Phase cubic phases

A central issue in the field of surfactant self-assembly is the structure of the liquid crystalline mesophases denoted bicontinuous cubic, and "intermediate" phases (i.e. rhombohedral, monoclinic and tetragonal phases). Cubic phases were detected by Luzzati et al. and Fontell in the 1960 s, although they were believed to be rare in comparison with the classical lamellar, hexagonal and micellar mesophases. It is now clear that these phases are ubiquitous in surfactant and Upid systems. Further, a number of cubic phases can occur within the same system, as the temperature or concentration is varied. Luzzati s group also discovered a number of crystalline mesophases in soaps and lipids, of tetragonal and rhombohedral symmetries (the so-called "T" and "R" phases). More recently, Tiddy et al. have detected systematic replacement of cubic mesophases by "intermediate" T and R phases as the surfactant architecture is varied [22-24]. The most detailed mesophase study to date has revealed the presence of monoclinic. 

Use of liquid crystalline phases Surfactants produce liquid crystalline phases at high concentrations. Three main types of Hquid crystals can be identified hexagonal phase (sometimes referred to as middle phase) cubic phase and lamellar (neat phase). All of these structures are highly viscous and also show elastic responses. If produced in the continuous phase of suspensions, they can eliminate sedimentation of the particles. These Hquid crystalline phase are particularly useful for application in liquid detergents which contain high surfactant concentrations. Their presence reduces sedimentation of the coarse builder particles (phosphates and silicates). 

Figure 29. Phase diagram of SDS/water (reproduced from [62]). (H, hexagonal phase two-dimensional monoclinic phase rhombo-hedral phase cubic phase tetragonal phase C, C and C" refer to different polymorphic varieties for the same SDS hydrate otherwise as for Fig. 14.)...

If we turn to the isotropic phases, several possibilities exist with respect to both liquid solution phases and cubic liquid crystalline phases. Cubic phases, which have long-range order, can be distinguished from microemulsions in giving rise to low-angle X-ray diffraction patterns. A number of different cubic phase structures are possible, but the X-ray low-angle... 

Cubic phases are often the solubility-limiting phase above the Krafft eutectic of monoglycerides [84] and possibly of other polyol surfactants. It is claimed that these cubic phases have an inverted (head group in) structure [85]. Often, they coexist with a more concentrated bicontinuous cubic phase [86] which lies next to the lamellar phase. Cubic phases are the solubility-limiting phase in the iV-acyl-JV-methylglucamines, but only at temperatures above the Ejafft eutectic (see later). Just above the Krafft eutectic, the solubility boundary of this surfactant is defined by the familiar hexagonal phase. 

Number of chains in meta position (Nm) Number of chains in para position (Np) Lamellar phase Cubic phase Columnar phase... 

Tricalcium aluminate reacts with water to form C2AH8 and C4AH13 (hexagonal phases). These products are thermodynamically unstable so that without stabilizers or admixtures they convert to the C3AH5 phase (cubic phase). In a paste, hydration is slightly retarded in the presence of CH. In dilute suspensions the first hydrate formed is C4AH19. 

Fork R L, Brito Cruz C H, Becker P C and Shank C V 1987 Compression of optical pulses to six femtoseconds by using cubic phase compensation Qpt. Lett. 12 483-5... 

Kane S, Squier J, Rudd J V and Mourou G 1994 Hybrid grating-prism stretcher-compressor system with cubic phase and wavelength tunability and decreased alignment sensitivity Opt. Lett. 19 1876-8... 

Figure B3.6.4. Illustration of tliree structured phases in a mixture of amphiphile and water, (a) Lamellar phase the hydrophilic heads shield the hydrophobic tails from the water by fonning a bilayer. The amphiphilic heads of different bilayers face each other and are separated by a thin water layer, (b) Hexagonal phase tlie amphiphiles assemble into a rod-like structure where the tails are shielded in the interior from the water and the heads are on the outside. The rods arrange on a hexagonal lattice, (c) Cubic phase amphiphilic micelles with a hydrophobic centre order on a BCC lattice.

Luzzati V, Tardieu A, Gulik-Krzywicki T, Rivas E and Reiss-Flusson F 1968 Structure of the cubic phases of lipid-water systems Nature 220 485-8... 

Luzzati V, Delacroix FI and Gulik A 1996 The micellar cubic phases of lipid-containing systems Analogies with foams, relations with the infinite periodic minimal surfaces, sharpness of the polar/apolar partition J. Physique. II 6 405-18... 

Seddon K M, Flogan J L, Warrender N A and Pebay-Peyroula E 1990 Structural studies of phospholipid cubic phases Prog. Colloid Polym. Sol. 81 189-97... 

Landau E M, Rummel G, Cowan-Jacob S W and Rosenbusch J P 1997 Crystallization of a polar protein and small molecules from the aqueous compartment of lipidic cubic phases J. Phys. Chem. B 101 1935-7... 

Completely miscible (O), partially miscible ia the cubic phase ( )), and not at all or very slightly miscible (O). 

A progressive etching technique (39,40), combined with x-ray diffraction analysis, revealed the presence of a number of a polytypes within a single crystal of sihcon carbide. Work using lattice imaging techniques via transmission electron microscopy has shown that a-siUcon carbide formed by transformation from the P-phase (cubic) can consist of a number of the a polytypes in a syntactic array (41). 

A continuous lipidic cubic phase is obtained by mixing a long-chain lipid such as monoolein with a small amount of water. The result is a highly viscous state where the lipids are packed in curved continuous bilayers extending in three dimensions and which are interpenetrated by communicating aqueous channels. Crystallization of incorporated proteins starts inside the lipid phase and growth is achieved by lateral diffusion of the protein molecules to the nucleation sites. This system has recently been used to obtain three-dimensional crystals 20 x 20 x 8 pm in size of the membrane protein bacteriorhodopsin, which diffracted to 2 A resolution using a microfocus beam at the European Synchrotron Radiation Facility. 

Landau, E.M., Rosenbuch, J.R Lipid cubic phases a concept for the crystallization of membrane proteins. 

Figure 3.16. WiditinnstiiUcn precipitation of a hexagonal close-packed phase from a face-centred cubic phase in i Cu Si alloy. Precipitation occurs on [ I I Ij planes of the matrix, and a simple epitaxial erystallographie correspondence is maintained. (0 0 0 Di, , (I I (after Barrett...

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. 

The initial configuration is set up by building the field 0(r) for a unit cell first on a small cubic lattice, A = 3 or 5, analogously to a two-component, AB, molecular crystal. The value of the field 0(r) = at the point r = (f, 7, k)h on the lattice is set to 1 if, in the molecular crystal, an atom A is in this place if there is an atom B, 0, is set to —1 if there is an empty place, j is set to 0. Fig. 2 shows the initial configuration used to build the field 0(r) for the simple cubic-phase unit cell. Filled black circles represent atoms of type A and hollow circles represent atoms of type B. In this case all sites are occupied by atoms A or B. 

FiG. 2 The initial configuration used to create structures of symmetry of simple cubic phase. 

The symmetry of the structure we are looking for is imposed on the field 0(r) by building up the field inside a unit cubic cell of a smaller polyhedron, replicating it by reflections, translations, and rotations. Such a procedure not only guarantees that the field has the required symmetry but also enables substantial reduction of independent variables 0/ the function F (f)ij k )- For example, structures having the symmetry of the simple cubic phase are built of quadrirectangular tetrahedron replicated by reflection. The faces of the tetrahedron lie in the planes of mirror symmetry. The volume of the tetrahedron is 1 /48 of the unit cell volume. 

FIG. 8 Multiply continuous cubic phases generated from the functional (1). 

Summarizing the detailed studies of the basic Landau-Ginzburg model presented in the preceding sections and in the present one suggest that this type of simplified model is not sufficient to describe all the effects related to the ordering in microemulsions. In particular, the only stable ordered phase in the model is the lamellar phase and all the cubic phases are only meta-... 

C. Stability of the Cubic Phases near the Bifurcation Line... 

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