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 and 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 form spirals in ac electric fields, whereas fingers of the first species (CF-1) crawl along their axes. In this article we show that CF-2's are much easier to nucleate in thick samples (with respect to the pitch) than in thin ones and may form loops like the CF-1's, with or without defects. We show that looped CF-1's always collapse in thick samples at increasing voltage, whereas they can form cholesteric bubbles in thin samples. By contrast, we never 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-1 segments always collapse at increasing voltage, whereas CF-2 segments systematically give cholesteric bubbles in similar conditions. To qualitatively explain these transformations, we use a simplified representation on the unit sphere S2 of the director field within the fingers. While the CF-1's are described within the standard model of Press and Arrot, we use for the CF-2's a recent model of Gil 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 with the spiral dynamics. Finally, we show experimentally and numerically that the CF-2's get abruptly thinner when the electric field exceeds the spinodal limit of the CF-1's. This transformation is reversible, but strongly hysteretic.