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Samo Kralj 1,2 , Riccardo Rosso 3 , Epifanio G. Virga 3

LIQUID CRYSTAL NEMATIC CONFIGURATIONS ON THIN FILMS. Samo Kralj 1,2 , Riccardo Rosso 3 , Epifanio G. Virga 3 1 Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia 2 Jozef Stefan Institute, Ljubljana, Slovenia 3 Department of Mathematics, University of Pavia, Italy.

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Samo Kralj 1,2 , Riccardo Rosso 3 , Epifanio G. Virga 3

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  1. LIQUID CRYSTAL NEMATIC CONFIGURATIONS ON THIN FILMS Samo Kralj1,2, Riccardo Rosso3, Epifanio G. Virga3 1Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia 2Jozef Stefan Institute, Ljubljana, Slovenia 3Department of Mathematics, University of Pavia, Italy

  2. Liquid crystal phases : • Important role in several natural systems. • Main advantages: • softness (= susceptibility) • optical transparency + anisotropy • richness of phases & structures • Confinement : • surface local interactions • (affecting translational&orientational ordering) • symmetry breaking • finite size effects

  3. LIQUID CRZSTALS Focus • 1) complex behavior in thin nematic hybrid films • (frustrations + topological defects) • new boojum structure • interaction of boojum with elastic distortions • boojum dragging towards cell interior • defect core enhancement

  4. 2) thin nematic shells • new 2D Q-tensor mesoscopic approach • character of the I-N transition • defect structures on ellipsoidal shells

  5. I) THIN NEMATIC HYBRID FILMS • Complex behavior : • Boojum • Frustration • Finite size effects • External field

  6. Expected boojum structure ? • Well known HEDGEHOG • biaxial structure • includes order reconstruction Half of hedgehog ?

  7. Order reconstruction: h<hc h > hc h < hc

  8. Mesoscopic modelling F Uniaxial states : Degree of biaxiality :

  9. Cylindrical coordinate system, parametrization (cylindrical symmetry, no twist) Phys. Rev. E 78, 031701 (2008); 81, 021702 (2010).

  10. Adequate parametrization for visualization of biaxial states TrQ=0 Phys. Rev. E 81, 021702 (2010). states with positive uniaxiality states with negative uniaxiality states with maximal biaxiality

  11. I) RESULS A B ? C A C

  12. Half uniaxial hedgehog

  13. Half biaxial hedgehog

  14. Observed boojum structure

  15. “Finger” boojum structure, 2(r,z)

  16. Naively expected biaxial boojum structure

  17. Interaction boojum : order reconstruction structure in thin films

  18. A D B C

  19. boojum can lift the order reconstruction structure

  20. Boojum pushed to the top, the order reconstruction structure locally follows it

  21. S S=0

  22. Width of the elongated boojum ?

  23. Planar radial with a negative uniaxial core Phys.Rev.E 60, 1858 (1999). ER = escaped radial

  24. Phys.Rev.E 66, 021703 (2002).

  25. Dimensionless excess free energy : Phys.Rev.E 60, 1858 (1999). External field contribution Bulk nematic ordering: =-/3 = negative uniaxiality

  26. def

  27. II) THIN NEMATIC SHELLS eigenframe general frame ei : chosen along the lines of principal curvatures of the surface

  28. The surface gradients:

  29. Symmetry invariant terms entering the free energy density Condensation term Elastic term, K: Gaussian curvature

  30. Uniaxial ellipsoidal surfaces obtained by rotating the ellipse v : meridians u : parallels

  31. In agreement with : Director field representation semi-microscopic simulations

  32. Oblate surfaces (sphere : =1)

  33. Prolate surfaces (sphere : =1)

  34. Prolate surfaces (sphere : =1)

  35. Conclusions • Complex nematic structures in thin films • Rich variety of structures -> interplay among geometrical constraints, elastic forces and finite size effects • Of interest for future nanobased electrooptic devices

  36. Nelson, Nano. Lett. 2, 1125 (2002) Nematic shells immersed in a solution of an isotropic liquid and flexible linkers = SCALED ATOMA (defect sites > determine valence)

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