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Chen Z, Aya S. Macroscopic Nematic Orientation Dictated by an Orientationally Frustrated Random-Field Surface: Equilibrium Structure and Kinetics. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:16118-16127. [PMID: 37921692 DOI: 10.1021/acs.langmuir.3c02251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/04/2023]
Abstract
Liquid crystals subjected to frustrated surfaces with mixed anchoring conditions demonstrate a rich variety of orientational patterns. Particularly, it would trigger either continuous or discontinuous variation of the bulk orientation, i.e., a phenomenon known as the anchoring or orientational transition. Despite its prime importance in developing novel optoelectronic devices, how the surface anchoring patterns dedicate the energy landscape of a system, thus the equilibrium state, still needs to be understood. Here, we designed a simulation to model boundary substrates with two randomly mixed anchoring domains in space, which exhibit planar and homeotropic preferences. We numerically obtain general bulk orientational state diagrams under various surface and electric field conditions, which reveal the roles of each domain's size and surface fraction and anchoring strength on the bulk orientational state. Furthermore, we examine how the external electric field modifies the orientational state diagram and uncovers a field-assisted anchoring transition. We discuss the observed bistability and compare it to experimental evidence.
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Affiliation(s)
- Zihua Chen
- South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
| | - Satoshi Aya
- South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China
- Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology, Guangzhou 510640, China
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2
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Eckert T, Schmidt M, de Las Heras D. Effect of sample height and particle elongation in the sedimentation of colloidal rods. SOFT MATTER 2023; 19:2214-2223. [PMID: 36883340 DOI: 10.1039/d3sm00191a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We study theoretically the effect of a gravitational field on the equilibrium behaviour of a colloidal suspension of rods with different length-to-width aspect ratios. The bulk phases of the system are described with analytical equations of state. The gravitational field is then incorporated via sedimentation path theory, which assumes a local equilibrium condition at each altitude of the sample. The bulk phenomenology is significantly enriched by the presence of the gravitational field. In a suspension of elongated rods with five stable phases in bulk, the gravitational field stabilizes up to fifteen different stacking sequences. The sample height has a non-trivial effect on the stable stacking sequence. New layers of distinct bulk phases appear either at the top, at the bottom, or simultaneously at the top and the bottom when increasing the sample height at constant colloidal concentration. We also study sedimentation in a mass-polydisperse suspension in which all rods have the same shape but different buoyant masses.
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Affiliation(s)
- Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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3
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Sammüller F, Hermann S, Schmidt M. Comparative study of force-based classical density functional theory. Phys Rev E 2023; 107:034109. [PMID: 37072997 DOI: 10.1103/physreve.107.034109] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.
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Affiliation(s)
- Florian Sammüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Sophie Hermann
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany
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4
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Salgado-Blanco D, Llanas-García AH, Díaz-Herrera E, Martínez-González JA, Mendoza CI. Structural properties and ring defect formation in discotic liquid crystal nanodroplets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:254001. [PMID: 35358952 DOI: 10.1088/1361-648x/ac630b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 03/31/2022] [Indexed: 06/14/2023]
Abstract
In this work, we performedNpTMonte Carlo simulations of a Gay-Berne discotic liquid crystal confined in a spherical droplet under face-on anchoring and fixed pressure. We find that, in contrast to the unbounded system, a plot of the order parameter as function of temperature does not show a clear evidence of a first-order isotropic-nematic transition. We also find that the impossibility of simultaneously satisfy the uniform director field requirement of a nematic phase with the radial boundary conditions, results in the appearance of a ring disclination line as a stress release mechanism in the interior of the droplet. Under further cooling, a columnar phase appears at the center of the droplet.
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Affiliation(s)
- Daniel Salgado-Blanco
- Cátedras CONACyT-Centro Nacional de Supercómputo, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San José 2055, 78216, San Luis Potosí, México
- División de Materiales Avanzados, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a Sección, San Luis Potosí, S. L. P., 78216, México
| | - Andrea H Llanas-García
- División de Materiales Avanzados, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4a Sección, San Luis Potosí, S. L. P., 78216, México
| | - Enrique Díaz-Herrera
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Ave. San Rafael Atlixco 186, Col. Vicentina, 09340 México, Ciudad de México, Mexico
| | - José A Martínez-González
- Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Parque Chapultepec 1570, San Luis Potosí 78210 SLP, Mexico
| | - Carlos I Mendoza
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apdo. Postal 70-360, 04510 México, Ciudad de México, Mexico
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5
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Yao X, Zhang L, Chen JZY. Defect patterns of two-dimensional nematic liquid crystals in confinement. Phys Rev E 2022; 105:044704. [PMID: 35590543 DOI: 10.1103/physreve.105.044704] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface-confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.
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Affiliation(s)
- Xiaomei Yao
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Lei Zhang
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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6
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Kaur J, Deb D. Pressure-tensor method evaluation of the interfacial tension between Gay-Berne isotropic fluid and a smooth repulsive wall. SOFT MATTER 2021; 17:10566-10579. [PMID: 34779475 DOI: 10.1039/d1sm01293b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The interfacial properties of a confined thermotropic liquid crystalline material are investigated using a molecular dynamics simulation technique. The pairwise interaction among the soft ellipsoidal particles is modeled by the Gay-Berne (GB) potential. The GB ellipsoids are confined by two soft, smooth, repulsive walls defined by the Weeks-Chandler-Andersen (WCA) potential. The aperiodic confinement due to walls makes the system mechanically anisotropic. Hence using the pressure-tensor method, the interfacial tension of an interface between the bulk isotropic (I) phase and WCA wall at various number densities (ρ) is calculated. From the pressure tensor and orientational order profiles, the arrangement of ellipsoids in the bulk and the vicinity of the wall is determined. The effect of system size and the wall-particle interaction strength (εW) on is also analyzed by varying the system size and εW.
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Affiliation(s)
- Jagroop Kaur
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Bhadson Road, Patiala, Punjab - 147004, India.
| | - Debabrata Deb
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Bhadson Road, Patiala, Punjab - 147004, India.
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7
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Kil KH, Yethiraj A, Kim JS. Nematic ordering of hard rods under strong confinement in a dense array of nanoposts. Phys Rev E 2020; 101:032705. [PMID: 32289982 DOI: 10.1103/physreve.101.032705] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Accepted: 02/26/2020] [Indexed: 11/07/2022]
Abstract
The effect of confinement on the behavior of liquid crystals is interesting from a fundamental and practical standpoint. In this work, we report Monte Carlo simulations of hard rods in an array of hard nanoposts, where the surface-to-surface separations between nanoposts are comparable to or less than the length of hard rods. This particular system shows promise as a means of generating large-scale organization of the nematic liquid by introducing an entropic external field set by the alignment of nanoposts. The simulations show that nematic ordering of hard rods is enhanced in the nanopost arrays compared with that in bulk, in the sense that the nematic order is significant even at low concentrations at which hard rods remain isotropic in bulk, and the enhancement becomes more significant as the passage width between two nearest nanoposts decreases. An analysis of local distribution of hard-rod orientations at low concentrations with weak nematic ordering reveals that hard rods are preferentially aligned along nanoposts in the narrowing regions between two curved surfaces of nearest nanoposts; hard rods are less ordered in the passages and in the centers of interpost spaces. It is concluded that at low concentrations the confinement in a dense array of nanoposts induces the localized nematic order first in the narrowing regions and, as the concentration further increases, the nematic order spreads over the whole region. The formation of a well-ordered phase at low concentrations of hard rods in a dense array of nanoposts can provide a new route to the low-concentration preparation of nematic liquid crystals that can be used as anisotropic dispersion media.
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Affiliation(s)
- Kye Hyoung Kil
- Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Arun Yethiraj
- Department of Chemistry, University of Wisconsin-Madison, Wisconsin 53706, USA
| | - Jun Soo Kim
- Department of Chemistry and Nanoscience, Ewha Womans University, Seoul 03760, Republic of Korea
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8
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Wu L, Malijevský A, Avendaño C, Müller EA, Jackson G. Demixing, surface nematization, and competing adsorption in binary mixtures of hard rods and hard spheres under confinement. J Chem Phys 2018; 148:164701. [DOI: 10.1063/1.5020002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Liang Wu
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Alexandr Malijevský
- Department of Physical Chemistry, University of Chemical Technology Prague, 166 28 Praha 6, Czech Republic
- Department of Microscopic and Mesoscopic Modelling, ICPF of the Czech Academy of Sciences, 165 02 Prague 6, Czech Republic
| | - Carlos Avendaño
- School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, United Kingdom
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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9
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Aliabadi R, Gurin P, Velasco E, Varga S. Ordering transitions of weakly anisotropic hard rods in narrow slitlike pores. Phys Rev E 2018; 97:012703. [PMID: 29448392 DOI: 10.1103/physreve.97.012703] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Indexed: 11/07/2022]
Abstract
The effect of strong confinement on the positional and orientational ordering is examined in a system of hard rectangular rods with length L and diameter D (L>D) using the Parsons-Lee modification of the second virial density-functional theory. The rods are nonmesogenic (L/D<3) and confined between two parallel hard walls, where the width of the pore (H) is chosen in such a way that both planar (particle's long axis parallel to the walls) and homeotropic (particle's long axis perpendicular to the walls) orderings are possible and a maximum of two layers is allowed to form in the pore. In the extreme confinement limit of H≤2D, where only one-layer structures appear, we observe a structural transition from a planar to a homeotropic fluid layer with increasing density, which becomes sharper as L→H. In wider pores (2D<H<3D) planar order with two layers, homeotropic order, and even combined bilayer structures (one layer is homeotropic, while the other is planar) can be stabilized at high densities. Moreover, first-order phase transitions can be seen between different structures. One of them emerges between a monolayer and a bilayer with planar orders at relatively low packing fractions.
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Affiliation(s)
- Roohollah Aliabadi
- Department of Physics, College of Science, Fasa University, 74617-81189 Fasa, Iran
| | - Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201 Hungary
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC) and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201 Hungary
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10
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Cortes LBG, Gao Y, Dullens RPA, Aarts DGAL. Colloidal liquid crystals in square confinement: isotropic, nematic and smectic phases. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:064003. [PMID: 28002038 DOI: 10.1088/1361-648x/29/6/064003] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We report on the confinement of colloidal liquid crystals in three dimensional chambers with a square footprint. To this end we use colloidal silica rods and exploit their relatively large density difference with respect to the dispersing solvent to study isotropic, nematic and smectic phases confined into a single chamber. Combining laser scanning confocal microscopy and soft-lithography techniques enables us to characterize the configurations down to the single particle level. We will focus on the smectic phase and compare to recent theories and simulations.
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Affiliation(s)
- Louis B G Cortes
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
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11
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Luzhbin DA, Chen YL. Shifting the Isotropic–Nematic Transition in Very Strongly Confined Semiflexible Polymer Solutions. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00986] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Dmytro A. Luzhbin
- Institute of Physics, Academia Sinica, Taipei, Taiwan, R.O.C
- Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, R.O.C
- Department of Physics, National Taiwan University, Taipei, Taiwan, R.O.C
| | - Yeng-Long Chen
- Institute of Physics, Academia Sinica, Taipei, Taiwan, R.O.C
- Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, R.O.C
- Department of Physics, National Taiwan University, Taipei, Taiwan, R.O.C
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12
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Ye S, Zhang P, Chen JZY. Nematic ordering of semiflexible polymers confined on a toroidal surface. SOFT MATTER 2016; 12:5438-5449. [PMID: 27248049 DOI: 10.1039/c6sm01098a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We study the isotropic-like and nematic states of wormlike liquid-crystal polymers embedded on the surface of a torus. The role played by surface curvature, which couples to the molecular rigidity, is reported as the main reason that causes the weak nematic ordering in an otherwise ordinary isotropic phase. The same coupling has a profound effect on the nematic states as well, which are stabilized by the Onsager excluded-volume interaction; the latter has been frequently used to study lyotropic liquid crystal polymers and is used here as an example of the physical mechanisms that drive the system to make orientational ordering. We identify important parameters in the system which are used as axes of the four-dimensional phase diagram. The numerical study demonstrates a strong correlation between the liquid-crystal defect-free and defect structures and the geometry of the liquid-crystal embedded surface.
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Affiliation(s)
- Shiwei Ye
- LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China.
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13
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Ye S, Zhang P, Chen JZY. Surface-induced phase transitions of wormlike chains in slit confinement. SOFT MATTER 2016; 12:2948-2959. [PMID: 26877230 DOI: 10.1039/c5sm02835c] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
On the basis of a self-consistent field theory treatment of semi-flexible polymer chains, we analyze the effects of the flexibility on the structure of polymers sterically confined between two parallel, structureless walls separated by a distance. The model is built from a wormlike chain formalism which crosses over from the rod limit to the flexible limit, and the Onsager-type interaction which describes the orientation-dependent excluded-volume interaction. Three surface states were obtained from the numerical solution to the theory: uniaxial, biaxial, and condensed. As the overall density increases in such a lyotropic system, first order phase transitions between uniaxial and biaxial states, biaxial and condensed states can occur.
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Affiliation(s)
- Shiwei Ye
- LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China.
| | - Pingwen Zhang
- LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China.
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada.
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14
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15
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Geigenfeind T, Rosenzweig S, Schmidt M, de las Heras D. Confinement of two-dimensional rods in slit pores and square cavities. J Chem Phys 2015; 142:174701. [DOI: 10.1063/1.4919307] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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16
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Santos-Silva T, Teixeira PIC, Anquetil-Deck C, Cleaver DJ. Neural-network approach to modeling liquid crystals in complex confinement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:053316. [PMID: 25353923 DOI: 10.1103/physreve.89.053316] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2012] [Indexed: 06/04/2023]
Abstract
Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.
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Affiliation(s)
- T Santos-Silva
- Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal
| | - P I C Teixeira
- Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal
| | - C Anquetil-Deck
- Materials and Engineering Research Institute, Sheffield Hallam University, Pond Street, Sheffield S1 1WB, United Kingdom
| | - D J Cleaver
- Materials and Engineering Research Institute, Sheffield Hallam University, Pond Street, Sheffield S1 1WB, United Kingdom
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17
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de Las Heras D, Velasco E. Domain walls in two-dimensional nematics confined in a small circular cavity. SOFT MATTER 2014; 10:1758-1766. [PMID: 24652373 DOI: 10.1039/c3sm52650j] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods inside a small circular cavity bounded by a hard wall, from the dilute regime to the high-density, layering regime. Both planar and homeotropic anchoring of the nematic director can be induced at the walls through a free-energy penalty. The circular geometry creates frustration in the nematic phase and a polar-symmetry configuration with a distorted director field plus two +1/2 disclinations is created. At higher densities, a quasi-uniform structure is observed with a (minimal) director distortion which is relaxed via the formation of orientational domain walls. This novel structure is not predicted by elasticity theory and is similar to the step-like structures observed in three-dimensional hybrid slit pores. We speculate that the formation of domain walls is a general mechanism to relax elastic stresses under the conditions of strong surface anchoring and severe spatial confinement.
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Affiliation(s)
- Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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18
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Ivanov VA, Rodionova AS, Martemyanova JA, Stukan MR, Müller M, Paul W, Binder K. Wall-induced orientational order in athermal semidilute solutions of semiflexible polymers: Monte Carlo simulations of a lattice model. J Chem Phys 2013; 138:234903. [DOI: 10.1063/1.4810745] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Zola RS, Evangelista LR, Yang YC, Yang DK. Surface induced phase separation and pattern formation at the isotropic interface in chiral nematic liquid crystals. PHYSICAL REVIEW LETTERS 2013; 110:057801. [PMID: 23414046 DOI: 10.1103/physrevlett.110.057801] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2012] [Indexed: 06/01/2023]
Abstract
We study the pattern formation of a chiral nematic liquid crystal under a wetting transition. In the isotropic-liquid crystal transition, a surface-enhanced effect happens and a thin liquid crystal layer forms at the substrates of the cell. In this confined system, chirality, elastic anisotropy, surface anchoring, and wetting strength interplay. A striped pattern is formed due to the chiral nature of the material and the tilted anchoring at the isotropic boundary. As the wetting layer grows from cooling the sample, first the stripes rotate through a process where dislocation defects are formed. As the wetting layer grows further, the periodicity of the stripe structure changes, and finally a splitting of the stripes occurs. Because of the unique properties of this system, new insights about pitch-thickness ratio, interface anchoring, and elastic anisotropy effect are found. Since the anchoring at the isotropic boundary is weak, the critical ratio between the thickness of the wetting layer and the helical pitch is different from that reported in the literature. We also discover that the elastic anisotropy and elastic constant ratios play a critical role in stripe formation. Because of the similarity with biological fibrous composites (twisted plywood), our system may be used as a synthetic version to mimic the naturally occurring one. We carry out a simulation study to explain the experimental results.
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Affiliation(s)
- R S Zola
- Chemical Physics Interdisciplinary Program and Liquid Crystal Institute, Kent State University, Ohio 44242, USA
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20
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Aya S, Araoka F, Ishikawa K, Takezoe H. Evolution of the discontinuous anchoring transition under an electric field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012507. [PMID: 23410349 DOI: 10.1103/physreve.87.012507] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2012] [Indexed: 06/01/2023]
Abstract
Anchoring transition (ATr), resulting in the orientational change of liquid crystal (LC) molecules at surfaces with temperature variation, is shown to be essentially affected by the application of an electric field (E field). By combining defocusing polarizing microscopy with retardation measurement, a detailed investigation of the molecular orientational change in the vicinity of ATr during a cooling process under an E field was performed. Two important conclusions can be made from our observations: (i) the ATr temperature exhibits a large downshift in the presence of an E field; (ii) the orientational change is always discontinuous from a planar (P) state to a homeotropic (H) state. If the applied E field is below the Freedericksz transition, P and H states are uniform, whereas the surface H state is influenced by the tilt in the bulk due to negative dielectric anisotropy, resulting in a bent-splay deformed state.
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Affiliation(s)
- Satoshi Aya
- Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1-S8-42 O-okayama, Meguro, Tokyo 152-8552, Japan
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Greschek M, Schoen M. Orientational prewetting of planar solid substrates by a model liquid crystal. J Chem Phys 2012; 135:204702. [PMID: 22128947 DOI: 10.1063/1.3660377] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present grand canonical ensemble Monte Carlo simulations of prewetting transitions in a model liquid crystal at structureless solid substrates. Molecules of the liquid crystal interact via anisometric Lennard-Jones potentials and can be anchored planar or homeotropically at the substrates. Fluid-substrate attraction is modeled by a Yukawa potential of variable range. By monitoring the grand-potential density and the nematic order parameter as functions of the chemical potential μ, several discontinuous prewetting, wetting, and isotropic-nematic phase transitions are observed. These transitions depend on both the range of the fluid-substrate attraction and the specific anchoring at the substrate. Our results show that at substrates characterized by degenerate anchoring prewetting occurs at lower μ compared with cases in which the anchoring is monostable. This indicates that prewetting transitions are driven by orientational entropy because degenerate anchoring allows for more orientationally distinct configurations of molecules compared with monostable anchoring. In addition, by analyzing local density and various local order parameters, a detailed picture of the structure of various phases emerges from our simulations.
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Affiliation(s)
- Manuel Greschek
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany.
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22
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Ivanov VA, Rodionova AS, An EA, Martemyanova JA, Stukan MR, Müller M, Paul W, Binder K. Orientational ordering transitions of semiflexible polymers in thin films: a Monte Carlo simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041810. [PMID: 22181168 DOI: 10.1103/physreve.84.041810] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2011] [Indexed: 05/31/2023]
Abstract
Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., "preferential orientation" along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film.
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Affiliation(s)
- V A Ivanov
- Faculty of Physics, Moscow State University, Moscow 119991, Russia
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Varga S, Martinez-Ratón Y, Velasco E. Competition between capillarity, layering and biaxiality in a confined liquid crystal. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 32:89-101. [PMID: 20521078 DOI: 10.1140/epje/i2010-10601-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2010] [Accepted: 05/03/2010] [Indexed: 05/29/2023]
Abstract
The effect of confinement on the phase behaviour and structure of fluids made of biaxial hard particles (cuboids) is examined theoretically by means of Onsager second-order virial theory in the limit where the long particle axes are frozen in a mutually parallel configuration. Confinement is induced by two parallel planar hard walls (slit-pore geometry), with particle long axes perpendicular to the walls (perfect homeotropic anchoring). In bulk, a continuous nematic-to-smectic transition takes place, while shape anisotropy in the (rectangular) particle cross-section induces biaxial ordering. As a consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases, can be stabilised as the cross-sectional aspect ratio is varied. On confining the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial or biaxial phases, separated by a continuous transition, can be present. Smectic ordering develops continuously from the walls for increasing particle concentration (in agreement with the supression of nematic-smectic second-order transition at confinement), but first-order layering transitions, involving structures with n and n + 1 layers, arise in the confined fluid at high concentration. Competition between layering and uniaxial-biaxial ordering leads to three different types of layering transitions, at which the two coexisting structures can be both uniaxial, one uniaxial and another biaxial, or both biaxial. Also, the interplay between molecular biaxiality and wall interactions is very subtle: while the hard wall disfavours the formation of the biaxial phase, biaxiality is against the layering transitions, as we have shown by comparing the confined phase behaviour of cylinders and cuboids. The predictive power of Onsager theory is checked and confirmed by performing some calculations based on fundamental-measure theory.
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Affiliation(s)
- S Varga
- Departamento de Física Téorica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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de las Heras D, Martínez-Ratón Y, Velasco E. Surface and smectic layering transitions in binary mixtures of parallel hard rods. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021706. [PMID: 20365581 DOI: 10.1103/physreve.81.021706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2009] [Indexed: 05/29/2023]
Abstract
The surface phase behavior of binary mixtures of colloidal hard rods in contact with a solid substrate (hard wall) is studied, with special emphasis on the region of the phase diagram that includes the smectic A phase. The colloidal rods are modeled as hard cylinders of the same diameter and different lengths, in the approximation of perfect alignment. A fundamental-measure density functional is used to obtain equilibrium density profiles and thermodynamic properties such as surface tensions and adsorption coefficients. The bulk phase diagram exhibits nematic-smectic and smectic-smectic demixing, with smectic phases having different compositions; in some cases they are microfractionated. The calculated surface phase diagram of the wall-nematic interface shows a very rich phase behavior, including layering transitions and complete wetting at high pressures, whereby an infinitely thick smectic film grows at the wall via an infinite sequence of stepwise first-order layering transitions. For lower pressures complete wetting also obtains, but here the smectic film grows in a continuous fashion. Finally, at very low pressures, the wall-nematic interface exhibits critical adsorption by the smectic phase, due to the second-order character of the bulk nematic-smectic transition.
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Affiliation(s)
- Daniel de las Heras
- Departamento de Física Teórica de Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
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Teixeira PIC, Barmes F, Anquetil-Deck C, Cleaver DJ. Simulation and theory of hybrid aligned liquid crystal films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:011709. [PMID: 19257054 DOI: 10.1103/physreve.79.011709] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Indexed: 05/27/2023]
Abstract
We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.
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Affiliation(s)
- P I C Teixeira
- Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal
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de las Heras D, Mederos L, Velasco E. Capillary and anchoring effects in thin hybrid nematic films and connection with bulk behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:011712. [PMID: 19257057 DOI: 10.1103/physreve.79.011712] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2008] [Revised: 12/24/2008] [Indexed: 05/27/2023]
Abstract
By means of a molecular model, we examine hybrid nematic films with antagonistic anchoring angles where one of the surfaces is in the strong anchoring regime. If anchoring at the other surface is weak, and in the absence of wetting by the isotropic phase, the anchoring transition may interact with the capillary isotropic-nematic transition. For general anchoring conditions on this surface we confirm the existence of the steplike biaxial phase and the associated transition to the linear constant-tilt-rotation, configuration. The steplike phase is connected with the bulk isotropic phase for increasing film thickness so that the latter transition is to be interpreted as the capillary isotropic-nematic transition in a hybrid film.
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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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Mima T, Narumi T, Kameoka S, Yasuoka K. Cell size dependence of orientational order of uniaxial liquid crystals in flat slit. MOLECULAR SIMULATION 2008. [DOI: 10.1080/08927020802256058] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Piñeiro MM, Galindo A, Parry AO. Surface ordering and capillary phenomena of confined hard cut-sphere particles. SOFT MATTER 2007; 3:768-778. [PMID: 32900141 DOI: 10.1039/b701463e] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Isothermal-isobaric and Gibbs ensemble Monte Carlo (GEMC) computer simulations of = 1500 and = 3000 hard cut spheres of aspect ratio / = 0.1, respectively, are carried out in order to investigate the effects of confinement on the isotropic (I)-nematic (N) phase transition. We first consider the free system, and confirm the stabilisation of isotropic (I), nematic (N) and columnar (Col) states. We examine in detail the I-N transition and find coexistence densities of =0.355 and =0.368. A slab geometry is then considered for two types of walls: a hard wall, which excludes the particles entirely, and an 'adsorbent' wall which excludes the centre of mass of the particles. The adsorbent wall is found to favour planar (edge-on) alignment, which results in the formation of a first layer of adsorbed molecules, which then acts as a rough hard wall for subsequent particles, and promotes disordered states. Using Gibbs ensemble simulations we determine the capillary phase diagram of the system, and the adsorption as a function of pore width. The capillary phase diagram obtained from Gibbs ensemble simulations corresponds to one with a first-order capillary isotropisation transition, with an associated capillary critical point for a wall separation of ∼3. The hard walls are seen to promote homeotropic (face-on) alignment of the cut spheres, and promote the stabilisation of the nematic phase. In this case the capillary phase diagram obtained from the GEMC simulations exhibits a first-order capillary nematisation transition, and a capillary critical point for a wall separation of ∼4.
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Affiliation(s)
- Manuel M Piñeiro
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London, UKSW7 2AZ
| | - Amparo Galindo
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London, UKSW7 2AZ
| | - Andrew O Parry
- Department of Mathematics, Imperial College London, South Kensington Campus, London, UKSW7 2AZ
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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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30
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de Las Heras D, Velasco E, Mederos L. Capillary smectization and layering in a confined liquid crystal. PHYSICAL REVIEW LETTERS 2005; 94:017801. [PMID: 15698132 DOI: 10.1103/physrevlett.94.017801] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2004] [Indexed: 05/24/2023]
Abstract
Using density-functional theory, we have analyzed the phase behavior of a model liquid crystal confined between two parallel, planar surfaces (i.e., the so-called slit pore). As a result of confinement, a rich phase behavior arises. The complete liquid-crystal phase diagram of the confined fluid is mapped out as a function of wall separation and chemical potential. Strong commensuration effects in the film with respect to wall separation lead to enhanced smectic ordering, which gives capillary smectization (i.e., formation of a smectic phase in the pore), or frustrated smectic ordering, which suppresses capillary smectization. These effects also produce layering transitions. Our nonlocal density-functional-based analysis provides a unified picture of all the above phenomena.
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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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Rodríguez-Ponce I, Romero-Enrique JM, Rull LF. Density functional theory study of the nematic–isotropic transition in an hybrid cell. J Chem Phys 2005; 122:14903. [PMID: 15638696 DOI: 10.1063/1.1829041] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We have employed the density functional theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyze the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropiclike to nematiclike states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interfacelike states which allow us to continuously transform the nematiclike phase to the isotropiclike phase without undergoing a sharp phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematiclike state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematiclike state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematiclike states.
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Affiliation(s)
- I Rodríguez-Ponce
- Physik Department, Technische Universität München, James-Franck-Strasse, D-85747 Munich, Germany
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