Menger-Portnoy model

The most straightforward of the various models describing micellar kinetics is the Menger-Portnoy model for (pseudo) unimolecular reactions.The Menger-Portnoy model assumes rapid equilibration of the reactant of interest over bulk water and the micellar pseudophase with equilibrium constant K. The reaction then proceeds in both pseudophases with rate constants and in bulk water and the micellar pseudophase, respectively (Scheme 4). 

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)]. " ... 

For the first case, one can use the so-called pseudophase ion exchange (PIE) model.The PIE model is based on the Menger-Portnoy model but additionally allows for ion exchange to occur in the micellar Stern region where a reactive counterion competes with nonreactive counterions (Scheme 5). 

The kinetic data are essentially always treated using the pseudophase model, regarding the micellar solution as consisting of two separate phases. The simplest case of micellar catalysis applies to unimolecTilar reactions where the catalytic effect depends on the efficiency of bindirg of the reactant to the micelle (quantified by the partition coefficient, P) and the rate constant of the reaction in the micellar pseudophase (k ) and in the aqueous phase (k ). Menger and Portnoy have developed a model, treating micelles as enzyme-like particles, that allows the evaluation of all three parameters from the dependence of the observed rate constant on the concentration of surfactant". ... 

In Menger and Portnoy s model, the variation of the rate constant with surfactant concentration has been treated on the basis of assumption that substrate S is distributed between aqueous and micellar pseudo-phase given as follows ... 

The rate constants for micelle-catalyzed reactions, when plotted against surfactant concentration, yield approximately sigmoid-shaped curves. The kinetic model commonly used quantitatively to describe the relationship of rate constant to surfactant, D, concentration assumes that micelles, D , form a noncovalent complex (4a) with substrate, S, before catalysis may take place (Menger and Portnoy, 1967 Cordes and Dunlap, 1969). An alternative model... 

The oxidation of D-fructose with cerium(IV) in sulfuric acid medium is inhibited by an increase in the acidity. A cationic surfactant, CTAB, catalyses the reaction, whereas SDS has no effect. The catalytic role of CTAB has been explained using the pseudophase model of Menger and Portnoy. A mechanism involving the formation of an intermediate complex between /3-D-fructopyranose and Ce(S04)32- has been proposed.61 The oxidation of cycloalkanones with cerium(IV) in sulfuric acid medium showed a negligible effect of acidity. Formation of an intermediate complex, which decomposes in the rate-determining step, has been suggested.62... 

Therefore, provided that there is an equilibrium between the micellar and aqueous pseudophases, the problem resolves itself into estimation of the distribution of reactants between aqueous and micellar pseudophase and calculation of the rate constants of reaction in each pseudophase. Menger and Portnoy [70] developed an equation which successfully accounted for micellar inhibited saponification of 4-nitrophenyl alkanoates. This model was also applied to spontaneous, unimolecular, hydrolyses of dinitrophenyl sulfate monoanions [66] and phosphate dianions [68] which are speeded by cationic micelles in water. 

Experimentally determined rate constants for various micellar-mediated reactions show either a monotonic decrease (i.e., micellar rate inhibition) or increase (i.e., micellar rate acceleration) with increase in [Suifl CMC, where [Surf]T represents total micelle-forming surfactant concentration (Figure 3.1). Menger and Portnoy obtained rate constants — [SurfJx plots — for hydrolysis of a few esters in the presence of anionic and cationic surfactants, which are almost similar to those plots shown in Figure 3.1. These authors explained their observations in terms of a proposed reaction mechanism as shown in Scheme 3.1 which is now called Menger s phase-separation model, enzyme-kinetic-type model, or preequilibrium kinetic (PEK) model for micellar-mediated reactions. In Scheme 3.1, Kj is the equilibrium... 

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