Abstract
Focal conic domains (FCDs) in smectic-A liquid crystals have drawn much attention, both for their exquisitely structured internal form and for their ability to direct the assembly of micromaterials and nanomaterials in a variety of patterns. A key to directing FCD assembly is control over the eccentricity of the domain. Here, we demonstrate a new paradigm for creating spatially varying FCD eccentricity by confining a hybrid-aligned smectic with curved interfaces. In particular, we manipulate interface behavior with colloidal particles in order to experimentally produce two examples of what has recently been dubbed the flower texture [C. Meyer et al., Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling, Materials 2, 499, 2009], where the focal hyperbolæ diverge radially outward from the center of the texture, rather than inward as in the canonical éventail or fan texture. We explain how this unconventional assembly can arise from appropriately curved interfaces. Finally, we present a model for this system that applies the law of corresponding cones, showing how FCDs may be embedded smoothly within a “background texture” of large FCDs and concentric spherical layers, in a manner consistent with the qualitative features of the smectic flower. Such understanding could potentially lead to disruptive liquid-crystal technologies beyond displays, including patterning, smart surfaces, microlens arrays, sensors, and nanomanufacturing.
- Received 23 October 2013
DOI:https://doi.org/10.1103/PhysRevX.3.041026
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Published by the American Physical Society
Synopsis
Planting a Liquid-Crystal Garden
Published 10 December 2013
Flower-shaped patterns in liquid crystals could be used to make small-scale optical elements.
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Popular Summary
Most of us have probably used the words “liquid crystals” when talking about our newly purchased flat-panel television sets. The scientific key to this display technology lies in the amazing fundamental ability of liquid-crystal materials to form a range of structural “textures” that display different contrasts under the illumination of polarized light. Such textures correspond to different physical states, in which the constituent anisotropically shaped molecules—rodlike molecules, for example—collectively, and spontaneously, orient and spatially arrange themselves. It turns out that the ability of liquid crystals to self-assemble does not stop at the molecular level: Even the defects in them are capable of self-organizing into ordered arrays. Such defect-based self-assemblies have found applications in optically selective photomasks and microlens arrays. In this experimental paper, informed by fundamental theoretical insights, we demonstrate a new experimental route to generating “flower textures” through controlled, defect-induced self-assembly in liquid crystals.
The class of liquid crystals we investigate are the so-called smectics, stacked layers of rodlike molecules well aligned along a common direction. It has been known that a colloidal particle inserted into a smectic liquid-crystal layer works as a defect by forcing the liquid-crystal molecules next to it to anchor themselves in particular orientations that differ from the orientations of those far away, giving rise to complicated geometries. Of particular interest are “focal conic domains,” geometric arrangements of layers studied nearly 150 years ago by Maxwell.
The key to our experiment is to generate these domains as desired by controlling the molecular alignment along the boundary of our smectic liquid-crystal sample using both nanoscale colloidal particles and the meniscus that forms between air and the liquid crystal. It is like finding a way to stack mattresses on an uneven bed frame—how do the lumps, bumps, and “peas” change the way they stack? Based on our insight of how to manipulate the local geometric properties of the “focal conical domains” created by such specially engineered settings, we can generate desired textures of radially distributed “flowers.” We have developed a concrete model to understand this flower geometry based on the elastic description of smectic liquid crystals.
Our findings provide local control over the geometrical properties of focal conic domains, meeting the great technological interest in manipulating these textures. In particular, our theoretical model should serve as a fundamental guideline to crafting smectic configurations of increased complexity.