Direct Computation of the Twist Elastic Coefficient of a Nematic Liquid Crystal Via Monte Carlo Simulations

A direct method for the computation of the twist Frank elasticity coefficient of a nematic liquid crystal is presented. The method, suitable for numerical calculations, is tested and applied in Monte Carlo simulations for a model system. The dependence of the elasticity coefficient on the temperature and density and its relation to the nematic order parameter are analyzed and discussed.

Figure 1

The nematic order parameter $S_2$ and the twist elastic coefficient $K_2$ versus the particle density $n$ for the isotherms $T=0.8$, $T=0.85$, $T=0.9$, $T=0.95$, and $T=1.0$.

Figure 2

Twist elastic coefficient $K_2$ versus the square of the product of particle density and nematic order parameter $(n{S}_2{)}^2$ for different temperatures and densities. The empty circles are the two-particle average value contributions $⟨K_2^{\mathrm{o}\mathrm{b}\mathrm{s}}⟩$. The line is the function $5.1(n{S}_2{)}^2$.

Figure 3

The coefficient $c$ at $T=10$ according to Refs. 7, 20 versus the anisotropy parameters. The filled circle marks the isotropic model $({\epsilon }_1,{\epsilon }_2)=(0,0)$, where $c$ vanishes. The “x” marks the point $({\epsilon }_1,{\epsilon }_2)=(0.04,-0.08)$. Between the lines there are regions with preferred side-side configuration (rods) and end-end configuration (discs).