Two methods to extract the Gibbs free energy based on the value of CMC and  exist; Phillips method based on the law of mass action and the pseudo-phase separation model. The law of mass action postulates that the micelle formation can be modeled as a chemical equilibrium process between the micelles  and its constituents, the surfactant monomers, :
where  is the average number of surfactant monomers in solution that associate into a micelle, commonly denoted the aggregation number.
The equilibrium is characterized by an equilibrium constant defined by , where  and  are the concentrations of micelles and free surfactant monomers, respectively. In combination with the law of conservation of mass, the system is fully specified by: , where  is the total surfactant concentration. Phillips defined the CMC as the point corresponding to the maximum change in gradient in an ideal property-concentration ( against ) relationship =0. By implicit differentiation of  three times with respect to  and equating to zero it can be shown that the micellization constant is given by  for . According to Phillips method the Gibbs free energy change of micellization is therefore given by:
The pseudo-phase separation model was originally derived on its own basis, but it has later been shown that it can be interpreted as an approximation to the mass-action model for large . That is, for micelles behaving in accordance with the law of mass-action, the pseudo-phase phase separation model is only an approximation and will only become asymptotically equal to the mass-action model as the micelle becomes a true macroscopic phase i.e. for →∞. However, the approximation that the aggregation number  is large is in most cases sufficient: