Bicontinuous cubic

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

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...

In the Hn phase and in the inverted micellar cubic phase, the water associated with the polar headgroups is trapped inside a ring structure and is not in rapid exchange with bulk water [18]. In a bicontinuous cubic phase, however, there is a continuous network of aqueous channels. 

It is believed that the Gaussian bending modulus k controls the membrane topology. In particular, a negative value of this constant is needed for stable bilayers. A positive value will induce nonlamellar topologies, such as bicontinuous cubic phases. Therefore, it is believed that k is negative for membranes. 

Bicontinuous cubic phase Lamellar phase Bicontinuous cubic phase Reverse hexagonal columnar phase Inverse cubic phase (inverse micellar phase)... 

Cyclic carbohydrates with two alkyl chains (e.g. 1,2-dialkyl (or 1,2-diacyl) glycerol 8 a (sug=Glcp, Galp) present structural similarities with glycerophospho-lipids. They form complex mesophases such as bicontinuous cubic phases, inverted hexagonal phases or myelin figures [58-61]. Other dialkyl derivatives... 

Figure 9.18 Idealized structures of hydrated didodecyl-phosphatidyl ethanolamine showing some typical bicontinuous cubic phases. (Adapted from Seddon et al, 1990 see this reference for the indicated crystallographic nomenclature.)...

Bicontinuous cubic phases have not, to date, been accounted for using SSL theory. The OBDD phase has been shown to be unstable with respect to lam and hex phases (Likhtman and Semenov 1994 Olmsted and Milner 1994a,b). As discussed above, it now appears that the OBDD was a misidentified gyroid phase however, SSL calculations for the gyroid structure have not been performed as yet. A perforated layer structure was found to be unstable by Fredrickson (1991), using SSL theory following Semenov s method. 

The phase behaviour of blends of PS-PI or PS-PB diblocks with PS homopolymer was summarized by Winey et al. (19926). Regions of stability of lamellar, bicontinuous cubic, hexagonal-packed cylindrical and cubic-packed spherical structures were mapped out as a function of homopolymer molecular weight, copolymer composition and homopolymer concentration. All blends were... 

Fig. 6.10 Phase diagrams for blends of PS homopolymers with PS-PI diblocks of approximately constant molecular weight (average M = 54.3 kgmol"L), annealed at 125 C (Winey et al. 1992ft). (a) Mn (PS) = 5.9kgmor (b) M (PS) = 14kgmol-1, (c) M (PS) = SVkgmor1. Here L, C and S denote lamellar, cylindrical and spherical microstructures respectively, DM indicates disordered micelles, BC a bicontinuous cubic structure and 2

Fig. 6.11 TEM images showing a sequence of morphologies on increasing PS homopolymer (M = 5.9kgmor ) concentration (wt%) in blends with a PS-PI diblock (Mr = 48.7kgmol-1,/PS = 0.51) (Winey et al. 1991c). The blends were annealed at 125 °C. (a) 10% PS, lamellae, (b) 30% PS, bicontinuous cubic, (c) 50% PS, hexagonal-packed cylinders, (d) 70% PS, cubic-packed spheres.

The stabilization of bicontinuous phases by addition of homopolymer to diblocks was studied in the strong segregation limit by Xi and Milner (19%).They found that a bicontinuous cubic structure (presumably the gyroid phase) is stable for 0,56 < f < 0.68, with corresponding optimal volume fractions of homopolymer ranging from 0.18 to 1.00 for this range of/. 

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)... 

Due to the rigidity of Rp-chains, in fluorinated LCs the transition from smectic to columnar organization often takes place via modulated smectic phases (ribbon phases, c2mm, p2gg, and Colob see Fig. 20, left) which completely or partly replace the bicontinuous cubic phases at the Sm-to-Col cross-over. Similarly, in columnar phases the circular columns can be deformed to an elliptic, rectangular, or square... 

An example of a special kind of mesogenic compound is provided by A,A -bis (4-alkoxybenzoylhydrazines) (e.g., compound 132a,) known to form bicontinuous cubic phases [247-249]. It is interesting that fluorination of only one chain of these compounds (compound 132b) removes the cubic phase which is restored if the second alkyl chain is also fluorinated (compound 132c, see Fig. 35a) [122]. 

Fig. 1 Schematic illustrations of LC nanostructures bicontinuous cubic, smectic, columnar and micellar cubic...

This behavior of the DPoPE/cationic PC mixtures is not surprising, because both the double bonds and hydrocarbon chain length variations are known to have considerable effect on the lamellar-to-nonlamellar transitions in lipids [113]. A specific structural characteristic of lipid arrays that exhibits distinct change around the chain length of 14 carbons is the formation of inverted bicontinuous cubic phases Qn. The latter phases tend to form in diacyl or dialkyl phospholipids... 

Templer RH, Seddon JM, Duesing PM et al (1998) Modeling the phase behavior of the inverse hexagonal and inverse bicontinuous cubic phases in 2 1 fatty acid phosphatidylcholine mixtures. J Phys Chem B 102 7262-7271... 

---