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Special issue: Commemorative Issue in honor of the late Professor Maurice Kleman

Manipulation of mechanically nanopatterned line defect assemblies in plane-parallel nematic liquid crystals

, , , , , , , & show all
Pages 98-122 | Received 28 Nov 2021, Accepted 12 Feb 2022, Published online: 03 Mar 2022

References

  • Mermin N. The topological theory of defects in ordered media. Rev Mod Phys. 1979;51:591–648.
  • Kibble TWB. Topology of cosmic domains and strings. J Phys A: Math. Gen. 1976;9(8):1387–1398.
  • Zurek WH. Cosmological experiments in superfluid helium? Nature. 1985;317:505–508.
  • Kleman M, Lavrentovich OD. Soft Matter physics: An introduction. New York (NY): Springer Science & Business Media; 2004.
  • Volovik GE, Lavrentovich OD. Topological dynamics of defects: boojums in nematic drops. Sov Phys JETP. 1983;58(6):1159–1166.
  • De Gennes PG, Prost J. The physics of liquid crystals. Oxford: Clarendon; 1994.
  • Palffy-Muhoray P. The diverse world of liquid crystals. Phys Today. 2007;6(9):54–60.
  • Lavrentovich OD. Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops. Liq Cryst. 1998;24(1):117–126.
  • Meiboom S, Sethna JP, Anderson PW, et al. Theory of the blue phase of cholesteric liquid crystals. Phys Rev Lett. 1981;46:1216–1219.
  • Wright DC, Mermin N. Crystalline liquids: the blue phase. Rev Mod Phys. 1989;61:385–432.
  • Lin IH, Miller DS, Bertics PJ, et al. Endotoxin-induced structural transformations in liquid crystalline droplets. Science. 2011;332:1297.
  • Lowe AM, Abbott NM. Liquid crystalline for biological applications. Chem Mater. 2012;24(5):746–758.
  • Guo D, Chen CW, Li CC, et al. Reconfiguration of three-dimensional liquid crystalline photonic crystals by electrostriction. Nat Mater. 2020;19:94–101.
  • Coursault D, Grand J, Zappone B, et al. Linear self-assembly of nanoparticles within liquid crystal defect arrays. Adv Mater. 2012;24:1461–1465.
  • Dubtsov AV, Pasechnik SV, Shmeliova DV, et al. Light and phospholipid driven structural transitions in nematic microdroplets. App Phys Lett. 2014;105:151606.
  • Klemenčič E, Trček M, Kutnjak Z, et al. Giant electrocaloric response in smectic liquid crystals with direct smectic-isotropic transition. Sci Rep. 2019;9:1721-1–1721-10.
  • Kikuchi H, Yokota M, Hisakado YH, et al. Polymer-stabilized liquid-crystals blue phases. Nat Mater. 2002;1:64–68.
  • Karatairi E, Rožič B, Kutnjak Z, et al. Nanoparticle-induced widening of the temperature range of liquid-crystalline blue phases. Phys Rev E. 2010;81:041703.
  • Wang X, Kim Y, Bukusoglu E, et al. Experimental insights into the nanostructure of the cores of topological defects in liquid crystals. Phys Rev Lett. 2016;116:147801.
  • Wang X, Miller DS, Bukusoglu E, et al. Topological defects in liquid crystals as templates for molecular self-assembly. Nat Mater. 2016;15:106–112.
  • Poulin P, Stark H, Lubensky TC, et al. Novel colloidal interactions in anisotropic fluids. Science. 1997;275:1770–1773.
  • Pires D, Fleury JB, Galerne Y. Colloid particles in the interaction field of a disclination line in a nematic phase. Phys Rev Lett. 2007;98:247801.
  • Tkalec U, Ravnik M, Čopar S, et al. Reconfigurable knots and links in chiral nematic colloids. Science. 2011;333:62–65.
  • Harth K, Stannarius R. Topological point defects of liquid crystals in quasi-two-dimensional geometries. Front. in Phys. 2020;8:112-131.
  • Shin MJ, Yoon DK. Role of stimuli on liquid crystalline defects: from defect engineering to switchable functional materials. Mater. 2020;13:5466. doi:10.3390/ma13235466.
  • Kulkarni S, Kumar S, Thareja P. Colloidal and fumed particles in nematic liquid crystals: self-assembly, confinement and implications on rheology. J Mol Liq. 2021;336:116241.
  • Stark H. Physics of colloidal dispersions in nematic liquid crystals. Phys Rep. 2001;351:387–474.
  • Lubensky TC, Pettey D, Currier N, et al. Topological defects and interactions in nematic emulsions. Phys Rev E. 1998;57:610.
  • Sanchez T, Chen DTN, DeCamp SJ, et al. Spontaneous motion in hierarchically assembled active matter. Nature. 2012;491:431–434.
  • Doostmohammadi A, Ignés-Mullol J, Yeomans JM, et al. Active nematics. Nat. Commun. 2018;9:3246.
  • Kralj S, Rosso R, Virga EG. Finite-size effects on order reconstruction around nematic defects. Phys Rev E. 2010;81:021702.
  • Kaiser P, Wiese W, Hess S. Stability and instability of a uniaxial alignment against biaxial distortions in the isotropic and nematic phases of liquid crystals. J. Non-Equilib. Thermodyn. 1992;17:153–169.
  • Kralj S, Žumer S. The saddle-splay surface elasticity of nematic structures confined to a cylindrical capillary. Phys Rev E. 1995;51:366–379.
  • Nobili M, Durand G. Disorientation-induced disordering at a nematic-liquid-crystal–solid interface. Phys Rev A. 1992;46:6174(R).
  • Virga EG. Variational theories for liquid crystals. London: Chapman Hall; 1994.
  • Nehring J, Saupe A. Calculation of the elastic constants of nematic liquid crystals. J Chem Phys. 1972;56:5527–5528.
  • Rapini A, Papoular M. Distorsion d'une lamelle nematique sous champ magnetique conditions d'ancrage aux Parois [Distortion of a nematic lamella under a magnetic field conditions of anchoring to the walls]. J. Phys Colloq. 1969;30(C4):54–56.
  • Selinger JV. Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals. Liq Cryst Rev. 2018;6(2):129–142.
  • Selinger JV. Director deformations, geometric frustration, and modulated phases in liquid crystals. Soft Condensed Matter (cond-mat.soft). 2021; arXiv:2103.03803.
  • Machon T, Alexander GP. Umbilic lines in orientational order. Phys Rev X. 2016;6:011033.
  • Ericksen JL. Inequalities in liquid crystal theory. Phys Fluids. 1966;9:1205–1207.
  • Gartland EC, Mkaddem S. Instability of radial hedgehog configurations in nematic liquid crystals under landau–de Gennes free-energy models. Phys Rev E. 1999;59:563.
  • Schopohl N, Sluckin TJ. Defect core structure in nematic liquid crystals. Phys Rev Lett. 1987;59:2582–2584.
  • Kralj S, Virga EG. Universal fine structure of nematic hedgehogs. J Phys A: Math. Gen. 2001;34:829–838.
  • Bisi F, Gartland EC, Rosso R, et al. Order reconstruction in frustrated nematic twist cells. Phys Rev E. 2003;6:021707.
  • Mori H, Nakanishi H. On the stability of topologically non-trivial point defects. J Phys Soc Jpn. 1988;57:1281–1286.
  • Terentjev EM. Disclination loops, standing alone and around solid particles, in nematic liquid crystals. Phys Rev E. 1995;51:1330–1337.
  • Bradač Z, Kralj S, Svetec M, et al. Annihilation of nematic point defects: postcollision scenarios. Phys Rev E. 2003;6:050702(R).
  • Zhou S, Shiyanovskii SV, Park HS, et al. Fine structure of the topological defect cores studied for disclinations in lyotropic chromonic liquid crystals. Nat Commun. 2017;8:14974–14981.
  • Hendry PC, Lawson NS, Lee RAM, et al. Generation of defects in superfluid 4He as an analogue of the formation of cosmic strings. Nature. 1994;368:315–317.
  • Dodd ME, Hendry PC, Lawson NS, et al. Nonappearance of vortices in fast mechanical expansions of liquid 4He through the lambda transition. Phys Rev Lett. 1998;81:3703–3706.
  • Kavoussanaki E, Monaco R, Rivers RJ. Testing the Kibble-Zurek scenario with annular josephson tunnel junctions. Phys Rev Lett. 2000;85:3452–3455.
  • Digal S, Ray R, Srivastava AM. Observing correlated production of defects and antidefects in liquid crystals. Phys Rev Lett. 1999;83:5030–5033.
  • Chuang I, Yurke B, Pargellis A, et al. Coarsening dynamics in uniaxial liwquid crystals. Phys Rev E. 1993;47:3343–3356.
  • Chuang I, Durrer R, Turok N, et al. Cosmology in the laboratory: defect dynamics in liquid crystals. Science. 1991;251:1336–1342.
  • Bradač Z, Kralj S, Žumer S. Early stage domain coarsening of the isotropic-nematic phase transition. J Chem Phys. 2011;135:024506.
  • Bradač Z, Kralj S, Žumer S. Molecular dynamics study of isotropic-nematic quench. Phys Rev E. 2002;65:021705-01–021705-10.
  • Billeter JL, Smondyrev AM, Loriot GB, et al. Phase-ordering dynamics of the Gay-Berne nematic liquid crystal. Phys Rev E. 1999;60:6831–6840.
  • Eakin JN, Xie Y, Pelcovits RA, et al. Zero voltage Freedericksz transition in periodically aligned liquid crystals. Appl Phys Lett. 2004;85:1671–1673.
  • Crawford GP, Eakin JN, Radcliffe RD, et al. Liquid-crystal diffraction gratings using polarization holography alignment techniques. J Appl Phys. 2005;98:123102.
  • Gorkhali SP. Intensity and polarization holography [dissertation]. Providence RI: Brown University; 2007.
  • Fleury J-B, Pires D, Galerne Y. Self-connected 3D architecture of microwires. Phys Rev Lett. 2009;103:267801.
  • Ackerman PJ, Qi Z, Smalyukh II. Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams. Phys Rev E. 2013;86:021703.
  • Ackerman PJ, Qi Z, Lin Y, et al. Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities. Sci Rep. 2012;2:414–422.
  • Evans JS, Ackerman PJ, Broer DJ, et al. Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles. Phys Rev E. 2013;87:032503.
  • Sohn HRO, Liu CD, Voinsecu R, et al. Optically enriched and guided dynamics of active skyrmions. Opt Expr. 2020;28(5):6306–6319.
  • Culbreath C, Glazar N, Yokoyama H. Note: automated maskless micro-multidomain photoalignment. Rev Sci Instr. 2011;82:126107.
  • Glazar N, Culbreath C, Li Y, et al. Switchable liquid-crystal phase-shift mask for super-resolution photolithography based on pancharatnam–Berry phase. Appl Phys Expr. 2015;8:116501.
  • Wang M, Li Y, Yokoyama H. Artificial web of disclination lines in nematic liquid crystals. Nat Comm. 2017;8:388–395.
  • Gao Y, Jiang M, Chehui P, et al. High-resolution and high-throughput plasmonic photopatterning of complex Molecular orientations in liquid crystal. Adv Mater. 2016;28(12):2353–2358.
  • Yu H, Jiang M, Guo Y, et al. Plasmonic metasurfaces with high UV–Vis transmittance for photopatterning of designer molecular orientations. Adv Opt Mater. 2019;7(11):1900117.
  • Guo Y, Jiang M, Afghah S, et al. Photopatterned designer disclination networks in nematic liquid crystals. Adv Opt Mater. 2021;9(16):2100181.
  • Peng C, Guo Y, Turiv T, et al. Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks. Adv Mater. 2017;29:1606112.
  • Ware TH, McConney ME, Jeong JW, et al. Voxelated liquid crystal elastomers. Science. 2015;347(6225):982–984.
  • You R, Choi Y-S, Shin MJ, et al. Reconfigurable periodic liquid crystal defect array via modulation of electric field. Adv Mater Techn. 2019;4:1900454.
  • Kim MS, Serra F. Tunable large-scale regular arrays of topological defects in nematic liquid crystals. RSC Adv. 2018;8:35640–35645.
  • Sasaki Y, Takahashi J, Tokoawa S, et al. A general control strategy to micropattern topological defects in nematic liquid crystals using ionically charged dielectric surface. Adv Mater Interfaces. 2021;8:2100379.
  • Sasaki Y, Jampani VSR, Tanaka C. Large-scale self-organization of reconfigurable topological defect networks in nematic liquid crystals. Nat Comm. 2016;7:13238.
  • Cattaneo L, Kos Z, Savoini M, et al. Electric field generation of Skyrmion-like structures in a nematic liquid crystal. Soft Matter. 2016;6:853–858.
  • Aya S, Salamon P, Eber N, et al. Reconfigurable large-scale pattern formation driven by topological defect separation in liquid crystals. Adv Mater Interfaces. 2020;7:2000139.
  • Missaoui A, Harth K, Salamon P, et al. Annihilation of point defect pairs in freely suspended liquid-crystal films. Phys Rev Res. 2020;2:013080.
  • Kim MS, Serra F. Tunable dynamic topological defect pattern formation in nematic liquid crystals. Adv Opt Mater. 2020;8(1):1900991.
  • Kim MS, Serra F. Topological defect arrays in nematic liquid crystals assisted by polymeric pillar arrays: effect of the geometry of pillars. Crystals. 2020;10:314–326.
  • Guo Y, Shahsava H, Davidson ZS, et al. Precise control of lyotropic chromonic liquid crystal alignment through surface topography. ACS Appl Mater Interfaces. 2019;11:36110–36117.
  • Rüetschi M, Grütter P, Fünfschilling J, et al. Creation of liquid crystal waveguides with scanning force microscopy. Science. 1994;265:512–514.
  • Kim J-H, Yoneya M, Yokoyama H. Tristable nematic liquid-crystal device using micropatterned surface alignment. Nature. 2002;420:159–162.
  • Wen B, Mahajan MP, Rosenblatt C. Ultrahigh-resolution liquid crystal display with gray scale. Appl Phys Lett. 2000;76:1240–1242.
  • Wen B, Petschek RG, Rosenblatt C. Nematic liquid-crystal polarization gratings by modification of surface alignment. Appl Opt. 2002;41(7):1246–1250.
  • Berreman DW. Solid surface shape and the alignment of an adjacent nematic liquid crystal. Phys Rev Lett. 1972;28:1683–1686.
  • Geary JM, Goodby JW, Kmetz AR, et al. The mechanism of polymer alignment of liquid-crystal materials. J Appl Phys. 1987;62:4100–4108.
  • Shioda T, Wen B, Rosenblatt C. Step-wise Freedericksz transition in a nematic liquid crystal. J Appl Phys. 2003;94(12):7502–7504.
  • Carbone G, Rosenblatt C. Polar anchoring strength of a tilted nematic: confirmation of the dual easy axis model. Phys Rev Lett. 2005;94:057802.
  • Vaughn KE, Sousa M, Kang D, et al. Continuous control of liquid crystal pretilt angle from homeotropic to planar. Appl Phys Lett. 2007;90:194102.
  • Missaoui A, Rosenblatt C. Unpublished.
  • Kim D-H, Seo S-S, Park H-G, et al. High pretilt angle effects on electro-optical property of Ion-beam irradiated liquid crystal cells on a blended polyimide surface. Ferroelectrics. 2010;396:67–75.
  • Nehring J, Saupe A. Schlieren texture in nematic and smectic liquid-crystals. J Chem Soc – n.a. Trans II. 1972;68(590):1–15.
  • Murray BS, Pelcovits RA, Rosenblatt C. Creating arbitrary arrays of two-dimensional topological defects. Phys Rev E. 2014;90:052501.
  • Syed IM, Carbone G, Rosenblatt C, et al. Planar degenerate substrate for micro- and nanopatterned nematic liquid-crystal cells. Phys Rev E. 2005;98:034303.
  • Kralj S, Murray BS, Rosenblatt C. Decomposition of strongly charged topological defects. Phys Rev E. 2017;95:04270291.
  • Murray BS, Kralj S, Rosenblatt C. Decomposition vs. escape of topological defects in a nematic liquid crystal. Soft Matter. 2017;13:8442–8450.
  • Harkai S, Murray BS, Rosenblatt C, et al. Electric field driven reconfigurable multistable topological defect patterns. Phys Rev Res. 2020;2:013176.
  • Ferris AJ, Afghah S, Selinger RLB, et al. Electric field-induced crossover from 3D to 2D topological defects in a nematic liquid crystal: experimental verification. Soft Matter. 2020;16:642–650.
  • Susser AL, Harkai S, Kralj S, et al. Transition from escaped to decomposed nematic defects, and vice versa. Soft Matter. 2020;16:4814–4822.
  • Susser, AL, Kralj S, Rosenblatt C. Co-revolving topological defects in a nematic liquid crystal. Soft Matter. 2021; 17:9616–9623. doi:10.1039/d1sm01124c.
  • Ondris-Crawford RJ, Crawford GP, Zumer S, et al. Curvature-induced configuration transition in confined nematic liquid crystals. Phys Rev Lett. 1993;70:194–197.
  • Cladis PE, Kleman M. Non-singular disclinations of strength S  = + 1 in nematics. J Phys. France. 1972;33(5-6):591–598.
  • Chiccoli C, Feruli I, Lavrentovich OD, et al. Topological defects in schlieren textures of biaxial and uniaxial nematics. Phys Rev E. 2002;66:030701.
  • Carbone G, Lombardo G, Barberi R, et al. Mechanically induced biaxial transition in a nanoconfined nematic liquid crystal with a topological defect. Phys Rev Lett. 2009;103:167801.
  • Martinot -Lagarde P, Dreyfus-Lambez H, Dozov I. Biaxial melting of the nematic order under a strong electric field. Phys Rev E. 2003;67:051710.
  • Smalyukh II, Pratibha R, Madhusudana NV, et al. Selective imaging of 3D director fields and study of defects in biaxial smectic A liquid crystals. Eur J Phys E. 2005;16:179–191.
  • Carr EF. Influence of electric and magnetic fields on dielectric constant and loss of liquid crystal anisaldazine. J Chem Phys. 1963;38:1536–1540.
  • Carr EF. Influence of electric fields on the molecular alignment in the liquid crystal p-(ansalamino)-phenyl acetate. Mol Cryst Liq Cryst. 1969;7:253–268.
  • Helfrich W. Conduction-induced alignment of nematic liquid crystals: basic model and stability considerations. J Chem Phys. 1969;51:4092–4105.
  • Pomeau Y, Manneville P. Intermittent transition to turbulence in dissipative dynamical systems. Comm Math Phys. 1980;74:189–197.
  • Oswald P, Dequidt A. Lehmann effect in chiral liquid crystals and langmuir monolayers: an experimental survey. Liq Cryst. 2009;36(10-11):1071–1084.
  • Backer AS, Callan-Jones AC, Pelcovits RA. Nematic cells with defect-patterned alignment layers. Phys Rev E. 2008;77(2):021701.
  • Afghah S, Selinger RLB, Selinger JV. Visualising the crossover between 3D and 2D topological defects in nematic liquid crystals. Liq Cryst. 2018;45(13-15):2022–2032.
  • Duzgun A, Selinger J, Saxena A. Comparing skyrmions and merons in chiral liquid crystals and magnets. Phys Rev E. 2018;97:062706.
  • Ambrožič M, Gudimalla A, Rosenblatt C, et al. Multiple twisted chiral nematic structures in cylindrical confinement. Crystals. 2020;10:576–591.
  • Fukuda J, Žumer S. Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal. Nat Commun. 2011;2:246–251.
  • Nych A, Fukuda J, Ognysta U, et al. Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film. Nat Phys. 2017;13:1215–1220.
  • Vitelli V, Turner AM. Anomalous coupling between topological defects and curvature. Phys Rev Lett. 2004;93:215301.
  • Bowick M, Nelson DR, Travesset A. Curvature-induced defect unbinding in toroidal geometries. Phys Rev E. 2004;69:041102.
  • Selinger RLB, Konya A, Travesset A, et al. Monte Carlo studies of the XY model on two-dimensional curved surfaces. J Phys Chem B. 2011;115:13989–13993.
  • Mesarec L, Góźdź W, Iglič A, et al. Effective topological charge cancelation mechanism. Sci Rep. 2016;6:1–12.
  • Mesarec L, Góźdź W, Iglič A, et al. Normal red blood cells’ shape stabilized by membrane’s in-plane ordering. Sci Rep. 2019;9:1–11.
  • Etchegoin P. Blue phases of cholesteric liquid crystals as thermotropic photonic crystals. Phys Rev E. 2000;62:1435–1437.
  • Cao W, Muñoz A, Palffy-Muhoray P, et al. Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II. Nat Mat. 2002;1:111–113.
  • Yoshida H, Tanaka Y, Kawamoto K, et al. Nanoparticle-stabilized cholesteric blue phases. Appl. Phys. Express. 2009;2:121501.
  • Cordoyiannis G, Losada-Pérez P, Tripathi CSP, et al. Blue phase III widening in CE6-dispersed surface-functionalized CdSe nanoparticles. Liq Cryst. 2010;11:1419–1426.
  • Dierking I, Blenkhorn W, Credland E, et al. Stabilising liquid crystalline blue phases. Soft Matter. 2012;8:4355–4362.
  • Rožič B, Tzitzios V, Karatairi E, et al. Theoretical and experimental study of the nanoparticle-driven blue phase stabilization. Eur Phys J E. 2011;3:17–28.
  • Cordoyiannis G, Lavrič M, Trček M, et al. Quantum Dot-driven Stabilization of liquid-crystalline blue phases. Front Phys. 2020;8:315–323.
  • Cordoyiannis G, Jampani VSR, Kralj S, et al. Different modulated structures of topological defects stabilized by adaptive targeting nanoparticles. Soft Matter. 2013;9:3956–3964.
  • Lavrič M, Tzitzios V, Kralj S, et al. The effect of graphene on liquid-crystalline blue phases. Appl Phys Lett. 2013;103:143116.
  • Lavrič M, Cordoyiannis G, Kralj S, et al. Effect of anisotropic MoS2 nanoparticles on the blue phase range of a chiral liquid crystal. Appl Opt. 2013;52:E47–E53.
  • Lavrič M, Tzitzios V, Cordoyiannis G, et al. Blue phase range widening induced by laponite nanoplatelets in the chiral liquid crystal CE8. Mol Cryst Liq Cryst. 2015;615:14–18.
  • Lavrič M, Cordoyiannis G, Tzitzios V, et al. Blue phase stabilization by CoPt-decorated reduced-graphene oxide nanosheets dispersed in a chiral liquid crystal. J Appl Phys. 2020;127:095101-1–095101-7.
  • Cordoyiannis G, Lavrič M, Tzitzios V, et al. Experimental advances in nanoparticle-driven stabilization of liquid-crystalline blue phases and twist-grain boundary phases. Nanomater. 2021;11:2968.
  • Čopar S, Ravnik M, Žumer S. Introduction to colloidal and microfluidic nematic microstructures. Crystals. 2021;11:956. https://doi.org/10.3390/cryst11080956.
  • Pasini P, Chiccoli C, Zannoni C. Liquid crystal lattice models II. confned systems. In: Pasini P, Zannoni C, editor. Advances in the computer simulations of liquid crystals. Dordrecth: Kluwer; 2000. p. 121–138.
  • Chiccoli C, Pasini P, Zannoni C, et al. From point to filament defects in hybrid nematic films. Sci Rep. 2019;9:17941. https://doi.org/10.1038/s41598-019-50948-w.
  • Svetec M, Kralj S, Bradač Z, et al. Annihilation of nematic point defects: pre-collision and post-collision evolution. Eur Phys J E. 2006;19:71–79.
  • Lubensky TC, Renn SR. Twist-grain-boundary phases near the nematic–smectic-A–smectic-C point in liquid crystals. Phys Rev A. 1990;41:4392.
  • Navailles L, Barois P, Nguyen HT. X-ray measurement of the twist grain boundary angle in the liquid crystal analog of the Abrikosov phase. Phys Rev Lett. 1993;71:545.
  • Renn SR, Lubensky TC. Existence of a Sm-C grain boundary phase at the chiral MAC point. Mol Cryst Liq Cryst. 1991;209:349–355.
  • Coursault D, Ibrahim BH, Pelliser L, et al. Modeling the optical properties of self-organized arrays of liquid crystal defects. Opt n.a. 2014;22:23182–23191.
  • Xia Y, Cedillo-Servin G, Kamien RD, et al. Guided folding of nematic liquid crystal elastomer sheets into 3D via patterned 1D microchannels. Adv Mater. 2016;28:9637–9643.
  • Senyuk B, Liu Q, He S, et al. Topological colloids. Nature. 2013;493:200–205.
  • Nelson DR. Toward a tetravalent chemistry of colloids. Nano Lett. 2002;2:1125–1129.
  • Vitelli V, Nelson DR. Nematic textures in spherical shells. Phys Rev E. 2006;74(2):021711.
  • Skačej G, Zannoni C. Controlling surface defect valence in colloids. Phys Rev Lett. 2008;100(19):197802.
  • Lopez-Leon T, Koning V, Devaiah KBS, et al. Frustrated nematic order in spherical geometries. Nat Phys. 2011;7(5):391–394.
  • Mesarec L, Iglič A, Kralj-Iglič V, et al. Curvature potential unveiled topological defect attractors. Cryst. 2021;11:539. https://doi.org/10.3390/cryst11050539.
  • Turner AM, Vitelli V, Nelson DR. Vortices on curved surfaces. Rev Mod Phys. 2010;82:1301–1348.
  • Rosso R, Virga EG, Kralj S. Parallel transport and 57defects on nematic shells. Continuum Mech Thermodyn. 2012;24:643–664.
  • Jesenek D, Kralj S, Rosso R, et al. Defect unbinding on a toroidal nematic shell. Soft Matter. 2015;11:2434–2444.
  • Song YM, Xie YZ, Malyarchuk V, et al. Digital cameras with designs inspired by the arthropod eye. Nature. 2013;497:95–99.
  • Chen L, Li Y, Fan J, et al. Photoresponsive monodisperse cholesteric liquid crystalline microshells for tunable omnidirectional lasing enabled by a visible light-driven chiral Molecular switch. Adv Optical Mater. 2014;2:845–848.
  • Liu D, Broer DJ. Self-assembled dynamic 3D fingerprints in liquid-crystal coatings towards controllable friction and adhesion. Angew Chem Int Ed. 2014;53:4542–4546.
  • Ge D, Lee E, Yang L, et al. A robust smart window: reversibly switching from high transparency to angle-independent structural color display. Adv Mater. 2015;27:2489–2495.
  • Jager EWH, Smela E, Inganas O. Microfabricating conjugated polymer actuators. Science. 2000;290:1540–1545.
  • Haan de LT, Schenning APHJ, Broer DJ. Programmed morphing of liquid crystal networks. Polym. 2014;55:5885–5896.
  • Keplinger C, Sun Y-E, Foo CC, et al. Stretchable, transparent, ionic conductors. Science. 2013;341:984–987.
  • Kim DH, Lu NS, Ma R, et al. Epidermal electronics. Science. 2011;333:838–843.
  • Xu S, Zhang YH, Cho J, et al. Stretchable batteries with self-similar serpentine interconnects and integrated wireless recharging systems. Nat Commun. 2013;4:1543–1551. https://doi.org/10.1038/ncomms2553.
  • Yin R, Xu W, Kondo M, et al. Can sunlight drive the photoinduced bending of polymer films? J Mater Chem. 2009;19:3141–3143.
  • Wilczek F. Majorana returns. Nat Phys. 2009;5:614–618.
  • Hobson A. There are no particles, there are only fields. Am J Phys. 2013;81:211–223.
  • Skyrme THR. A unified field theory of mesons and baryons. Nucl Phys. 1962;31:556–569.
  • Smalyukh II. Review: knots and other new topological effects in liquid crystals and colloids. Rep Prog Phys. 2020;83:106601.

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