The Cholesteric Blue Phases
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The Cholesteric Blue Phases P.H. Keyes Introduction In 1888, the year commonly taken as the birthdate of liquid crystal research, F. Reinitzer1 wrote to O. Lehmann to describe the curious properties of cholesteryl benzoate, a "substance [which] has two melting points, if it can be expressed in such a manner." Throughout most of the 33°C interval between thèse two "melting points" this material is in the biréfringent fluid state now known as the cholesteric liquid crystal. Today it is common to find compounds showing a whole cascade of liquid crystalline mesophases as the température is increased, but it is not customary to refer to any of the phase changes between them as "melting points" except for the lowest température transition where the crystalline lattice dissolves. In récent years, however, it has been discovered that many cholesteric liquid crystals, including cholesteryl b e n z o a t e , do something very strange in a température interval of only a degree or so just before they yield up their last bit of liquid crystalline order: they form complex structures having the symmetries of cubic lattices — they "freeze"! — and then "melt" at a higher température into either the ordinary amorphous liquid or else into a new kind of amorphous liquid which in turn undergoes a sharp transition into the ordinary amorphous liquid at still higher température. The reasons for this bizarre behavior and the natures of thèse unusual structures, which hâve corne to be known as the blue phases, are the subjects of this article. The theory needed to understand this phenomenon has been developed only over the last décade or so, and the essential éléments will be reviewed hère. Also briefly reviewed are the experiments that measure the unique properties of thèse blue phases and that détermine which of the many structures predicted by theory are correct. Finally, o u t s t a n d i n g problems, particularly related to the new amor-
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phous phase, known as blue phase III, are mentioned. Other récent review articles containing more of the détails of thèse théories a n d e x p e r i m e n t s are listed in the références.2"6
Qd> = ( y » V « 0 - j ô « W
O)
where m is a unit vector pointing along the long axis of a molécule and the brackets dénote the ensemble average. In a suitable coordinate, frame Qa/3 can be diagonalized and may look like '2Q 1 Qa, = j \ 0 0
0
0
0 -Q+P 0 -Q-P/
(2)
where P is zéro if the nematic liquid crystal is optically uniaxial, and nonzero if it is biaxial. Most nematic liquid crystals are uniaxial and the preferred direction along which the molécules align is called the director and is given the symbol n. In Equation 2 it is understood that with P = 0 the director is along the x axis. If now the coordinate frame should be rotated the order parameter tensor for the uniaxial nematic liquid will look like Qap = Q h r "
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