Saddle-splay term induced orientational instability in nematic liquid crystal cells and director fluctuations at substrates

摘要

We analyze stability of the planar orientational structure in a nematicliquid crystal (NLC) cell with planar anchoring conditions at both substrates.Specifically, we study the instabilities of the ground state caused by surfaceelasticity at large saddle-splay elastic constant, $K_{24}$. For relativelysmall $K_{24}$ violating the Ericksen inequalities the theory predicts that thecritical fluctuation mode of the wavelength, $\lambda_c$, will render thestructure unstable when the thickness of the cell is below its critical value,$d_c$. The parity of the critical mode changes as the twist-splay ratio$K_2/K_1$ is passing through the unity. Further increase of $K_{24}$ beyond thesecond threshold value, $4K_1K_2/(K_1+K_2)$, leads to the instability withrespect to the short wavelength fluctuations regardless of the cell thickness.We compute the critical thickness and the critical wavelength as functions of$K_{24}$, the twist-splay ratio and the azimuthal anchoring strength.