The Landau-de Gennes approach revisited: A minimal self-consistent microscopic theory for spatially inhomogeneous nematic liquid crystals

Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang-Landau Method

We study the nature of the smectic-isotropic phase transition using a mobile 6-state Potts model. 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 a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang-Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.

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.