Isotropic—lamellar phase

Phase transitions in condensed phases are characterized by symmetry changes, i.e. by transformations in orientational and translational ordering in the system. Many soft materials form a disordered (isotropic) phase at high temperatures but adopt ordered structures, with different degrees of translational and orientational order, at low temperatures. The transition from the isotropic phase to ordered phase is said to be a symmetry breaking transition, because the symmetry of the isotropic phase (with full rotational and translational symmetry) is broken at low temperatures. Examples of symmetry breaking transitions include the isotropic-nematic phase transition in hquid crystals (Section 5.5.2) and the isotropic-lamellar phase transition observed for amphiphiles (Section 4.10.2) or block copolymers (Section 2.11). 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

Similarly, N-allcylammonium [28] and alkylphosphonium [29] salts form lamellar phases with smectic bilayer structures. In both cases. X-ray scattering also showed the isotropic liquid not to be completely disordered and still displaying similar features to the mesophase. Buscio et al. [28] showed that in N-allcylammonium chlorides the feature was not only much broader than that observed in the mesophase but increased in width with decreasing chain length. 

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 14 Schematic representation of the microphase separation of block copolymers. The left graph shows atomic-scale details of the phase separation at intermediate temperatures, and the right graph shows a lamellar phase formed by block copolymers at low temperatures. The block copolymers have solid-like properties normal to the lamellae, because of a well-defined periodicity. In the other two directions, the system is isotropic and has fluid-like characteristics. From reference 54.

At vv = 20, an isotropic phase appears. By increasing the water content vv from 20 to 29, the lamellar phase progressively disappears, giving rise to two phases consisting of isooclaiie and the isotropic phase. The latter is attributed to intcrdigitaled reverse micelles. Syntheses at various water... 

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.

The behavior of a series of polyoxyethylene alkyl ether nonionic surfactants is also illustrative. According to Figure 11 the dioxyethylene (A) compound does not form liquid crystals when combined with water. Its solutions with decane dissolve water only in proportion to the amount of emulsifier. The tetraoxyethylene dodecyl ether (B) forms a lamellar liquid crystalline phase and is not soluble in water but is completely miscible with the hydrocarbon. The octaoxyethylene compound (C) is soluble in both water and in hydrocarbon and gives rise to three different liquid crystals a middle phase, an isotropic liquid crystal, and a lamellar phase containing less water. If the hydrocarbon p-xylene is replaced by hexadecane (D), a surfactant phase (L) and a lamellar phase containing higher amounts of hydrocarbon are formed in combination with the tetraoxyethylene compound (B-D). 

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))...

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 21.6 Ternary phase diagram of the sodium octanoate-decanol-water system at 25°C. There are two isotropic solution phases, micellar and reversed micellar (rev mic), and three liquid crystalline phases, hexagonal (hex), lamellar (lam), and reversed hexagonal (rev hex) (from Ref. 17). 

On the other hand, studies with three-dimensional isotropic lamellar matrices have shown that Azone is a weakly polar molecule, which can occupy the interfacial region as well as the hydrocarbon interior of bilayers [86,87]. The contrasting observations of Azone promoting the assembly of reversed-type liquid-crystal phases (e.g., reversed hexagonal and reversed micellar) in simple model lipid systems [88-90], while also favoring the formation of lamellar structures in one of these mixtures [91], adds further confusion to the discussion [92]. This notwithstanding, the studies by Schiickler and co-workers [91] emphasize the differences in the calorimetric profiles of intact human stratum comeum (HSC) and model SC lipid mixtures Although these systems are clearly useful and versatile, extrapolation of inferences from model lipids to the intact membrane must be performed with caution. 

Figure 12.25 Phase diagram of didodecyldimethylammonium bromide (DDAB) in water and styrene at 20°C. The phases include an oil-rich isotropic phase L2, lamellar phases, and five distinct cubic strut phases, including the G, D, P, C(P), and an unknown phase C5. Above the cubic phases are regions of two- and three-phase coexistence. (From Strom and Anderson 1992, reprinted with permission from Langmuir 8 691. Copyright 1992, American Chemical Society.)...

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