Pseudophase diagram

Fig. 7. Three-dimensional pseudophase diagram of an oil or coal-tar pitch (49).

The Diels-Alder reaction of methyl methacrylate with cyclopentadiene was studied [72] with solutions from three different regions of the pseudophase diagram for toluene, water and 2-propanol, in the absence and in the presence of surfactant [sodium dodecyl sulfate (SDS) and hexadecyltrimethylammonium bromide (HTAB)]. The composition of the three solutions (Table 6.11) corresponds to a W/O-fiE (A), a solution of small aggregates (B) and a normal ternary solution (C). The diastereoselectivity was practically constant in the absence and in the presence of surfactant a slight increase of endo adduct was observed in the C medium in the presence of surfactant. This suggests that the reaction probably occurs in the interphase and that the transition state has a similar environment in all three media. 

Figure 5. The pseudophase diagram for the toiuene/water/2-propanoi system...

FIG. 11 Pseudophase diagram for 30 wt% cyclohexane in water stabilized by PAA (Carbopol 980). The c values are shown as the curve drawn in the bottom left-hand corner of the diagram. (Reprinted from Colloids and Surfaces A Physicochem Eng Aspects, 88, Lockhead RY, Rulinson CJ, An investigation of the mechanism by which hydrophobically modified hydrophilic polymers act as primary emulsifiers for oil in water emulsions. 1. Poly(acrylic acids) and hydroxyethyl celluloses. 27-32, Copyright (1994), with permission from Elsevier Science.)... 

Pseudophase Diagram. A phase diagram for a system in which there are more phases present than are allowed to vary in the diagram. A pseudophase diagram is thus only one of several that are needed to completely describe a system. 

FIGURE 1.10 Two main representations of the microemulsion pseudophase diagram. The left depiction (a) is the Ekwall-Gillberg approach, which treats the hydrocarbon/ cosurfactant liquid as one component, while the right model (b) combines the surfactant and cosurfactant into one component. 

Pseudophase diagram of a flexible polymer near an attractive substrate... 

The Icolor code in Fig, 13,2 encodes the value of the specific heat and the brighter the shading, the larger the value of cy. Black and white lines emphasize the ridges of the profile. The specific heat profile typically is a reasonable quantity for the identification of pseudophases and, therefore, these ridges mark pseudophase boundaries. As expected, the pseudophase diagram is divided into two main parts - the phases of adsorption and desorption. The two desorbed pseudophases DC (desorbed-compact conformations) and DE (desorbed-expanded structures) are separated by the collapse transition line which... 

To summarize all the information gained from the different observables, we construct the approximate boundaries of different regimes in the T-(s plane. The pseudophase diagram is displayed in Fig. 13.12 and the different pseudophases are denoted by the abbreviations introduced in the previous subsections. Transitions between conformational phases are indicated by stripes. It must be noted that their thickness is due to the the different locations of peaks when considering different fluctuating quantities. This is a typical feature of a finite system, where different indicators of transitions (e.g., transition temperatures) do... 

Representative examples of conformations for a 20mer in the different regions of the T-es pseudophase diagram, shown in Fig. 13.12. DE, DG, and DC represent bulk "phases" where the polymer is preferably desorbed. In regions AE1, AE2, AC1, AG, AC2a, and AC2b, conformations are favorably adsorbed. From [304]. 

Pseudophase diagram of a lattice polymer with 179 monomers as in Fig. Z2, but here parametrized by the surface attraction strength e and the temperature 7. The color encodes the specific-heat profile the darker the color, the larger Its value. From [304]. 

We may conclude that, in particular, the high-temperature pseudophases DE, DC/DG, AG, AE, nicely correspond to each other in both models. Noticeable qualitative deviations occur, as expected, in those regions of the pseudophase diagram where compact conformations are dominant and (unphysical) lattice effects are influential. Thus, the choice of the appropriate model depends on the question one wants to answer. Unlike temperatures are not too small and the polymer chain not too short, lattice models are perfectly suitable for the investigation of structural phases. This is particularly true for scaling analyses toward the thermodynamic limit. However, if the focus is more on finite-size effects and the behavior at low temperatures, off-lattice models should generally be preferred. 

We will now take a closer look at the adsorption transition in the phase diagram (Fig. 13.12) and we do this by a microcanonical analysis [307, 308]. As we have discussed in detail in Section 2,7, the microcanonical approach allows for a unique identification of transition points and a precise description of the energetic and entropic properties of structural transitions in finite systems. The transition bands in canonical pseudophase diagrams are replaced by transition lines. Figure 13.15 shows the microcanonical entropy per monomer s e)=N lng e) as a function of the energy per monomer e=EfN for a polymer with N=, 20 monomers and a surface attraction strength = 5, as obtained from multicanonical simulations of the model described in Section 13.6. 

Starting at very low temperatures, we know from the pseudophase diagram in Fig. 14.1(a) that the system resides in pseudophase ACT This means that the macrostate of the peptide is dominated by the class of compact, filmlike single-layer conformations. The system obviously prefers surface contacts at the expense of hydrophobic contacts. Nonetheless, the formation of compact hydrophobic domains in the two-dimensional topology is energetically favored, but maximal compactness is hindered by the steric influence of the substrate-binding polar residues. 

The anionic fluorinated surfactant (SPFO) forms with the nonionic or the amphoteric hydrocarbon surfactant mixed micelles containing both types of surfactants. Both systems exhibit a negative deviation from ideality. Changes of the F and H chemical shifts of the two surfactants upon mixing are consistent with pseudophase diagrams, calculated from the cmc dependence on the fluorinated surfactant mole fraction. The interpretation of data was based a modified regular solution theory and the phase-separation model. 

---