Liquidlike cells free energy

The essence of the free-volume theory described in Section III is that the only change in free energy associated with a redistribution of free volume is in the entropy of the probability distribution of the free volume. This arises from the decomposition of the free energy into a sum of terms depending only on the volume of a single cell, the local free energy /(u,), and from the linearity of /(u,) in v, for liquidlike cells. Of the two, the former is the more serious approximation. 

Fig. 10. Sketches of the free energy 9 p) as a function of the liquidlike cell fraction p. Curves a, b, and c correspond to those so labeled in Fig. 9. The positions of the solutions of Fig. 9 are indicated by dots. Curve a corresponds to (Pi) (Pi) at the temperature 7, where the first-order phase transition occur. Crosses emphasize the infinite negative slope of S at p, the percolation threshold.

---