Lamellar phases hexagonal

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. 

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.

Another phase which has attracted recent interest is the gyroid phase, a bicontinuous ordered phase with cubic symmetry (space group Ia3d, cf. Fig. 2 (d) [10]). It consists of two interwoven but unconnected bicontinuous networks. The amphiphile sheets have a mean curvature which is close to constant and intermediate between that of the usually neighboring lamellar and hexagonal phases. The gyroid phase was first identified in lipid/ water mixtures [11], and has been found in many related systems since then, among other, in copolymer blends [12]. 

For a certain choice of g cj)) and f 4>) the above equation can be solved analytically for simple spatially modulated phases, such as lamellar or hexagonal [22]. This is possible for the piecewise parabolic model of /(0) ... 

FIG. 7 Structures of various liquid-crystalline phases of membrane lipids. (A) Normal hexagonal phase (Hi) (B) lamellar phase (C) inverted hexagonal phase (Hu). Cubic phases consisting of (D) spherical, (E) rod-shaped, and (F) lamellar units. The hydrocarbon regions are shaded and the hydrophilic regions are white. (Reprinted by permission from Ref. 11, copyright 1984, Kluwer Academic Publishers.)... 

For nearly symmetric compositions the unlike blocks form domains composed of alternating layers, known as lamellar phase (L). Slightly off-symmetry composition results in the formation of a different layered structure. The structure is known as perforated layers (PI) or catenoid phase. Despite an earlier assignment as an equilibrium phase, it is now known to be in a long-lived metastable state that facilitates the transition from I to G phases [9-14], The PL structure consists of alternating minority and majority component layers in which hexagonally packed channels of the majority component extend through the minority component. 

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

Figure 4.23 Synthesis space diagram for a ternary system composed of tetraethylorthosilicate (TEOS), cetyltrimethylammonium bromide (CTAB), and sodium hydroxide (H, hexagonal phase [MCM-41] C, cubic phase [MCM-48] L, lamellar phase [MCM-50] H20/Si02 = 100, reaction temperature 100°C, reaction time 10 days). (Reprinted from Science, Vol. 267, A. Firouzi, D. Kumar, L.M. Bull, T. Besier, R Sieger, Q. Huo, S.A. Walker, J.A. Zasadzinski, C. Glinka, J. Nicol, D.l. Margolese, G.D. Stucky, B.F. Chmelka, Cooperative Organization of Inorganic-Surfactant and Biomimetic Assemblies, pp. 1138-1143. Copyright 1995. With permission of AAAS.)...

In addition to the cubic and/or inverse cubic forms described above, further transitional forms exist between the lamellar phase and the hexagonal mesophase (cubic, type II) or inverse hexagonal mesophase (cubic, type III) [6]. In contrast to the discontinuous phases of types I and IV, cubic mesophases of type II and III belong to the bieontinuous phases (Fig. 4f). A range of lyotropic mesophases are possible, depending on the mesogen concentration, the lipophilic or hydrophilic characteristics of the solvent, and the molecule itself [6]. 

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

At higher concentrations, micelles assemble in turn, to form hexagonal or cubic phases while longer chains or multi-chain compounds afford lamellar phases in which the amphiphilic derivative is arranged in parallel bilayers, separated by water. The succession of mesophases depending on temperature and concentration of the amphiphile can be visualized in a phase diagram (Fig. 3 c). 

When layers of certain block copolymers of ethylene oxide and butylene oxide are contacted with water, there is an initial period when the position of the interface is proportional to tm, where m < 0.5 [32]. That is, initial swelling is not controlled by diffusion but instead by hydration and rearrangement of the long molecules to form the various phases. In the case of (EO)i6(BO)22 small-angle X-ray scattering did detect evidence of both reverse hexagonal and lamellar phases during this initial period, but it was not clear whether all the swollen block copolymer layer consisted of these phases or how the... 

Seddon, J. M. (1990). Structure of the inverted hexagonal (HII) phase, and non-lamellar phase transitions of lipids, Biochim. Biophys. Acta, 1031, 1-69. 

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