Nematic and Smectic Phases: Dynamics and Phase Transition

We study in this paper the dynamics of molecules leading to the formation of nematic and smectic phases using a mobile 6-state Potts spin model with Monte Carlo simulation. Each Potts state represents a molecular orientation. We show that, with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by 6-state Potts spins, we obtain the structure of the smectic phase by cooling the molecules from the isotropic phase to low temperatures: molecules are ordered in independent equidistant layers. The isotropic-smectic phase transition is found to have a first-order character. The nematic phase is also obtained with the choice of another microscopic Hamiltonian. The isotropic-nematic phase transition is a second-order one. The real-time dynamics of the molecules leading to the liquid-crystal ordering in each case is shown by a video.