Biaxial nematic

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A biaxial nematic is a spatially homogeneous liquid crystal with three distinct optical axes. This is to be contrasted to a simple nematic, which has a single preferred axis, around which the system is rotationally symmetric. The symmetry group of a biaxial nematic is <math>D_</math> i.e. that of a rectangular right parallelepiped, having 3 orthogonal <math>C_2</math> axes and three orthogonal mirror planes. In a frame co-aligned with optical axes the second rank order parameter tensor of a biaxial nematic has the form
Q=begin-fracS+T & 0 &0 \0 &-fracS-T & 0 \0 & 0& S\end</math>


<math>S</math> is the standard nematic scalar order parameter

<math>T</math> a measure of the biaxiality.

The first report of a biaxial nematic appeared in 2004 based on a boomerang shaped oxadiazole 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 phases.

It is also found that this material can segregate into chiral 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<sub>u</sub> to a biaxial nematic N<sub>b</sub> mesophase, as predicted...
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