Lamellar phases transitions between

Fig. 6.22 Phase diagram for blends of PE and PEP homopolymers (A/j, - 392 and 409 respectively) with a PE-PEP diblock (iVc = 1925) (Bates et al. 1995). Open and filled circles denote experimental phase transitions between ordered and disordered states measured by SANS and rheology respectively. Phase boundaries obtained from self-consistent field calculations are shown as solid lines. The diamond indicates the Lifshitz point (LP), below which an unbinding transition (UT) separates lamellar and two-phase regions in mean field theory.

At temperatures below the main transition, a basic equilibrium stracture is the subgel (crystalline) Lc phase. Its formation usually requires prolonged low-temperature incubation. In addition to the Lc phase, many intermediate stable, metastable, and transient lamellar gel structures are adopted by different lipid classes—with perpendicular or tilted chains with respect to the bilayer plane, with fully interdigitated, partially interdigitated, or noninterdigitated chains, rippled bilayers with various ripple periods, and so forth. (Fig. 1). Several polymorphic phase transitions between these structures have been reported. Well-known examples of polymorphic transitions are the subtransition (Lc- L ) and the pretransition (Lp/- Fp/) in phosphatidylcholines (33). Recently, a polymorphic transition that included rapid, reversible transformation of the usual gel phase into a metastable, more ordered gel phase with orthorhombic hydrocarbon chain-packing (so-called Y-transition) was reported to represent a common pathway of the bilayer transformation into a subgel (crystalline) Lc phase (62). 

Nakamura, N., Tagawa, T., Kihara, K., Tobita, I., and Kunieda, H. (1997) Phase transition between microemulsion and lamellar liquid crystal. Langmuir, 13, 2001-2006. 

Examples of anisotropy parameters are shown in Fig. 9 (left). They are clearly suited to characterize the phase transition between the disordered phase at low and the lamellar phase at high xN. For comparison, the same system was also examined with complex Langevin simulations. The results are shown in Fig. 9 (right). The transition points are the same. 

The second chapter, by D. Vollmer (Germany), brings a quantitative comparison of experimental data and theoretical predictions on thermodynamic and kinetic properties of microemulsions based on nonionic surfactants. Phase transitions between a lamellar and a droplet-phase microemulsion are discussed. The work is based on evaluation of the latent heat and the specific heat accompanying the transitions. The author focuses on the kinetics of phase separation when inducing emulsification failure by constant heating. The chapter is a comprehensive, detailed study of all the aspects related to the phase separation phenomenon in microemulsions. 

Leibler also predicted phase transitions between three different microdomains (from the disordered phase to spherical microdomains, from spherical to cylindrical microdomains, and from cylindrical to lamellar microdomains) using the fourth-order expansion of the vertex function in terms of the order parameter. Figure 7 displays... 

The second difference is related to the structure of the lamellar phase. The Euler characteristic has been assumed zero in the whole lamellar phase by Gompper and Kraus [47], whereas we show that it fluctuates strongly in the lamellar phase between the transition line and the topological disorder fine. The notion of the topological disorder line has not appeared in their paper. We think that the topological disorder line is much closer to the transition... 

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

Figure 7. Topological fluctuations of the lamellar phase at different points of the phase diagram, (a) Single fusion between the lamellae by a passage (this configuration is close to the topological disorder line), (b) Configuration close to the transition to the disordered microemulsion phase the Euler characteristic is large and negative.

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]. 

Figure 4.16 Phase diagram of poly(isoprene-Z>-2-vinylpyridine) with octyl gallate, indicating the transition between different morphologies with octyl gallate content and temperature (D, disordered S, spherical H, hexagonal L, lamellar L2, lamellar with reduced spacing I, intermediate state). Reprinted ftomBondzic et al. (2004). Copyright2004 American Chemical Society.

Until recently, very little quantitative information was available on blends of block copolymers. The literature is summarized in Table 6.3. Hoffman et al. (1970) reported microscopic demixing of blends of PS-PB diblocks, with two maxima in the domain size distribution, but with no evidence tor macrophase separation. These findings must be treated with caution in the light of more recent results. Hadziioannou and Skoulios (1982) used SAXS and SANS to investigate the morphology of binary blends of PS-PI diblocks, and binary PS-PI/PS-PI-PS or PS-PI/PI-PS-PI blends or blends of the two types of triblock. They found that the blends were microphase separated, and that the sharpness of the interface was not reduced in blends compared to neat copolymers. The transition between a lamellar and a cylindrical structure was shown to depend primarily on blend composition. In contrast, the transition from a lamellar to a disordered phase at... 

The phase behavior of a synthetic lecithin, dipalmitoyllecithin, as analyzed by Chapman and co-workers (5), is diagrammed in Figure 3. The main features are the same as in the phase diagram of egg lecithin a mixture of numerous homologs. As a consequence of the variation in fatty acid chain length, the chain melting point is lowered which means that the critical temperature for formation of liquid crystalline phases is reduced. This temperature is about 42 °C for dipalmitoyllecithin, and, if the lamellar liquid crystal is cooled below this temperature, a so-called gel phase is formed. The hydrocarbon chains in the lipid bilayers of this phase are extended, and they can be regarded as crystalline. The gel phase and the transitions between ordered and disordered chains are considered separately. 

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