Molecular Dynamics Simulations of Gay-Berne Liquid Crystals in Two Dimensions - Bharti (My University, 2023)
The melting phenomenon in a three-dimensional (3D) system is well understood. The nature of melting in 2D, however, is still being debated. The aim of the thesis is to understand the melting in a two-dimensional (2D) liquid crystalline (LC) system. We have simulated the LC system consisting of soft ellipses. The pair interaction is modeled by using the Gay–Berne (GB) potential. Our specific interest was to understand how the orientational degrees of freedom of the GB ellipses influence melting behavior. Hence we have considered a dense GB system where the orientational order exists in the system up to very high temperatures. We varied boththe density and temperature of the system. We identified different phases using different correlation functions and order parameters. We identified the existence of an intermediate hexatic phase when the 2D GB crystal melts into a nematic phase. We created a phase diagram of the dense 2D GB system from these studies. Next, we studied the effect of an underlying periodic substrate on the phase behavior of the 2D GB system. To this end, we varied the substrate parameters like substrate-particle interaction strength(A1) and substrate periodicity (as ). While keeping A1 fixed, as we varied the as, we observed that a positionally disordered nematic phase first gets stabilized, and its positional order increases for low values of as . However, when as is increased, the stabilized system melts into a modulated-smectic phase. Then finally, when as crosses a critical value (equal to the GB ellipses’ aspect ratio), the system undergoes a depinning transition and re-melts into a nematic phase. These findings then get summarised into a one-dimensional (as as axis) isothermal phase diagram. Finally, we systematically varied both as and A1 . We showed that when a GB system in the nematic phase is subjected to substrates with specific as and A1, the system transitions into different novel smectic phases. We finally show that by applying a substrate with large as, A1 can be used as a control parameter to steer the LC director.
Keywords: Liquid crystal; Gay-Berne potential; Melting; Two-dimension; KTHNY theory; Molecular dynamics; LAMMPS; Computer simulation