Isotropic cubic phase

The other mesophases which may be formed are the viscous isotropic, cubic phase and the hexagonal II phase described in Chapter 8. 

As shown before, using/ /os = 0 and dfcjos/3 2 (2) = 0, gives the reduced isotropic-cubic phase transition temperature ... 

The viscous isotropic cubic phase, which is periodic in three dimensions, is produced with monogylceride-water systems at chain lengths above C14. This isotropic phase has a bicontinuous structure, consisting of a lamellar bilayer, which... 

Figure 11.25 Schematic phase diagram of a binary system surfactant/water. Inverse hexagonal phase Hn, lamellar phase Lo, hexagonal phase Hj, isotropic (cubic) phases a, b, c, d.

Dodecyltrimethylammonium chloride in water, for example, shows the presence of two distinct viscous isotropic cubic phases at room temperature. Similar results are found for the decyl and tetradecyl analogs, while the hexadecyl and octadecyl members of the series do not exhibit these phases. The cubic phases are apparently absent in the corresponding bromides of aU members of the series. 

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. 

Example The following compound exhibits a crystalline phase (Cr), smectic SmC, cubic (Cub), smectic SmA mesophases, and an isotropic (I) phase, with transitions at the specified temperatures ... 

Lindblom, G. and Rilfors, L. (1989). Cubic phases and isotropic structures formed by membrane lipids - possible biological relevance. Biochem. Biophys. Acta, 988, 221-56. 

The phase behaviour established for concentrated aqueous solutions of PEO-PPO-PEO copolymers has its counterpart in PEO/PBO copolymer solutions. A phase diagram for PE058PB0i7PE0M based on tube inversion experiments is shown in Fig. 4.14 (Luo et al. 1992). The hard gel is isotropic under the polarizing microscope and can be characterized as a cubic phase formed from spherical micelles of a similar size to those in the dilute micellar solution. 

Fig. 4.44 Phase diagram for aqueous solutions of Pluronic P104 (PEOi7PP05,PFX)27) (Noolandi et al. 1996). Notation iso, isotropic (polymer poor) solution cubic, cubic phase hex[, hexagonal phase lam, lamellar phase, hex2, inverse hexagonal phase, cubicj, inverse cubic phase, iso2, isotropic (polymer rich) solution. The solid and dashed lines are calculated from the continuum and lattice versions of self-consistent field theory respectively.

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... 

Colhd columnar hexagonal phase, Colborh columnar body-centred orthorhombic phase, Colbsorh columnar base centred orthorhombic phase, Cub cubic phase, SmA smectic A phase, I isotropic phase... 

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))...

The optical properties of ferroelectric materials are characterized by birefringence. Barium titanate is isotropic only in the cubic phase. The tetragonal and the rhombohedral phases are... 

Fig. 3.23 NM R spectra for macroscopic polymorphic phases of phospholipids in bilayers, hexagonal HM, and isotropic phases (small vesicles, micelles, inverted micelles, and cubic phases). Similar spectra are recorded for any one phase regardless of which...

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