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Ngo VT, Nguyen PT, Diep HT. Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang-Landau Method. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1232. [PMID: 33286999 PMCID: PMC7711670 DOI: 10.3390/e22111232] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Revised: 10/18/2020] [Accepted: 10/26/2020] [Indexed: 11/16/2022]
Abstract
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.
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Affiliation(s)
- V. Thanh Ngo
- Center for Informatics and Computing, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10000, Vietnam;
- Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10000, Vietnam;
| | - Phuong-Thuy Nguyen
- Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi 10000, Vietnam;
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi 10000, Vietnam
| | - Hung T. Diep
- Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université (Formerly, University of Cergy-Pontoise), CNRS, UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France
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Zakharov AV, Vakulenko AA. Orientational relaxation in free-standing smectic C film driven by rotating circular frame. J Chem Phys 2015; 143:104902. [PMID: 26374057 DOI: 10.1063/1.4930085] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The pecularities in the cˆ-director reorientation in free-standing smectic C film without of defects and stretched between two circular frames, the rest outer and rotating inner, have been investigated theoretically based on the hydrodynamic theory including the cˆ-director motion and with accounting for backflow. Since the orientation of the cˆ-director is fixed at the rims of the smectic film, the shear flow induced by rotating frame winds up of the cˆ-director field. It is found that the higher shearing flow produces the greater twisting rotation of the cˆ-director around the normal to the smectic film directed in the opposite sense with respect to the direction of the angular velocity. Calculations also show that the relaxation dynamics of the cˆ-director field depends crucially on the curvature of the inner rotating frame.
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Affiliation(s)
- A V Zakharov
- Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia
| | - A A Vakulenko
- Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia
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Zakharov AV, Sliwa I. Squeezing-out dynamics in free-standing smectic films. J Chem Phys 2015; 142:214703. [PMID: 26049512 DOI: 10.1063/1.4921960] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We have carried out a theoretical study of the dynamics of the removal of one smectic layer from the N-layer free-standing smectic film during the layer-thinning process. Squeezing-out is initiated by a thermally activated nucleation process in which a density fluctuation forms a small hole. The dynamics of the bounding area during the layer-thinning transition N → N - 1, when the nucleation occurs in the center of the circular smectic film and the squeezed-out area increases up to the edge of the circular smectic area, is studied by the use of the conservation laws for mass and linear momentum. The disjoining pressure is the main factor that is responsible for the driving out of one smectic layer from the N-layer smectic film.
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Affiliation(s)
- A V Zakharov
- Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia
| | - Izabela Sliwa
- Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznaǹ, Poland
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`Sliwa I, Zakharov A. Surface tension, disjoining pressure and layer compression of free-standing smectic films in water. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2014.12.032] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Zakharov AV, Vakunenko AA. Influence of an external field on the surface tension of free-standing smectic films. Phys Rev E 2012; 86:031701. [PMID: 23030927 DOI: 10.1103/physreve.86.031701] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Revised: 08/01/2012] [Indexed: 11/07/2022]
Abstract
We have carried out a theoretical study of the effect of the electric field E on the thermodynamical properties and surface tension γ of free-standing smectic films. Calculations, based upon the extended McMillan approach with anisotropic forces, show a stepwise reduction and increase of the values of the Helmholtz free energy f and γ, respectively, per partially fluorinated 5-n-alkyl-2-[4-n-(perfluoroalkyl-metheleneoxy)phenyl] (H10F5MOPP) molecule, as the temperature is raised above that for the bulk smectic-A-isotropic transition. Calculations show that E may not only affect the layer-thinning transition sequence, but also change the first multilayer jump in the thickness and increase the value of γ per H10F5MOPP molecule. Reasonable agreement between the theoretically predicted and the experimentally obtained data on γ of the partially fluorinated H10F5MOPP film has been obtained.
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Affiliation(s)
- A V Zakharov
- Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia.
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Zakharov AV, Sullivan DE. Transition entropy, Helmholtz free energy, and heat capacity of free-standing smectic films above the bulk smectic-A-isotropic transition temperature: a mean-field treatment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041704. [PMID: 21230292 DOI: 10.1103/physreve.82.041704] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2009] [Revised: 07/02/2010] [Indexed: 05/30/2023]
Abstract
We have carried out a numerical study of both the structural and thermodynamic properties of free-standing smectic films (FSSFs) for two cases of enhanced pair interactions in the bounding layers. Calculations, based upon the extended McMillan's approach with anisotropic forces, shows a stepwise reduction of the value of the heat capacity as the temperature is raised above the bulk smectic A-isotropic transition. The effects of surface "enhanced" pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy, and entropy of FSSFs have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained--by means of calorimetric techniques--data on the heat capacity of the partially fluorinated 5-n-alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) (H10F5MOPP) films has been obtained.
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Affiliation(s)
- A V Zakharov
- Saint Petersburg Institute for Machine Sciences, The Russian Academy of Sciences, Saint Petersburg 199178, Russia.
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Martínez-Ratón Y. Capillary ordering and layering transitions in two-dimensional hard-rod fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051708. [PMID: 17677085 DOI: 10.1103/physreve.75.051708] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2006] [Revised: 11/23/2006] [Indexed: 05/16/2023]
Abstract
We calculate the surface phase diagram of a two-dimensional hard-rod fluid confined between two hard lines. In the first stage we study a semi-infinite system consisting of an isotropic fluid in contact with a single hard line. We have found complete wetting by the columnar phase at the wall-isotropic fluid interface. When the fluid is confined between two hard walls, capillary columnar ordering occurs via a first-order phase transition. For higher chemical potentials the system exhibits layering transitions even for very narrow slits (near the one-dimensional limit). The theoretical model used was a density-functional theory based on the fundamental-measure functional applied to a fluid of hard rectangles in the restricted-orientation approximation (Zwanzig model). The results presented here can be checked experimentally in two-dimensional granular media made of rods, where vertical motions induced by an external source and excluded volume interactions between the grains allow the system to explore those stationary states which entropically maximize packing configurations. We claim that some of the surface phenomena found here can be present in two-dimensional granular-media fluids.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, Madrid, Spain.
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de Las Heras D, Velasco E, Mederos L. Capillary effects in a confined smectic phase of hard spherocylinders: influence of particle elongation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011709. [PMID: 16907113 DOI: 10.1103/physreve.74.011709] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2006] [Indexed: 05/11/2023]
Abstract
A system of hard rods confined into a pore with slit geometry (two parallel planar substrates) is studied theoretically in the regime of high packing fraction. In this regime the bulk system exhibits a nematic phase as well as a smectic-A (spatially layered) phase. When the system is confined, strong commensuration effects between the layer spacing and the pore width bring about a rich phenomenology, with a phase diagram showing layering and capillary transitions. The latter include capillary smectization transitions whereby a confined smectic phase occurs at conditions of saturation different from those of the corresponding bulk fluid. These transitions are seen to be intimately connected with layering transitions involving discontinuous changes in the number of layers inside the pore. This rich phenomenology is obtained by use of a sophisticated density-functional, Onsager-theory-based approach, especially suited to deal with strongly inhomogeneous fluids. The theory allows for a unified description of ordering and phase behavior of the fluid in confined geometry, and permits us to correlate the above behavior with the wetting properties of the fluid on a single substrate.
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Affiliation(s)
- D de Las Heras
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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Dolganov PV, Cluzeau P, Joly G, Dolganov VK, Nguyen HT. Interaction of surfaces in smectic membranes and their instability near thinning transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:031713. [PMID: 16241466 DOI: 10.1103/physreve.72.031713] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2005] [Indexed: 05/05/2023]
Abstract
We report measurements of the interaction between surfaces of the presmectic membrane above the temperature of transition to the phase without layer ordering. Investigations were performed employing cholesteric droplets embedded in the membrane in the temperature range of thinning transitions. Upon heating, the difference between the membrane tension and surface tension of the bulk sample decreases sufficiently, which leads to membrane instability. After the thinning transition, the membrane returns to a stable state with a larger value of surface interaction.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow Region, Russia
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Sullivan DE, Shalaginov AN. First-order Landau-de Gennes model for layer thinning in presmectic free-standing films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:011707. [PMID: 15324072 DOI: 10.1103/physreve.70.011707] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2003] [Indexed: 05/24/2023]
Abstract
A Landau theory for surface enhanced ordering in free-standing smectic-A films is described, based on a generalization of de Gennes's "presmectic" model to systems which undergo a first-order smectic-isotropic transition in bulk. As found in related work on phase transitions in thin films, the system exhibits three phases, an isotropic liquid, a bulk-like ordered (smectic-A) phase, and a surface-ordered ("quasismectic") phase. Over much of its range, the temperature-thickness boundary between the bulk-ordered and surface-ordered phases is effectively characterized by a power-law relation similar to those observed for layer-thinning transitions in overheated free-standing smectic-A films.
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Affiliation(s)
- D E Sullivan
- Department of Physics and Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario, Canada N1G 2W1
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Shalaginov AN, Sullivan DE. Dislocation loops in overheated free-standing smectic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:031715. [PMID: 11909089 DOI: 10.1103/physreve.65.031715] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2001] [Revised: 11/08/2001] [Indexed: 05/23/2023]
Abstract
Static and dynamic phenomena in overheated free-standing smectic-A films are studied theoretically. The work is based on a generalization, introduced recently by the authors, of de Gennes' theory for a confined presmectic liquid. In this approach, smectic ordering in an overheated film is caused by an intrinsic surface contribution to the film free energy and vanishes at some temperature depending on the number of layers. Here the theory is further generalized to study the dynamics of films with planar inhomogeneities. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated free-standing films, namely, "uniform thinning" versus nucleation of dislocation loops. It is concluded that the nucleation mechanism dominates provided there is a sufficiently large pressure difference arising from meniscus curvature. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.
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Affiliation(s)
- A N Shalaginov
- Department of Physics and Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario, Canada N1G 2W1
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Shalaginov AN, Sullivan DE. Landau-de Gennes theory of surface-enhanced ordering in smectic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:031704. [PMID: 11308663 DOI: 10.1103/physreve.63.031704] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2000] [Indexed: 05/23/2023]
Abstract
A Landau theory for surface-enhanced ordering in smectic-A free-standing films is described, based on a generalization of de Gennes' model for a "presmectic" fluid confined between two walls. According to the theory, smectic ordering in free-standing films heated above the bulk smectic melting temperature is due to an intrinsic surface contribution rather than an external field. The theory yields a persistent finite-size effect, in that the film melting temperatures do not tend to the bulk transition temperature in the limit of infinite film thickness. It also predicts that a continuous transition from (N+1)- to N-layer films is impossible without an external field. The theory closely fits existing experimental data on layer-thinning transitions in compounds which exhibit a bulk smectic-A to nematic phase transition. Possible origins of the intrinsic surface contribution are discussed.
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Affiliation(s)
- A N Shalaginov
- Department of Physics and Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ontario, Canada N1G 2W1
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Mills SJ, Care CM, Neal MP, Wilson MR, Allen MP, Cleaver DJ. Formation of a nematic monodomain in a model liquid crystal film. J Mol Liq 2000. [DOI: 10.1016/s0167-7322(99)00176-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Martínez-Ratón Y, Somoza AM, Mederos L, Sullivan DE. Smectic-A ordering in liquid crystal films. Faraday Discuss 1996. [DOI: 10.1039/fd9960400111] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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