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Nascimento ES, Henriques EF, Vieira AP, Salinas SR. Maier-Saupe model for a mixture of uniaxial and biaxial molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062503. [PMID: 26764707 DOI: 10.1103/physreve.92.062503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2015] [Indexed: 06/05/2023]
Abstract
We introduce shape variations in a liquid-crystalline system by considering an elementary Maier-Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature T, concentration c of intrinsically biaxial molecules, and a parameter Δ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structure, including uniaxial and biaxial nematic phases, a reentrant ordered region, and many distinct multicritical points. Also, we use the formalism to write an expansion of the free energy in order to make contact with the Landau-de Gennes theory of nematic phase transitions.
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Affiliation(s)
- E S Nascimento
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil
| | - E F Henriques
- Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, 96010-900 Pelotas, RS, Brasil
| | - A P Vieira
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil
| | - S R Salinas
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil
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Belli S, Dijkstra M, van Roij R. Depletion-induced biaxial nematic states of boardlike particles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:284128. [PMID: 22739023 DOI: 10.1088/0953-8984/24/28/284128] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
With the aim of investigating the stability conditions of biaxial nematic liquid crystals, we study the effect of adding a non-adsorbing ideal depletant on the phase behavior of colloidal hard boardlike particles. We take into account the presence of the depletant by introducing an effective depletion attraction between a pair of boardlike particles. At fixed depletant fugacity, the stable liquid-crystal phase is determined through a mean-field theory with restricted orientations. Interestingly, we predict that for slightly elongated boardlike particles a critical depletant density exists, where the system undergoes a direct transition from an isotropic liquid to a biaxial nematic phase. As a consequence, by tuning the depletant density, an easy experimental control parameter, one can stabilize states of high biaxial nematic order even when these states are unstable for pure systems of boardlike particles.
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Affiliation(s)
- S Belli
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands.
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Trojanowski K, Pająk G, Longa L, Wydro T. Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011704. [PMID: 23005434 DOI: 10.1103/physreve.86.011704] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Revised: 05/22/2012] [Indexed: 06/01/2023]
Abstract
We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [L. Longa, G. Pająk, and T. Wydro, Phys. Rev. E 79, 040701(R) (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (N(T)), and chiral nematic tetrahedratic (N(T)(*)) phases of global T(d), D(2d), and D(2) symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the N(T)(*) phase is also given.
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Affiliation(s)
- Karol Trojanowski
- Marian Smoluchowski Institute of Physics, Department of Statistical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, Reymonta 4, Kraków, Poland
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Grzybowski P, Longa L. Biaxial nematic phase in model bent-core systems. PHYSICAL REVIEW LETTERS 2011; 107:027802. [PMID: 21797641 DOI: 10.1103/physrevlett.107.027802] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2010] [Revised: 05/05/2011] [Indexed: 05/31/2023]
Abstract
We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.
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Affiliation(s)
- Piotr Grzybowski
- Marian Smoluchowski Institute of Physics, Department of Statistical Physics and Mark Kac Center for Complex Systems Research, Jagellonian University, Reymonta 4, Kraków, Poland
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do Carmo E, Vieira AP, Salinas SR. Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011701. [PMID: 21405699 DOI: 10.1103/physreve.83.011701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2010] [Indexed: 05/30/2023]
Abstract
We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results.
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Affiliation(s)
- E do Carmo
- Instituto de Física, Universidade de São Paulo, São Paulo, Brazil
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Polymerization in Liquid Crystal Medium: Preparation of Polythiophene Derivatives Bearing a Bulky Pyrimidine Substituent. Polymers (Basel) 2010. [DOI: 10.3390/polym2040393] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Longa L, Pajak G, Wydro T. Chiral symmetry breaking in bent-core liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:040701. [PMID: 19518164 DOI: 10.1103/physreve.79.040701] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2008] [Indexed: 05/27/2023]
Abstract
By molecular modeling we demonstrate that the nematic long-range order discovered in bent-core liquid-crystal systems should reveal further spatially homogeneous phases. Two of them are identified as a tetrahedratic nematic (N_{T}) phase with D_{2d} symmetry and a chiral tetrahedratic nematic (N_{T};{ *}) phase with D2 symmetry. These phases were found for a lattice model with quadrupolar and octupolar anisotropic interactions using mean-field theory and Monte Carlo simulations. The phase diagrams exhibit tetrahedratic (T) , N_{T} , and N_{T};{ *} phases, in addition to ordinary isotropic (I) , uniaxial nematic (N_{U}) , and biaxial nematic (N_{B}) phases.
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Affiliation(s)
- Lech Longa
- Marian Smoluchowski Institute of Physics, Department of Statistical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, Reymonta 4, Kraków, Poland.
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Berardi R, Muccioli L, Orlandi S, Ricci M, Zannoni C. Computer simulations of biaxial nematics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:463101. [PMID: 21693834 DOI: 10.1088/0953-8984/20/46/463101] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Biaxial nematic (N(b)) liquid crystals are a fascinating condensed matter phase that has baffled, for more than thirty years, scientists engaged in the challenge of demonstrating its actual existence, and which has only recently been experimentally found. During this period computer simulations of model N(b) have played an important role, both in providing the basic physical properties to be expected from these systems, and in giving clues about the molecular features essential for the thermodynamic stability of N(b) phases. However, simulation studies are expected to be even more crucial in the future for unravelling the structural features of biaxial mesogens at the molecular level, and for helping in the design and optimization of devices towards the technological deployment of N(b) materials. This review article gives an overview of the simulation work performed so far, and relying on the recent experimental findings, focuses on the still unanswered questions which will determine the future challenges in the field.
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Affiliation(s)
- Roberto Berardi
- Dipartimento di Chimica Fisica e Inorganica, and INSTM-CRIMSON, Università di Bologna, Viale Risorgimento 4, 40136 Bologna, Italy
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Allender D, Longa L. Landau-de Gennes theory of biaxial nematics reexamined. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011704. [PMID: 18763970 DOI: 10.1103/physreve.78.011704] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2008] [Indexed: 05/16/2023]
Abstract
Recent experiments report that the long-looked-for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations, we concentrate on some elementary theoretical issues concerned with the classical sixth-order Landau-de Gennes free energy expansion in terms of the symmetric and traceless tensor order parameter Q alpha beta. In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple, critical, and tricritical points and with multiple (reentrant) biaxial and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.
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Affiliation(s)
- David Allender
- Department of Physics and Liquid Crystal Institute, Kent State University, PO Box 5190, Kent, Ohio 44242-0001, USA.
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Cordoyiannis G, Apreutesei D, Mehl GH, Glorieux C, Thoen J. High-resolution calorimetric study of a liquid crystalline organo-siloxane tetrapode with a biaxial nematic phase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011708. [PMID: 18763974 DOI: 10.1103/physreve.78.011708] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2008] [Indexed: 05/26/2023]
Abstract
High-resolution adiabatic scanning calorimetry and differential scanning calorimetry have been employed to study the thermal behavior of an organo-siloxane tetrapode reported to exhibit a biaxial nematic phase. No signature of the uniaxial to biaxial nematic phase transition could be retraced in sequential heating and cooling runs under different scanning rates, within the experimental resolution. The results obtained reveal that an extremely small heat should be involved in the uniaxial to biaxial nematic phase transition. The isotropic to uniaxial nematic transition at 318+/-0.01 K is very stable, and it is weakly first order with a rather small latent heat of 0.20+/-0.02 J/g .
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Affiliation(s)
- George Cordoyiannis
- Laboratorium voor Akoestiek en Thermische Fysica, Departement Natuurkunde en Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, Leuven, Belgium
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