Identification of first-order transitions by Maxwell construction

2 Identification of first-order transitions by Maxwell construction 

Traditionally, transitions with phase coexistence are analyzed by means of Maxwell s construction. It was introduced to cure and interpret the unphysical backbending branch that occurs for real gases described by the van der Waals equation in the pressure (p) versus 

Since the depletion region of the entropy has an energetic width Ag 0 and coimects energetic spaces which are associated with different phases of reduced thermodynamic activity, the extended region in-between accommodates macrostates, in which two phases coexist. It is therefore common to interpret Ag as the latent heat and to associate the entropic suppression in this region with a first-order transition, in analogy to thermodynamic first-order phase transitions in the thermodynamic limit. 

As Fig, 2,3(b) also shows, the curve resembles a third-order polynomial. For that reason, the Maxwell line jStr possesses a third intersection point with P(E), denoted by Eti. It can be considered as the separation point, where the entropic weight of each of the two phases in the coexistence region is identical. In this formalism, it defines the transition state. The total entropy change in the order-dominated coexistence regime is  

Free-energy profiles f (f) for temperatures below, at, and above the transition point Tan = h. 

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