Topological Polymer Dispersed Liquid Crystals with Bulk Nematic Defect Lines Pinned to Handlebody Surfaces

Michael G. Campbell, Mykola Tasinkevych, and Ivan I. Smalyukh

Phys. Rev. Lett. 112, 197801 – Published 16 May 2014

Abstract

Polymer dispersed liquid crystals are a useful model system for studying the relationship between surface topology and defect structures. They are comprised of a polymer matrix with suspended spherical nematic drops and are topologically constrained to host defects of an elementary hedgehog charge per droplet, such as bulk or surface point defects or closed disclination loops. We control the genus of the closed surfaces confining such micrometer-sized nematic drops with tangential boundary conditions for molecular alignment imposed by the polymer matrix, allowing us to avoid defects or, on the contrary, to generate them in a controlled way. We show, both experimentally and through numerical modeling, that topological constraints in nematic microdrops can be satisfied by hosting topologically stable half-integer bulk defect lines anchored to opposite sides of handlebody surfaces. This enriches the interplay of topologies of closed surfaces and fields with nonpolar symmetry, yielding new unexpected configurations that cannot be realized in vector fields, having potential implications for topologically similar defects in cosmology and other fields.

Received 18 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.197801

Authors & Affiliations

Michael G. Campbell^1,2, Mykola Tasinkevych^3,4, and Ivan I. Smalyukh^1,2,5,6,*

¹Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
²Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA
³Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany
⁴Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
⁵Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA
⁶Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA

^*To whom all correspondence should be addressed. ivan.smalyukh@colorado.edu

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Vol. 112, Iss. 19 — 16 May 2014

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Images

Figure 1
TPDLC with $g = 1$ nematic drops. (a) and (b) POM micrographs obtained (a) without and (b) with an additional phase retardation plate. Polarizer and analyzer orientations are shown using white double arrows, and the slow axis of the phase retardation plate is shown by a blue double arrow. (c) and (d) 3D representation of $n (r)$ at the surface of a $g = 1$ drop based on (c) numerical modeling and (d) experiments, with the color-coded scheme of azimuthal orientations shown in the inset of (e). (e) Computer-simulated $n (r)$ of a defect-free equilibrium configuration. (f)–(h) $n (r)$ in the vicinity of self-compensating defects found in metastable states of some drops as depicted (f) at the LC-polymer interface, (g) in drop’s interior, and (h) in a plane intersecting the defect lines. Disclinations are shown as red tubes and filled circles representing regions of reduced scalar order parameter.
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Figure 2
Nematic $g = 2$ drops. (a) and (b) POM micrographs obtained (a) without and (b) with an additional phase retardation plate. (c) and (d) 3D representation of $n (r)$ at the surface of a $g = 2$ drop based on (c) numerical modeling and (d) experiments. The color-coded scheme of azimuthal orientations is shown in the inset of (c). (e) and (f) Nematic configurations and defects at the junction of two tori, with (e) $n (r)$ at the LC-polymer interface depicted using rods and the line defect cores in the bulk of the $g = 2$ drop shown using regions of reduced scalar order parameter. (g) and (h) A metastable configuration with a pair of additional self-compensating defects probed using POM (g) without and (h) with an additional phase retardation plate. (i) The corresponding experimental 3D representation of $n (r)$ at the surface of a $g = 2$ drop. (j) $n (r)$ in the vicinity of a defect in a midplane of a $g = 2$ drop.
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Figure 3
Nematic $g = 3$ drops. (a)–(d) 3PEF-PM images obtained for a midplane of the handlebody-shaped drops at different linear polarizations of excitation light (white double arrows). (e–i) Optical micrographs of two different $g = 3$ drops obtained (e) without polarizers, (f) and (h) between crossed polarizers, and (g) and (i) between crossed polarizers and with an additional phase retardation plate. (j) and (k) 3D representations of $n (r)$ at the LC-polymer interface obtained (j) by numerical modeling and (k) experimentally; the color-coded scheme of azimuthal orientations is shown in the inset. (l) and (m) Defect lines at tori junctions and (m) $n (r)$ shown for one of them. (n) Co-existence of a line defect at the triple junction with boojums in other locations of a larger drop. The red tubelike defect regions are defect cores with reduced scalar order parameter.
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Figure 4
Nematic $g = 4$ and $g = 5$ drops. (a) POM micrograph and (b) and (c) 3D $n (r)$ for two different $g = 4$ drops. (d) and (e) the corresponding numerical results depicting (d) defect lines in the junction regions and (e) $n (r)$ at the LC-polymer interface, with two defect lines marked by red filled circles. (f)–(i) POM micrographs showing two different $g = 5$ drops obtained (f) and (h) without and (g) and (i) with an additional phase retardation plate. (j) 3D representation of $n (r)$ of a $g = 5$ drop; the color-coded scheme of azimuthal orientations is shown in the inset.
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