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Lebovka NI, Tatochenko MO, Vygornitskii NV, Tarasevich YY. Confinement effects on the random sequential adsorption packings of elongated particles in a slit. Phys Rev E 2021; 104:054104. [PMID: 34942691 DOI: 10.1103/physreve.104.054104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 10/22/2021] [Indexed: 11/07/2022]
Abstract
The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, ɛ=l/d) of the particles was varied within the range ɛ∈[1;32] while the distance between the walls was varied within the range h/d∈[1;80]. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of ɛ and h significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage φ(ɛ) or φ(h) were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.
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Affiliation(s)
- Nikolai I Lebovka
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Mykhailo O Tatochenko
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Nikolai V Vygornitskii
- Laboratory of Physical Chemistry of Disperse Minerals, F. D. Ovcharenko Institute of Biocolloidal Chemistry, NAS of Ukraine, Kyiv 03142, Ukraine
| | - Yuri Yu Tarasevich
- Laboratory of Mathematical Modeling, Astrakhan State University, Astrakhan 414056, Russia
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Velasco E, Mederos L. Anisotropic line tension of domains in lipid monolayers. Phys Rev E 2019; 100:032413. [PMID: 31639977 DOI: 10.1103/physreve.100.032413] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Indexed: 06/10/2023]
Abstract
We formulate a simple effective model to describe molecular interactions in a lipid monolayer and calculate the line tension between coexisting domains. The model represents lipid molecules in terms of two-dimensional anisotropic particles on the plane of the monolayer. These particles interact through forces that are believed to be relevant for the understanding of fundamental properties of the monolayer: van der Waals interactions originating from lipid chains and dipolar forces between dipole groups in the molecular heads. The model stresses the liquid-crystalline nature of the ordered phase in lipid monolayers and explains coexistence properties between ordered and disordered phases in terms of molecular parameters. Thermodynamic and interfacial properties of the model are analyzed using density-functional theory. In particular, the line tension at the interface between ordered and disordered phases turns out to be highly anisotropic with respect to the angle between the nematic director and the interface separating the coexisting phases. This important feature mainly results from the tilt angle of lipid chains and, to a lesser extent, from dipolar interactions perpendicular to the monolayer. The role of the two dipolar components, parallel and perpendicular to the monolayer, is assessed by comparing with computer simulation results for lipid monolayers.
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Affiliation(s)
- E 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
| | - L Mederos
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, C/Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain
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Bautista-Carbajal G, Gurin P, Varga S, Odriozola G. Phase diagram of hard squares in slit confinement. Sci Rep 2018; 8:8886. [PMID: 29891959 PMCID: PMC5995855 DOI: 10.1038/s41598-018-26922-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Accepted: 05/21/2018] [Indexed: 12/02/2022] Open
Abstract
This work shows a complete phase diagram of hard squares of side length σ in slit confinement for H < 4.5, H being the wall to wall distance measured in σ units, including the maximal packing fraction limit. The phase diagram exhibits a transition between a single-row parallel 1-\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\diamond }$$\end{document}◇ˆ structures. For regions Hc(3) < H < Hc(4) and Hc(4) < H < Hc(5), very similar pictures arise. There is a (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ structures. The similarities found for n = 2, 3 and 4 lead us to propose a tentative phase diagram for Hc(n) < H < Hc(n + 1) (n ∈ \documentclass[12pt]{minimal}
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Affiliation(s)
- Gustavo Bautista-Carbajal
- Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 07160, México, Distrito Federal, Mexico
| | - Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201, Hungary
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201, Hungary
| | - Gerardo Odriozola
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200, CD, México, Mexico.
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Gurin P, Varga S, González-Pinto M, Martínez-Ratón Y, Velasco E. Ordering of hard rectangles in strong confinement. J Chem Phys 2017; 146:134503. [DOI: 10.1063/1.4979497] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Affiliation(s)
- Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
| | - Miguel González-Pinto
- 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
| | - Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain
| | - 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
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5
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Sitta CE, Smallenburg F, Wittkowski R, Löwen H. Hard rectangles near curved hard walls: Tuning the sign of the Tolman length. J Chem Phys 2016; 145:204508. [DOI: 10.1063/1.4967876] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Christoph E. Sitta
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Frank Smallenburg
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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6
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Windows-Yule CRK, Scheper BJ, den Otter WK, Parker DJ, Thornton AR. Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles. Phys Rev E 2016; 93:020901. [PMID: 26986277 DOI: 10.1103/physreve.93.020901] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2015] [Indexed: 11/07/2022]
Abstract
The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.
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Affiliation(s)
- C R K Windows-Yule
- Multiscale Mechanics (MSM), CTW and MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.,School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - B J Scheper
- Multiscale Mechanics (MSM), CTW and MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - W K den Otter
- Multiscale Mechanics (MSM), CTW and MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.,Computational Biophysics, TNW and MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - D J Parker
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - A R Thornton
- Multiscale Mechanics (MSM), CTW and MESA+, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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de las Heras D, Velasco E, Martínez-Ratón Y. Capillary and winding transitions in a confined cholesteric liquid crystal. SOFT MATTER 2015; 11:7038-7045. [PMID: 26246247 DOI: 10.1039/c5sm01036e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We consider a Lebwohl-Lasher model of chiral particles confined in a planar cell (slit pore) under different boundary conditions, and solve it using mean-field theory. The phase behaviour of the system with respect to temperature and pore width is studied. Two phenomena are observed: (i) an isotropic-cholesteric transition, which exhibits an oscillatory structure with respect to pore width, and (ii) an infinite set of winding transitions caused by commensuration effects between cholesteric pitch and pore width. The latter transitions have been predicted and analysed by other authors for cholesterics confined in a fixed pore and subjected to an external field promoting the uniaxial nematic phase; here we induce winding transitions solely from geometry by changing the pore width at zero external field (a setup recently explored in atomic-force microscopy experiments). In contrast with previous studies, we obtain the phase diagram in the temperature vs. pore width plane, including the isotropic-cholesteric transition, the winding transitions and their complex relationship. In particular, the structure of winding transitions terminates at the capillary isotropic-cholesteric transition via triple points where the confined isotropic phase coexists with two cholesterics with different helix indices. For symmetric and asymmetric monostable plate anchorings the phase diagrams are qualitatively similar.
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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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Mederos L, Velasco E, Martínez-Ratón Y. Hard-body models of bulk liquid crystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:463101. [PMID: 25335432 DOI: 10.1088/0953-8984/26/46/463101] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.
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Affiliation(s)
- Luis Mederos
- Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain
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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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11
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González-Pinto M, Martínez-Ratón Y, Velasco E. Liquid-crystal patterns of rectangular particles in a square nanocavity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032506. [PMID: 24125284 DOI: 10.1103/physreve.88.032506] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Indexed: 06/02/2023]
Abstract
Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length H composed of hard inner walls. Patterning in the cavity is governed by surface-induced order as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio κ≡L/σ, with L the length and σ the width of the rectangles (L≥σ), and cavity size H. Ordering may be very different from bulk (H→∞) behavior when H is a few times the particle length L (nanocavity). Bulk and confinement properties are obtained for the cases κ=1, 3, and 6. In bulk the isotropic phase is always stable at low packing fractions η=Lσρ_{0} (with ρ_{0} the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher η depending on κ: For increasing η the sequence of isotropic to columnar is obtained for κ=1 and 3, whereas for κ=6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by 90^{∘}); this configuration is necessary to stabilize periodic phases. For κ=1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case κ=3 the commensurate transitions involve columnar phases with different number of columns. In the case κ=6 the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing.
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Affiliation(s)
- Miguel González-Pinto
- Departamento de Física Teórica de la Materia Condensada, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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de las Heras D, Martínez-Ratón Y, Mederos L, Velasco E. Two-dimensional nematics in bulk and confined geometries. J Mol Liq 2013. [DOI: 10.1016/j.molliq.2012.08.014] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Bakhti B, Müller G, Maass P. Interacting hard rods on a lattice: distribution of microstates and density functionals. J Chem Phys 2013; 139:054113. [PMID: 23927249 DOI: 10.1063/1.4816379] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The derivation, constructed from conditional probabilities in a Markov chain approach, yields the exact joint probability distribution for the positions of the rods as a functional of their density profile. For contact interaction ("sticky core model") between rods, we give a lattice fundamental measure form of the density functional and present explicit results for contact correlators, entropy, free energy, and chemical potential. Our treatment includes inhomogeneous couplings and external potentials.
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Affiliation(s)
- Benaoumeur Bakhti
- Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, 49076 Osnabrück, Germany
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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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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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de las Heras D, Martínez-Ratón Y, Velasco E. Phase transitions in nanoconfined binary mixtures of highly oriented colloidal rods. Phys Chem Chem Phys 2010; 12:10831-41. [PMID: 20631968 DOI: 10.1039/c003448g] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We analyse a binary mixture of colloidal parallel hard cylindrical particles with identical diameters but dissimilar lengths L(1) and L(2), with s = L(2)/L(1) = 3, confined by two parallel hard walls in a planar slit-pore geometry, using a fundamental-measure density functional theory. This model presents nematic (N) and two types of smectic (S) phases, with first- and second-order N-S bulk transitions and S-S demixing, and surface behaviour at a single hard wall which includes complete wetting by the S phase mediated (or not) by an infinite number of surface-induced layering (SIL) transitions. In the present paper the effects of confinement on this model colloidal fluid mixture are studied. Confinement brings about profound changes in the phase diagram, resulting from competition between the three relevant length scales: pore width h, smectic period d and length ratio s. Four main effects are identified: (i) second-order bulk N-S transitions are suppressed; (ii) demixing transitions are weakly affected, with small shifts in the mu(1)-mu(2) (chemical potentials) plane; (iii) confinement-induced layering (CIL) transitions occurring in the two confined one-component fluids in some cases merge with the demixing transition; (iv) surface-induced layering (SIL) transitions occurring at a single surface as coexistence conditions are approached are also shifted in the confined fluid. The trends with pore size are analysed by means of complete mu(1)-mu(2) and p-x[combining macron] (pressure-mean pore composition) phase diagrams for particular values of pore size. This work, which is the first one to address the behaviour of liquid-crystalline mixtures under confinement, could be relevant as a first step to understand the self-assembling properties of mixtures of metallic nanoparticles under external fields in restricted geometry.
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Affiliation(s)
- Daniel de las Heras
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
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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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Varga S, Gurin P, Armas-Pérez JC, Quintana-H J. Nematic and smectic ordering in a system of two-dimensional hard zigzag particles. J Chem Phys 2009; 131:184901. [DOI: 10.1063/1.3258858] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tarazona P, Cuesta J, Martínez-Ratón Y. Density Functional Theories of Hard Particle Systems. THEORY AND SIMULATION OF HARD-SPHERE FLUIDS AND RELATED SYSTEMS 2008. [DOI: 10.1007/978-3-540-78767-9_7] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Martínez-Ratón Y, Capitán JA, Cuesta JA. Fundamental-measure density functional for mixtures of parallel hard cylinders. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051205. [PMID: 18643058 DOI: 10.1103/physreve.77.051205] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2008] [Indexed: 05/26/2023]
Abstract
We obtain a fundamental-measure density functional for mixtures of parallel hard cylinders. For this purpose we first generalize to multicomponent mixtures the fundamental-measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of those authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step, we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain
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Triplett DA, Fichthorn KA. Monte Carlo simulation of two-dimensional hard rectangles: confinement effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011707. [PMID: 18351866 DOI: 10.1103/physreve.77.011707] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2007] [Revised: 09/24/2007] [Indexed: 05/26/2023]
Abstract
We use orientational-bias Monte Carlo simulations to examine the phase behavior of two-dimensional hard rectangles in the bulk and under confinement by hard walls. For all of the rod aspect ratios and area fractions studied, we find that confinement increases the degree of nematic ordering over the bulk, as confined rods tend to align their long axes parallel to the confining walls. The extent of nematic ordering increases as the separation between the confining walls decreases. If the aspect ratio of the rectangles is sufficiently large, they exhibit nematic ordering in both the bulk and under confinement, where the nematic director is set by the walls. Rods with a small aspect ratio are isotropic in the bulk and exhibit weak tetratic tendencies for sufficiently high densities. From studies of density profiles, angular distributions, and orientational correlation functions for confined, low-aspect-ratio rods, it is apparent that they align their long axes parallel to the wall in the near-wall region, where layering occurs for sufficiently high rod densities. However, confined rods with low aspect ratios still exhibit weak tetratic (isotropic) tendencies near the center of the confined region for all but the smallest wall separations. We note that although our studies probe the ordering of hard rectangles, the entropic tendencies that we observe here will be present for rods with energetic interactions. Thus, these studies serve as a general starting point for understanding and controlling the assembly of rods in two-dimensional confining geometries.
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Affiliation(s)
- Derek A Triplett
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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de las Heras D, Martínez-Ratón Y, Velasco E. Demixing and orientational ordering in mixtures of rectangular particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031704. [PMID: 17930260 DOI: 10.1103/physreve.76.031704] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2007] [Indexed: 05/25/2023]
Abstract
Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyze the stability of phases with orientational order and the demixing phase behavior of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilized, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares, in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard disks or discorectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behavior, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.
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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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