# A Molecular Meanfield Model for the Biaxial Rectangular Discotic Phase with Herring-Bone Packing of Tilted Molecules

01 May 1995-Molecular Crystals and Liquid Crystals (Taylor & Francis Group)-Vol. 264, Iss: 1, pp 165-179

TL;DR: In this article, a molecular mean field model for a rectangular columnar to hexagonal columnar phase transition is presented, assuming the molecules basically to be biaxial objects.

Abstract: A molecular meanfield model for a rectangular columnar to hexagonal columnar phase transition, as observed in case of the HAT series, is presented here assuming the molecules basically to be biaxial objects The theory is developed for a rectangular lattice having herring-bone packing of the tilted molecules Various types of phase diagrams for a homologous series are reproduced for different values of molecular biaxiality Some of them are very similar to the experimentally observed cases but others, particularly involving biaxial nematic phase, are not yet observed It is shown that a gradual lowering of biaxiality with the addition of flexible chain segments can lead to the full phase sequence observed in the HAT series

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TL;DR: In this paper, the structures of columnar mesophases that depend on the presence of either N-H⋯O, or H-O-Bonds (subsumed under the term ‘N|H|O-bonds') are reviewed.

Abstract: The structures of supramolecular columnar mesophases that depend on the presence of either N–H⋯O, or N⋯H–O– hydrogen bonds (subsumed under the term ‘N|H|O-bonds’) are reviewed. The thesis is supported that supramolecular mesogenes bridge different fields of liquid crystal research, offering the opportunity to create a unified picture of thermotropic, and lyotropic mesomorphism. With the examples of N|H|O hydrogen bond mesogenes the molecular structures of the respective mesogenes are presented, and general principles to rationally construct such molecules are discussed. A connection is drawn to systems from isolated columns as found in low molecular weight organogels. Perspectives, and outlooks for possible applications of N|H|O hydrogen bonded columnar phases are given.

117 citations

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TL;DR: The results point to the formation of dynamical structural defects along the columns in stacks of liquid-crystalline tetraalkoxy-substituted, metal-free phthalocyanines.

Abstract: We present a joint molecular dynamics (MD)/kinetic Monte Carlo (KMC) study aimed at the atomistic description of charge transport in stacks of liquid-crystalline tetraalkoxy-substituted, metal-free phthalocyanines. The molecular dynamics simulations reproduce the major structural features of the mesophases, in particular, a phase transition around 340 K between the rectangular and hexagonal phases. Charge transport simulations based on a Monte Carlo algorithm show an increase by 2 orders of magnitude in the hole mobility when accounting for the rotational and translational dynamics. The results point to the formation of dynamical structural defects along the columns.

82 citations

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TL;DR: In this article, a simple scheme of nomenclature is suggested for the six different types of columnar phase requiring only two structural parameters: firstly the symmetry of the lattice (hexagonal: Dh, rectangular: Dr, oblique: Dob), and secondly the order or disorder within the column.

Abstract: Among the various mesogenic polyaromatic cores, only benzene, triphenylene, truxene and anthraquinone hexasubstituted derivatives exhibit one or several D columnar phases and/or a ND lenticular nematic phase. A simple scheme of nomenclature is suggested for the six different types of columnar phase requiring only two structural parameters: firstly the symmetry of the lattice (hexagonal: Dh, rectangular: Dr, oblique: Dob), and secondly the order or disorder within the column. Several examples of disc-like compounds which form phases Dho, Dhd, Drd(P21/a) , Drd(P2/a), Drd(C2/m), Dod.d are described and a discussion of the specificity of the corresponding optical textures is given. Then the complex polymorphism of these new mesogenic materials (normal, inverse, reentrant columnar-nematic sequences) is reviewed. Finally, a simple classification of the various types of lyotropic and thermotropic phase is proposed, based on the shape of the structural element (finite or infinite cylinder, disc, infinite...

287 citations

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TL;DR: In this article, five mesomorphic phases are described in several disc-like liquid-crystals, which are hexalkanoyloxy benzenes, triphenylenes or truxenes, hexa-alkoxy triphenynylenes, Hexa-benzoates of triphenylene.

Abstract: Five mesomorphic phases are described in several disc-like liquid-crystals. They are hexalkanoyloxy benzenes, triphenylenes or truxenes, hexa-alkoxy triphenylenes, hexa-benzoates of triphenylene. Several of these compounds exhibit a complex polymorphism. Informations on the structures of these phases have been obtained by means of X-Ray diffraction; except a Nd namatic phase all the others one are columnar phases. At the same time a systematic study has been performed by the well known method of isomorphy. All these results allow us to propose a general classification of these phases.

219 citations

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Yale University

^{1}TL;DR: In this paper, a model for a fluid of biaxial particles within a type of mean-field approximation was solved. And the results suggest that the phase diagram of such a fluid exhibits a special critical point where two second-order critical lines meet a first-order phase boundary in a sharp cusp.

Abstract: A model is solved for a fluid of biaxial particles within a type of mean-field approximation. The results suggest that the phase diagram of such a fluid exhibits a special critical point where two second-order critical lines meet a first-order phase boundary in a sharp cusp. The features of the phase diagram suggest a new way to look for critical phase transitions and biaxial phases in liquid crystals.

196 citations

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TL;DR: In this paper, the authors examined the possibility that plate-like molecules might give rise to biaxial liquid crystal order by considering a molecular field lattice model in which molecules are represented by rectangular plates.

Abstract: The possibility that the repulsive interaction between platelike molecules might give rise to biaxial liquid crystal order is examined by considering a molecular‐field lattice model in which molecules are represented by rectangular plates. We find that plates which are neither very square nor very rodlike in shape may exist in a phase characterized by biaxial long‐range order in the orientation of the plates. This biaxial phase occurs at high pressure. At some lower pressure the biaxial phase undergoes a second order phase transition to a uniaxial phase. At a still lower pressure the uniaxial phase undergoes a transition to an isotropic phase. This last phase transition is usually first order in that there are discontinuities in the density and the orientational order in going through the transition. However the size of the discontinuities depend strongly on the shape of the plates. For example for plates of length 6 and width approximately 2.22 and thickness 1, the discontinuities are zero, and the transition is accidentally second order. The discontinuities at this uniaxial‐isotropic transition are always very small for plates which have the potential to give rise to a biaxial phase. This last result is shown to have a direct physical basis which should transcend the limitations imposed by the approximate nature of our calculation. Thus we conclude that for real substances likely to have biaxial phases of the type we have studied, the value of the nematic order parameter at the nematic‐isotropic transition should be much lower than for other nematic liquid crystals.

105 citations

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IBM

^{1}TL;DR: In this paper, the energy of interaction between two asymmetric molecules is considered and a generalization of the Maier-Saupe model of a nematic liquid is proposed, where the exact state of minimum internal energy is found to be biaxial.

Abstract: The general form of the energy of interaction between two asymmetric molecules is considered. This leads to a generalization of the Maier-Saupe model of a nematic liquid. The exact state of minimum internal energy of the system is found to be biaxial. In the molecular field approximation the consistency relations yield two distinct ordered states, a uniaxial state and a biaxial state. It is shown that with decreasing temperature the fluid will have two successive transitions according to the scheme: isotropicuniaxial orderbiaxial order.

78 citations