Berezins Pseudophase Model

In the early 1970s, the Russian school of Berezin et attempted to rationalize 

In Equation 3.63, F is the Faraday constant Zr, an ionic valence state of ion R and RT, the multiple of gas constant and absolute temperature. An excellent agreonent between the calculated values of Kqh from Equation 3.11 as well as Equation 3.62 and Equation 3.63 has been reported, which validates the use of Equation 3.11 for ionic nticeUar-mediated semiionic reactions. Distribution of reactive counterions, discussed in terms of micellar surface potentials, has led to equations similar to those based on the ion-exchange model. 

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According to the simple pseudophase model of Berezin (8), the binding constants between the ligands and the micelles have been calculated using the following equation ... 

Various experimental observations, obtained by studies of diverse nature, indirectly suggest that micellar pseudophase is not homogeneous in terms of micropolarity, water concentration, dielectric constant, and ionic strength (for ionic micelles). " This fact has not been considered in the classical pseudophase kinetic model hrst suggested by Berezin et al. " and Martinek et al. It is therefore logical for Davies et al. to suggest that the micellar pseudophase should be divided up into an arbitrary number of pseudophases, each with a different mean partition coefficient for the reactant or reactants and each with a different mean rate constant. This generalization of the classical (Berezin s) pseudophase model is referred to as the multiple micellar pseudophase (MMPP) model and leads to a kinetic equation similar to Equation 3.61 or Equation 3.11 with modified definitions of kinetic parameters such as kM (= (kMW]y,)KRKs) = E(kM iA Mr)KR iKs i with i = 1, 2, 3,. .., q Kr = S Kr, with i = 1, 2, 3,. .., q and Kg = X K i with i = 1,2, 3,..., q, where q represents an arbitrary number of micelle pseudophases. 

The Menger-Portnoy model is closely related to the Berezin model employing partition coefficients instead of equilibrium constants.For the case where only two pseudophases (bulk water and micelle) are considered, the partitioning of the reactant is given by the partition coefficient P. This leads to Equation (4) describing observed rate constants as a function of surfactant concentration. 

Both the Menger-Portnoy model and the model by Berezin were effectively derived on the assumption that micellar solutions contain two pseudophases, namely the micellar pseudophase and bulk water. However, both models can be expanded to take more than one micellar pseudophase into account. For example, this could be done when the micellar pseudophase is seen to consist of two separate pseudophases (zones) itself, namely a pseudophase corresponding to the hydrophobic core and a pseudophase corresponding to the micellar Stern region. " If one then assumes a reaction to occur with a rate constant k in the Stern region while the reaction does not occur in the micellar core, the expression for k includes the distribution of the reactant over different zones [Equation (6)]. " ... 

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