141
Views
3
CrossRef citations to date
0
Altmetric
Mathematical Modelling, Symmetry and Topology

Spiralling defect cores in chromonic hedgehogs

ORCID Icon & ORCID Icon
Pages 1498-1516 | Received 19 Jan 2023, Published online: 10 Apr 2023

References

  • Lydon J. Chromonic liquid crystal phases. Curr Opin Colloid Interface Sci. 1998;3(5):458–466.
  • Lydon J. Chromonics. In: Demus D, Goodby J, Gray GW, Spiess H-W, Vill V, editors. Handbook of liquid crystals: low molecular weight liquid crystals II. Chapter XVIII. Weinheim, Germany: John Wiley & Sons; 1998. p. 981–1007.
  • Lydon J. Chromonic review. J Mater Chem. 2010;20:10071–10099.
  • Lydon J. Chromonic liquid crystalline phases. Liq Cryst. 2011;38(11–12):1663–1681.
  • Dierking I, Martins Figueiredo Neto A. Novel trends in lyotropic liquid crystals. Crystals. 2020;10(7):604.
  • Nayani K, Chang R, Fu J, et al. Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders. Nat Commun. 2015 8;6:8067.
  • Davidson ZS, Kang L, Jeong J, et al. Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity. Phys Rev E. 2015;91:050501(R). See also Erratum [47] and Supplementary Information. https://journals.aps.org/pre/supplemental/10.1103/PhysRevE.91.050501/Supplementary_Info_Planar_Davidson_et_al.pdf
  • Fu J, Nayani K, Park J, et al. Spontaneous emergence of twist and formation of monodomain in lyotropic chromonic liquid crystals confined to capillaries. Npg Asia Mater. 2017;9:e393.
  • Javadi A, Eun J, Jeong J. Cylindrical nematic liquid crystal shell: effect of saddle-splay elasticity. Soft Matter. 2018;14:9005–9011.
  • Ericksen JL. Inequalities in liquid crystal theory. Phys Fluids. 1966;9(6):1205–1207.
  • Paparini S, Virga EG. Stability against the odds: the case of chromonic liquid crystals. J Nonlinear Sci. 2022;32:74.
  • Long C, Selinger JV. Violation of Ericksen inequalities in lyotropic chromonic liquid crystals. J Elast. 2022. DOI:10.1007/s10659-022-09899-z
  • Paparini S, Virga EG. Paradoxes for chromonic liquid crystal droplets. Phys Rev E. 2022;106:044703.
  • Tortora L, Park HS, Kang SW, et al. Self-assembly, condensation, and order in aqueous lyotropic chromonic liquid crystals crowded with additives. Soft Matter. 2010;6:4157–4167.
  • Tortora L, Lavrentovich OD. Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals. Proc Natl Acad Sci, USA. 2011;108(13):5163–5168.
  • Peng C, Lavrentovich OD. Chirality amplification and detection by tactoids of lyotropic chromonic liquid crystals. Soft Matter. 2015;11:7221–7446.
  • Nayani K, Fu J, Chang R, et al. Using chiral tactoids as optical probes to study the aggregation behavior of chromonics. Proc Natl Acad Sci, USA. 2017;114(15):3826–3831.
  • Shadpour S, Vanegas JP, Nemati A, et al. Amplification of chirality by adenosine monophosphate-capped luminescent gold nanoclusters in nematic lyotropic chromonic liquid crystal tactoids. ACS Omega. 2019;4:1662–1668.
  • Paparini S, Virga EG. An elastic quartic twist theory for chromonic liquid crystals. J Elast. 2023. DOI:10.1007/s10659-022-09983-4
  • Nehring J, Saupe A. On the elastic theory of uniaxial liquid crystals. J Chem Phys. 1971;54(1):337–343.
  • Oldano C, Barbero G. An ab initio analysis of the second-order elasticity effect on nematic configurations. Phys Lett A. 1985;110(4):213–216.
  • Dozov I. On the spontaneous symmetry breaking in the mesophases of achiral banana-shaped molecules. Europhys Lett. 2001;56(2):247.
  • Meyer RB. Structural problems in liquid crystal physics. In: Balian R Weill G, editors. Molecular fluids. (Les houches summer school in theoretical physics; Vol. XXV-1973). New York: Gordon and Breach; 1976. p. 273–373.
  • Cestari M, Diez-Berart S, Dunmur DA, et al. Phase behavior and properties of the liquid-crystal dimer 1’‘,7’’-bis(4-cyanobiphenyl-4’-yl) heptane: a twist-bend nematic liquid crystal. Phys Rev E. 2011;84:031704.
  • Lelidis I, Barbero G. Nematic phases with spontaneous splay–bend deformation: standard elastic description. Liq Cryst. 2016;43(2):208–215.
  • Barbero G, Lelidis I. Fourth-order nematic elasticity and modulated nematic phases: a poor man’s approach. Liq Cryst. 2019;46(4):535–542.
  • Lelidis I, Barbero G. Nonlinear nematic elasticity. J Mol Liq. 2019;275:116–121.
  • Spina L, De Santo MP, Tone CM, et al. Intercalation or external binding: how to torque chromonic sunset yellow. J Mol Liq. 2022;359:119265.
  • Lavrentovich OD, Terent’ev EM. Phase transition altering the symmetry of topological point defects (hedgehogs) in a nematic liquid crystal. Sov Phys JEPT. 1986;64:1237–1244. Russian original: Zh. Eksp. Teor. Fiz. 91, 2084–2086 (December 1986).
  • Ball JM, Virga EG. A brief hedgehog review. Unpublished. 2023.
  • Oseen CW. The theory of liquid crystals. Trans Faraday Soc. 1933;29(4):883–899.
  • Frank FC. On the theory of liquid crystals. Discuss Faraday Soc. 1958;25:19–28.
  • Virga EG. Variational theories for liquid crystals. (Applied mathematics and mathematical computation; Vol. 8). London: Chapman & Hall; 1994.
  • Selinger JV. Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals. Liq Cryst Rev. 2018;6:129–142.
  • Machon T, Alexander GP. Umbilic lines in orientational order. Phys Rev X. 2016 Mar;6:011033.
  • Virga EG. Uniform distortions and generalized elasticity of liquid crystals. Phys Rev E. 2019;100:052701.
  • Kléman M, Lavrentovich OD. Topological point defects in nematic liquid crystals. Philos Mag. 2006;86(25–26):4117–4137.
  • Kléman M. Defect densities in directional media, mainly liquid crystals. Philos Mag. 1972;27(5):1057–1072.
  • Mermin ND. The topological theory of defects in ordered media. Rev Mod Phys. 1979 Jul;51:591–648.
  • Sonnet AM, Virga EG. Reorientational dynamics of conjugated nematic point defects. Liq Cryst. 2010;37:785–797.
  • Ericksen JL. General solutions in the hydrostatic theory of liquid crystals. Trans Soc Rheol. 1967;11(1):5–14.
  • Cohen R, Taylor M. Weak stability of the map x/|x| for liquid crystal functionals. Comm PDE. 1990;15(5):675–692.
  • Kinderlehrer D, Ou B. Second variation of liquid crystal energy at x/|x|. Proc R Soc Lond A. 1992;437(1900):475–487.
  • Kinderlehrer D. Recent developments in liquid crystal theory. (IMA preprint series; Vol. 493). Minneapolis (MN): Institute for Mathematics and its Applications; 1989.
  • Zhou S, Nastishin YA, Omelchenko MM, et al. Elasticity of lyotropic chromonic liquid crystals probed by director reorientation in a magnetic field. Phys Rev Lett. 2012;109:037801.
  • Revignas D, Ferrarini A. Spontaneous twisting of achiral hard rod nematics. Phys Rev Lett. 2023;130:028102.
  • Davidson ZS, Kang L, Jeong J, et al. Erratum: chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity [Phys. Rev. E 91, 050501(R) (2015)]. Phys Rev E. 2015;92(1):019905.
  • Ince IL. Ordinary differential equations. New York: Dover Publications; 1956.
  • Sastry S. Nonlinear systems: analysis, stability, and control. (Interdisciplinary applied mathematics; Vol. 10). New York: Springer-Verlag; 1999.
  • Markus L. Asymptotically autonomous differential systems. In: Lefschetz S, editor. Contributions to the theory of nonlinear oscillations III. (Annals of Mathematics Studies, Vol. 23). Princeton: Princeton University Press; 1956. p. 17–29.
  • Thieme HR. Convergence results and a poincaré-bendixson trichotomy for asymptotically autonomous differential equations. J Math Bio. 1992;30:755–763.
  • Thieme HR. Asymptotically autonomous differential equations in the plane. Rocky Mountain J Math. 1994;24(1):351–380.
  • Longa L, Monselesan D, Trebin HR. An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals. Liq Cryst. 1987;2(6):769–796.
  • Golovaty D, Novack M, Stenberg P. A novel landau-de gennes model with quartic elastic terms. Eur J Appl Math. 2021;32(1):177–198.
  • Zocher H. The effect of a magnetic field on the nematic state. Trans Faraday Soc. 1933;29:945–957.
  • Selinger JV. Director deformations, geometric frustration, and modulated phases in liquid crystals. Ann Rev Condens Matter Phys. 2022;13:49–71. First posted online on October 12, 2021. Volume publication date, March 2022. DOI:10.1146/annurev-conmatphys-031620-105712.
  • Pedrini A, Virga EG. Liquid crystal distortions revealed by an octupolar tensor. Phys Rev E. 2020 Jan;101:012703.
  • Long C, Selinger JV. Explicit demonstration of geometric frustration in chiral liquid crystals. Soft Matter. 2023;19:519–529.
  • Zhou S. Lyotropic chromonic liquid crystals. Cham, Switzerland: Springer; 2017.
  • Stanley CB, Hong H, Strey HH. DNA cholesteric pitch as a function of density and ionic strength. Biophys J. 2005;89(4):2552–2557.
  • Tortora MMC, Mishra G, Prešern D, et al. Chiral shape fluctuations and the origin of chirality in cholesteric phases of DNA origamis. Sci Adv. 2020;6(31):5163–5168.
  • Harris AB, Kamien RD, Lubensky TC. Microscopic origin of cholesteric pitch. Phys Rev Lett. 1997;78:1476–1479.
  • Harris AB, Kamien RD, Lubensky TC. Molecular chirality and chiral parameters. Rev Mod Phys. 1999;71:1745–1757.
  • Kornyshev A, Leikin S, Malinin S. Chiral electrostatic interaction and cholesteric liquid crystals of DNA. Eur Phys J E. 2002;7:83–93.
  • Grelet E, Fraden S. What is the origin of chirality in the cholesteric phase of virus suspensions? Phys Rev Lett. 2003;90:198302.
  • Gurtin ME, Fried E, Anand L. The mechanics and thermodynamics of contiuna. Cambridge: Cambridge University Press; 2010.
  • Rudinger A, Stark H. Twist transition in nematic droplets: a stability analysis. Liq Cryst. 1999;26(5):753–758.
  • Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. 2nd ed. ( Texts in Applied Mathematics, Vol. 2). New York: Springer-Verlag; 2003.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.