The temperature dependence of the helical pitch in a cholesteric liquid crystal

Abstract

We investigate the temperature dependence of the helical pitch of a cholesteric liquid crystal by means of Monte Carlo simulations. We carry out both lattice and off-lattice simulations to assess the impact of geometric and modelling constraints on the properties of the cholesteric phase. For the off-lattice simulations we develop boundary conditions commensurate with the cholesteric phase and derive an analytic expression for the helical wavenumber q that works well qualitatively. We find that the common simplification of constraining the orientation of the mesogens to planes normal to the helical axis makes q temperature-independent, as predicted by a mean-field theory of van der Meer et al. [J. Chem. Phys. $\mathbf{65}$, 3935 (1976)]. However, if mesogens are allowed to rotate in three dimensions, q will increase with temperature, as the isotropic-cholesteric transition is approached from below, in agreement with experiments for a number of substances. Our simulations indicate that the temperature-independent q is merely a consequence of the overly restricted orientational degrees of freedom to points on the unit circle in the model on which the mean-field theory is based.

GRAPHICAL ABSTRACT

Keywords:

• Cholesteric liquid crystal
• temperature dependence of helical pitch
• lattice and off-lattice Monte Carlo simulation

Acknowledgments

This article is dedicated to the memory of the late Professor Gerhard H. Findenegg, outstanding scientist and inspiring academic teacher. One of us (M. S.) mourns the loss of a wonderful colleague, and, above all, of a dear friend. It was a privilege and honour to know Gerhard personally.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 CID: circular intensity differential.