Berezin model

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. 

The immediate success of the Berezin model in accounting almost quantitatively for the observed catalysis effect of micelles has an interesting implication. Is this truly a case of catalysis In many instances, the micelles bring about considerable shifts in equilibrium positions, which forced Berezin to admit that the term micellar catalysis was somewhat incorrect [2]. He justified its continued use on the basis that the surfactant is not consumed in the reaction and that for most surfactants the concentration required to bring about marked effects is usually very low. Some workers in the field have opted for less controversial terms such as micellar rate enhancement or rate promotion. The title of a recent review, Micellar Catalysis, a Useful Misnomer [3], sums up the prevalent attitude of researchers today. 

The emphasis placed on the last assumption is responsible for the name of the model. It is now well known that these assumptions, especially the first two, are reliable with impunity only over very narrow and dilute micellar concentration ranges. Nevertheless, the PIE model has provided invaluable insight over the past 25 years in elucidating micellar catalysis. Its failures [27-31] are usually attributable to clear-cut violations of its simple assumptions. Refinements or alternatives to these basic premises such as solving the nonlinear Poisson Boltzmann equation for the cell model have not proved to be particularly enlightening nor more helpful [32]. The extension of the PIE model to complicated micellar systems where anomalous rate behavior is more often than not the rule rather than the exception is probably unwarranted [33]. Sudhdlter et al. [34] have critically reviewed the Berezin model and its Romsted variation, the PIE model, as matters stood 20 years ago. In... 

The kinetics and mechanism of a range of slow metal-ligand substitution processes have been investigated, and a generalized theory was proposed that was very similar to the Berezin model for the interpretation of micelle kinetics in aqueous solutionsJ Ligands of different hydrophobicity were studied in terms of their reaction with Ni +(aq), and it was found that for p3rridine-2-azo-p-phenol (PAP), the rate constants kf for reaction in SDS micellar solution and water/Na-AOT/heptane systems were comparable, as shown in Table 10.2. kf is expressed as a first-order rate constant in the microemulsion.)... 

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)]. " ... 

Martinek, K., Levashov, A. V, Pantin, V. I., and Berezin, I. V. (1978). Model of biological membranes or surface-layer (active center) of protein globules (enzymes) - reactivity of water solubilized by reversed micelles of aerosol OT in octane during neutral hydrolysis of picrylchloride. Doklady Akademii Nauk SSSR, 238, 626-9. 

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 ... 

AE Shilov and TS Dzablev (1984) Models of photosynthesis. In IV Berezin (ed) Solar Energy Bloconverslon, pp 22-34. ONTI AN SSSR, Pushchino... 

Associated Adsorbate ModeV° This model, which leads to the Berezin-Kiselev equation, accounts for lateral interactions within the adsorbed phase by proposing the formation of associates in the monolayer. The equation may be written as ... 

A recent study that adopts the associated adsorbate model of Berezin and Kiselev may prove particularly useful in elucidating heterogeneity topK>l-ogy. In their theoretical treatise, Jaroniec and Borowko assumed a dual adsorbent surface and the possibility of double associates. Thus by formulating quasi-chemical reactions ... 

The oxidation of dextrose by A -bromothalimide in H2SO4 both in the absence and in the presence of surfactants (sodium dodecylsulfate, tritonX-100) is fractional order in dextrose and negative fractional order in H+ the role of anionic and non-ionic micelle is best explained by Berezin s model. ... 

Over 40 years ago, Kiselev [30] presented an interesting concept of the associating adsorbate. He assumed that all interactions in the monolayer might be described as a series of reversible quasichemical reactions between admolecules and adsorption sites and between adsorbate molecules in the monolayer. These interactions were characterized by means of suitable reaction constants. This theory was extended by Berezin and Kiselev [31] their final isotherm involves dispersive interactions according to the Fowler-Guggenheim model and specific interactions which cause formation different associates in the surface phase. 

Apart from the Fowler-Guggenheim local adsorption isotherm, the Berezin-Kiselev equation has been extended to adsorption on heterogeneous surfaces by Jaroniec and Borowko [89]. Their results have an instructive character the method allow us to investigate the influence of various geometrical distributions of active sites on adsorption in the fi amework of simple and clearly constructed model. They have considered localized monolayer adsorption on the siuface consisting of two types of adsorption site. The lateral interactions caused the formation of double associates. The total adsorption was the sum of the surface coverage on adsorption sites of both kinds, which may be calculated fi om... 

A comparison of the Berezin and PSIE approaches has recently been carried out. However, there are a number of cases where the PSIE model is inappropriately applied. ... 

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. 

Martinek, K., Levashov, A.V., Berezin, I.V. Mechanism of catalysis by functional micelles containing a hydroxyl group model of action of serine proteases. Tetrahedron Lett. 1975 (15), 1275-1278. 

---