Second-order rate constants in the micellar pseudophase

Second-order rate constants in the micellar pseudophase 

As noted earlier comparison of second-order rate constants requires that one assume an arbitrary measure of concentration. Eqn. 6 was derived using concentration in mole ratios, which leads to a convenient form of the equation, but the rate constants, kf, sec , cannot be compared directly with values of in water, for 

If one assumes that reaction occurs in the Stem layer, whose molar volume is 0.14 

Values of k 2 would be approximately doubled if a molar volume of ca. 0.3 1 was used. 

The second order rate constants, A and k, for reactions in the micellar and aqueous pseudophases have the same dimensions, and can now be compared directly, and within all the uncertainties of the treatment it seems that A and k are of similar magnitudes for most reactions, and in some systems A A . This generalization is strongly supported by evidence for reactions of relatively hydro-phobic nucleophilic anions such as oximate, imidazolide, thiolate and aryloxide, typically with carboxylate or phosphate esters [61,82-85]. These similarities of second-order rate constants in the aqueous and micellar pseudophases are consistent with both reactants being located near the micellar surface in a water-rich region. Therefore the micellar rate enhancements of bimolecular reactions are due largely to concentration of the reactants in the small volume of the micelles. Some examples are in Table 3 for reactions of or hydrophilic nucleophilic anions and in Table 4 for reactions of more hydrophobic nucleophiles. 

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Herein k js is the observed pseudo-first-order rate constant. In the presence of micelles, analogous treatment of the experimental data will only provide an apparent second-order rate constant, which is a weighed average of the second-order rate constants in the micellar pseudophase and in the aqueous phase (Equation 5.2). 

Unfortunately, more detailed kinetic studies aimed at the determination of the second-order rate constants in the micellar pseudophase have not been published. 

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 ... 

Second-order rate constant in the micellar pseudophase (s-1), with concentration expressed as mole ratio... 

An impressive body of evidence supports these generalizations. This evidence has been reviewed (Romsted, 1984) and it does not seem necessary to discuss it in detail here, but some examples will be given and some exceptions to these generalizations will be mentioned. Some reactions of OH- are shown in Table 3 for both inert and reactive ion surfactants, and Table 4 gives data for reactions of other hydrophilic ions. Reactions of hydrophobic nucleophiles are shown in Table 2. For all these reactions second-order rate constants in the micellar pseudophase are compared with those in water. For some reactions we also give values of krcl, i.e. the rate constant relative to that in water. These values depend upon the reactant concentration and are included merely to provide an indication of the micellar rate effects. Other examples of micellar rate effects are given in the Appendix. 

First-order rate constant in the micellar pseudophase (s ) Second-order rate constant in the micellar pseudophase (s ), with concentration expressed as mole ratio Second-order rate constant in the micellar pseudophase (M-is- ) k S = kMKM... 

The derivation can alternatively be given using a second-order rate constant in the micellar pseudophase based on the volume of that pseudophase [25,61,72]. The rate equation then includes the micellar molar volume, and this formulation is often used. 

For both systems the data can be fitted with an ion exchange constant = 4, and the second order rate constant in the micellar pseudophase is about one-third of this in water, probably because the high ionic content of the Stern layer exerts a negative salt effect upon the reaction. 

So far as I know there was no reaction in the literature for which the second-order rate constants in the micellar pseudophase are much larger than those in water. However aromatic substitution by azide ion upon 2,4-dinitrochlorobenzene and naphthalene in cationic micelles is such a reaction. The second-order rate constants, kf, in the micellar pseudophase are much larger than those in water [88]. However this high reactivity is not observed in deacylation or an 8 2 displacement and it is not obvious why aromatic substitution by azide ion should be an exception to generalizations about rate constants in aqueous and micellar pseudophases. 

The situation is more complicated for nonspontaneous bimolecular reactions involving a second reactant, whose distribution between the two pseudophases has to be considered. The simplest situation is that for reaction of a hydrophobic species whose solubility in water is sufficiently low that it is incorporated essentially quantitatively in the association colloid. For example, for reactions of nucleophilic amines in aqueous micelles, second-order rate constants in the micellar pseudophase calculated in terms of local concentrations are lower than in water [103,104], because these reactions are inhibited by a decrease in medium polarity and micelle/water interfaces are less polar than bulk water [59,60,99101]. Nonetheless, these bimolecular reactions are generally faster in micellar solutions than in water because the nucleophile is concentrated within the small volume of the micelles. Similar results were obtained for the reaction of 2,4-dinitrochlorobenzene (5) with the cosurfactant -hexylamine in O/W microemulsions with CTABr and w-octane [99], again consistent with the postulated similarities in the interfacial regions of aqueous micelles and O/W microemulsions. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

This reaction is reversible [93], but the high concentration of CN at the micellar surface allows one to neglect the reverse reaction in CTACN. The rate constants for addition increase smoothly with increasing [CTACN] to values which are almost independent of the hydrophobicity of the substrate. The second-order rate constants in the micelle are very similar to that for reaction of the n-propyl derivative in water [93], consistent with the generalization that rate enhancements of bimolecular reactions are due to concentration of the reactants in the micellar pseudophase. 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Another approach is to define concentration in the micellar pseudophase in terms of a mole ratio. Concentration is then defined unambiguously, and the equations take a simple form (Bunton, 1979a,b Romsted, 1984). However, this approach does not allow direct comparison of second-order rate constants in aqueous and micellar pseudophases and by evading one problem one faces another. 

Analysis of the variation of the overall rate constant of reaction with [surfactant] was discussed in Section 3 (p. 222) and the treatment allows calculation of the second-order rate constants of reaction in the micellar pseudophase. These rate constants can be compared with second-order rate constants in water provided that both constants are expressed in the same dimensions and typically the units are M-1 s-1. Inevitably the comparison... 

The similarity for many reactions of second-order rate constants in aqueous and micellar pseudophases, and the observation that substrate hydrophobicity usually affects binding and not inherent reactivity in the micelle, suggests that substrate location or orientation is relatively unimportant. This conclusion is strongly supported by a quantitative analysis of the effects of CTABr micelles on the reaction of OH- and arylsulfonylalkyl arenesulfonates (16) (van der Langkruis and Engberts, 1984). 

Here variables are defined as before,, 2 and ni,2 are the (second order) rate constants in water and in the micellar pseudophase, respectively, Pm, and Pni,B are the partition coefficients for reactants A and B, respectively. 

A detailed examination of relative second-order rate constants in micellar and aqueous pseudophases is outside the scope of this discussion, but for anionic reagents it seems that (Tables 3 and 4) deviates from unity when the substrate is very hydrophobic and the anion more hydrophilic, suggesting that, on the average, they are not located in the same region of the micelle. However, more evidence will be needed on micelle-solute interactions for this question to be answered. 

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