Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2003-09-09
Physical Review E 69, 041701 (2004)
Physics
Condensed Matter
Soft Condensed Matter
extended version, uses revtex4, 29 pages, 13 figures
Scientific paper
10.1103/PhysRevE.69.041701
We analyze stability of the planar orientational structure in a nematic liquid crystal (NLC) cell with planar anchoring conditions at both substrates. Specifically, we study the instabilities of the ground state caused by surface elasticity at large saddle-splay elastic constant, $K_{24}$. For relatively small $K_{24}$ violating the Ericksen inequalities the theory predicts that the critical fluctuation mode of the wavelength, $\lambda_c$, will render the structure 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 the second threshold value, $4K_1K_2/(K_1+K_2)$, leads to the instability with respect 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.
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