The blue phases

The blue phases occur in cholesteric systems of sufficiently low pitch, less than about 5000 A. They exist over a narrow temperature range, usually 1 C, between the cholesteric liquid crystal phase and the isotropic liquid phase (see (1.3.5)). The first observation of a blue phase was described by Reinitzer himself in his historic letter to Lehmann as follows On cooling (the liquid phase of cholesteryl benzoate) a violet and blue phenomenon appears, which then quickly disappears leaving the substance cloudy but still liquid. Although Lehmann recognized it as a stable phase, not until the 1970s was it generally accepted that the blue phases are thermodynamically distinct phases. The nature of these phases has now become a subject of considerable interest to condensed matter physicists. 

Striking confirmation of the cubic structures of BP I and BP II was obtained by Onusseit and Stegemeyer and others, who succeeded in growing beautiful single crystals of up to a few hundred microns in size (fig. 4.8.2(a)). Optical Kossel diagrams, analogous to the Kossel lines observed in X-ray diffraction from crystals, have confirmed their symmetry (fig. 4.8.2(f))). 

Topologically, it turns out that the helical structure of the cholesteric cannot be deformed continuously to produce a cubic lattice without creating defects. Thus BP I and BP II are unique examples in nature of a regular three-dimensional lattice composed of disclination lines. Possible unit cells of such a disclination network, arrived at by minimizing the Oseen-Frank free energy, are shown in fig. 4.8.3. The tubes in the diagram represent disclination lines, whose cores are supposed to consist of isotropic (liquid) material. Precisely which of these configurations represents the true situation is a matter for further study. 

The occurrence of the BPs can also be described in terms of the Landau theory. The free energy expansion contains the usual nematic terms 

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A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

Fig. 5 Induction of the blue phase by doping a N material with (a) a rod-shaped molecule MHPOBC and (b) a bent-shaped molecule P8-PIMB. In both cases, the blue phase is induced above the N phase. The bent-shape of the antiferroelectric molecule is responsible for the blue phase induction in (a), since the doping of a real rod-shaped molecule (TBBA) does not induce the blue phase [26]...

Alexander GP, Yeomans JM (2006) Stabilizing the blue phases. Phys Rev E 74 061706-1-9... 

Whether quasicrystalline structures are limited to alloys remains an open question. It is possible that their occurrence is much more widespread than had been previously thought. Indeed there is evidence for quasicrystallinity in both thermotropic and lyotropic liquid crystals. Diffraction patterns of decagonal symmetry have been recorded in lyotropic liquid crystals [K. Fontell, private communication], (Fig. 2.19), and there is theoretical evidence for the existence of a quasicrystalline structure within the blue phase of cholesterol (Chapters 4, 5). (The decagonal structure has quasisymmetry perpendicular to the tenfold axes, and translation symmetry along them.) Viruses crystallise in icosahedral clusters and the list continues to grow. In addition to five-fold symmetry, it has been shown that eight and ten- fold quasisymmetry is possible. ... 

The structure of the blue phase is of some importance. Among the lipoproteins carrying lipids in the blood, low-density lipoproteins (LDL) have attracted much attention. They are the factors mainly responsible for plaque formation, which ultimately leads to atheriosclerotic changes and heart disease. The major components of the LDL-particles are cholesterol fatty acid esters. A remarlmble property is the constant size of LDL particles [28], which indicates that the interior must possess some degree of order. It seems probable that the structure proposed above for cholesterol esters in the cholesteric liquid-crystalline structure should occur also in the LDL-particle. In that case the LDL particle can be viewed as a dispersed blue phase, whose size is related to the periodicity of the liquid-crystalline phase, and the protein coat at the surface is oriented parallel to adjacent specific crystallographic planes of the blue phase. These amphiphilic proteins will expose lipophilic segments inwards emd expose hydrophilic groups towards tiie enviroiunent. 

The compound CigHxaNs [43, 49] has already been mentioned as the product obtained on boiling the primary diazo-compound of phenosaffranine with alcohol. Its salts have a magenta-red colour and do not fluoresce in alcoholic solution. Concentrated sulphuric acid dissolves them with a yellowish-green colour, and on dilution the colour changes through green to redj the blue phase does not occur. 

PolyTCDU (X = C5H5) can be synthesized so that the red, high-temperature phase is stable at room temperature (12). Conversion to the blue phase can be achieved at low temperatures (at least partially) (13) or under a strain field (14). The optical properties of the red aTi blue phases of polyTCDU are nearly identical to those of polyETCD and polylUPDO (9,J ). The X-ray structure of polyTCDU (2 ) suggested that thTs polymer existed in the butatriene conformation, -(R)C C=C=C(R)-, rather than the commonly observed (and theoretically more stable) acetylenic conformation, =(R)C-C5C-C(R)=. This led to the suggestion that thermochromism involved an acetylenic-to-butatrienic conformational change (10). 

Recently, direct observations of the blue phase lattice structure have been attempted by freeze-fracture electron microscopy [ 13,14] (Fig. 7), atomic force microscopy for quenched blue phases [15], and confocal laser scanning microscopy [ 16] (Fig. 8). 

Kitzerow et al. in 1993 formed blue phases of polymeric liquid crystal monomers and polymerized these monomers while maintaining the blue-phase structure, leading to a solid resin of fixed blue-phase structure [22]. Such a substance, although maintaining the blue-phase structure, provided none of the dynamics of liquid crystal, since all the constituent molecules were polymerized. 

Chirality is also an important aspect of liquid crystals. The introduction of chiral moieties into the chiral smectic phases induces functions such as ferroelectricity and antiferroelectricity. A few of the unconventional chiral liquid crystals are described in Chapter 1. The blue phase is one of the exotic chiral liquid crystalline phases. In Chapter 3, Kikuchi introduces the basic aspects and recent progress in research of the blue phase. Recently, the materials exhibiting the blue phases have attracted attention because significant photonic and electro-optic functions are expected from the materials. 

Some cholesteric materials show the blue phase as the temperature increases from that of the cholesteric phase and before it reaches that of the isotropic phase. The blue phase is a cubic phase. There have been three blue phases found so far BP I, BP II and BP III phases. It is now understood that the BP I phase is a body-centered cubic, the BP II phase is a primitive cubic and the BP III phase is a fog phase with no structural symmetry. Generally the temperature range of the blue phase is quite narrow, less than 1 degree... 

The blue phase has a similar structure to that of the D phase, in spite of the remarkable difference in the lattice parameter. The lattice parameter of the former is hundreds of nm while that of the latter is less than 10 nm. 

S. Meiboom, J.P. Sethna, P. Anderson, W. Brinkman, Theory of the blue phase of cholesteric liquid crystals. Phys. Rev. Lett. 46, 1216-1219 (1981)... 

These phases were an enigma of the centuries. Since the experiments of Reinitzer [ 19] up to recent times it was not clear whether it was a special texture of the known cholesteric phase or a thermodynamically new phase. The textures of the blue phases are often of blue color. Fig. 4.31. Properties of the blue phases are very interesting from the fundamental point of view. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Earlier in Section 4.8 we discussed the blue phases observed in cholesterics close to the transition to the isotropic phase. The whole appearance of the blue phase is owed to the defects, which form a three dimensional lattice. 

Blue phases exist in a narrow temperamre region between the isotropic and cholesteric phases. As temperamre is decreased, the order of appearance of the blue phases is BPIII, BPII, and BPI [15-17]. Whether a chiral liquid crystal has a blue phase depends on its molecular stmcmre and chirality. The blue phases can be identified by an optical microscope under reflection mode. BPI and BPII have bright and colorful multi-domain crystal plate textures, while BPIII has a dim uniform foggy texmre [5,18]. Therefore, BPIII is also called the fog phase. As will be discussed later, BPI and BPII have cubic crystal structures while BPIII has an amorphous stmcmre. 

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