Labyrinthine instability in polar free-standing liquid crystalline films

We report the first study of fingering and labyrinthine instabilities in freely suspended polar liquid-crystalline films. This phenomenon is in a way the electric analogy to the labyrinthine instability in thin films of magnetic fluids. Because of the existence of a permanent polarization in the smectic films, an external electric field is not required for the spontaneous formation of the instability. It forms upon temperature controlled transitions between mesophases with different polarizations in the films. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. In case of our materials, we assume, that the labyrinthine pattern is intrinsically related to regular splay deformations of the local polarization field, coupled to the local director.