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Müller M. Memory in the relaxation of a polymer density modulation. J Chem Phys 2022; 156:124902. [DOI: 10.1063/5.0084602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marcus Müller
- Institute for Theoretical Physics, Georg August University Gottingen Faculty of Physics, Germany
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2
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Peters VFD, Vis M, Wensink HH, Tuinier R. Algebraic equations of state for the liquid crystalline phase behavior of hard rods. Phys Rev E 2020; 101:062707. [PMID: 32688562 DOI: 10.1103/physreve.101.062707] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 06/01/2020] [Indexed: 05/24/2023]
Abstract
Based on simplifications of previous numerical calculations [H. Graf and H. Löwen, Phys. Rev. E 59, 1932 (1999)1063-651X10.1103/PhysRevE.59.1932], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.
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Affiliation(s)
- V F D Peters
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - M Vis
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Laboratoire de Chimie, École Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France
| | - H H Wensink
- Laboratoire de Physique des Solides - UMR 8502, CNRS & Université Paris-Saclay, Orsay, France
| | - R Tuinier
- Laboratory of Physical Chemistry, Department of Chemical Engineering and Chemistry & Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
- Van t Hoff Laboratory for Physical and Colloid Chemistry, Department of Chemistry & Debye Institute for Nanomaterials Science, Utrecht University, 3584 CH Utrecht, The Netherlands
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3
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Chrzanowska A. Computational aspects of the smectization process in liquid crystals: An example study of a perfectly aligned two-dimensional hard-boomerang system. Phys Rev E 2017; 95:063316. [PMID: 28709360 DOI: 10.1103/physreve.95.063316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2017] [Indexed: 11/07/2022]
Abstract
A replica method for calculation of smectic liquid crystal properties within the Onsager theory has been presented and applied to an exemplary case of two-dimensional perfectly aligned needlelike boomerangs. The method allows one to consider the complete influence of the interaction terms in contrast to the Fourier expansion method which uses mostly first or second order terms of expansion. The program based on the replica algorithm is able to calculate a single representative layer as an equivalent set of layers, depending on the size of the considered width of the sample integration interval. It predicts successfully smectic density distributions, energies, and layer thicknesses for different types of layer arrangement-of the antiferroelectric or of the smectic A order type. Specific features of the algorithm performance and influence of the numerical accuracy on the physical properties are presented. Future applications of the replica method to freely rotating molecules are discussed.
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Affiliation(s)
- Agnieszka Chrzanowska
- Institute of Physics, Kraków University of Technology, ulica Podchorążych 1, 30-084 Kraków, Poland
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4
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Marechal M, Dussi S, Dijkstra M. Density functional theory and simulations of colloidal triangular prisms. J Chem Phys 2017; 146:124905. [DOI: 10.1063/1.4978502] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthieu Marechal
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Simone Dussi
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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5
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Wittmann R, Marechal M, Mecke K. Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244003. [PMID: 27115987 DOI: 10.1088/0953-8984/28/24/244003] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Density functional theory (DFT) for hard bodies provides a theoretical description of the effect of particle shape on inhomogeneous fluids. We present improvements of the DFT framework fundamental measure theory (FMT) for hard bodies and validate these improvements for hard spherocylinders. To keep the paper self-contained, we first discuss the recent advances in FMT for hard bodies that lead to the introduction of fundamental mixed measure theory (FMMT) in our previous paper (2015 Europhys. Lett. 109 26003). Subsequently, we provide an efficient semi-empirical alternative to FMMT and show that the phase diagram for spherocylinders is described with similar accuracy in both versions of the theory. Finally, we present a semi-empirical modification of FMMT whose predictions for the phase diagram for spherocylinders are in excellent quantitative agreement with computer simulation results.
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Affiliation(s)
- René Wittmann
- Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland. Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstr 7, 91058 Erlangen, Germany
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6
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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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7
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Wittmann R, Marechal M, Mecke K. Fundamental measure theory for smectic phases: Scaling behavior and higher order terms. J Chem Phys 2014; 141:064103. [PMID: 25134547 DOI: 10.1063/1.4891326] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- René Wittmann
- Institute for Theoretical Physics, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Matthieu Marechal
- Institute for Theoretical Physics, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Klaus Mecke
- Institute for Theoretical Physics, Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
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8
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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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9
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Wittmann R, Mecke K. Surface tension of isotropic-nematic interfaces: Fundamental measure theory for hard spherocylinders. J Chem Phys 2014; 140:104703. [DOI: 10.1063/1.4867277] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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de las Heras D, Varga S, Vesely FJ. Mesophase formation in a system of top-shaped hard molecules: Density functional theory and Monte Carlo simulation. J Chem Phys 2011; 134:214902. [DOI: 10.1063/1.3596749] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Cinacchi G, De Gaetani L. Diffusion in the lamellar phase of a rod-sphere mixture. J Chem Phys 2009. [DOI: 10.1063/1.3207951] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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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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13
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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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14
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Cinacchi G, Martínez-Ratón Y, Mederos L, Velasco E. Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders. J Chem Phys 2007; 124:234904. [PMID: 16821950 DOI: 10.1063/1.2207141] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A second-virial Onsager theory, based on Parsons-Lee rescaling and suitably extended to deal with multicomponent systems and smectic phases, has been used to calculate the phase diagram of a collection of binary mixtures of thin and thick hard spherocylinders. In particular, two types of phase diagrams are investigated. First, a number of binary mixtures where the two components have the same total length have been considered; in addition, the phase diagram of a binary mixture where the two components have the same volume has been calculated. For the particles of one of the two components, the length of the cylindrical part and the diameter have always been set equal to 5 and 1, respectively. Spherocylinders of the same total length and different diameter tend to demix considerably as soon as the diameter ratio deviates from unity. This happens especially at high pressures, when at least the phase richer in the thicker component is smectic. In the case where the two components have equal volumes, demixing is further increased due to the disparity not only in particle diameter but also in particle lengths. The incorporation of inhomogeneous layered phases is seen to alter significantly the phase diagrams calculated if only homogeneous phases are allowed, since transitions to a smectic phase often preempt those to a nematic or an isotropic phase. The apparent versatility of the recent experimental techniques suggests that the phase diagram features predicted by the theory might be also observed in real systems.
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Affiliation(s)
- Giorgio Cinacchi
- Dipartimento di Chimica, Università di Pisa, Via Risorgimento 35, I-56126 Pisa, Italy.
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15
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Rex M, Wensink HH, Löwen H. Dynamical density functional theory for anisotropic colloidal particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021403. [PMID: 17930035 DOI: 10.1103/physreve.76.021403] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2007] [Indexed: 05/25/2023]
Abstract
We generalize the formalism of dynamical density functional theory for translational Brownian dynamics toward that of anisotropic colloidal particles which perform both translational and rotational Brownian motion. Using a mean-field approximation for the density functional and a Gaussian-segment model for the rod interaction, the dynamical density functional theory is then applied to a concentrated rod suspension in a confined slab geometry made by two parallel soft walls. The walls are either expanded or compressed and the relaxation behavior is investigated for an equilibrated starting configuration. We find distinctly different orientational ordering during expansion and compression. During expansion we observe preferential parallel ordering of the rods relative to the wall while during compression there is homeotropic ordering perpendicular to the wall. We find a nonexponential relaxation behavior in time. Furthermore, an external field which aligns the rods perpendicular to the walls is turned on or switched off and similar differences in the relaxational dynamics are found. Comparing the theoretical predictions to Brownian dynamics computer simulation data, we find good agreement.
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Affiliation(s)
- M Rex
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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16
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Abstract
We consider the anisotropic interaction between two line segments consisting of a homogeneous distribution of Lennard-Jones centers. The potential energy of such a pair cannot be expressed in closed form. However, we show that it may be approximated in a way that renders this intuitively appealing model competitive both for simulations and theory.
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Affiliation(s)
- Franz J Vesely
- Computational Physics Group, Department of Experimental Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria.
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17
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Cao D, Zhu M, Wang W. Microstructure and Self-Assembly of Inhomogeneous Rigid Rodlike Chains between Two Neutral Surfaces: A Hybrid Density Functional Approach. J Phys Chem B 2006; 110:21882-9. [PMID: 17064154 DOI: 10.1021/jp064040m] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.
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Affiliation(s)
- Dapeng Cao
- Lab of Molecular and Materials Simulation, College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, P R China.
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18
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Murat M, Kantor Y. Elasticity of a system with noncentral potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031124. [PMID: 17025611 DOI: 10.1103/physreve.74.031124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2006] [Indexed: 05/12/2023]
Abstract
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via noncentral two-body potentials as thermal averages of products of first and second partial derivatives of the interparticle potentials and components of the interparticle separation vectors. These results are adapted to hard potentials, where the stress and the elastic constants are expressed as thermal averages of the components of normals to contact surfaces between the particles and components of vectors separating their centers. The averages require knowledge of the simultaneous contact probabilities of two pairs of particles. We apply the expressions to particles for which a contact function can be defined, and demonstrate the feasibility of the method by computing the stress and the elastic constants of a two-dimensional system of hard ellipses using Monte Carlo simulations.
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Affiliation(s)
- Michael Murat
- School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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19
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Abstract
We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.
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Affiliation(s)
- Victor Pryamitsyn
- Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
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20
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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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21
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Wu J. Density functional theory for chemical engineering: From capillarity to soft materials. AIChE J 2006. [DOI: 10.1002/aic.10713] [Citation(s) in RCA: 299] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Cuetos A, Martínez-Haya B, Lago S, Rull LF. Parsons−Lee and Monte Carlo Study of Soft Repulsive Nematogens. J Phys Chem B 2005; 109:13729-36. [PMID: 16852720 DOI: 10.1021/jp051834c] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
A general approach based on the Parsons-Lee theory for soft repulsive molecular fluids is employed to investigate the nematogenic behavior of prolate thermotropic liquid crystals over a broad temperature range. The theory is solved for the particular case of the Kihara soft repulsive spherocylinder model, which is mapped into an effective hard core interaction with a temperature-dependent molecular diameter, expected to resemble the average size and shape of the soft molecules at a given temperature. The reduction of the effective molecular diameter with temperature in the Kihara soft repulsive fluid implies implicitly an increase of the elongation of the molecule and induces the stabilization of the nematic phase at smaller effective packing fractions, contrary to what is found for other fluid models. The rationalization of this effect in terms of excluded volume steric arguments is corroborated by the good general agreement between the Parsons-Lee approach and Monte Carlo simulations for the equation of state of the fluid in the vicinity of the isotropic-nematic transition.
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Affiliation(s)
- A Cuetos
- Departamento de Ciencias Ambientales, Universidad Pablo de Olavide, 41013 Seville, Spain
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23
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Cinacchi G, De Gaetani L, Tani A. Diffusion and viscosity of a calamitic liquid crystal model studied by computer simulation. J Chem Phys 2005; 122:184513. [PMID: 15918735 DOI: 10.1063/1.1895718] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We report a molecular dynamics simulation study on an ensemble of rod-like particles, each composed of nine soft spheres held rigidly along a line. We have calculated translational mean square displacements and velocity autocorrelation functions in the fluid phases exhibited by the model, i.e., smectic A, nematic and isotropic. These quantities have then been used to compute diffusion coefficients. In addition, we have calculated viscosities in the nematic and isotropic phases. Despite its crude nature, the model is capable of providing a faithful reproduction of many features of the transport behavior observed in real liquid-crystalline materials. The simulation results have been compared with the predictions of the modified affine transformation theory, finding only a fair agreement.
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Affiliation(s)
- Giorgio Cinacchi
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, I-56126 Pisa, Italy
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del Río EM, de Miguel E. Smectic phase in a system of hard ellipsoids with isotropic attractive interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051710. [PMID: 16089554 DOI: 10.1103/physreve.71.051710] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2005] [Indexed: 05/03/2023]
Abstract
The smectic phase is studied for a thermotropic fluid model consisting of aligned hard ellipsoids with superimposed square-well attractive interactions of variable range. The system is analyzed using a density functional theory in which the hard-core contributions to the free-energy functional are treated within a nonlocal weighted density approximation and the attractive contributions are considered at a mean-field level. In the absence of attractions the model reduces, under appropriate scaling, to a fluid of hard spheres and therefore does not exhibit smectic ordering. It is shown that above a certain value of the square-well range, smectic ordering is stable relative to the nematic state at densities well inside the fluid region. The nematic-smectic-A transition is found to be continuous at high temperatures and first order at low temperatures, these two regimes being separated by a tricritical point at an intermediate temperature. These predictions have been confirmed by computer simulation of the model fluid. The results highlight that smectic ordering can be stabilized by coupling anisotropic short-range repulsions with the isotropic contribution of the soft attractive interactions. By increasing the pressure, the range of stability of the smectic phase is seen to decrease. At sufficiently high pressure, the smectic phase is suppressed, and the solid phase dominates. Our calculations show that smectic ordering is no longer stable if the range of the attractions is made too long ranged.
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Affiliation(s)
- Elvira Martín del Río
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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Hidalgo RC, Sullivan DE, Chen JZY. Smectic ordering of homogeneous semiflexible polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041804. [PMID: 15903694 DOI: 10.1103/physreve.71.041804] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2004] [Indexed: 05/02/2023]
Abstract
A self-consistent-field theory for fluids of homogeneous wormlike polymers exhibiting a one-dimensional spatial variation is presented. We have extended the treatment of excluded-volume effects by adding an effective interaction term which describes the excluded volume between wormlike cylindrical segments and terminal (or end) segments of the polymer molecules. This enables us to find a smectic-A phase in the case of homogeneous semiflexible polymers. Using this framework, we have investigated the occurrence of smectic-A, nematic, and isotropic phases in the second-virial (Onsager) approximation. Phase diagrams are calculated for systems characterized by different rigidities (i.e., persistence lengths). For the case of infinitely rigid molecules, the nematic-smectic transition appears to be mostly second order. Systems of semiflexible molecules exhibit mainly a first-order smectic-nematic transition, and their isotropic-nematic-smectic triple points are accessed for different rigidity values. The nematic-smectic transition line is in good agreement with previous analytical calculations, which were also performed assuming the second-virial approximation. However, the values of the volume fraction at the nematic-smectic transition are large compared with computer simulation results, indicating limitations of the second-virial approximation.
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Affiliation(s)
- Raul Cruz Hidalgo
- Department of Physics, University of Guelph, Guelph, Ontario, Canada N1G2W1.
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Cinacchi G, De Gaetani L, Tani A. Numerical study of a calamitic liquid-crystal model: phase behavior and structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:031703. [PMID: 15903443 DOI: 10.1103/physreve.71.031703] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2004] [Indexed: 05/02/2023]
Abstract
We have studied an idealized calamitic liquid-crystal model, consisting of a linear rigid array of nine soft repulsive spheres, employing both theory and molecular dynamics simulation. The phase behavior (which includes crystalline, smectic, nematic, and isotropic phases) and structure of a collection of these rodlike particles have been determined by molecular dynamics simulation in an isothermal-isobaric ensemble. The liquid crystalline part of the phase diagram has been compared to that emerging from an Onsager-type density-functional theory. We have found a fair agreement between theory and computer simulation results, with a similar accuracy for the smectic to nematic and nematic to isotropic phase transitions.
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Martínez-Ratón Y, Velasco E, Mederos L. Effect of particle geometry on phase transitions in two-dimensional liquid crystals. J Chem Phys 2005; 122:064903. [PMID: 15740404 DOI: 10.1063/1.1849159] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.
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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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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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Cinacchi G, Mederos L, Velasco E. Liquid–crystal phase diagrams of binary mixtures of hard spherocylinders. J Chem Phys 2004; 121:3854-63. [PMID: 15303954 DOI: 10.1063/1.1774153] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have built the liquid crystal phase diagram of several binary mixtures of freely rotating hard spherocylinders employing a second-order virial density functional theory with Parsons scaling, suitably generalized to deal with mixtures and smectic phases. The components have the same diameter and aspect ratio of moderate value, typical of many mesogens. Attention has been paid to smectic-smectic demixing and the types of arrangement that rods can adopt in layered phases. Results are shown to depend on the aspect ratio of the individual components and on the ratio of their lengths. Smectic phases are seen not to easily mix together at sufficiently high pressures. Layered phases where the longer rods are the majority component have a smectic-A structure. In the opposite case, a smectic-A(2) phase is obtained where the shorter particles populate the layers and the longer ones prefer to stay parallel to the latter in the interlayer region.
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Affiliation(s)
- Giorgio Cinacchi
- Dipartimento di Chimica, Universita di Pisa, Via Risorgimento 35, I-56126 Pisa, Italy.
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Martínez-Ratón Y. Bulk inhomogeneous phases of anisotropic particles: a fundamental measure functional study of the restricted orientations model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061712. [PMID: 15244603 DOI: 10.1103/physreve.69.061712] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2003] [Indexed: 05/24/2023]
Abstract
The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through minimization of the fundamental measure functional (FMF) of hard parallelepipeds. The study of parallel hard cubes (PHC's) as a particular case is also included motivated by recent simulations of this system. As a result a rich phase behavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called here discotic smectic) which was already found in the only existing simulation of the model, and which turns out to be stable because of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level with simulation results of other anisotropic particle systems.
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Affiliation(s)
- Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés, Madrid, Spain.
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De Las Heras D, Velasco E, Mederos L. Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal. J Chem Phys 2004; 120:4949-57. [PMID: 15267357 DOI: 10.1063/1.1646374] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A fluid of hard spherocylinders of length-to-breadth ratio L/D=5 confined between two identical planar, parallel walls--forming a pore of slit geometry--has been studied using a version of the Onsager density-functional theory. The walls impose an exclusion boundary condition over the particle's centers of mass, while at the same time favoring a particular anchoring at the walls, either parallel or perpendicular to the substrate. We observe the occurrence of a capillary transition, i.e., a phase transition associated with the formation of a nematic film inside the pore at a chemical potential different from micro(b)-the chemical potential at the bulk isotropic-nematic transition. This transition terminates at an Ising-type surface critical point. In line with previous studies based on the macroscopic Kelvin equation and the mesoscopic Landau-de Gennes approach, our microscopic model indicates that the capillary transition is greatly affected by the wetting and anchoring properties of the semi-infinite system, i.e., when the fluid is in contact with a single wall or, equivalently, the walls are at a very large distance. Specifically, in a situation where the walls are preferentially wetted by the nematic phase in the semi-infinite system, one has the standard scenario with the capillary transition taking place at chemical potentials less than micro(b) (capillary nematization transition or capillary ordering transition). By contrast, if the walls tend to orientationally disorder the fluid, the capillary transition may occur at chemical potentials larger than micro(b), in what may be called a capillary isotropization transition or capillary disordering transition. Moreover, the anchoring transition that occurs in the semi-infinite system may affect very decisively the confinement properties of the liquid crystal and the capillary transitions may become considerably more complicated.
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Affiliation(s)
- D De Las Heras
- Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid, Spain
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Withers IM. Effects of longitudinal quadrupoles on the phase behavior of a Gay–Berne fluid. J Chem Phys 2003. [DOI: 10.1063/1.1615768] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Galindo A, Haslam AJ, Varga S, Jackson G, Vanakaras AG, Photinos DJ, Dunmur DA. The phase behavior of a binary mixture of rodlike and disclike mesogens: Monte Carlo simulation, theory, and experiment. J Chem Phys 2003. [DOI: 10.1063/1.1598432] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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de las Heras D, Mederos L, Velasco E. Wetting properties of a hard-spherocylinder fluid on a substrate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:031709. [PMID: 14524790 DOI: 10.1103/physreve.68.031709] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2003] [Indexed: 05/24/2023]
Abstract
A density-functional theory is used to analyze the wetting properties of a fluid made up of hard spherocylinders of a length-to-breadth ratio L/D=5 on a model substrate. The substrate imposes an exclusion boundary condition over the molecular centres of mass, while at the same time favoring a definite molecular orientation, either parallel or perpendicular to the substrate, in a region next to the substrate. The wetting properties of this system are seen to depend on the strength with which the substrate orients the molecules: as the latter is increased, wetting by nematic phase is followed by a region of partial wetting which then leads to reentrant wetting by nematic. The two wetting transitions correspond to wetting films with nematic director perpendicular and parallel to the substrate, respectively. Also, in the region of partial wetting, an anchoring transition occurs in the substrate-nematic interface between two different director configurations (parallel and perpendicular to the substrate). Finally, a metastable wetting transition by isotropic is also obtained. This model considerably enriches the wetting phenomenology of the hard-spherocylinder fluid on substrates, of which only the pure hard wall, with no surface control parameter available, has been considered so far.
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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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36
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Velasco E, Mederos L, Sullivan DE. Density-functional study of the nematic-isotropic interface of hard spherocylinders. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:021708. [PMID: 12241197 DOI: 10.1103/physreve.66.021708] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2002] [Indexed: 05/23/2023]
Abstract
The Somoza-Tarazona density-functional theory is applied to the isotropic-nematic interface of hard spherocylinders with length (L)-to-diameter (D) ratios in the range L/D=5-20. Properties such as the density and orientational order-parameter profiles and the variation of interfacial tension with bulk nematic tilt angle agree qualitatively with results of previous studies at larger values of L/D using both computer simulation and the Onsager second-virial approximation. The minimum interfacial tension is obtained at a tilt angle of 90 degrees. For values of L/D approximately 5, it is found that the Onsager approximation predicts a spurious minimum in the interfacial tension at small tilt angles.
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Affiliation(s)
- E Velasco
- Departamento de Física Teórica de la Materia Condensada and Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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