Ordering Kinetics of Canted and Uniform States in Nematic Liquid Crystals

We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3-dimensions $(d=3)$ by performing deep quenches from the isotropic $(T>T_c)$ to the nematic $(T<T_c)$ phase. The inter-molecular potential between the nematogens, represented by continuous $O(3)$ spins with inversion symmetry, is accurately mimicked by the {\it generalised Lebwohl Lasher} (GLL) model. It incorporates second and fourth order Legendre interactions, and their relative interaction strength is $\lambda$. For $\lambda <-0.3$, we observe {\it canted} morphologies with a $\lambda$-dependent angle-of-tilt between the neighbouring rod-like molecules. For $\lambda \geq-0.3$, the molecules align to yield {\it uniform} states. The coarsening morphologies obey {\it generalized dynamical scaling} in the two regimes, but the scaling function is not robust with respect to $\lambda$. The structure factor tail in the canted regime follows the {\it Porod law}: $S(k,t)\sim k^{-4}$, implying that the coarsening dynamics is due to the annihilation of interfacial defects. This is unexpected, as the GLL model is characterised by a continuous order parameter. The uniform regime on the other hand, exhibits the expected {\it generalized Porod decay}: $S(k,t)\sim k^{-5}$, characteristic of scattering from {\it string defects}. Finally, the domain growth obeys the {\it Lifshitz-Allen-Cahn law}: $L(t)\sim t^{1/2}$ for all values of $\lambda$. Our results for the novel {\it canted} regime are relevant for a large class of systems with orientational ordering, e.g. active matter, membranes, LC elastomers, etc. We hope that our work triggers-off stimulating investigations in them.