A Schematic Phase Diagram

In Fig. 7.1, the phase diagram of water is presented schematically. We emphasize that we are dealing with a single compound, or as addressed in thermodynamics, we are dealing with a system composed of one component. At low pressures, there is a region where water exists only as gas. At low pressures and low temperatures, water appears as ice. Between ice and gas, there is the liquid region. Every two regions are separated by border lines. 

In the inner part of a region, we may change pressure and temperature arbitrarily, i.e., independently, and the phase does not disappear. But there is only one phase, that is, solid ice, liquid water, or water vapor, respectively. 

If there should be two phases, we must choose a pair of temperature and pressure so that this tuple lies on a border line. If we want now to change either the temperature or the pressure, the two phases being still there, then we must change the temperature together with the pressure in such a way that the tuple remains on the border line. 

we cannot change temperature and pressure arbitrarily independently. Otherwise, if we are moving away from the border line, one phase will disappear. There is still another unique point, the triple point. At the triple point there are ice, liquid 

---

Fig. IV-17. A schematic phase diagram illustrating the condensed mesophases found in monolayers of fatty acids and lipids.

Figure A3.3.2 A schematic phase diagram for a typical binary mixture showmg stable, unstable and metastable regions according to a van der Waals mean field description. The coexistence curve (outer curve) and the spinodal curve (iimer curve) meet at the (upper) critical pomt. A critical quench corresponds to a sudden decrease in temperature along a constant order parameter (concentration) path passing through the critical point. Other constant order parameter paths ending within tire coexistence curve are called off-critical quenches.

Another interesting class of phase transitions is that of internal transitions within amphiphilic monolayers or bilayers. In particular, monolayers of amphiphiles at the air/water interface (Langmuir monolayers) have been intensively studied in the past as experimentally fairly accessible model systems [16,17]. A schematic phase diagram for long chain fatty acids, alcohols, or lipids is shown in Fig. 4. On increasing the area per molecule, one observes two distinct coexistence regions between fluid phases a transition from a highly diluted, gas -like phase into a more condensed liquid expanded phase, and a second transition into an even denser... 

Figure 2a shows a schematic phase diagram for lyotropic liquid crystals. This figure shows the formation of micelles, cubic phases, bicontinuous cubic phases, and lamellar phases as the concentration of surfactant increases. Also shown in this figure is a schematic diagram of an ordered bicontinuous cubic phase (Fig. 2b). Another interesting example in...

Recently, new ordered mesoporous silicas have also been synthesized by using self-organization of amphiphilic molecules, surfactants and polymers either in acidic or basic condition. A schematic phase diagram of water-surfactant is shown in the figure. 

Similar to the derivation of schematic phase diagrams showing an UCST or LCSTbehavior, as shown in the previous section, it is now possible to plot a schematic phase diagram as a function of conversion, q, such as shown in Fig. 5. The binodal and spinodal curves are obtained by interconnecting all the coexisting points and inflection points of the AG -curves as a function of q similar to the procedure described in [67-69]. 

Figure 7 A schematic phase diagram of a binary system...

A schematic phase diagram of MBE growth is depicted in fig. 4 (Ohno 1998 Shen et al. 1999). Recently it was shown that metallic (Ga,Mn)As with x = 0.1 can be obtained by the use of a modified MBE growth technique at 7s = 150°C, migration-enhanced epitaxy (MEE), where the beam fluxes of source materials are precisely controlled (Sadowski et al. 2001a, 2001b). 

A schematic phase diagram summarizing the three temperature regions (Ff, Fnf and melt) is shown in Fig. 9. For VF2 compositions below 82%, at room temperature, one observes the predominant ferroelectric phase. With increasing temperature, the paraelectric phase appears and at higher temperatures one obtains the molten state of the paraelectric crystallites. The Tm values of the copolymers are considerable lower than those of both homopolymers and show... 

Figure 1. A schematic phase diagram for CaO- Na 0-P20 system based on published diagrams. [Published diagrams Na20- P2Os, CaO- P205, (4) and...

Figure 6. A schematic phase diagram for the cuprates. The Tc line is determined by the pairing line (7pair), decreasing with x, and the coherence line f/COii), increasing with x. Broken lines should not be regarded as sharp lines (except when T 0), but as crossover regimes. The MIT point is where a metal-insulator transition occurs at T = 0 when SC is suppressed.

Figure 8 A schematic phase diagram for the carbonaceous mesophase ...

In this connection let us consider a fragment of a schematic phase diagram in the region of high concentrations of a polymer capable of forming the liquid crystalUne phase (Fig. 2). In a crystalUne polymer containing no solvent (100% polymer, vf), the transition from the crystalline state (c) to the Uquid crystalline state (Ic) must take place at the temperature T -.ic and further transition into isotropic state (i), at the temperature Such transitions are called thermotropic, and the system formed at I, is called the thermotropic liquid crystal. The transition to the Uquid crystalline state can also occur by adding to a polymer a solvent at a temperature below T -. c-... 

Fig. 2 A schematic phase diagram of Lai cSr cCu04 (LSCO). 7n, 7c, and T indicate the Neel, superconducting, and pseudogap temperatures, respectively...

Fig. 9 is a schematic phase diagram of a dilute aqueous cationic surfactant solution showing temperature and concentration effects on its microstructures. When the temperature is lower than the Krafft point [the temperature at which the solubility equals the critical micelle concentration (CMC)], the surfactant is partially in crystal or in gel form in the solution. At temperatures above the Krafft point and concentrations higher than the CMC, spherical micelles form in the surfactant solution. With further increase in concentration and/or on addition of counterions, the micelles form cylindrical rods or threads or worms with entangled thread-like and sometimes branched threadlike structures. 

Fig. 48. (a) Schematic phase diagram of the surface of a semi-infinite anisotropic ferromagnel, showing the plane of variables temperature T and enhancement A = - 1 of the surface... 

Fig. 56. (a) Schematic phase diagrams of a semi-infinite lsing magnet in the vicinity of the bulk critical point Tc as a function of temperature T, bulk field H, and surface field Hi. In the shaded part of the plane H 0 the system (for T < rc) is non-wet, while outside of it (For T < Tc) it is wet. The wetting transition is shown by a thin line where it is second order and by a thick line where it is first order. First-order prewetting surfaces terminate in the plane H = 0 at the first-order wetting line. Critical and multicritical points are indicated... 

Figure 8.19 shows a schematic phase diagram of the solution of immiscible polymer pair. A single phase is formed above the binodal (full line). During evaporation of a solvent, the system crosses the phase boundary and it is thmsted into the two-phase... 

A schematic phase diagram indicating the three qualitatively different types of solids discussed in the book. The phase boundaries are topologically correct but details of shape are only schematic. 

Figure 27.1 shows a schematic phase diagram for binary blends showing the relationship between free energy of mixing AG ) and blend composition cp). For sample A, an immiscible system is obtained (AG j > 0), for sample B a fully miscible system is obtained in which AG < 0, and C represents a partially miscible system that satisfies AG < 0 for all compositions, but d AG Idcpi is lower than 0 at certain compositions, indicating that at these compositions the blend will be immiscible. 

Figure 9 A schematic phase diagram of a cut at constant surfactant concentration through the temperature-composition phase prism of a ternary system with nonionic surfactant showing the characteristic X-like extension of the isotropic liquid phase L. (O is the volume fraction of oil in the solvent mixture.) Schematic drawings of the various microstructures are also shown. (Courtesy of Ulf Olsson.)...

Fig. 28. A schematic phase diagram of the domain walls of Au/Si(lll) system at gold coverage above 0.76 ML...

Figure 3 A schematic phase diagram cut at equal amoimts of water and oil (Fish plot), plotted as temperature vs. surfactant concentration. Fq is the balance temperature and O j is the minimum siu -factant concentration needed to mix equal amoimts of water and oil at Fq. The lower the more efficient is the surfactant.

---