Pseudophase model

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". ... 

The catalytic effect on unimolecular reactions can be attributed exclusively to the local medium effect. For more complicated bimolecular or higher-order reactions, the rate of the reaction is affected by an additional parameter the local concentration of the reacting species in or at the micelle. Also for higher-order reactions the pseudophase model is usually adopted (Figure 5.2). However, in these systems the dependence of the rate on the concentration of surfactant does not allow direct estimation of all of the rate constants and partition coefficients involved. Generally independent assessment of at least one of the partition coefficients is required before the other relevant parameters can be accessed. 

Figure 5.2. Kinetic analysis of a bimolecular reaction A + B 7 C according to the pseudophase model.

In order to interpret the data in Table 5.1 in a quantitative fashion, we analysed the kinetics in terms of the pseudophase model (Figure 5.2). For the limiting cases of essentially complete binding of the dienophile to the micelle (5.If in SDS and 5.1g in CTAB solution) the following expression can be derived (see Appendix 5.2) ... 

Figure 5.3 shows the dependence of the apparent second-order rate constants (koi "/[5.2]i) on the concentration of surfactant for the Diels-Alder reactions of 5.If and 5.1 g with 5.2. The results of the analysis in terms of the pseudophase model are shown in the inset in Figure 5.3 and in the first two... 

Table 5.2. Analysis using the pseudophase model partition coefficients for 5.2 over CTAB or SDS micelles and water and second-order rate constants for the Diels-Alder reaction of 5.If and 5.1g with 5.2 in CTAB and SDS micelles at 25 C.

This conclusion seems in coirflict with the outcome of the analysis using the pseudophase model. Here we do not speculate on the origins of this discrepancy. Instead, an extensive discussion is provided in Section 5.2.3. 

Figure 5.6. Plots of the apparent second-order rate constant (kap-p) versus the concentration of Cu(DS )2 for the Diels-Alder reaction of S.lc ( ), 5.1 f (f ) and 5.1 g (jsC) with 5.2 at 25 C. The inset shows the treatment of the data for the reaction of 5.1g according to the pseudophase model.

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],... 

The following discussion of chemical reactivity and mechanism will be based on the premise that for most thermal reactions equilibrium is maintained between water and the micelles, which can be regarded as distinct reaction media, and most kinetic treatments are based on this so-called pseudophase model (Cordes and Gitler, 1973 Bunton, 1973b). Reaction... 

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

An example of the application of the pseudophase model to imidazolide ion dephosphorylation is shown in Fig 1. The areneimidazole is a weak acid,... 

The pseudophase model is often applied to reactions of hydrophobic ionic substrates, e.g. pyridinium ion in solutions of cationic micelles (Tables 3 and 4) with the hydrophobic attraction between micelle and substrate over-... 

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). 

Mechanistic studies of organic reactivities in vesicles have focused on two questions the first is the application of the pseudophase model to reactions in vesicles and the second that of reaction at the inner and outer vesicular surfaces. 

A 5/Arw = 0.5-1 a = 0.27 CTABr, CTAF + OH". Relative rate effects of CTABr and CTAF did not fit simple pseudophase model... 

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 second case of a bimolecular reaction occurring between two uncharged reactants A and B requires further extensions of the pseudophase model. The simplest of the possible expansions involves bimolecular reactions not involving reactions crossing the interface between the pseudophases, in other words, reactant A in the aqueous pseudophase reacts only with reactant B in the aqueous pseudophase while reactant A in the micellar pseudophase reacts only with reactant B in the micellar pseudophase (Scheme 6). 

Lantz, A.W., Pino, V., Anderson, J.L., and Armstrong, D.W., Determination of solute partition behavior with room-temperature ionic liquid based micellar gas-liquid chromatography stationary phases using the pseudophase model, /. Chromatogr. A, 1115, 217-224, 2006. 

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... 

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 ... 

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