Liquid-crystal cubic

Figure 4. Schematic phase diagram of metastable silicon in the pressure-temperature (P, T) plane discussed in [20,113]. The thick solid line represents the liquid-crystal (cubic diamond) transition line, extended into the j6-Tin phase. The dotted lines represent the liquid-/S-Tin and the Cubic diamond-yS-Tin transition lines. The thin line is the liquid-liquid phase transition line ending at a critical point represented by a filled circle. The dashed lines represent the spinodals associated with the liquid-liquid transition. The oval symbol represents the amorphous-liquid transition as predicted by some of the earlier experiments. [With permission from McMillan [20,113].]...

Figure 2a shows a schematic phase diagram for lyotropic liquid crystals. This figure shows the formation of micelles, cubic phases, bicontinuous cubic phases, and lamellar phases as the concentration of surfactant increases. Also shown in this figure is a schematic diagram of an ordered bicontinuous cubic phase (Fig. 2b). Another interesting example in...

The family of primary silver thiolate compounds AgSC H2n+1 ( = 4, 6, 8, 10, 12, 16, or 18), which in the solid state consists of 2x,[AgSR] layers, behaves as thermotropic liquid crystals. On heating, they display successively lamellar (smectic A), cubic, and micellar mesophases.969... 

Lyotropic lamellar (La) liquid crystals (LC), in a form of vesicle or planar membrane, are important for membrane research to elucidate both functional and structural aspects of membrane proteins. Membrane proteins so far investigated are receptors, substrate carriers, energy-transducting proteins, channels, and ion-motivated ATPases [1-11], The L liquid crystals have also been proved useful in the two-dimensional crystallization of membrane proteins[12, 13], in the fabrication of protein micro-arrays[14], and biomolecular devices[15]. Usefulness of an inverted cubic LC in the three-dimensional crystallization of membrane proteins has also been recognized[16]. 

Figures 9a-c represent transmission electron micrographs of different lyotropic liquid crystals after freeze fracture without etching. The layer structure of the lamellar mesophase including confocal domains, hexagonal arrangement of rodlike micelles within the hexagonal mesophase, as well as close-packed spherical micelles within the cubic liquid crystal can be clearly seen.

Different types of liquid crystals exhibit different rheological properties [16,17]. With an increase in organization of the microstructure of the liquid crystal its consistency increases and the flow behavior becomes more viscous. The coefficient of dynamic viscosity r, although a criterion for the viscosity of ideal viscous flow behavior (Newtonian systems), is high for cubic and hexagonal liquid crystals but fairly low for lamellar ones. However, the flow characteristics are not Newtonian but plastic or pseudoplastic, respectively. 

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). 

Note 4 Cubic mesophases have long been known in thermotropic salt-like compounds and in lyotropic liquid-crystals. 

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. 

The cubic amphiphilic mesophases (Sic, Vi, and V2) from their interposition in the succession of mesophases Sic, Mi, Vi, G, V2, and M2, have generally been termed liquid crystalline like the optically anisotropic amphiphilic mesophases Mi, G, and M2. The cubic mesophases formed by non-amphiphilic globular molecules have however usually been termed plastic crystals. This nomenclature has obscured the fact that these plastic crystals are fundamentally liquid crystals rather than solid cyrstals and bear a relationship to the optically anisotropic non-amphiphilic smectic and nematic liquid crystals similar to that born by the amphiphilic cubic mesophases to the optically anisotropic neat (G) and middle (Mi and M2) liquid crystalline phases. 

Figure 6. Phases for systems which give I, crystal, anisotropic liquid, and isotropic liquid II, crystal and isotropic liquid III, crystal, cubic plastic crystal, and isotropic liquid (8)...

Keywords Columnar mesophase Cubic mesophase Dendrimer Liquid crystal Metallomesogen Micro-segregation Organic semiconductor Perfluorinated molecule Polyphilic molecule Self-assembly... 

Cr Cub, Cubv d E G HT Iso Isore l LamN LaniSm/col Lamsm/dis LC LT M N/N Rp Rh Rsi SmA Crystalline solid Spheroidic (micellar) cubic phase Bicontinuous cubic phase Layer periodicity Crystalline E phase Glassy state High temperature phase Isotropic liquid Re-entrant isotropic phase Molecular length Laminated nematic phase Correlated laminated smectic phase Non-correlated laminated smectic phase Liquid crystal/Liquid crystalline Low temperature phase Unknown mesophase Nematic phase/Chiral nematic Phase Perfluoroalkyl chain Alkyl chain Carbosilane chain Smectic A phase (nontilted smectic phase)... 

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. 

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