Phase-behavior diagram, representation

While classical phase diagrams provide a powerful methodology for grasping the thermodynamic behavior of few-component systems, it is evident that the restricted 2D or 3D realm of human graphical intuition cannot adequately cope with the complexities of many-component systems. Hence, it is important to find generalized analytical techniques that can accurately represent many-component phase behavior for arbitrary values of c. Such techniques will be considered in the metric geometric representation of multicomponent phenomena (Chapter 12). 

A phase diagram is a graphic representation of the phase behavior of a system under study. The behavior of a single component as a function of temperature and pressure can be represented on a phase diagram, which will show the conditions under which a material is a solid, liquid, or gas. More complex phase diagrams may involve several components. Phase diagrams are very useful tools for formulation, as they allow one to define not only the acceptable composition range of a product but also enable one to optimize the order of addition of the different raw materials. 

A schematic representation of type-I ternary phase behavior is shown in figure 3.29. The three diagrams in this figure represent mixtures at a fixed temperature slightly higher than the critical temperature of the SCF but at three different pressures. The distinguishing feature of type-I ternary phase behavior is the absence of LLV immiscibility regions within the ternary... 

This study supports the assumption that the alcohol influences the phase behavior of oil-brine-surfactant system and its effect is related to the saturation concentration in the water-phase. On the other hand, the ternary phase diagram with a constant amount of the cosolvent seems to be more valuable for selecting microemulsion formulations than the pseudo-ternary representation in which both alcohol and surfactant are varied simultaneously. 

In connection with these experiments, data are presented on how the surfactant-brine-oil phase behavior is influenced by small amounts of a polysaccharide polymer dissolved in the brine. This polymer apparently complicates phase behavior considerably in principle a fourth axis is required in the phase diagram. However, in view of the approximate nature of the ternary representation of the surfactant-brine-oil system, we shall not attempt to draw sys-... 

Experimentally, polymer solutions as well as mixtures of small molecules may show a wide range of phase behavior. A schematic representation of possible phase diagrams for binary mixtures of small molecules and polymers in solution is given in Figure 6. For some systems, eg water/triethylamine solutions, miscibility decreases with increasing temperature, phase separation taking place above a... 

Representation of three-component systems as a set of quasi-binary cross-sections is not quite rigorous for the most real ternary mixtures because a ratio of second and third components in equibbrium phases is not usually constant. However, if we intend to study the phase behavior from the point of view of topological schemes, the sequence of binary phase diagrams of quasi-binary sections (including the sections through the ternary nonvariant points) give an exhaustive description of possible phase equilibria and phase transformations in ternary systems. 

To obtain a valid representation of the entire domain of liquid-liquid phase behavior, it is necessary to take accoxmt of the concentrations of all three components. This is done by using the trilinear coordinate system, which leads to a construction known as a triangular diagram, shown in Figure 6.8. 

Subsequently, we employ the Gibbs-Duhem method as first proposed by Kofke [31,32] to determine the phase coexistence lines in the (rj, kct) plane for a fixed Pe. Using these methods, we study the phase behavior of hard-core Yukawa particles, whose interactions are described by the pair potential given by Equation 8.8. The phase diagrams are calculated for fixed contact values Pe and they are given in the (ri, l/xa) representation. We calculate the phase diagram for four contact... 

Figure 9.49 Schematic representation of the P-T behavior of a polymer-organic solvent mixture. The inset shows the full phase diagram. The hatched area is expanded to show more detail near the critical point of the solvent (McClellan, Bauman, and McHugh, 1985).

---