Equilibrium phases and domain growth kinetics of calamitic liquid crystals

N Birdi and TL Underwood and NB Wilding and S Puri and V Banerjee, PHYSICAL REVIEW E, 105, 024706 (2022).

DOI: 10.1103/PhysRevE.105.024706

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter kappa' has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of kappa' on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T-c(1) and (ii) Nm to Sm at T-c(2) < T-c(1). kappa' decreases T-c(1) significantly but has relatively little effect on T-c(2). Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t) similar to t(1/2) and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to kappa'. We find that the Sm phase at the quench temperatures T (T > T-c(1) -> T < T-c(2)) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t) similar to t(1/2) at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t) similar to t(1/4) in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in kappa', but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

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