Chirality and biaxiality in cholesteric liquid crystals

We investigate the statistical mechanics of chirality and biaxiality in liquid crystals through a variety of theoretical approaches, including Monte Carlo simulations, lattice mean-field theory, and Landau theory. All of these calculations show that there is an important interaction between cholesteric twist and biaxial order: The twist acts as a field on the biaxial order, and conversely, the biaxial order increases the twist, that is, reduces the pitch. We model the behavior of chiral biaxial liquid crystals as a function of temperature and discuss how the predictions can be tested in experiments.

Figure 1

(a) Achiral and (b) chiral biaxial molecular structures studied in this work. (c) Cholesteric phase of chiral molecules, showing the macroscopic twist.

Figure 2

Monte Carlo results. (a) Uniaxial and biaxial order parameters as functions of temperature $T$ for achiral biaxial molecules with ellipsoid separation $h=0.24$. (b) Phase diagram for achiral biaxial molecules, in terms of $h$ and $T$. (c) Order parameters as functions of $T$, for chiral biaxial molecules with $h=0.24$ and molecular twist angle $\chi =0.08$. (Inset shows results for $h=0.28$ and $\chi =0.08$, with axis labels same as main figure.) (d) Boundary twist angle $\Phi$ as a function of $T$. For achiral molecules, $\Phi$ is locked at $\pi$, indicating that system is not twisted. For chiral molecules, $\Phi$ is not a multiple of $\pi$, indicating that system is twisted, and cholesteric twist increases as $T$ decreases. (Inset shows results for $h=0.28$ and $\chi =0.08$.)

Figure 3

Theoretical results for cholesteric twist as a function of temperature (in units of interaction strength $A$): Monte Carlo simulations, mean-field theory, and Landau theory.