystal droplets

Cholesteric liquid crystals can be switched reversibly between planar and focal-conic textures, a property enabling their application in bistable displays, liquid crystal writing tablets, e-books, and color switching ``e-skins.'' To explore voltage-pulse induced switching in cholesteric droplets, we perform simulation studies of director dynamics in three dimensions. Electrostatics calculations are solved at each time step using an iterative relaxation method. We demonstrate that as expected, a low amplitude pulse drives the transition from planar to focal conic, while a high amplitude pulse drives the transition from focal conic back to the planar state. We use the model to explore the effects of droplet shape, aspect ratio, and anchoring conditions, with the goal of minimizing both response time and energy consumption.   

Necklaces of Liquid Crystal Beads: Nematic Drops Constrained on Thin Cellulosic Fibers

Liquid crystal droplets dispersed in a continuous matrix have important applications in electro-optical devices. They also produce intriguing topological defect structures due to the confinement of the liquid crystal by closed boundaries that impose alignment at the interface. In this work we use a simple method to generate stable liquid crystal droplets topologically equivalent to a toroid by depositing tiny volumes of a nematic liquid on cellulosic micro-fibers (1 $\mu $m diameter) suspended in air. This system can exhibit non-trivial point topological defects which can be energetically unstable against expanding into ring defects, depending on the fibers constraining geometries. By changing temperature, the system remains stable and allows the study of the defects evolution near the nematic-isotropic transition showing qualitatively different behavior on cooling and heating processes. The necklaces of such liquid crystal drops constitute excellent systems for fundamental studies and open new perspectives for applications. This work was sponsored by Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-10-1-3020. The US Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon. Other support includes the Portuguese Science and Technology Foundation grant SFRH/BD/63574/2009 and projects PEst-C/CTM/LA0025/2011 (Strategic Project - LA 25 - 2011-2012, PTDC/CTM/099595/2008, PTDC/FIS/110132/2009 and Windsor Treaty grant 2009-10 UR55.   

Controlling the location of defects in nematic shells

We study nematic shells with four s=+1/2 defects and vary the elastic constant anisotropy of the liquid crystal by approaching the nematic-to-smectic phase transition temperature. We find the defects ultimately arrange themselves along a great circle, consistent with recent expectations. Changing the elastic constant anisotropy provides an alternative route to changing the shell thickness inhomogeneity for controlling the defects location.   

Structures in liquid crystalline shells at a nematic-smectic transition

Liquid crystalline shells display phenomena that are fascinating from a fundamental physics point of view and they also hold promise for innovative applications e.g. for advanced colloids. The key feature of these shells is the unavoidable presence of topological defects, the types and numbers of which depend on the phase as well as the geometrical features of the shell. Here we present our investigation of the complex internal reordering phenomena occurring in a liquid crystalline shell undergoing a transition between the nematic and smectic phases. In the smectic phase, the topological and geometrical constraints of a spherical shell with symmetric boundary conditions imposed on the developing 1D quasi-long-range order create a conflict that triggers a series of buckling instabilities, resulting in two different characteristic defect patterns. We will also show very recent results on shells with asymmetric boundary conditions, giving rise to beautiful complex patterns, some transitory, some stable. The phase transition between nematic and smectic order yields varying textures depending on the shell size and thickness, and on the specific alignment types at the shell in- and outside, respectively.   

Visualizing, manipulating, and imprinting $\pi$-wall defects in self-assembled colloidal membranes

Geometric frustration and the resulting topological defects play an important role in determining the structural, mechanical and optical properties of materials. Here we describe the behavior of a new type of defect, called a $\pi$-wall, in a model system of colloidal membranes composed of chiral rod-like \textit{fd} viruses. We use complimentary optical microscopy techniques to study the structure and energetics of $\pi$-walls, and develop a model based on the analogy between liquid-crystals and superconductors to determine the structure and energetics of $\pi$-walls. We then focus on $\pi$-wall formation, showing that $\pi$-walls naturally assemble through a unique coalescence process in which chiral frustration plays an essential role. $\pi$-walls can also be artificially created and engineered using externally applied optical forces.