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. , 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
![](/cms/asset/1be35c35-1c14-466c-b803-7cae4233e3c5/tmph_a_1881638_uf0001_oc.jpg)
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.