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-...

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Bibliographic Details
Main Authors: V. Thanh Ngo, Phuong-Thuy Nguyen, Hung T. Diep
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/22/11/1232
Description
Summary: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 (<i>T</i>). In order to elucidate the order of the transition and the low-<i>T</i> 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 <i>T</i>. At a higher <i>T</i>, 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 <i>T</i> 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.
ISSN:1099-4300