STATIC AND DYNAMIC TEXTURES OBTAINED UNDER AN ELECTRIC-FIELD IN THE NEIGHBORHOOD OF THE WINDING TRANSITION OF A STRONGLY CONFINED CHOLESTERIC

In recent work, Oswald and collaborators describe the thermodynamical phase diagrams of a large pitch cholesteric, confined between glass plates with homeotropic alignment conditions, in the neighborhood of the critical confinement and in the presence of an AC electric field. In the case of a negative dielectric anisotropy, and with a low confinement ratio C, they have shown both experimentally and theoretically that the electrical destabilization possesses a second order character, as in the case of the nematic Freedericksz transition. It is consequently possible to describe and to simulate numerically the equilibrium (under an AC field) and dissipative, out of equilibrium (under a DC field) patterns obtained experimentally, by the use of a Ginzburg-Landau model, deduced from symmetry arguments. The order parameter used here is the projection of the director in the mid-plane of the sample. The spiral shaped textures obtained in the out of equilibrium case are probably among the first simple physical analogues to the chemical and biological phenomena observed in the area of excitable media.