Local/global phase diagram

The regions within the local/global "phase diagram" for which these hyperbolic bilayer structures can be realised within a surfactant-water mixture are plotted in Fig. 4.8. 

The resulting local/global "phase diagram" for elliptic, parabolic and hyperbolic monolayers, together with bilayers (flat, as in the classical lamellar La phase, and hyperbolic) is shown in fig. 4.11. To generate specific data, die value of the tail length, I, is set to 14A, which is characteristic of a molten 12-carbon tail, for which the fully stretched length is about IbA. 

Figure 16.15. Local/global phase diagram for a rang of discrete micellar I2 mesophases (cf. Figure 16.8) fee (Fm3m) (or hep (P63/mmc), bee (Im3m), and clathrate (Pm3n, Fd3m) packings. The ordinate is the apolar volume fraction...

Figure 16.19. Local/global phase diagrams for a range of observed bicontinuous cubic mesophases, the P, D and G (gyroid) phases (cf. Figure 16.8) (a) Type VI (b) Type V2 (cf. Figures 16.7, 16.15, 16.17)...

Figure 5.24 Model of hierarchical self-assembly of chiral rodlike monomers.109 (a) Local arrangements (c-f) and corresponding global equilibrium conformations (c -f) for hierarchical selfassembling structures formed in solutions of chiral molecules (a), which have complementary donor and acceptor groups, shown by arrows, via which they interact and align to form tapes (c). Black and the white surfaces of rod (a) are reflected in sides of helical tape (c), which is chosen to curl toward black side (c ). (b) Phase diagram of solution of twisted ribbons that form fibrils. Scaled variables relative helix pitch of isolated ribbons h hh /a. relative side-by-side attraction energy between fibrils eaur/e. Reprinted with permission from Ref. 109. Copyright 2001 by the National Academy of Sciences, U.S.A.

Copper ions have been reduced in colloidal assemblies differing in their structures (55,56). In all cases, copper metal particles are obtained. Figure 9.3.1 shows the freeze-fracture electron microscopy (FFEM) for the various parts of the phase diagram. Their structures have been determined by SAXS, conductivity, FFEM, and by predictions of microstructures that require only notions of local curvature and local and global packing constraints. 

Figure 4. Section of the pseudobinary phase diagram of the sulfuric acid SLP catalytic material. The data were taken from Ref. 16. The data points were derived from anomalies of the conductivity versus temperature curves of the respective mixtures. At the high compositional resolution and in the range of the global eutectic, the formation of a vanadate-sulfato complex causes the local maximum in the solidus curve. It is noted that extreme precision in the experimental procedures was necessary to derive this result illustrating the characteristic of fused systems that compound formation can well occur in the molten state.

Figure 4.12. (Top ) The binary phase diagram of didodecyl phosphatidylethanolamine -water mixtures. (Adapted from [15].) Single-phase regions are white, two-pha% regions shaded. The thermotropic behaviour at about 20% w/w water is illustrated by die line ABC. (Bottom ) The trajectory of the line ABC in the local/global domain (see previous figure), showing the variation of molecular shape as a function of temperature for this l d. The phase diagram can be reconciled with the local/global behaviour if the "lamellar" (L) phase is in fact a mesh structure, i.e. porous lamellae.

Figure 4.13. (Left ) The binary phase diagram of AOT-water mixtures (after (17,18]). The lyotropic behaviour at room temperature is illustrated by the line ABC. (Right) The trajectory of die line ABC in the local/global domain.

The model is not necessary utilized directly. The model was not referred sequentially for control. In this study, the method was proposed for bringing out global dynamics from local dynamics equation. The input was symbolized in chapter 7, and operators were arranged in chapter 8. With symbols and operators, phase diagram or global map of the system was drawn. In this way, the model can be converted into dynamic rules. Models theoretically support the dynamics-based control. 

---