Nonlinear analysis of flexodomains in nematic liquid crystals

We investigate flexodomains, which are observed in planar layers of certain nematic liquid crystals, when a dc voltage $U$ above a critical value ${U}_{c}$ is applied across the layer. They are characterized by stationary stripelike spatial variations of the director in the layer plane with a wave number $p(U)$. Our experiments for different nematics demonstrate that $p(U)$ varies almost linearly with $U$ for $Ug{U}_{c}$. That is confirmed by a numerical analysis of the full nonlinear equations for the director field and the induced electric potential. Beyond this numerical study, we demonstrate that the linearity of $p(U)$ follows even analytically, when considering a special parameter set first used by Terent'ev and Pikin [Sov. Phys. JETP 56, 587 (1982)]. Their theoretical paper serves until now as the standard reference on the nonlinear analysis of flexodomains, since it has arrived at a linear variation of $p(U)$ for large $U\ensuremath{\gg}{U}_{c}$. Unfortunately, the corresponding analysis suffers from mistakes, which in a combination led to that result.