Gibbs phase triangle

Fig. 2. Oil-rich region of the Gibbs phase triangle of the ternary mixture Tween 85, cyclohexane and water...

In Section 4.3.3, it was explained how to construct the reaction (diffusion) path for ternary and higher solid solution systems. In practice, one plots, for example, in a ternary system, the composition variables (measured along the pertinent space coordinate of the reacting solid) into a Gibbs phase triangle, noting that the spatial information is thereby lost. For certain boundary conditions, such a reaction path is independent of reaction time and therefore characterizes the diffusion process. For a one dimensional ternary system with stable interfaces, these boundary conditions are c,-( = oo,f) = c°( oo) q( <0,0) = c (-oo) c,(f>0,0) = c (+oo). 

FIG. 2 Schematic drawing of the Gibbs phase triangle for a mixture of water, alkane, and nonionic surfactant (CjEj). 14>, 2, and 3 stand for a single-phase microemulsion, a microemulsion coexisting with a water- or oil-rich phase, and a microemulsion coexisting with a water-rich phase and an oil-rich phase. 

FIG. 7 The latent heat AQ per cubic centimeter of sample volume for the transition lam — Li is plotted as a function of ( )s at a fixed ratio < )o/< >w = 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle. 

As with the example presented for cosolvency in the case of polymer solutions in mixed solvents (Fig. 27), the origin of cosolvency for polymer blends in a common solvent can be interpreted as a dissection of a miscibility gap that would normally bridge the Gibbs phase triangle from one binary subsystem to the other binary system (here from 1/B to A/B) by special interactiMis between the completely miscible components (here 1/A). With the example of Fig. 32, the thermodynamic quality of the solvent for polymer A is almost marginal in this manner polymer B becomes completely miscible with certain solutions of polymer A in solvent 1. 

Fig. 8. Solubility of polymers in mixed solvents Simplicity. These phsise diagrams were calculated by means of the eqs. 23-25 in combination with eq. 22, setting E = 0.7 and X = 0.5 furthermore it weis assumed that the low molecular weight liquids mix combinatorial. The numbers of segments of the components are stated at the comers and the binary interaction parameters are indicated at the edges of the Gibbs phase triangle. The composition areas within which homogeneous mixtures are unstable (spinodal regime) are displayed in gray or black. The full circle shows a critical point some compositions of coexisting phases are represented by open circles.

It was shown some time ago that one can also use a similar thermodynamic approach to explain and/or predict the composition dependence of the potential of electrodes in ternary systems [22-25], This followed from the development of the analysis methodology for the determination of the stability windows of electrolyte phases in ternary systems [26]. In these cases, one uses isothermal sections of ternary phase diagrams, the so-called Gibbs triangles, upon which to plot compositions. In ternary systems, the Gibbs Phase Rule tells us... 

Figure 1.2 Isothermal Gibbs triangles of the system water (A)-oil (B)-non-ionic surfactant (C) at different temperatures. Increasing the temperature leads to the phase sequence 2-3-2. A large miscibility gap can be found both at low and high temperatures. While at low temperatures a surfactant-rich water phase (a) coexists with an oil-excess phase (b), a coexistence of a surfactant-rich oil phase (b) with a water-excess phase (a) is found at high temperatures. At intermediate temperatures the phase behaviour is dominated by an extended three-phase triangle with its adjacent three two-phase regions. The test tubes illustrate the relative change in phase volumes.

Fig. 5.15. Schematic E-diagram for the reaction A B C, including an absorbance triangle according to a distorted Gibbs phase diagram.

The solvent components in the feed and in the EA are chosen such that (a) the entire system formed by the starting polymer and the solvent components exhibits a miscibility gap at the temperature of operatimi (b) that, in the Gibb s phase triangle, the composititMi of the feed corresponds to a point outside of this miscibility gap and (c) that the EA is composed in such a way that the straight line drawn between feed and EA (working line) intersects the miscibility gap (Fig. 6). 

Figure 9-2. Schematic A-B-0 phase diagram (Gibbs triangle) with tie lines between the following phases of complete solubility (A,B), (A,B)0, (A, B)304, (A,B)203. B-oxides are more stable than A-oxides. I, II, III denote two-phase fields.

At a given temperature, die Gibbs free energy of each phase in a ternary system may be represented in a graphical form with the composition triangle as base and the free energy as vertical axis. Then it would look like this ... 

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