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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MDPI AG
2020-10-01
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1232 |
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| author | V. Thanh Ngo Phuong-Thuy Nguyen Hung T. Diep |
| author_facet | V. Thanh Ngo Phuong-Thuy Nguyen Hung T. Diep |
| author_sort | V. Thanh Ngo |
| collection | DOAJ |
| description | 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. |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:14:33Z |
| publishDate | 2020-10-01 |
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| spelling | doaj.art-19576598c9b14480be2ce1bbc5f4d32e2023-11-20T19:02:48ZengMDPI AGEntropy1099-43002020-10-012211123210.3390/e22111232Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau MethodV. Thanh Ngo0Phuong-Thuy Nguyen1Hung T. Diep2Center for Informatics and Computing, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10000, VietnamGraduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10000, VietnamLaboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université (Formerly, University of Cergy-Pontoise), CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise, FranceWe 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.https://www.mdpi.com/1099-4300/22/11/1232Potts modelMonte Carlo simulationWang–Landau methodsmectic phasedynamicsisotropic-smectic phase transition |
| spellingShingle | V. Thanh Ngo Phuong-Thuy Nguyen Hung T. Diep Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method Entropy Potts model Monte Carlo simulation Wang–Landau method smectic phase dynamics isotropic-smectic phase transition |
| title | Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method |
| title_full | Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method |
| title_fullStr | Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method |
| title_full_unstemmed | Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method |
| title_short | Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang–Landau Method |
| title_sort | statistical physics approach to liquid crystals dynamics of mobile potts model leading to smectic phase phase transition by wang landau method |
| topic | Potts model Monte Carlo simulation Wang–Landau method smectic phase dynamics isotropic-smectic phase transition |
| url | https://www.mdpi.com/1099-4300/22/11/1232 |
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