Biaxial Nematic Research Articles

New type of cholesteric liquid crystal.

We discuss the defects and the macroscopic properties which can result when a biaxial nematic is chiralized. A "biaxial" cholesteric phase is possible, where two axes of the triad of unit vectors spiral around the third one. In contrast to "ordinary" cholesteric liquid crystals, $\ensuremath{\lambda}$ defects have a singular core. Probably this type of cholesteric liquid crystal has been observed very recently.

Relation Between Molecular Structure and Liquid Crystalline Properties

Abstract The paper draws attention to a few selected problems that are of interest from the molecular point of view. In particular, the following topics are discussed briefly: (i) the activation energy for low frequency dielectric relaxation in the nematic and smectic A phases, (ii) near-neighbor correlation and some of its consequences, e.g., reentrant polymorphism, and (iii) the possibility of producing new kinds of thermotropic phases, e.g., biaxial nematics and discotic smectics, by bridging the gap between rod-like and disk-like mesogens.

Erratum: Elastic continuum theory of biaxial nematics

Erratum: Elastic continuum theory of biaxial nematics

Molecular correlation in thermotropic copolyesters

Uniaxially oriented samples of thermotropic random copolyesters of hydroxybenzoic and hydroxynaphthoic acids, and of hydroxybenzoic acid and ethylene terephthalate, have been characterised in detail using wide-angle X-ray diffraction. The technique was used to measure the global chain orientation, and in the case of the first polymer the meridional scattering has been analysed in terms of diffraction from an isolated straight random chain. Optical microstructures were observed between crossed polars, with circularly polarized light and in plane-polarised light with no analyser present. Interpretation of the contrast seen shown that the material is optically biaxial and leads to the conclusion that, in the liquid-crystalline phase, there is long-range correlation of the rotations of the molecules about their chain axes. The polymers are examples of ‘biaxial nematics’. Thermal analysis indicates that the solid phase has a higher level of conformational order than the melt and that the melting range is very broad. Annealing below the melting point leads to the development of localised regions of enhanced order, especially in specimens with a high degree of overall orientation. The combination of electron diffraction and electron microscopy provides evidence that the lateral growth of ordered entities does not necessarily require regular sequences within the otherwise random copolymer molecules. Small crystals based on identical but non-periodic sequences within the molecules are (NPL crystals) proposed as being consistent with the experimental evidence and the implications of a brief statistical analysis.

Macroscopic behaviour of a biaxial mixture of uniaxial nematics versus hydrodynamics of a biaxial nematic liquid crystal

We discuss to what extent it is possible to distinguish macroscopically a truly biaxial nematic liquid crystal from a biaxial mixture of uniaxial aggregates in lyotropic systems. We propose for some cases simple experiments to resolve this question. The behaviour in an external magnetic field and the flow alignment in a shear flow experiment is discussed. We find that for small shear the flow alignment angle varies linearly with the shear rate S whereas for truly biaxial nematics it is independent of S. In a static external magnetic field the orthorhombic symmetry can be lost above a first critical field and uniaxiality can be reached above a second critical field. The complete set of hydrodynamic equations for a biaxial mixture of uniaxial aggregates is presented in an appendix.

Théorie hydrodynamique des cristaux liquides nématiques biaxes

A hydrodynamic theory of biaxial nematic liquid crystals is presented. The equations of motion are deduced from the principle of virtual power and constitutive equations are proposed by applying the method of local state within the framework of the irreversible thermodynamics. Hence it follows that the dissipative part of the stress tensor contains generally twelve independent viscosity coefficients. The resulting theory is a generalization of the well-known theory of uniaxial nematics.

Defects and their relationship to molecular configurations in nematic polymers

Some recent observations of defects in main-chain nematic and chiral polymers are reviewed in order to obtain a better understanding of the nature of molecular configurations. Important parameters are (a) the chain length, the density of free ends and the length of flexible spacers and (b) the orientational correlations between chains. The first topic, (a), is discussed with respect to observations of defects in uniaxial nematics; the second, (b), is discussed in the light of observations of biaxial nematics and of cholesteric textures of rigid polymers of biological interest. The elements of a geometrical (structural) model which includes local competitions between coiling and orientational correlations and which uses the methods developed for the representation of frustration in curved spaces are given.

Isothermal Hydrodynamics of Biaxial Nematics

Abstract Differential equations governing elastic and flow behavior of compressible biaxial nematics are derived using the Ericksen-Leslie approach (ELA). Expressions of the free energy density F, viscous stress [sgrave] 1 ji and flexoelectric polarisation Pi (f) are derived for monoclinic and triclinic nematics using the principal axes approach utilised by Saupe. The expression of [sgrave] 1 ji derived using ELA can be reduced to that derived from Saupe's approach by adopting a procedure which was developed in an earlier communication. For biaxial nematics, the number of elastic constants seems to be the same as the number of viscosity coefficients, in general.

Elastic continuum theory of biaxial nematics

The elastic-distortion free-energy density of biaxial nematics is derived with use of the formalism of tensor analysis. The macroscopic description of biaxial nematics involves 12 bulk elastic constants. The appearance of chirality introduces an additional number of 5 twist terms.

Landau Theory of Biaxial Nematic Liquid Crystals

Abstract The orientational order of molecules in a liquid crystal is traditionally described by spatial or temporal averages of functions that are quadratic in the direction cosines of molecular axes with respect to laboratory fixed axes. The free energy describing the nematic phase must be independent of the choice of coordinate systems and therefore rotationally invariant with respect to both laboratory and molecular frames. A Landau theory for biaxial and uniaxial nematics based on six fundamental invariants is developed which is properly rotationally invariant. Four possible nematic phases, two uniaxial and two biaxial, result. NMR experiments should be able to identify which of these actually occur in specific materials.

Isothermal Hydrodynamics of Orthorhombic Nematics

Abstract Differential equations governing elastic and flow behaviour of compressible orthorhombic biaxial nematics are derived using the Ericksen-Leslie approach for uniaxial nematics. The preferred direction of orientation is represented by a mutually orthogonal triad of unit vectors (directors), each of which is a diad axis of symmetry. The expression for non-dissipative stress is deduced as a consequence of entropy inequality; the free energy density is found to satisfy a symmetry relation similar to that for uniaxial nematics. The expression for viscous stress derived on general symmetry assumptions depends on 21 viscosity coefficients. Use of the dissipative function approach reduces this number to 15 via three Onsager relations and three symmetry relations; the viscous stress becomes identical to that derived by Saupe.2 Under uniaxial symmetry about one director, the expression for the viscous stress reduces to that for a compressible uniaxial nematic. It seems possible to determine combinations of ...

Topological Symmetry Breakdown in Cholesterics, Nematics, andHe3

Cholesterics, uniaxial and biaxial nematics, and the dipole-free $A$ phase of superfluid $^{3}\mathrm{He}$ are characterized by order parameters which are left invariant by suitable "symmetry" groups $H$. We show that in the presence of defects, the full group $H$ may not be implementable on the states because of topological obstructions. Thus $H$ is topologically broken in the presence of suitable defects.

Erratum - Theory of flow alignment in biaxial nematics and nematic discotics

Erratum - Theory of flow alignment in biaxial nematics and nematic discotics

Number of elastic coefficients in a biaxial nematic liquid crystal

Number of elastic coefficients in a biaxial nematic liquid crystal

Uniaxial and biaxial lyotropic nematic liquid crystals

Experimental evidence for the existence of optically biaxial lyotropic nematics is presented. The first experimental measurements of the optical uniaxial birefringence $\ensuremath{\Delta}n$ versus the temperature in a discotic nematic are reported; they show a discontinuity of $\ensuremath{\Delta}n$ at the discotic-calamitic phase transition.

Hydrodynamics of biaxial nematics with arbitrary nonsingular textures

The hydrodynamics of biaxial nematics has been obtained in the presence of an external field $\stackrel{\ensuremath{\rightarrow}}{H}$. By working with the triad order parameter, we obtain results valid for arbitrary nonsingular textures. We also present the bending energy for biaxial nematics. Our derivation of the hydrodynamics explicitly includes angular momentum conservation. The resulting hydrodynamic equations clearly possess a rotating-equilibrium solution. In an Appendix we discuss extending the theory to include the internal angular momentum of the molecules which constitute the biaxial nematic.

Theory of flow alignment in biaxial nematics and nematic discotics

Theory of flow alignment in biaxial nematics and nematic discotics

Broken symmetries and hydrodynamics of superfluidP23-neutron-star matter

We investigate spontaneously broken symmetries and their conseqeunces for the static and dynamic behavior of $^{3}P_{2}$-neutron-star matter. Apart from a broken gauge symmetry, which is characteristic of any superfluid, the total rotational symmetry of spin and orbit space is spontaneously broken, a property unique to $^{3}P_{2}$-neutron-star matter. The additional hydrodynamic variables are discussed, especially their commutator relations and their anholonomity properties. A complete set of nonlinear hydrodynamic equations is derived, and a procedure for guaranteeing total angular momentum conservation locally is presented. As unusual hydrodynamic excitations we find three pairs of damped spin-orbit waves which reflect the intricate coupling of orbit and spin space in $^{3}P_{2}$-neutron-star matter. Its hydrodynamics shares some properties with biaxial nematic liquid crystals on the one hand and with $^{3}\mathrm{He}$-B on the other. Finally, we discuss the consequences of a reversible current connecting the vortices of the magnetic field with the density of linear momentum which can influence the magnetohydrodynamics of a neutron star.

Hydrodynamics of Biaxial Nematic Liquid Crystals

Abstract The linearized hydrodynamic equations and the elastic part of the free energy density for a biaxial nematic liquid crystal are derived. The equations are then used to predict the attenuation of low frequency sound waves.

Elastic and flow properties of biaxial nematics

Elastic and hydrodynamic properties of biaxial nematics of D2 symmetry are theoretically studied. The treatment follows closely the classical formalism used for solids which is extended by inclusion of director fields. The resulting theory is a generalization of the well-established theory of uniaxial nematics. The elasticity and viscosity coefficients have similar physical meanings. The theory for incompressible biaxial nematics contains 12 relevant elastic constants and 12 viscosity coefficients. Three of the elastic constants can be assigned to twist deformations, six to bend deformations, and three to coupling between bend and twist. Nine of the viscosity coefficients can be determined in simple shear flow experiments. The remaining three describe the friction connected with the rotation of alignment axes.