Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling

Meyer, Claire; Cunff, L. Le; Belloul, Malika; Foyart, Guillaume

doi:10.3390/ma2020499

Cited by 33 publications

(39 citation statements)

References 23 publications

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“…Outside the circular base, the molecules are perpendicular to the bottom substrate (homeotropic alignment in between the TFCDs). The filling of the substrate with the circular bases of the TFCD is of an iterative type, with the smaller domains filling the gaps between the larger ones, similar to the well‐known Apollonius packing of circles,36, 37 in which one starts with a system of large touching circles and then fills the interstices between them with smaller circles that are tangent to those already present and then repeats this iteration process. Blanc and Kleman reported about tiling or assembly of the plane non‐congruous TFCDs 29.…”

Section: Periodic Array Of Fcdsmentioning

confidence: 99%

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Smectic Liquid Crystal Defects for Self‐Assembling of Building Blocks and Their Lithographic Applications

Kim

Yoon

Jeong

et al. 2011

Adv Funct Materials

100

111

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crystal (LC) fi lm containing an ordered, periodic array of smectic LC defects. [ 9,10 ] Unlike previously reported self-assembling materials, which have been geared toward defect-free systems of the ordered structures, these approaches rely on the order of artifi cially made defects as building blocks to create templates. The proposed approaches based on LC defects have signifi cant advantages over existing methods to micro/nanopatterning applications, including easy fabrication, the creation of long-range surface ordering, very rapid formation of periodic arrays, and the ability to generate various featured sizes ranging from the micrometer to the sub-micrometer scale. Furthermore, the ordered array of LC defects occurs rapidly due to reversible and non-covalent interactions between the LC molecules and can easily be generated by controlling surface anchoring, which is a very simple and costeffective mechanism that is well suited to mass production. In addition, this process should not be limited to specifi c rodlike LC materials and it should be applicable to other smectic LC systems forming similar defect structures. Accordingly, such defect orders of LC materials can be very strong candidates for the periodic templates, compared to other soft-building blocks such as block copolymers, colloids, and surfactants.To introduce this new type of building block based on LC defect order, fi rstly we will describe various types of LC phases and their versatile defect structures. In particular, focal conic domains (FCDs), which are typical defect structures of the smectic phase, will be demonstrated in Section 2, since FCDs were fi rstly used to create defect orders. Next, we deal with defect arrays from three different FCDs including toric FCD (TFCD), parabolic FCD (PFCD), and cylindrical oily streak (OS). The TFCDs, which are generated in an antagonistic surface anchoring condition, will be described in detail. Then, the mechanism of TFCD formation is described in terms of surface anchoring, direct internal structure observation, and energetics in Section 3. In Section 4, the template-assisted self-assembling approaches, including some manipulating methods for the domain size, arrangement, and selective patterning of TFCDs, are demonstrated. Finally, we discuss their applications in soft lithographic templates, superhydrophobic surfaces, microlens arrays, organic photomasks, and trapping templates for colloidal particles based on large-area TFCD-array patterning in Section 5.As the fi eld of information displays is maturing, LC materials research is undergoing a modern-day renaissance. Devices Smectic Liquid Crystal Defects for Self-Assembling of Building Blocks and Their Lithographic ApplicationsRecently, it has been reported that liquid crystal (LC) defects can be used to create highly periodic templates by controlling the surface anchoring and the elastic properties of LC molecules. The self-assembled defect ordering of the LC materials takes advantage of the ability to achieve fast stabilization of molecular orde...

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Section: Periodic Array Of Fcdsmentioning

confidence: 99%

Section: Periodic Array Of Fcdsmentioning

confidence: 99%

Smectic Liquid Crystal Defects for Self‐Assembling of Building Blocks and Their Lithographic Applications

Kim

Yoon

Jeong

et al. 2011

Adv Funct Materials

100

111

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“…Confined smectic A liquid crystals (SmA LCs) form geometric defects called focal conic domains (FCDs) that focus light as gradient‐index lenses . Here, we exploit surface curvature to self‐assemble FCDs in a single step into a hierarchical structure (coined a “flower pattern”) molded by the fluid interface that is pinned at the top of a micropillar.…”

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confidence: 99%

“…In this self‐assembled structure, most of the small FCDs are far away from the pillars, whereas progressively larger FCDs are found near the pinned edge. Some small FCDs are also found close to the pillar edge because they improve the packing of the larger domains, as in Apollonius tiling . The range of FCD diameters is approximately 3–40 μm, which is remarkably similar to the ommatidia in insects .…”

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confidence: 99%

Curvature‐Driven, One‐Step Assembly of Reconfigurable Smectic Liquid Crystal “Compound Eye” Lenses

Serra

Gharbi

Luo

et al. 2015

Advanced Optical Materials

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Confined smectic A liquid crystals (SmA LCs) form topological defects called focal conic domains (FCDs) [1] that focus light as gradient-index lenses [2][3][4][5]. Here, we exploit surface curvature to self-assemble FCDs in a single step into a hierarchical structure [6,7] (coined "flower pattern") molded by the fluid interface that is pinned at the top of a micropillar. The structure resembles the compound eyes of some invertebrates, which consist of hundreds of microlenses on a curved interface, able to focus and construct images in three dimensions (3D) [8]. Here we demonstrate that these flowers are indeed "compound eyes" with important features which have not been demonstrated previously in the literature. The eccentric FCDs gradually change in size with radial distance from the edge of the micropillar, resulting in a variable microlens focal length that ranges from a few microns to a few tens of microns within a single "flower". We show that the microlenses can construct a composite 3D image from different depth of field (DOF). Moreover, the smectic "'compound eye" can be reconfigured by heating and cooling at the LC phase transition temperature; its field of view (FOV) can be manipulated by tuning the curvature of the LC interface, and the lenses are sensitive to light polarization.Insects' eyes are comprised of hundreds of microlenses (ommatidia) arranged on a curved surface [8]. Despite having modest resolution in comparison to single aperture lenses (like the human eyes), the compound eye offers attractive optical properties, including exceptionally wide FOV, fast motion detection, and polarization sensitivity. Artifical compound eyes have been created with angular sensitivity [9] and with a hemispheric FOV and near infinite DOF [10]. Typically, multiple top-down fabrication steps are required, including photolithography, replica molding, or complex micromachining processes [9][10][11]. For practical applications with wide FOV, lenses which self-align are highly desirable. * These authors contributed equally to the work † kstebe@seas.

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“…One can enclose the smectic by curved surfaces (11)(12)(13) or confine it between two flat surfaces with antagonistic surface anchoring, say, perpendicular and tangential (14, 15) (earlier works are reviewed in ref. 16).…”

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confidence: 99%

Designing Dupin cyclides in micro and macro worlds

Lavrentovich

2012

Proc. Natl. Acad. Sci. U.S.A.

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Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling

Cited by 33 publications

References 23 publications

Smectic Liquid Crystal Defects for Self‐Assembling of Building Blocks and Their Lithographic Applications

Smectic Liquid Crystal Defects for Self‐Assembling of Building Blocks and Their Lithographic Applications

Curvature‐Driven, One‐Step Assembly of Reconfigurable Smectic Liquid Crystal “Compound Eye” Lenses

Designing Dupin cyclides in micro and macro worlds

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