Looped finger transformation in frustrated cholesteric liquid crystals

Localized structures named "fingers" form in the vicinity of the unwinding transition of a cholesteric liquid crystal subjected to an electric field a nd to homeotropic boundary conditions. Several types of fingers exist, with different static and dynamic properties. For instance, cholesteric fingers of the second species (CF-2) can drift perpendicular to their axes and for m spirals in ac electric fields, whereas fingers of the first species (CF-I ) crawl along their axes. In this article we show that CF-2's are much easi er to nucleate in thick samples (with respect, to the pitch) than in thin o nes and may form loops like the CF-l's, with or without defects. We show th at looped CF-l's always collapse in thick samples at increasing voltage, wh ereas they can form cholesteric bubbles in thin samples. By contrast, we ne ver observe the formation of a bubble from a loop of a CF-2 except when it possesses a point defect. We also recall that CF-I segments always collapse at increasing voltage, whereas CF-2 segments systematically give cholester ic bubbles in similar conditions. To qualitatively explain these transforma tions, we use a simplified representation on the unit sphere S2 of the dire ctor field within the fingers. While the CF-l's are described within the st andard model of Press and Arrot, we use for the CF-2's a recent model of Gi l and Gilli, which we prove to explain most observations. We also describe the growth and collapse dynamics of a loop of a CF-2 in close connection wi th the spiral dynamics. Finally, we show experimentally and numerically tha t the CF-2's get abruptly thinner when the electric field exceeds the spino dal limit of the CF-1's. This transformation is reversible, but strongly hy steretic. [S1063-651X(99)08205-7].