Enthelpic Excess Function - Phase Separation in Regular solutions

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The discussion centers on the interpretation of a phase diagram related to mixing and phase separation. The professor asserts that for β > +2, two minima indicate phase separation due to unfavorable enthalpic interactions. However, there is a counterargument that for Δmix G/nRT < 0, mixing is spontaneous, suggesting that at β = 2.5, the components should be fully miscible. The conversation also questions the relationship between phase behavior at maxima and minima, particularly whether the presence of one phase at the maxima contradicts the idea of unfavorable mixing when Δmix G/nRT is positive. Clarification is sought on these points regarding miscibility and phase behavior.
elemis
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My professor, in his handout (picture below), says the following about this diagram :

For \beta&gt;+2 there are two minima and phase separation occurs driven
by unfavourable enthalpic interactions.

I disagree with him partly. For \Delta_{mix} G/nRT&lt;0 mixing is spontaneous and hence there solutions would be miscible. Hence at \beta=2.5 should we not expect the components to be fully miscible. ?

Following on from this logic; for \beta=3 the components are only miscible for \Delta_{mix} G/nRT&lt;0 so the maxima represents a phase separation between the two components.

Who is correct ?

Additionally,the webpage below indicates that at the maxima there is one phase whilst at the minima there are two. Does this mean at the maxima the solutions are miscible ? If so, how can this be true given that \Delta_{mix} G/nRT&lt;0 is positive and hence mixing is unfavourable ?

http://www.chm.bris.ac.uk/~chdms/Teaching/Chemical_Interactions/page_17.htm


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