Analysis of nonlocal electrostatic effects in chiral smectic C liquid crystals

SIAM Journal on Applied Mathematics

Volumn 66, Issue 6, 2006, Pages 2107-2126

  Park, Jinhae ^a   Calderer, M Carme ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Chiral; Electrostatic self interaction; Energy minimizer; Ferroelectricity; Helical filaments; Liquid crystals; Nonlocal effects; Smectic C phase; Smectic layers; Vortex tubes

Indexed keywords

ELECTROSTATIC SELF-INTERACTION; ENERGY MINIMIZER; HELICAL FILAMENTS; NONLOCAL EFFECTS; SMECTIC C PHASE; SMECTIC LAYERS; VORTEX TUBES;

ELECTROSTATICS; FERROELECTRICITY; POLARIZATION;

SMECTIC LIQUID CRYSTALS;

EID: 33845545452     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050641120     Document Type: Article

References (40)

1. P. BAUMAN, M. C. CALDERER, C. LIU, AND D. PHILLIPS, The phase transition between chiral and smectic A* liquid crystals, Arch. Ration. Mech. Anal., 165 (2002), pp. 161-186.
2. P. BISCARI AND M. C. CALDERER, Telephone-cord instabilities in thin smectic capillaries, Phys. Rev. E, 71 (2005), paper 051701.
3. J. CHEN AND T. C. LUBENSKY, Landau-Ginzburg mean-field theory for the nematic to smectic C and nematic to smectic A liquid crystal transitions, Phys. Rev. A, 14 (1976), pp. 1202-1297.
4. N. A. CLARK AND S. T. LAGERWALL, Submicrosecond bistable electro-optic switching in liquid crystals, Appl. Phys. Lett., 36 (1980), pp. 899-901.
5. D. A. COLEMAN, J. FERNSLER, N. CHATTHAM, M. NAKATA, Y. TAKANISHI, E. KÖBLOVA, D. R. LINK, R. F. SHAO, W. G. JANG, J. E. MACLENNAN, O. MONDAINN-MONVAL, C. BOYER, W. WEISSFLOG, G. PETZEL, L. C. CHIEN, J. ZASADZINSKI, J. WATANABE, D. M. WALBA, H. TAKEZOE, AND N. A. CLARK, Polarization-modulated liquid crystal phases, Science, 301 (2003), pp. 1204-1211.
6. P. J. COLLINGS AND J. S. PATEL, EDS., Handbook of Liquid Crystal Research, Oxford University Press, New York, 1997.
7. P. G. DE GENNES AND J. PROST, The Physics of Liquid Crystals, Clarendon Press, Oxford, UK, 1993.
8. Z. DOGIC AND S. FRADEN, Development of model colloidal liquid isotropic-smectic transition, Philos. Trans. Roy. Soc. London Ser. A, 359 (2001), pp. 997-1015.
9. F. C. FRANK, On the theory of liquid crystals, Discuss. Faraday Soc., 25 (1958), pp. 19-28.
10. M. GLOGAROVA, J. FOUSEK, L. LEJCEK, AND J. PAVEL, The structure of ferroelectric liquid crystals in planar and its response to electric fields, Ferroelectrics, 58 (1984), pp. 161-178.
11. M. GLOGAROVA, L. LEJCEK, AND J. PAVEL, The influence of an external electric field on the structure of chiral Sm C* liquid crystals, Mol. Cryst. Liq. Cryst., 91 (1983), pp. 309-325.
12. M. GLOGAROVA AND J. PAVEL, The structure of chiral Sm C* liquid crystals in planar samples and its change in an electric field, J. Physique, 45 (1984), pp. 143-149.
13. J. W. GOODY, R. BLINC, N. A. CLARK, S. T. LAGERWALL, M. A. OSIPOV, S. A. PIKIN, T. SAKURAI, K. YOSHINO, AND B. ZEKS, Ferroelectric Liquid Crystals, Principles, Properties and Applications, Gordon and Breach, New York, 1991.
14. M. A. HANDSCHY AND N. A. CLARK, Structures and responses of ferroelectric liquid crystals in the surface-stabilized geometry, Ferroelectrics, 59 (1984), pp. 69-116.
15. R. HARDT, D. KINDERLEHRER, AND F. H. LIN, Existence and partial regularity of static liquid crystal configurations, Comm. Math. Phys., 105 (1986), pp. 547-570.
16. A. JÁKLI, CH. LISCHKA, W. WEISSFLOG, G. PELZL, AND A. SAUPE, Helical filamentary growth in liquid crystals consisting of banana-shaped molecules, Liq. Cryst., 27 (2000), pp. 1405-1409.
17. A. JÁKLI, D. KRÜERKE, AND G. G. NAIR, Liquid crystal fibers of bent-core molecules, Phys. Rev. E, 67 (2003), paper 051702.
18. S. JOO AND D. PHILLIPS, The phase transitions between chiral nematic, smectic A*, and C* liquid crystals, Comm. Math, Phys., to appear.
19. A. G. KHACHATURYAN, Development of helical cholesteric structure in a nematic liquid crystal due to the dipole-dipole interaction, J. Phys. Chem. Solids, 36 (1975), pp. 1055-1061.
20. X. Y. KONG AND Z. L. WANG, Polar-surface dominated ZnO nanobelts and the electrostatic energy induced nanohelixes, nanosprings, and nanospirals, Appl. Phys. Lett., 84 (2004), pp. 975-977.
21. S. T. LAGERWALL, Ferroelectric and Antiferroelectric Liquid Crystals, Wiley-VCH, New York, 1999.
22. L. D. LANDAU, E. M. LIFSHITZ, AND L. P. PITAEVSKII, Electrodynamics of Continuous Media, Butterworth-Heinemann, Oxford, UK, 1998.
23. L. LONGA, D. MONSELESAN, AND H. R. TREBIN, An extension of the Landau-Ginzburgde Gennes theory for liquid crystals, Liq. Cryst., 2 (1987), pp. 769-796.
24. I. LUKYANCHUK, Phase transition between the cholesteric and twist grain boundary C phases, Phys. Rev. E, 57 (1998), pp. 574-581.
25. R. B. MEYER, L. LIEBERT, L. STRZELECKI, AND P. KELLER, Ferroelectric liquid crystals, J. Physique Lettres, 36 (1975), pp. L69-L71.
26. I. MUŠEVIČ, R. BLINC, AND B. ŽEKŠ, The Physics of Ferroelectric and Antiferroelectric Liquid Crystals, World-Scientific, Singapore, NJ, London, Hong Kong, 2000.
27. J. PARK AND M. C. CALDERER, Variational problems and modeling of ferroelectricity in chiral smectic liquid crystals, in Modeling of Soft Matter, IMA Vol. Math. Appl. 141, Springer, New York, 2005, pp. 169-188.
28. J. PARK AND M. C. CALDERER, Phase Transitions between Ferroelectric and Antiferroelectric Liquid Crystal Phases: Static and Dynamical Problems, preprint, 2004.
29. J. PAVEL, M. GLOGAROVA, AND S. S. BAWA, Dielectric permittivity of ferroelectric liquid crystals influenced by a biasing electric field, Ferroelectrics, 76 (1987), pp. 221-232.
30. J. PAVEL AND M. GLOGAROVA, The effect of biasing electric field on relaxations in FLC investigated by the dielectric and optical methods, Ferroelectrics, 121 (1991), pp. 45-53.
31. J. PAVEL, Behavior of thin planar Sm C* samples in an electric field, J. Physique, 45 (1984), pp. 137-141.
32. S. A. PIKIN, Structural Transformations in Liquid Crystals, Gordon and Breach, New York, 1991.
33. H. R. BRAND, P. E. CLADIS, AND H. PLEINER, Fluid biaxial banana smectics: Symmetry at work, Liquid Crystal Today, 9 (1999), pp. 1-10.
34. H. R. BRAND, P. E. CLADIS, AND H. PLEINER, Symmetry and defects in CM phase of polymeric liquid crystals, Macromolecules, 25 (1992), pp. 7223-7226.
35. Y. SHU AND K. BHATTACHARYA, Domain patterns and macroscopic behavior of ferroelectric materials, Phil. Mag. B, 81 (2001), pp. 2021-2051.
36. R. A. SONES, R. PETSCHEK, D. W. CRONIN, AND E. M. TERENTJEV, Twisting transition in a fiber composed of chiral smectic-C liquid crystal polymer, Phys. Rev. E, 53 (1996), pp. 3611-3617.
37. I. STEWART, The Static and Dynamic Continuum Theory of Liquid Crystals, Taylor and Francis, London, New York, 2004.
38. J. V. STEWART, Intermediate Electromagnetic Theory, World Scientific, Singapore, NJ, London, Hong Kong, 2001.
39. T. P. RIEKER, N. A. CLARK, AND S. LAGERWALL, Chevron local layer structure in surface stabilized ferroelectric smectic-C cells, Phys. Rev. Lett., 59 (1987), pp. 2658-2672.
40. D. M. WALBA, Ferroelectric liquid crystal conglomerate, Materials-Chirality, 24 (2003), pp. 457-518.