Critical Point

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Entry by Andrew Capulli

Definition: Critical Point

The Critical Point indicates the Chi value X (Chi is an energy of interaction parameter) that separates the situation where mixtures are always stable and the situations where mixtures are unstable or metastable where the resultant mixtures then separate into components (eventually if metastable and instantly is unstable).

Example Discussion of the Critical Point

For AP225 students, this discussion is based on the diagrams used in the course notes. Here we are looking at the Chi Parameter as a function of temperature T. We can likewise look at it as a function of pressure for example

The critical point is where the spinodal line and the coexist curve are equal (Spinodal1.jpg as defined in the Jones text used in Soft Matter AP225). The critical point is where the either a stable or unstable solution can occur (X=2 in figures below). At the critical point the free energy of the system is a straight line with no minima; at any X less than 2, no contribution is given to the production of the diagram showing X versus composition. Given the curves in [A], the diagram X versus composition ([B]) can be created. Points on the metastable portions of the curves (the concave down portions) construct the inner parabola seen in [B] while points in the stable regions of the curves (the concave up portions)construct the outer parabola in [B]. To obtain [C] (the phase diagram as we know it!) it is assumed that X goes as 1/temperature so [C] is [B] inverted; essentially X is increased with temperature decrease and decreased with temperature increase. So, the critical point represents the 'situation' where mixtures are stable and where they are not stable (ie metastable or completely unstable which will then separate into phases). As seen in this phase diagram, and what is somewhat intuitive, this system of arbitrary components is miscible at any concentration ratio given a high enough temperature (the critical point or critical temperature!).

CriticalPoint1.jpg

Reference:

The Science of Chocolate: interactive activities on phase transitions, emulsification, and nucleation