Pseudophase micellar model

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

The pseudophase kinetic models for speeded or inhibited bimolecular, second-order, reactions are more complex. Here the focus is on reaction between a neutral organic substrate and a reactive counterion in micellar solutions in the absence of oil (d>o = 0, Scheme 4). Micellar effects on reactions of substrates with reactive counterions are important because they illustrate the general differences of micellar effects on spontaneous and bimolecular reactions and also how specific counterion effects influence the results. Pseudophase models also work for bimolecular reactions between two uncharged organic substrates and third-order reactions, reactions in vesicles and microemulsions, which may include partitioning into and reaction in the oil region, reactions of substrates with an ionizable (e.g., deprotonatable) second reactant, and the effect of association colloids on indicator equilibria. ... 

This equation states that the interfacial molarity of counterion is eqnal to the initial molarity in the absence of added salt, first term, plus the molarity of the stoichiometric concentration of the counterion added as salt, second term. This inteipietation qualitatively fits both kinetic and chemical trapping results above about 0.2 M of added salt and indicates that the micellar interfaces (and by implication other association colloid interfaces) do not saturate with counterions as originally assumed in pseudophase kinetic models. ... 

Here we have undertaken a study of the effects of SDS micellar systems and added organic solvents on the electrochemical behaviour of relevant antioxidants. In the last years we have taken great interest in determining the distribution of antioxidants in the emulsified systems, and for that purpose we have developed a novel kinetic method based on the reaction between a hydrophobic arenediazonium ion and the antioxidants which allows to determine the partition constants of the antioxidant between the oU, water and interfacial regions of the emulsified system [10-12]. The kinetic results are interpreted using the pseudophase kinetic model based on the hypothesis that the rates of chemical reactions are not limited by transport of reactants, i.e., that all reactants are in the dynamic equilibrium throughout the reaction. This hypothesis was experimentally proved by fitting the kinetic data to the equations derived from the pseudophase model, but determination of the diffusion coefficients of the reactants in the studied system will be very useful from the conceptual point of view to confirm or discard the mentioned idea. 

The pseudophase separation model of micellar solutions considers a micelle to be a pseudophase in a liquid state. Because the micelles are assumed to have a liquidlike core, the mutual solubility of a fluorinated surfactant and a hydrocarbon surfactant in mixed micelles is, according to the pseudophase model, governed by the miscibility of the fluorocarbon and hydrocarbon chain. For example, heptane and perfluoroheptane are immiscible at 25°C, but above 50°C, these liquids are miscible in all proportions [75]. A terminal substitution of a hydrophilic group depresses the enthalpy of mixing and makes the components miscible at 25°C. 

Kamrath and Franses [85] developed a single-micelle-size mass action model for binary solutions of surfactants with the same hydrophilic group and counterion. The mass action model predicts micellar behavior more accurately than the pseudophase separation model [73] if the number of surfactant monomers in the mixed micelle is less than about 50. 

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. 

Broxton, T.J., Sango, D.B. Micellar catalysis of organic reactions. X. Further evidence for the partial failure of the pseudophase kinetic model of micellar catalysis for reactions of hydroxide ions. Aust. J. Chem. 1983, 36(4), 711-717. 

Perhaps one of the first of the very few systematic kinetic studies on the effects of mixed micelles on the bimolecular reaction rates is one on the effects of mixed CTABr/C,oE4 where C10E4 = C,oH2,(OCH2CH2)30CH2CH20H on the rate of an 8 2 reaction of methyl naphthalene-2-sulfonate (1) with counterions of cationic surfactant (Br). Pseudophase (PP) model, i.e., Equation 5.11 has been used to explain quantitatively the deaease in k bs with increase in Xp p = [C,oE4]x/([CioE4]x + [CTABrJj). In Equation 5.11, Kj is CTABr micellar binding constant of nonionic substrate 1,... 

Recently, Davies and Foggo studied the effects of mixed anionic (SDS)/non-ionic (C12E23) micelles on the rate of reaction of m-chloroperbenzoic acid and iodide. The observed data have been treated using a combined multiple micellar pseudophase (MMPP) model and transition state pseudoequilibrium constant approach. It is interesting to note that proportionately weighted nonlinear regression was used for the kinetic model fitting to a kinetic equation of nine disposable parameters, and it is almost certain that the reliability of the values of calculated disposable parameters from a kinetic equation derived based upon a kinetic model decreases with an increase in the number of such disposable parameters. 

Surfactants have also been of interest for their ability to support reactions in normally inhospitable environments. Reactions such as hydrolysis, aminolysis, solvolysis, and, in inorganic chemistry, of aquation of complex ions, may be retarded, accelerated, or differently sensitive to catalysts relative to the behavior in ordinary solutions (see Refs. 205 and 206 for reviews). The acid-base chemistry in micellar solutions has been investigated by Drummond and co-workers [207]. A useful model has been the pseudophase model [206-209] in which reactants are either in solution or solubilized in micelles and partition between the two as though two distinct phases were involved. In inverse micelles in nonpolar media, water is concentrated in the micellar core and reactions in the micelle may be greatly accelerated [206, 210]. The confining environment of a solubilized reactant may lead to stereochemical consequences as in photodimerization reactions in micelles [211] or vesicles [212] or in the generation of radical pairs [213]. 

Solubilisation is usually treated in terms of the pseudophase model, in which the bulk aqueous phase is regarded as one phase and tire micellar pseudophase as another. This allows the affinity of the solubilisate for the micelle to be quantified by a partition coefficient P. Different definitions of P can be found in the literature, differing in their description of the micellar phase. Frequently P is... 

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 retrospect, this study has demonstrated the limitations of two commonly accepted methods of analysing solubilisation and micellar catalysis, respectively. It has become clear that solubilisate ririg-current induced shifts need to be interpreted with due caution. These data indicate a proximity of solubilisate and parts of the surfactant and, strictly, do not specify the location within the micelle where the encounter takes place. Also the use of the pseudophase model for bimolecular reactions requires precaution. When distribution of the reactants over the micelle is not comparable, erroneous results are likely to be obtained... 

Assuming complete binding of the dienophile to the micelle and making use of the pseudophase model, an expression can be derived relating the observed pseudo-first-order rate constant koi . to the concentration of surfactant, [S]. Assumirg a negligible contribution of the reaction in the aqueous phase to the overall rate, the second-order rate constant in the micellar pseudophase lq is given by ... 

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

We have demonstrated that due to inhomogeneous distribution of both reaction partners in the micelles, the pseudophase model leads to erroneous estimates of the second-order rate Constantin the micellar pseudophase, so that conclusions regarding the medium of the reaction cannot be derived through this model. However, analysis of substituent effects and endo-exo ratios of the Diels-Alder adducts indicate that the reaction experiences a water-like medium. 

A kinetic study of the basic hydrolysis in a water/AOT/decane system has shown a change in the reactivity of p-nitrophenyl ethyl chloromethyl phosphonate above the percolation threshold. The applicability of the pseudophase model of micellar catalysis, below and above the percolation threshold, was also shown [285],... 

Micellar effects upon reaction rates and equilibria have generally been discussed in terms of a pseudophase model, and this approach will be followed here. 

Some examples of micellar rate enhancements of bimolecular reactions of electrophiles are shown in Table 5. Generally the surfactant was SDS with added electrophile, e.g. H30+ or a metal ion, but sulfonic acids were also used so that HaO+ was the counterion and there was no interionic competition. The maximum rate enhancements, knl, depend upon the specific conditions of the experiment, and, as predicted by the pseudophase ion-exchange model, generally decrease with increasing concentration of the electrophilic ion. In some cases the reactions were too fast for measurement... 

The acid hydrolysis of micellized alkyl sulfates (Kurz, 1962 Motsavage and Kostenbauder, 1963) has recently been very carefully reinvestigated (Garnett et al., 1983). For relatively dilute micellized alkyl sulfate, salt inhibition follows the predictions of the pseudophase ion-exchange model, with the expected salt order. But this order is not followed with more concentrated alkyl sulfate, and these results are a very interesting deviation from the widely observed pattern of micellar salt effects. 

Despite our reservations as to the validity of the various pseudophase models of micellar rate effects they provide a convenient mental scaffolding for discussion of the data and we use them for that purpose (Mortimer, 1982). 

An alternative approach to this problem is to assume that deprotonation of a weak acid in the micellar pseudophase will be related to the concentration of bound OH-, which should follow the ion-exchange model (Section 5). As a result much of the work has been based on the use of very weak acids which are deprotonated only at high pH. 

The hexadecyltrimethylammonium cation causes a modest increase in rate constant for the anion-anion reaction [Fe(CN)5(4-CNpy)]3-+CN-. This can equally well be interpreted according to the pseudophase model developed from the Olson-Simonson treatment of kinetics in micellar systems or by the classical Bronsted equation (135). 

The impact of salt concentration on the formation of micelles has been reported and is in apparent accord with the interfacial tension model discussed in Sect. 4.1, where the CMC is lowered by the addition of simple electrolytes [ 19,65, 280,282]. The existence of a micellar phase in solution is important not only insofar as it describes the behavior of amphipathic organic chemicals in solution, but the existence of a nonpolar pseudophase can enhance the solubility of other hydrophobic chemicals in solution as they partition into the hydrophobic interior of the micelle. A general expression for the solubility enhancement of a solute by surfactants has been given by Kile and Chiou [253] in terms of the concentrations of monomers and micelles and the corresponding solute partition coefficients, giving... 

A pseudophase ion exchange model has been applied to reactions in micellar systems with varying success (1-7). According to this model, the distribution of nucleophile is considered to depend on the ion-exchange equilibrium between the nucleophile and the surfactant counterion at the micelle surface. This leads to a dependence on the ion-exchange constant (K g) as well as on the degree of dissociation (a) of the surfactant counterion. The ion exchange (IE) model has recently been extended to oil in water microemulsions (8). 

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