Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders

The presumed ground state of a nematic fluid confined in a cylindrical geometry with planar anchoring corresponds to that of an axial configuration, wherein the director, free of deformations, is along the long axis of the cylinder. However, upon confinement of lyotropic chromonic liquid crystals in cylindrical geometries, here we uncover a surprising ground state corresponding to a doubly twisted director configuration. The stability of this ground state, which involves significant director deformations, can be rationalized by the saddle-splay contribution to the free energy. We show that sufficient anisotropy in the elastic constants drives the transition from a deformation-free ground state to a doubly twisted structure, and results in spontaneous symmetry breaking with equal probability for either handedness. Enabled by the twist angle measurements of the spontaneous twist, we determine the saddle-splay elastic constant for chromonic liquid crystals for the first time.

[1]  Oleg D. Lavrentovich,et al.  Soft Matter Physics: An Introduction , 2002 .

[2]  A. Arrott,et al.  Theory and Experiments on Configurations with Cylindrical Symmetry in Liquid-Crystal Droplets , 1974 .

[3]  Ingo Dierking,et al.  Chiral Liquid Crystals: Structures, Phases, Effects , 2014, Symmetry.

[4]  Charles Mauguin,et al.  Sur les cristaux liquides de M. Lehmann , 2022 .

[5]  Tom C. Lubensky,et al.  Chiral structures from achiral liquid crystals in cylindrical capillaries , 2015, Proceedings of the National Academy of Sciences.

[6]  Takahiro Yamamoto,et al.  A liquid crystalline chirality balance for vapours , 2014, Nature Communications.

[7]  Paul Drzaic,et al.  Liquid Crystal Dispersions , 1995 .

[8]  F. C. Frank,et al.  I. Liquid crystals. On the theory of liquid crystals , 1958 .

[9]  Jagdish K. Vij,et al.  Advances in liquid crystals , 2000 .

[10]  P. Yeh.  Optics of Liquid Crystal Displays , 2007, 2007 Conference on Lasers and Electro-Optics - Pacific Rim.

[11]  G. Berry,et al.  Frank Elastic Constants and Leslie-Ericksen Viscosity Coefficients of Nematic Solutions of a Rodlike Polymer , 1987 .

[12]  A. Fernández-Nieves,et al.  Stable nematic droplets with handles , 2012, Proceedings of the National Academy of Sciences.

[13]  Slobodan Žumer,et al.  Microscope textures of nematic droplets in polymer dispersed liquid crystals , 1991 .

[14]  D. Kondepudi,et al.  Chiral Symmetry Breaking in Sodium Chlorate Crystallizaton , 1990, Science.

[15]  O. Lavrentovich,et al.  Self-assembly of lyotropic chromonic liquid crystal Sunset Yellow and effects of ionic additives. , 2008, The journal of physical chemistry. B.

[16]  O. Lavrentovich,et al.  Parity-breaking phase transition in tangentially anchored nematic drops , 1990 .

[17]  D. J. Carter,et al.  Structural Correspondence of Solution, Liquid Crystal, and Crystalline Phases of the Chromonic Mesogen Sunset Yellow , 2014 .

[18]  Clark,et al.  Spontaneous formation of macroscopic chiral domains in a fluid smectic phase of achiral molecules , 1997, Science.

[19]  Doane,et al.  Surface elastic and molecular-anchoring properties of nematic liquid crystals confined to cylindrical cavities. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[20]  Petra Koenig.  Waves And Grains Reflections On Light And Learning , 2016 .

[21]  J. Hough,et al.  Circular polarization in star-formation regions: implications for biomolecular homochirality. , 1998, Science.

[22]  D. Dupré,et al.  Temperature, concentration, and molecular weight dependence of the twist elastic constant of cholesteric poly‐γ‐benzyl‐L‐glutamate , 1975 .

[23]  P. van der Schoot,et al.  Parity breaking in nematic tactoids , 2004, cond-mat/0411015.

[24]  P. Drzaic.  A case of mistaken identity: spontaneous formation of twisted bipolar droplets from achiral nematic materials , 1999 .

[25]  O. Lavrentovich,et al.  Elasticity of lyotropic chromonic liquid crystals probed by director reorientation in a magnetic field. , 2012, Physical review letters.

[26]  J. Lydon.  Chromonic mesophases : Lyotropic liquid crystals , 2003 .

[27]  Friedrich Reinitzer,et al.  Beiträge zur Kenntniss des Cholesterins , 1888 .

[28]  Žumer,et al.  Chiral nematic liquid crystals in cylindrical cavities. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  T. Lubensky,et al.  Chiral symmetry breaking and surface faceting in chromonic liquid crystal droplets with giant elastic anisotropy , 2014, Proceedings of the National Academy of Sciences.

[30]  O. Lavrentovich,et al.  Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals , 2011, Proceedings of the National Academy of Sciences.

[31]  Meyer,et al.  Crossover behavior of the elastic coefficients and viscosities of a polymer nematic liquid crystal. , 1988, Physical Review Letters.

[32]  Liu,et al.  Effect of chirality on liquid crystals in capillary tubes with parallel and perpendicular anchoring. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  Symmetry breaking: an epistemological note , 2004 .

[34]  Pierce,et al.  Influence of the surface on magnetic domain-wall microstructure. , 1989, Physical review letters.

[35]  R. Kamien,et al.  Saddle-splay screening and chiral symmetry breaking in toroidal nematics. , 2013, Soft matter.

[36]  T. Lubensky,et al.  Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  A. Arrott,et al.  ELASTIC ENERGIES AND DIRECTOR FIELDS IN LIQUID CRYSTAL DROPLETS, I. CYLINDRICAL SYMMETRY , 1975 .

[38]  O. Lavrentovich,et al.  PATTERNS IN THIN LIQUID CRYSTAL FILMS AND THE DIVERGENCE ("SURFACELIKE") ELASTICITY , 1995 .

[39]  Kralj,et al.  Saddle-splay elasticity of nematic structures confined to a cylindrical capillary. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[40]  Roy Williams,et al.  Two transitions in tangentially anchored nematic droplets , 1986 .

[41]  Meyer,et al.  New ground state for the Splay-Fréedericksz transition in a polymer nematic liquid crystal. , 1985, Physical review letters.