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 o-lattice simulations to assess the impact of geometric and modelling constraints on the properties of the cholesteric phase. For the o-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 nd that the common simplication of constraining the orientation of the mesogens to planes normal to the helical axis makes q temperature-independent, as predicted by a mean-eld 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-eld theory is based.

Flow-assisted self-healing of the helical structure in a cholesteric liquid crystal

“…Thus, we simply assume for convenience the distance dependence of u chir aniso to be the same as the one derived rigorously for u achir aniso in Eq. (2.4) [23]. We note in passing that the orientation dependence described by the triple scalar product is the same as the one used in earlier studies of chiral liquid crystals [23,[27][28][29].…”

“…Again, as detailed in Ref. 23, we eventually obtain by a similar expansion in terms of the rotational invariants the expression…”

“…As we discuss in detail elsewhere [23], the achiral contribution u achir aniso can be expanded in terms of (a subset of) the so-called rotational invariants S 00 ll0 as suitable basis functions because of the assumed uniaxial symmetry of the molecules [23,24].…”

“…Using the relation between the rotational invariants and the spherical harmonics {Y lm }, on the one hand, and between the spherical harmonics and the set of Legendre polynomials {P l }, on the other hand, it is relatively straightforward to show [23] that the achiral contribution u achir aniso can be cast as…”

“…The robust order of cholesterics invites the question of whether it is possible to control its structure under more general nonequilibrium conditions. We know that temperature is a good control variable for the pitch of the cholesteric helix [23]. In this work we explore the limits of the stability of the cholesteric structure under strong out-of-equilibrium conditions.…”