Theory of a helicoidal cholesteric phase induced by an external field

ABSTRACT

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.

Graphical Abstract

KEYWORDS:

• Helicoid
• cholesteric phase
• phase separation
• twist-bend nematic

Acknowledgement

The author thanks Junji Watanabe for helpful discussions on chiral and achiral molecules.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by JSPS KAKENHI [grant number 26400435].