Experimental study of coarsening dynamics of the zigzag wall in a nematic liquid crystal with negative dielectric anisotropy.

When a homeotropically aligned nematic liquid crystal cell is placed above two permanent magnets forming a magnetic quadrupole, a straight splay-bend wall, or a so-called Ising wall, is formed. With a material of positive dielectric anisotropy, it has been shown that the application of an electric field perpendicular to the plates leads to a zigzag instability of the wall, exclusively related to the elastic anisotropy of the liquid crystal. In this case, the coarsening process of the zigzag is very slow, which in turn leads to experimental difficulties concerning its quantitative investigation. If a material of negative dielectric anisotropy is used under an electric field with low voltage and low frequency, two convective rolls appear along the Ising wall due to the charge focusing effect, which is also responsible, at a higher voltage in the homogenous tilted regions, for the appearance of Williams domains electrohydrodynamic instability. If the voltage is higher than a threshold value, the straight Ising wall spontaneously breaks into a zigzag shape and a fast coarsening of the zigzag proceeds, associated with the annihilation of two neighboring vertices. In the present paper, the coarsening dynamics of this system, which can be considered as a one-dimensional Ising situation, are investigated experimentally. At late times, the average width of the zigzag increases logarithmically with time. This finding is consistent with the theory and also with the numerical simulation of a one-dimensional Cahn-Hilliard situation having a conserved order parameter. The scaling analysis of size distribution of the Ising domain, the shape of the power spectrum, and of the correlation function of the Ising order parameter, as well as the number density correlation functions of kinks also confirms that the dynamical scaling law predicted for one-dimensional conservative systems holds for the coarsening process. As supposed from symmetry arguments, it is confirmed that this experiment constitutes a one-dimensional analog of spinodal decomposition.