Phase diagram for different

Figure 3. Phase diagrams for different form-factor models Gaussian (solid lines), Lorentzian a = 2 (dashed lines) and NJL (dash-dotted). In /3-equilibrium, the colorsuperconducting phase does not exist for Co Gi. In the inset we show for the Gaussian model the comparison of the numerical result with the modified BCS formula Tf = 0.57 A(T = 0, fiq) g(Hq) for the critical temperature of the superconducting phase transition.

Fig. 1. The H — T phase diagrams for different S/F systems, (a) Structure with narrow domains. The solid (dashed) line corresponds to an isolated superconducting nucleus at the domain boundary (far from the domain boundary), (b) Isolated superconducting nucleus in a structure with wide domains BoD2/To = 25). (c) Periodic domain structure for ttBow2/To = 5 (solid line) and -nBow2 /To = 1 (dashed line), (d) Ferromagnetic dot over the superconducting film (N = 10).

Fig. 4.4 Theoretical diblock copolymer phase diagrams for different levels of polydispersity. a An increase of the overall PDI with identical block PDIs results in a shift towards lower xA values while the phase diagram stays symmetrical (Adapted with permission from Cooke et al. [20]. Copyright 2013 American Chemical Society), b An asymmetrical increase of PDI with PD/a > PDIs shifts the phase boundaries towards decreasing xA and increasing /a values, and creates biphasic regions 2-4>. Note that the phase space of the pure gyroid morphology is even narrower for asymmetric block polydispersities (Reprinted with permission from Matsen et al. [21]. Copyright 2013 by the American Physical Society)...

Although all copolymer phase diagrams are qualitatively similar, they vary quantitatively from copolymer to copolymer, and they are generally not perfectly symmetric about /a = 0.5. The small differences in phase diagrams for different molecules of the same architectures, for example, diblock PS-PI versus diblock PS-PDB, can thus be characterized in terms of different conformational asymmetries of the polymers. 

Lyotropic liquid crystals also progressed during this second phase. Lawrence s paper at the 1933 Faraday meeting discussed the phase diagrams for different compositions... 

Fig. 4. 8. Phase diagrams for different PS/PB-mixtures, exhibiting lower miscibility gaps, (a) M(PS) = 2250gmol, M(PB) = 2350gmol (b) M(PS) = 3500gmol , M(PB) = 2350gmon (c) M(PS) = 5200gmol , M(PB) = 2350gmol . Data from Roe and Zin [19]...

The SiC phase diagram has a peritectical charactCT (Fig. 3). The temperature of peritectical transformation = 3103 K. The SiC compound is the only solid phase for the Si-C binary system. Figure 3b and c represent parts of the diagram that border with silicon and carbon. In the part of the diagram that borders with Si (Fig. 3b) is a decrease in the liquidus temperature ATi versus increasing carbon concentration Cl in the solution. The equilibrium distribution coefficient of carbon in silicon is ko = 0.07. It is hard to define phase diagrams for different polytype structures because the physical-chemical analysis is not sufficiently accurate. 

Figure 13.17 Calculated phase diagram for different GaAs(OOl) surface structures displaying the total surface energy per (1x1) unit cell versus the variation of the gallium chemical potential A/x(A) with respect to the bulk value (From Refs. [50].). The stable surface structures are at the lower border of the phase diagram.

Practically, the addition of a nonadsorbing polymer to a dispersion can induce flocculation of dispersed particles due to the depletion attraction. This was first observed by Cowell, Lin-In-On, and Vincent [1434]. When large amounts of poly (ethylene oxide) are added to an aqueous dispersion of hydrophilized polystyrene latex particles, the particles start to flocculate. For an organic dispersion, namely, hydrophobized silica particles in cyclohexane, de Hek and Vrij [1435] observed depletion-induced flocculation when dissolved polystyrene was added. Other combinations of particles and polymers followed [1436]. Phase diagrams for different particle-solvent-polymer systems were successfully drawn using the depletion potential of Asakura as interaction potential between dispersed spheres [1437] and for dissolved polymers using statistical mechanics [1438]. 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

Figure A1.12 shows the phase diagram for ice. (The pressures are so large that steam appears only at the extreme upper left.) There are eight different solid phases of ice, each with a different crystal structure. 

Stadler et al. [150,151] have performed Monte Carlo simulations of this model at constant pressure and calculated the phase behavior for various different head sizes. It turns out to be amazingly rich. The phase diagram for chain length N = 1 and heads of size 1.2cr (cr being the diameter of the tail beads) is shown in Fig. 8. A disordered expanded phase is found as well as... 

As yet, models for fluid membranes have mostly been used to investigate the conformations and shapes of single, isolated membranes, or vesicles [237,239-244], In vesicles, a pressure increment p between the vesicle s interior and exterior is often introduced as an additional relevant variable. An impressive variety of different shapes has been found, including branched polymer-like conformations, inflated vesicles, dumbbell-shaped vesicles, and even stomatocytes. Fig. 15 shows some typical configuration snapshots, and Fig. 16 the phase diagram for vesicles of size N = 247, as calculated by Gompper and Kroll [243]. 

FIGURE 8.9 The phase diagram for water drawn with a logarithmic scale for pressure, in order to show the different solid phases of water in the high-pressure region. 

The phase diagram constructed in this way, with the assumption that the difference in free energy of liquid lead and solid lead, Fo(l) — Fg(c), is a linear function of the temperature, and that the other parameters remain unchanged, is shown as Fig. 8. It is seen that it is qualitatively similar to the phase diagram for the lead-thallium system in the range 0-75 atomic percent thallium. 

All phase diagrams share the ten common features listed above. However, the detailed appearance of a phase diagram is different for each substance, as determined by the strength of the intermolecular interactions for that substance. Figure 11-40 shows two examples, the phase diagrams for molecular nitrogen and for carbon dioxide. Both these substances are gases under normal conditions. Unlike H2 O, whose triple point lies close to 298 K,... 

The phase diagram for silica shows six different forms of the solid, each stable under different temperature and pressure conditions. 

In phase diagrams for two-component systems the composition is plotted vs. one of the variables of state (pressure or temperature), the other one having a constant value. Most common are plots of the composition vs. temperature at ambient pressure. Such phase diagrams differ depending on whether the components form solid solutions with each other or not or whether they combine to form compounds. 

Fig. 59 Phase diagram for blend consisting of two symmetric PS-6-PI block copolymers of different molecular weights in parameter space of temperature and fraction of higher molecular weight copolymer, . disordered state lamella A PS cylinder. From [179]. Copyright 2001 American Chemical Society... 

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