Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch(H)) is derived as a function of a usual orientational order parameter and an order parameter of the Ch(H) phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch(H) phase. Depending on the temperature and the strength of the external field, we find the second-order N-Ch(H) and Ch(H)-Ch phase transitions and the first-order paranematic (pN)-N, pN-Ch(H) and pN-Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field. [GRAPHICS] .