Liquid crystal nematic configurations on thin films
Samo Kralj1,2, Riccardo Rosso3, Epifanio G. Virga3, and Dalija Jesenek2
1 Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
2 Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
3 Department of Mathematics, University of Pavia, via Ferrata 1, I-27100 Pavia, Italy
We shall be concerned with the influence of surface geometry on orientational ordering in liquid
crystal thin films. We will focus on universal mechanisms, such as merging and splitting of topological defects,
reshaping of defect cores, positioning of defects and defect induced global system transformations. All phenomena
are analyzed in the frame of 2D or 3D Landau-de Gennes theory in terms of a tensorial order parameter. For the cases
studied we discuss future research trends and possible applications.
We first consider possible defect structures and merging of defects in thin nematic shells of various geometries
using a 2D approach , which has been recently developed by the Pavia group. It is well known  that the equilibrium
texture of a spherical film exhibits four defects of winding number 1/2 sitting at the vertices of a regular tetrahedron
to maximize their mutual distance. By varying the film geometry, the position of the defects and their structure could be
altered. Among others things, we show that for sufficiently prolate ellipsoidal shells the four defects merge pairwise at the
poles leaving only two +1 defects.
We next consider external field induced transformations of defect cores, positioning of defects, and defect induced
or suppressed surface transitions in 3D. For this purpose we consider a hybrid cylindrical cell where we topologically
stabilize a boojum in the center of the upper confining plate . If an external electric field is applied, the boojum
could be either stretched towards the cell interior or expelled from the cell, depending on the sign of the field
anisotropy constant. The stretching of the boojum is also accompanied by a substantial widening of the defect core.
Depending on conditions, the presence of the boojum could either substantially increase or depress an external field
driven surface biaxial transition.
Finally we consider temperature driven surface wetting and dewetting transitions in a thin film. We show that for
appropriate conditions the temperature difference between the surface and bulk phase transition could be anomalously
increased with respect to already reported related phenomena.
 S. Kralj, R. Rosso, and E. G. Virga, Curvature control of valence on nematic shells, submitted to Soft Matter.
 V Vitelli and D. R. Nelson, Nematic textures in spherical shells, Phys. Rev. E 74, 021711 (2006).
 S. Kralj, R. Rosso, and E. G. Virga, Finite-size effects on order reconstruction around nematic defects, Phys. Rev. E 81, 021702 (2010).