Ordering and finite-size effects in the dynamics of one-dimensional transient patterns

Arising of magnetic walls in the vicinities of the Frèedericksz transition

In this paper, the dynamical formation of twist-bend periodic walls at the neighborhoods of the Frèedericksz critical point of a nematic sample of liquid crystals is studied. The theory that describes the arising of these periodic structures affirms that the mode with the fastest initial growth will fix the observed properties of these patterns. But, just above the Frèedericksz threshold there is a region where this leading mode becomes null and, therefore, a homogeneous bending of the director may be detected. This prediction was not confirmed by the experiment, and walls with very well defined wavelength were found. We will show here that the fastest growing mode cannot be defined around the Frèedericksz threshold and, therefore, a new way to compute the observed periodicity must be formulated. We assume that the observed wall results from a sum of a continuum and nonsharp distribution of modes in which the null mode is at the center.

Comment on "Corresponding states of periodic structures in nematic liquid crystals"

Palangana, Simões, Evangelista, and Arrotéia [Phys. Rev. E 56, 4282 (1997)] (PSEA) propose a general scaling model for periodic wall patterns in the magnetic twist Fréedericksz transition of nematics, performing an elastic energy analysis. We demonstrate that this model is incorrect because it does not consider consistently the hydrodynamic wavelength selection of the observed structures, but is based on the assumption of inappropriate model functions instead. It is shown that experimental data actually contradict the proposed theory. The approach of PSEA is particularly not suited to determine elastic constant ratios of nematic liquid crystals.