Cubic liquid crystal phase

Refractive index data are very useful for the quantitation of isotropic (liquid and cubic liquid crystal) phases, and for the calibration of cell thickness and nonflatness. Hovever, the analysis of birefringent phases using refractive index data has been found to be unreliable (9). A problem arises from the fact that the orientation of such phases relative to the direction of the light path, as veil as the system variables, influence refractive indices. In order to use refractive index data for quantitation, a phase must spontaneously orient in a reproducible fashion. Such orientation does occur in the case of fluid lamellar phases (as in short chain polyoxyethylene nonionic systems (7)), but viscous lamellar phases, hexagonal phases, and crystal phases do not orient to a sufficient degree. 

The D phase is the one cubic liquid crystal phase which was discovered independently in 1957 by G. Gray (Gray et al., 1957) and D. Demus (1957) when they were studying the following compounds... 

Figure 3.4 The temperature-concentration phase diagrams of BPS-m (m=5,10,20, and 30) with BmimPFj. The phase abbreviations are as follows micellar phase (1 ), discontinuous cubic liquid crystal phase (1 ), hexagonal liquid crystal phase (H ), lamellar liquid crystal phase (L ), lamellar gel phase (L ), reverse micellar phase (L ), ionic liquid phase (IL), and two-phase separation (II). The chemical structure of j0-sitosterol ethoxylates as a typical example of BPS-m is also shown in this figure. Reproduced from Sakai et al. [37] with permission from Japan Oil Chemists Society.

FIG. 11. Transmission electron micrographs of freeze fractured oily droplets dispersed (a) in a hexagonal and (b) in a cubic liquid crystalline phase, bar 100 nm. From Mueller-Goymann, C., Liquid crystals in emulsions, creams and gels, containing ethoxylated sterols as surfactant, Pharm. Res. 1 154-158 (1984). 

The association of block copolymers in a selective solvent into micelles was the subject of the previous chapter. In this chapter, ordered phases in semidilute and concentrated block copolymer solutions, which often consist of ordered arrays of micelles, are considered. In a semidilute or concentrated block copolymer solution, as the concentration is increased, chains begin to overlap, and this can lead to the formation of a liquid crystalline phase such as a cubic phase of spherical micelles, a hexagonal phase of rod-like micelles or a lamellar phase. These ordered structures are associated with gel phases. Gels do not flow under their own weight, i.e. they have a finite yield stress. This contrasts with micellar solutions (sols) (discussed in Chapter 3) which flow readily due to a liquid-like organization of micelles. The ordered phases in block copolymer solutions are lyotropic liquid crystal phases that are analogous to those formed by low-molecular-weight surfactants. 

Depending on temperature, transitions between distinct types of LC phases can occur.3 All transitions between various liquid crystal phases with 0D, ID, or 2D periodicity (nematic, smectic, and columnar phases) and between these liquid crystal phases and the isotropic liquid state are reversible with nearly no hysteresis. However, due to the kinetic nature of crystallization, strong hysteresis can occur for the transition to solid crystalline phases (overcooling), which allows liquid crystal phases to be observed below the melting point, and these phases are termed monotropic (monotropic phases are shown in parenthesis). Some overcooling could also be found for mesophases with 3D order, namely cubic phases. The order-disorder transition from the liquid crystalline phases to the isotropic liquid state (assigned as clearing temperature) is used as a measure of the stability of the LC phase considered.4... 

Finally, an area that will most likely see an explosive growth over the next few years is the self-assembly of nanoparticles covered with mesogenic and pro-mesogenic capping agents. A number of different approaches have been summarized in this review, and the formation of nematic, smectic-like, cubic, and columnar phases and/or superstructures have been demonstrated. Once more, the possibilities to produce such metamaterials using nanoparticles and liquid crystal motifs are endless, and future research will surely discover other, in part, more complex phase morphologies as well as uniquely tunable nanoscale properties as a result of liquid crystal phase formation. 

Fig. 2.18. Phase diagram of the dodecyltrimethylammonium chloride-water system. F denotes isotropic solution phase, M normal hexagonal liquid crystal, N lamellar liquid crystal and C and C cubic liquid crystalline phases. (From Ref.84))...

Micellar solutions are isotropic microstructured fluids which form under certain conditions. At other conditions, liquid crystals periodic in at least one dimension can form. The lamellar liquid crystal phase consists of periodically stacked bilayers (a pair of opposed monolayers). The sheetlike surfactant structures can curl into long rods (closing on either the head or tail side) with parallel axes arrayed in a periodic hexagonal or rectangular spacing to form a hexagonal or a rectangular liquid crystal. Spherical micelles or inverted micelles whose centers are periodically distributed on a lattice of cubic symmetry form a cubic liquid crystal. 

SBA-1 and SBA-6 were synthesized by using different surfactants and from acidic and basic synthesis media, respectively. They have the same structure and show the similar XRD patterns. Their structure is similar with cubic Ij phase, spherical micelles packed in Pm3n symmetry, in lyotropic liquid-crystal phase diagram for surfactant-water systems. 

In Fig. 2, a variety of micelle structures are shown. Typical shapes of micelles are spherical, rod-like, and worm-like. At high concentrations of surfactant or at high concentrations of counterions, liquid crystals are usually formed. Hexagonal, cubic, and lamellar are common liquid crystal phases that occupy much of a... 

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