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 U > 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 [Soy. 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 >> U-c. Unfortunately, the corresponding analysis suffers from mistakes, which in a combination led to that result.