Segment molar Gibbs energy

For mixtures of two types of linear chain molecules, A and B, the segment molar Gibbs energy of mixing is usually formulated as ... 

The segment molar Gibbs energy of mixing for three component (indices i,j, and k) with Ni, Nj, and segments, respectively, as formulated on the basis of the Hory-Huggins theory reads in its general form ... 

The double-indexed g parameters are for binary interaction parameters. The first line of the above relation represents the combinatorial part, and the second line the residual part of the reduced segment molar Gibbs energy of mixing. This relation also contains a ternary interaction parameter tij that accounts for the expectation that the interaction between two components of the ternary mixture may change in the presence of a third component. 

Fig. 1. Three qualitatively distinguishable composition dependencies of the reduced segment molar Gibbs energy for mixtures of a liquid polsnmer P and liquid solvent 1. (i) Complete miscibility of the components, (ii) Coexistence of two liquids (with the compositions indicated by the full circles) and two points of inflection (open circles), (iii) Occurrence of a critical point (half filled circle).

Fig. 2. Composition dependence of the reduced segment molar Gibbs energy for mixtures of a solid, crystalline polymer and a liquid solvent.

Under the (unrealistic) assumption that eq. 6 describes the entropy part of the mixing process adequately, the expression for the segment molar Gibbs energy of mixing can be obtained by simply adding the enthalpy part of the mixing process... 

Figure 3 How to construct a phase diagram knowing the composition dependence of segment molar Gibbs energy of mixing.

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