A biaxial nematic is a spatially homogeneous

liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. T ...

with three distinct optical axes. This is to be contrasted to a simple

nematic Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. The ...

, which has a single preferred axis, around which the system is rotationally symmetric. The

symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...

of a biaxial nematic is

D_

i.e. that of a rectangular right parallelepiped, having 3 orthogonal

C_2

axes and three orthogonal mirror planes. In a frame co-aligned with optical axes the second rank

order parameter In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...

of a biaxial nematic has the form :

Q=
\begin
-\fracS+T & 0 &0 \\
0 &-\fracS-T & 0 \\
0 & 0& S\\
\end

where

S

is the standard nematic scalar order parameter and

T

is a measure of the biaxiality. The first report of a thermotropic biaxial nematic appeared in 2004 based on a

boomerang A boomerang () is a thrown tool, typically constructed with aerofoil sections and designed to spin about an axis perpendicular to the direction of its flight. A returning boomerang is designed to return to the thrower, while a non-returning b ...

shaped

oxadiazole Oxadiazoles are a class of heterocyclic aromatic chemical compound of the azole family; with the molecular formula C2H2N2O. There are four isomers of oxadiazole: File:1,2,3-oxadiazole.svg, 1,2,3-oxadiazole File:1,2,4-oxadiazole.svg, 1,2,4-oxadiazo ...

bent-core mesogen. The biaxial nematic phase for this particular compound only occurs at temperatures around 200 °C and is preceded by as yet unidentified

smectic Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. The ...

phases.

It is also found that this material can segregate into

chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...

domains of opposite handedness. For this to happen the boomerang shaped molecules adopt a helical superstructure. In one azo bent-core mesogen a thermal transition is found from a uniaxial N_u to a biaxial nematic N_b mesophase, as predicted by theory and simulation. This transition is observed on heating from the N_u phase with Polarizing optical microscopy as a change in Schlieren texture and increased light transmittance and from

x-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...

as the splitting of the nematic reflection. The transition is a second order transition with low energy content and therefore not observed in

differential scanning calorimetry Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature. Both the sample and ref ...

. The positional order parameter for the uniaxial nematic phase is 0.75 to 1.5 times the mesogen length and for the biaxial nematic phase 2 to 3.3 times the mesogen length. Biaxialnematic2005

Another strategy towards biaxial nematics is the use of mixtures of classical rodlike mesogens and disklike discotic mesogens. The biaxial nematic phase is expected to be located below the minimum in the rod-disk phase diagram. In one study a miscible system of rods and disks is actually found although the biaxial nematic phase remains elusive.

References

{{reflist Phases of matter Crystallography Liquid crystals

See also

References