Extension of the PP Model

The total number of bound molecules, Xn, is proportional, through the proportionality constant o, to the micelhzed surfactant concentration C i.e., Xuj, = aC, where n represents number of molecules or moles, subscript b stands for bound (i.e., in the micellar pseudophase), and C,i is the analytical concentration of the nticelUzed surfactant in moles L.  

All the assumptions involved in the Debye-Huckel approximation (DH) are incorporated in this model because approximations have been used to establish the relationship between the electrostatic transfer constant Kj and (Tb/Tf)j (where Tj is the activity coefficient of the j-th species) in terms of measurable parameters. 

Minero et al. avoided exchange model formalism in the definition of exchange constants and used simple ratios between transfer constants because simple measurements of counterion activities showed that two kinds of counterions can independently associate with or dissociate from micelles even when they have the same charge. This model contains a fairly large number of assumptions, and experimentally usable kinetic equations could be obtained after several approximations. The quality of a model is not strictly proved by the fact that it is able to fit the data, especially if the model involves many approximations and assumptions that cannot be validated with convincing evidence. 

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The PIE model is essentially an extension of the PP model and therefore contains all the assumptions involved in the PP model and a few more, as clearly expressed in several excellent reviews. These additional assumptions may be summarized as follows ... 

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