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

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. 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.