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I have three components, $A,B,C$, with 3 Flory-Huggins exchange parameters: $\chi _{AB}, \chi _{BC}, \chi _{AC}$. I want to create a ternary diagram to see how such a mixture behaves and how phase separation takes place i.e find points on the ternary plot where I will see $(A+B,C), (A+C,B), (B+C,A), (A+B+C), (A,B,C)$, where $I+J$ represents a mixed phase of $I,J$ and a separation by a comma $","$ indicates the third species is in a different phase.

The ternary spinodal condition is: $$D=\frac{\partial ^2 f}{\partial \phi _B ^2}\Bigg|_{N,T,\phi_A}\frac{\partial ^2 f}{\partial \phi _A ^2}\Bigg|_{N,T,\phi _B} - \left( \frac{\partial ^2 f}{\partial \phi _B \partial \phi _A} \Bigg| _{N,T}\right)^2 = 0$$

My question is, how do I find the regions on the ternary plot indicated above? How do I find the region where two species are mixed while the third one is not?

I am not quite sure what it means when A+B is in a mixed state and when C is not. Does this mean that $\mu _A = \mu _B \neq \mu _C$?

This is basically the figure I want to make from this paper: enter image description here

I would appreciate any advice you have for me.

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  • $\begingroup$ I gave my +1 long ago, but since it has been more than 6 months, is there any update you can provide us? Are you still urgently or actively in need of an answer to this question? Please let us know! $\endgroup$ Dec 1, 2023 at 17:47

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