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We consider helical configurations of a cholesteric liquid crystal (CLC)sandwiched between two substrates with homogeneous director orientation favoredat both confining plates. We study the CLC twist wavenumber $q$ characterizingthe helical structures in relation to the free twisting number $q_0$ whichdetermines the equilibrium value of CLC pitch, $P_0=2\pi/q_0$. We investigatethe instability mechanism underlying transitions between helical structureswith different spiral half-turn numbers. Stability analysis shows that forequal finite anchoring strengths this mechanism can be dominated by in-planedirector fluctuations. In this case the metastable helical configurations areseparated by the energy barriers and the transitions can be described as thedirector slippage through these barriers. We extend our analysis to the case ofan asymmetric CLC cell in which the anchoring strengths at the two substratesare different. The asymmetry introduces two qualitatively novel effects: (a)the intervals of twist wavenumbers representing locally stable configurationswith adjacent helix half-turn numbers are now separated by the instabilitygaps; and (b) sufficiently large asymmetry, when the difference betweenazimuthal anchoring extrapolation lengths exceeds the thickness of the cell,will suppress the jump-like behaviour of the twist wavenumber.Comment: uses revtex4, 23 pages, 8 figure

Twist of cholesteric liquid crystal cells: Stability of helical structures and anchoring energy effects