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2014-01-22T14:28:31Z

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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_{2h}</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
:<math>
Q=
\begin{pmatrix}
-\frac{1}{2}S+T & 0 &0 \\
0 &-\frac{1}{2}S-T & 0 \\
0 & 0& S\\
\end{pmatrix}
</math>

where

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

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

The first report of a thermotropic biaxial nematic appeared in 2004<ref>
{{cite journal
|last1=Madsen |first1=L. A.
|last2=Dingemans |first2=T. J.
|last3=Nakata |first3=M.
|last4=Samulski |first4=E. T.
|year=2004
|title=Thermotropic Biaxial Nematic Liquid Crystals
|journal=[[Physical Review Letters]]
|volume=92 |pages=145505
|doi=10.1103/PhysRevLett.92.145505 |pmid=15089552 |bibcode=2004PhRvL..92n5505M
|issue=14
}}</ref><ref>
{{cite journal
|last1=Prasad |first1=V.
|last2=Kang |first2=S.-Woong
|last3=Suresh |first3=K. A.
|last4=Joshi |first4=Leela
|last5=Wang |first5=Qingbing
|last6=Kumar |first6=Satyendra
|year=2005
|title=Thermotropic Uniaxial and Biaxial Nematic and Smectic Phases in Bent-Core Mesogens
|journal=[[Journal of the American Chemical Society]]
|volume=127 |pages=17224
|doi=10.1021/ja052769n
|issue=49
}}</ref> 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.

[[Image:Biaxialnematic.gif|center|Biaxial nematic boomerang liquid crystal]]

It is also found that this material can segregate into [[Chirality (chemistry)|chiral]] domains of opposite handedness.<ref>
{{cite journal
|last1=Görtz |first1=V.
|last2=Goodby |first2=J. W.
|year=2005
|title=Enantioselective segregation in achiral nematic liquid crystals
|journal=[[Chemical Communications]]
|pages=3262
|doi=10.1039/B503846D
|issue=26
}}</ref> 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 Nu to a biaxial nematic Nb mesophase,<ref>
{{cite journal
|last1=Prasad |first1=V.
|last2=Kang |first2=S.-W.
|last3=Suresh |first3=K. A.
|last4=Joshi |first4=L.
|last5=Wang |first5=Q.
|last6=Kumar |first6=S.
|year=2005
|title=Thermotropic Uniaxial and Biaxial Nematic and Smectic Phases in Bent-Core Mesogens
|journal=[[Journal of the American Chemical Society]]
|volume=127 |pages=17224
|doi=10.1021/ja052769n
|issue=49
}}</ref> as predicted by theory and simulation.<ref>
{{cite journal
|last1=Bates |first1=M.
|last2=Luckhurst |first2=G.
|year=2005
|title=Biaxial nematic phases and V-shaped molecules: A Monte Carlo simulation study
|journal=[[Physical Review E]]
|volume=72 |pages=051702
|doi=10.1103/PhysRevE.72.051702
|bibcode = 2005PhRvE..72e1702B
|issue=5 }}</ref> This transition is observed on heating from the Nu phase with [[Polarizing optical microscopy]] as a change in [[Schlieren texture]] and increased light transmittance and from [[x-ray diffraction]] as the splitting of the nematic reflection. The transition is a [[Phase transition|second order transition]] with low energy content and therefore not observed in [[differential scanning calorimetry]]. 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.

[[Image:Biaxialnematic2005.png|center|600px|Azo bent-core mesogen thermal transitions in °C: K 82.8 Sy 93.4 Sx 104.3 Sc 118.5 Nb 149 Nu 176.5 I]]

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<ref>
{{cite journal
|last1=Apreutesei |first1=D.
|last2=Mehl |first2=G. H.
|year=2006
|title=Completely miscible disc and rod shaped molecules in the nematic phase
|journal=[[Chemical Communications]]
|pages=609
|doi=10.1039/b512120e
|issue=6
}}</ref> a miscible system of rods and disks is actually found although the biaxial nematic phase remains elusive.

==See also==
* [[Chromonic]]
* [[Liquid crystal]]
* [[Liquid crystal display]]
* [[Liquid crystal polymer]]
* [[Lyotropic liquid crystal]]
* [[Plastic crystallinity]]
* [[Smart glass]]
* [[Thermochromics]]

== References ==
{{reflist}}

[[Category:Phases of matter]]
[[Category:Crystallography]]
[[Category:Liquid crystals]]

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