Structure of Blue Phase

From the experimental results discussed in the above section, it is known that BPI and BPII have cubic structures. There are two theories that have successfully explained the existence of the blue phases and predict their symmetry and physical properties. One is known as the defect theory, in which the blue phases consist of packed double-twist cylinders and there 

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Fig. 5 Structures of Blue Phases I and II. The rods in (a) and (c) represent double-twist cylinder. The black lines in (b) and (d) represent disclination lines...

O. Henrich, K. Stratford, M.E. Cates, D. Marenduzzo, Structure of blue phase IB of cholesteric liquid crystals. Phys. Rev. Lett. 106, 107801(1-4) (2011)... 

V. A. Belyakov, E. I. Demikhov, V. E. Dmitrienko, and V. K. Dolganov, Optical activity, transmission spectra, and structure of blue phases of liquid crystals, Sov. Phys. JETP, 62, 1173 (1985). 

The three-dimensional crystalline structure of blue phases with lattice periods comparable to the wavelength of visible Ught results in the optical diffraction dependent on the orientation of the light wave vector with respect to the crystalline planes [93]. Thus, the selective reflection of light occurs in a different spectral range for different experimental geometry. This is well illustrated by Fig. 6.24 taken from [94] where selective reflection maxima (normalized to 1.6n)... 

Blue phases I and II show cubic 3D lattice stmctures. Figure 8.14a-d shows the unit cell structures of blue phases 1 and n, respectively. Blue phases I and II have a body-centered cubic lattice structure and a simple cubic lattice structure, respectively, with lattice constants of several 100 nm. 

Recent progress in material science, notably with the development of new materials exhibiting blue phases, has generated a renewed interest in the incorporation of the functional properties with the unique structure of frustrated phases. Synthesis of a monosubstituted ferrocene-based chiral Schiff s base derivative which exhibits TGBA and blue phases has been reported [17] (Fig. 9). Other metallomesogens leading to blue phases have been found for palladium complexes [18] (Fig. 10). Optically active materials incorporating... 

Fig. 12 Chemical structure of T-shaped dimeric liquid crystal molecules that broadened the temperature range of blue phases to 13 K [24]...

A screw dislocation is similar in structure to that of a double twist cylinder which is the basis for the formation of Blue Phases [24], The equivalent of the... 

This is the typical optical rotatory power of cholesteric liquid crystals with pitch shorter than the hght wavelength. In the blue phases, the double-twist cylinders orient along many different directions, and therefore the optical rotatory power is smaller than that of cholesteric phase. The thickness of blue phases displays are typically a few microns, and over this distance the hehcal structure in the blue phases does not change much the polarization state of light. 

In the vicinity of the transition into the isotropic phase, optically isotropic uniform textures are often observed. These so-called blue phases are cubi-cally symmetric defect structures of cholesteric liquid crystals. With decreasing temperature three blue phases occur [13, 14]. All of them are optically active but not birefringent. The observation of the optical Bragg refiections allowed the determination of the structure of these phases. They are formed by a special packing of pieces of the helix into various cubic lattices. An example is shown in Fig. 1.5(b) [15]. Parameters of the lattices are of the order of the helical pitch. Due to the optical Bragg refiection firom the cubic lattice these phases are blue colored. 

Physical properties of blue phases are due to such a structure. From the point of view of the light diffraction, the pertinent quantity is the dielectric tensor j,(r) which is a periodic function of r which, therefore, can be decomposed into a Fourier series. This decomposition was done for the first time by Dick Hornreich et al. [10] who used the traceless part of the dielectric tensor as the order parameter for a Landau-type theory of blue phases. The traceless part of the symmetric dielectric tensor has five independent coefficients. For this reason, for each q(Ak/) vector of the reciprocal lattice, five independent Fourier components have to be considered. We already know one of them from the section on cholesteric liquid crystals (2.25). Let... 

The blue phases of types BPI and BPn are modeled as regular networks of disclination lines with periodicity of order p. Indeed, the three-dimensional periodic structure of these phases is revealed in their nonzero shear moduli, their ability to grow well-faceted monocrystals and Bragg reflection in the visible part of the spectrum (which is natural since p is of the order of a few tenths of a micron). The third identified phase, BPIH, that normally occurs between the isotropic melt and BPII, is less understood. It might be a melted array of disclinations. Note that although most blue phases have been observed in thermotropic systems, double-twist geometries are relatively frequently met in textures of biological polymers, like DNA. 

An important question to ask of blue phases is whether they are liquid or solid. The cubic structure is not one of atoms in fixed positions as in a conventional crystal—rather, the molecules are free to diffuse randomly throughout the blue phase lattice, changing their orientation en route so as to conform to the blue phase s spatially dependent order. 

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. 

Figure 4.11 Optimized structures of CH cO species, as indicated, over aqueous-solvated Pt(lll) as determined by DFT in Cao et al. [2005]. Horizontal and vertical arrows indicate C—H and O—H cleavage steps, respectively. Reaction energies are included for the aqueous phase [Cao et al., 2005] and the vapor phase (in parentheses) [Desai et al., 2002]. The thermodynamically preferred aqueous phase pathway is indicated by bold arrows (in blue). (See color insert.)...

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