Gibbs free energy ternary systems

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 ... 

For isothermal ternary systems, Geveke and Danner (1991) have modified the Flory-Huggins theory to account for the concentration dependency of the parameters. The reduced total Gibbs free energy of mixing is given by... 

Application of stability criteria to the ternary system via differentiation of Gibbs free energy reveals that compressibility plays a central role. Specifically, the system is destabilized as compressibility increases. Compressibility can in turn be calculated using an appropriate equation of state. We choose the Sanchez-Lacombe which can be written... 

Another model describing the thermodynamics of polymer solutions was introduced by Flory and Huggins [5,6]. In the Flory-Huggins theory, the non-ideality of the polymer solutions due to the large difference in molecular size between the solute and solvent is taken into account. Based on this theory, the Gibbs free energies of binary and ternary systems are expressed in Equations 15.7 and 15.8, respectively [7] as follows ... 

The subject matter is introduced by a short exposition of the Gibbs phase rule in Sec. 8.2. Unary component systems are discussed in Sec. 8.3. Binary and ternary systems are addressed in Secs. 8.4 and 8.5, respectively. Sec. 8.6 makes the connection between free energy, temperature, and composition, on one hand, and phase diagrams, on the other. 

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